Abstract:
The invention discloses a method of dynamically configuring linear density and blending ratio of yarn by three-ingredient asynchronous/synchronous drafted, comprising: a drafting and twisting system, which includes a first stage drafting unit, a successive second stage drafting unit and an integrating and twisting unit. The first stage drafting unit includes a combination of back rollers and a middle roller. The second stage drafting unit includes a front roller and the middle roller. Blending proportion and linear densities of three ingredients are dynamically adjusted by the first stage asynchronous drafting mechanism, and reference linear density is adjusted by the second stage synchronous drafting mechanism. The invention can not only accurately control linear density change, but also accurately control a color change of the yarn. Further, the rotation rate of the middle roller is constant, ensuring a reproducibility of the patterns and colors of the yarn with a changing linear density.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a national phase entry application of International Application No. PCT/CN2015/085269, filed on Jul. 28, 2015, which is based upon and claims priority to NO. CN201510140910.4, filed on Mar. 27, 2015, claims another priority to NO. CN201510140466.6, filed on Mar. 27, 2015, the entire contents of which are incorporated herein by reference. 
     
    
     TECHNICAL FIELD 
       [0002]    The invention relates to a ring spinning filed of a textile industry, and particularly relates to a method and device of dynamically configuring a linear density and a blending ratio of a yarn by three-ingredient asynchronous/synchronous drafted. 
       BACKGROUND 
       [0003]    Yarn is a long and thin fiber assembly formed by orienting in parallel and twisting of fiber. The characteristic parameters generally include fineness (linear density), twist, blending ratio (color blending ratio), etc. The characteristic parameters are important features which should be controlled during a forming process. 
         [0004]    The yarn can be divided into four categories:
       (1) yarn with a constant linear density and a variable blending ratio, such as a color yarn of constant liner density, with a gradient or segmented color;   (2) yarn with a constant blending ratio and variable linear density, such as a slub yarn, a big-belly yarn, a dot yarn, etc.;   (3) yarn with a variable linear density and blending ratio, such as segmented a color slub yarn, a segmented color big-belly yarn, a segmented color dot yarn, etc.;   (4) blended yarn or mixed color yarn mixed at any rate, with a constant linear density and blending ratio.       
 
         [0009]    The development of yarn processing technology mainly relates to the problems of special yarns. The existing spinning technology and the patent applications fail to guide the spinning production of the above four types of yarns, challenging the existing spinning theories. Specifically, it is analyzed as follows: 
         [0010]    (1) Yarn with a Constant Linear Density and a Variable Blending Ratio (Color Blending Ratio) 
         [0011]    The yarn with a constant linear density and a variable blending ratio (color blending ratio) can be assumed as a color yarn of constant liner density, with a gradient or segmented color. No existing patent application is related to this type of yarn. 
         [0012]    (2) Yarn with a Constant Blending Ratio and Variable Linear Density 
         [0013]    The yarn with a constant blending ratio and variable linear density, can be such as a slub yarn, a big-belly yarn, a dot yarn, etc. The existing method of manufacturing the ring spun yarn with a variable linear density comprises feeding one roving yarn each to the middle roller and back roller, and discontinuously spinning to manufacture the yarns with variable linear density by uneven feeding from the back roller. For example, a patent entitled “a discontinuous spinning process and yarns thereof” (ZL01126398.9), comprising: feeding an auxiliary fiber strand B from the back roller; unevenly drafting it via the middle roller and back roller; integrating with another main fiber strand A fed from the middle roller, and entering into the drafting area; drafting them by the front roller and middle roller, and outputting from the jaw of the front roller; entering into the twisting area to be twisted and form yarns. Because the auxiliary fiber strand is fed from the back roller intermittently and integrates with the main fiber strand, under the influence of the front area main drafting ratio, the main fiber strand is evenly attenuated to a certain linear density, and the auxiliary fiber strand is attached to the main fiber strand to form a discontinuous and uneven linear density distribution. By controlling the fluctuation quantity of the uneven feeding from the back roller, different effects such as a dot yarn, a slub yarn, a big-belly yarn, etc. are obtained finally on the yarn. The deficiencies of this method are that the main and auxiliary fiber strands cannot be exchanged and a range of slub thickness is limited. 
         [0014]    (3) Yarn with a Variable Linear Density and Blending Ratio 
         [0015]    No existing patent application relates to this type of yarn. 
         [0016]    (4) Blended Yarn or Mixed Color Yarn Mixed at any Rate, with a Constant Linear Density and Blending Ratio 
         [0017]    The blended yarn or mixed color yarn mixed at any rate, with a constant linear density and blending ratio, are disclosed. The current method comprises blending two or more than two different ingredients to obtain a roving yarn at a certain blending ratio, by fore-spinning process, then spinning the roving yarn to form a spun yarn by spinning process to obtain a yarn with a constant linear density and a blending ratio. Usually spinning processes can only achieve several conventional proportions, such as 50:50, 65:35, 60:40. The deficiencies are that they cannot be blended at any rate and two or more than two fibers cannot be blended at any rate in a single step. 
       SUMMARY OF THE INVENTION 
       [0018]    To solve the above problems, the objective of this invention is to disclose a process of providing three-ingredient asynchronous/synchronous two-stage drafting fiber strands, and then integrating and twisting to form a yarn. The linear density and blending ratio of a ring spun yarn can be adjusted arbitrarily. The invention can adjust the linear density and blending ratio of the yarn at the same time to produce the above four types of yarns, overcoming the limitation of being unable to adjust characteristic parameters of a yarn on line. 
         [0019]    To achieve the above objectives, the invention discloses a method of dynamically configuring linear density and blending ratio of yarn by three-ingredient asynchronous drafting, comprising: 
         [0020]    1) An actuating mechanism mainly includes a three-ingredient asynchronous/synchronous two-stage drafting mechanism, a twisting mechanism and a winding mechanism. The three-ingredient asynchronous/synchronous two-stage drafting mechanism includes a first stage asynchronous drafting unit and a successive second stage synchronous drafting unit; 
         [0021]    2) The first stage asynchronous drafting unit includes a combination of back rollers and a middle roller. The combination of back rollers has three rotational degrees of freedom and includes a first back roller, a second back roller, a third back roller, which are set abreast on a same back roller shaft. A first back roller, a second back roller, a third back roller move at the speeds V h1 , V h2 , and V h3  respectively. The middle roller rotates at the speed V z . The second stage synchronous drafting unit includes a front roller and the middle roller. The front roller rotates at the surface linear speed V q . 
         [0022]    Assuming the linear densities of a first roving yarn ingredient, a second roving yarn ingredient, a third roving yarn ingredient drafted by a first back roller, a second back roller, a third back roller are respectively ρ 1 , ρ 2 , and ρ 3 , the linear density of the yarn Y drafted and twisted by the front roller is ρ y . 
         [0000]    
       
         
           
             
               
                 
                   
                     ρ 
                     y 
                   
                   = 
                   
                     
                       1 
                       
                         V 
                         q 
                       
                     
                      
                     
                       ( 
                       
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           * 
                           
                             ρ 
                             1 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           * 
                           
                             ρ 
                             2 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                           * 
                           
                             ρ 
                             3 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0023]    The blending ratios of the first roving yarn ingredient, the second roving yarn ingredient, and the third roving yarn ingredient are respectively k 1 , k 2 , and k 3 . 
         [0000]    
       
         
           
             
               k 
               1 
             
             = 
             
               
                 
                   ρ 
                   1 
                   ″ 
                 
                 
                   
                     ρ 
                     1 
                     ″ 
                   
                   + 
                   
                     ρ 
                     2 
                     ″ 
                   
                   + 
                   
                     ρ 
                     3 
                     ″ 
                   
                 
               
               = 
               
                 
                   
                     ρ 
                     1 
                     ′ 
                   
                   
                     
                       ρ 
                       1 
                       ′ 
                     
                     + 
                     
                       ρ 
                       2 
                       ′ 
                     
                     + 
                     
                       ρ 
                       3 
                       ′ 
                     
                   
                 
                 = 
                 
                   
                     
                       ρ 
                       1 
                     
                     * 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                   
                     
                       
                         ρ 
                         1 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                     + 
                     
                       
                         ρ 
                         2 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           2 
                         
                       
                     
                     + 
                     
                       
                         ρ 
                         3 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           3 
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               2 
             
             = 
             
               
                 
                   ρ 
                   2 
                   ″ 
                 
                 
                   
                     ρ 
                     1 
                     ″ 
                   
                   + 
                   
                     ρ 
                     2 
                     ″ 
                   
                   + 
                   
                     ρ 
                     3 
                     ″ 
                   
                 
               
               = 
               
                 
                   
                     ρ 
                     2 
                     ′ 
                   
                   
                     
                       ρ 
                       1 
                       ′ 
                     
                     + 
                     
                       ρ 
                       2 
                       ′ 
                     
                     + 
                     
                       ρ 
                       3 
                       ′ 
                     
                   
                 
                 = 
                 
                   
                     
                       ρ 
                       2 
                     
                     * 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                   
                   
                     
                       
                         ρ 
                         1 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                     + 
                     
                       
                         ρ 
                         2 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           2 
                         
                       
                     
                     + 
                     
                       
                         ρ 
                         3 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           3 
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               3 
             
             = 
             
               
                 
                   ρ 
                   3 
                   ″ 
                 
                 
                   
                     ρ 
                     1 
                     ″ 
                   
                   + 
                   
                     ρ 
                     2 
                     ″ 
                   
                   + 
                   
                     ρ 
                     3 
                     ″ 
                   
                 
               
               = 
               
                 
                   
                     ρ 
                     3 
                     ′ 
                   
                   
                     
                       ρ 
                       1 
                       ′ 
                     
                     + 
                     
                       ρ 
                       2 
                       ′ 
                     
                     + 
                     
                       ρ 
                       3 
                       ′ 
                     
                   
                 
                 = 
                 
                   
                     
                       ρ 
                       3 
                     
                     * 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                   
                   
                     
                       
                         ρ 
                         1 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                     + 
                     
                       
                         ρ 
                         2 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           2 
                         
                       
                     
                     + 
                     
                       
                         ρ 
                         3 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           3 
                         
                       
                     
                   
                 
               
             
           
         
       
     
         [0024]    3) Keeping the ratio of linear speeds of the front roller and the middle roller V q /V z  constant, the speeds of the front roller and the middle roller depend on reference linear density of the yarn; 
         [0025]    4) The linear density of yarn Y or/and blending ratio can be dynamically adjusted on line, by adjusting the rotation rates of the first back roller, the second back roller. 
         [0026]    Further, according to the changes of the blending ratio K of the yarn Y with time t, and the changes of the linear density ρ y  of the yarn Y with the time t, the changes of the surface linear speeds of a first back roller, a second back roller, a third back roller are derived. The blending ratios of the first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient are set respectively as k 1 , k 2 , and k 3 . 
         [0027]    The ratios of blending ratios of the yarn Y are respectively K 1 , and K 2 . 
         [0000]    
       
         
           
             
               
                 K 
                 1 
               
               = 
               
                 
                   
                     k 
                     1 
                   
                   
                     k 
                     2 
                   
                 
                 = 
                 
                   
                     
                       ρ 
                       1 
                     
                      
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                   
                     
                       ρ 
                       2 
                     
                      
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                   
                 
               
             
             , 
             
               
 
             
              
             
               
                 K 
                 2 
               
               = 
               
                 
                   
                     k 
                     1 
                   
                   
                     k 
                     3 
                   
                 
                 = 
                 
                   
                     
                       ρ 
                       1 
                     
                      
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                   
                     
                       ρ 
                       3 
                     
                      
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                   
                 
               
             
           
         
       
     
         [0028]    Linear density of yarn Y is 
         [0000]    
       
         
           
             
               ρ 
               y 
             
             = 
             
               
                 
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       1 
                     
                   
                   * 
                   
                     ρ 
                     1 
                   
                 
                 + 
                 
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   * 
                   
                     ρ 
                     2 
                   
                 
                 + 
                 
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       3 
                     
                   
                   * 
                   
                     ρ 
                     3 
                   
                 
               
               
                 V 
                 q 
               
             
           
         
       
     
         [0029]    Then a surface linear speed of the back roller  1 : 
         [0000]    
       
         
           
             
               V 
               
                 h 
                  
                 
                     
                 
                  
                 1 
               
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                  
                 
                   V 
                   q 
                 
               
               
                 
                   ρ 
                   1 
                 
                  
                 
                   ( 
                   
                     1 
                     + 
                     
                       1 
                       
                         K 
                         1 
                       
                     
                     + 
                     
                       1 
                       
                         K 
                         2 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
         [0030]    a surface linear speed of the back roller  2 : 
         [0000]    
       
         
           
             
               V 
               
                 h 
                  
                 
                     
                 
                  
                 2 
               
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                  
                 
                   V 
                   q 
                 
               
               
                 
                   ρ 
                   2 
                 
                  
                 
                   ( 
                   
                     1 
                     + 
                     
                       K 
                       1 
                     
                     + 
                     
                       
                         K 
                         1 
                       
                       
                         K 
                         2 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
         [0031]    a surface linear speed of the back roller  3 : 
         [0000]    
       
         
           
             
               V 
               
                 h 
                  
                 
                     
                 
                  
                 3 
               
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                  
                 
                   V 
                   q 
                 
               
               
                 
                   ρ 
                   3 
                 
                  
                 
                   ( 
                   
                     1 
                     + 
                     
                       K 
                       2 
                     
                     + 
                     
                       
                         K 
                         2 
                       
                       
                         K 
                         1 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
         [0032]    wherein ρ 1 , ρ 2 , and ρ 3  are constants, and K i  and ρ y  are functions changing with time t. 
         [0033]    Further, let ρ 1 =ρ 2 =ρ 3 =ρ y , then: 
         [0034]    1) change the speed of any one of the first back roller, the second back roller, and the third back roller, and keep the speeds of the other two backer rollers unchanged. The yarn ingredient and the linear density thereof of the yarn Y drafted by this back roller change accordingly. The linear density ρ′ y  of the yarn Y is adjusted as: 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   ( 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                     + 
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           3 
                         
                       
                     
                   
                   ) 
                 
                  
                 
                     
                 
                  
                 or 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   ( 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                     + 
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           2 
                         
                       
                     
                   
                   ) 
                 
                  
                 
                     
                 
                  
                 or 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   ( 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                     + 
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
         [0035]    wherein Δρ y  is a linear density change of the yarn, ΔV h1 , ΔV h2  and ΔV h3  is a speed change of the first back roller, the second back roller, and the third back roller respectively. 
         [0036]    2) change the speeds of any two back rollers of the first back roller, the second back roller, and the third back roller, and keep the speeds of the other backer rollers unchanged. The yarn ingredients of the yarn Y drafted by these any two back rollers and the linear densities thereof change accordingly. The linear density ρ′ y  of yarn Y is adjusted as: 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 or 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 or 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δρ 
                   y 
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
               
             
           
         
       
     
         [0037]    3) change the speeds of three back rollers of the first back roller, the second back roller, and the third back roller simultaneously. The yarn ingredients of the yarn Y drafted by these any three back rollers and the linear densities thereof change accordingly. The linear density ρ′ y  of the yarn Y is adjusted as: 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δρ 
                   y 
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
               
             
           
         
       
     
         [0000]    further, change the speeds of the first back roller, the second back roller, and the third back roller, and make the speed of any of back rollers equal to zero, while the speeds of the other two backer rollers unequal to zero. The yarn ingredient of the yarn Y drafted by the any one of back rollers is thus discontinuous, while the other two yarn ingredients are continuous. The linear density ρ′ y  of yarn Y is adjusted as: 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     0 
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δρ 
                   y 
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     
                       T 
                       1 
                     
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       2 
                     
                   
                   ) 
                 
                  
                 
                     
                 
                  
                 or 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δρ 
                   y 
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     
                       T 
                       1 
                     
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       2 
                     
                   
                   ) 
                 
                  
                 
                     
                 
                  
                 or 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                           
                         
                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                         ) 
                       
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    wherein T 1  and T 2  are time points, and t is a time variable. 
         [0038]    Further, change the speeds of the first back roller, the second back roller, and the third back roller, make the speeds of any two back rollers equal to zero successively, while the speeds of the other one backer rollers unequal to zero. The yarn ingredients of the yarn Y drafted by the any two back rollers are thus discontinuous, while the other yarn ingredients are continuous. The linear density ρ′ y  of the yarn Y is adjusted as: 
         [0039]    1) When the First Back Roller is Unequal to Zero 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     0 
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                         
                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                           
                         
                         ) 
                       
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                    
                   
                       
                   
                    
                   or 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                         
                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                         ) 
                       
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    wherein T 3  is time pons and T 1 ≦T 2 ≦T 3    
         [0040]    2) When the Second Back Roller is Unequal to Zero 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     0 
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                         
                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                           
                         
                         ) 
                       
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                    
                   
                       
                   
                    
                   or 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                           
                         
                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                         ) 
                       
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0041]    3) When the Third Back Roller is Unequal to Zero 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     0 
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                         
                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                         ) 
                       
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                    
                   
                       
                   
                    
                   or 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                           
                         
                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                         ) 
                       
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0042]    Further change the speeds of the first back roller, the second back roller, and the third back roller, make the speeds of any two back rollers equal to zero simultaneously, while the speeds of the other one backer rollers unequal to zero. The yarn ingredients of the yarn Y drafted by the any two back rollers are thus discontinuous, while the other one yarn ingredients are continuous. The linear density ρ′ y  of the yarn Y is adjusted as: 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     0 
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                    
                   
                       
                   
                    
                   or 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                    
                   
                       
                   
                    
                   or 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δρ 
                     y 
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0043]    Further, change the speeds of the first back roller, the second back roller, and the third back roller, and keep 
         [0000]        V   h1 *ρ 1   +V   h2 *ρ 2   +V   h3 *ρ 3 =constant
 
         [0000]      and ‘ρ 1 =ρ 2 =ρ 3 =ρ’
 
         [0000]    then the linear density of the yarn Y is thus fixed while the blending ratios of the ingredients thereof change; the blending ratios of the first yarn ingredient, the second yarn ingredient, and the third yarn ingredient are k 1 , k 2 , k 3 . 
         [0000]    
       
         
           
             
               k 
               1 
             
             = 
             
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     1 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       1 
                     
                   
                 
               
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     1 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       1 
                     
                   
                 
                 + 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       2 
                     
                   
                 
                 + 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     3 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       3 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               2 
             
             = 
             
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       2 
                     
                   
                 
               
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     1 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       1 
                     
                   
                 
                 + 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       2 
                     
                   
                 
                 + 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     3 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       3 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               3 
             
             = 
             
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     3 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       3 
                     
                   
                 
               
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     1 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       1 
                     
                   
                 
                 + 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       2 
                     
                   
                 
                 + 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     3 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       3 
                     
                   
                 
               
             
           
         
       
     
         [0044]    Further, according to the set blending ratio and/or linear density, divide the yarn Y into n segments. The linear density and blending ratio of each segment of the yarn Y are the same, while the linear densities and blending ratios of the adjacent segments are different. When drafting the segment i of the yarn Y, the linear speeds of a first back roller, a second back roller, a third back roller are V h1i , V h2i , V h3i , wherein iε(1, 2, . . . , n); The first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient are two-stage drafted and twisted to form segment i of the yarn Y, and the blending ratios k 1i , k 2i  and k 3i  thereof are expressed as below: 
         [0000]    
       
         
           
             
               
                 
                   
                     k 
                     
                       1 
                        
                       i 
                     
                   
                   = 
                   
                     
                       
                         ρ 
                         1 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           1 
                            
                           i 
                         
                       
                     
                     
                       
                         
                           ρ 
                           1 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                              
                             i 
                           
                         
                       
                       + 
                       
                         
                           ρ 
                           2 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                              
                             i 
                           
                         
                       
                       + 
                       
                         
                           ρ 
                           3 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                              
                             i 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       2 
                        
                       i 
                     
                   
                   = 
                   
                     
                       
                         ρ 
                         2 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           2 
                            
                           i 
                         
                       
                     
                     
                       
                         
                           ρ 
                           1 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                              
                             i 
                           
                         
                       
                       + 
                       
                         
                           ρ 
                           2 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                              
                             i 
                           
                         
                       
                       + 
                       
                         
                           ρ 
                           3 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                              
                             i 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       3 
                        
                       i 
                     
                   
                   = 
                   
                     
                       
                         ρ 
                         3 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           3 
                            
                           i 
                         
                       
                     
                     
                       
                         
                           ρ 
                           1 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                              
                             i 
                           
                         
                       
                       + 
                       
                         
                           ρ 
                           2 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                              
                             i 
                           
                         
                       
                       + 
                       
                         
                           ρ 
                           3 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                              
                             i 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
       
         
           
             the linear density of segment i of yarn Y is: 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     ρ 
                     
                       y 
                        
                       
                           
                       
                        
                       i 
                     
                   
                   = 
                   
                     
                       
                         
                           V 
                           z 
                         
                         
                           V 
                           q 
                         
                       
                       * 
                       
                         ( 
                         
                           
                             
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   i 
                                 
                               
                               
                                 V 
                                 z 
                               
                             
                             * 
                             
                               ρ 
                               1 
                             
                           
                           + 
                           
                             
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   i 
                                 
                               
                               
                                 V 
                                 z 
                               
                             
                              
                             
                               ρ 
                               2 
                             
                           
                           + 
                           
                             
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   3 
                                    
                                   i 
                                 
                               
                               
                                 V 
                                 z 
                               
                             
                              
                             
                               ρ 
                               3 
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         1 
                         
                           e 
                           q 
                         
                       
                       * 
                       
                         ( 
                         
                           
                             
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   i 
                                 
                               
                               
                                 V 
                                 z 
                               
                             
                             * 
                             
                               ρ 
                               1 
                             
                           
                           + 
                           
                             
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   i 
                                 
                               
                               
                                 V 
                                 z 
                               
                             
                              
                             
                               ρ 
                               2 
                             
                           
                           + 
                           
                             
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   3 
                                    
                                   i 
                                 
                               
                               
                                 V 
                                 z 
                               
                             
                              
                             
                               ρ 
                               3 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
       
         
           
             wherein 
           
         
       
     
         [0000]    
       
         
           
             
               e 
               q 
             
             = 
             
               
                 V 
                 q 
               
               
                 V 
                 z 
               
             
           
         
       
     
         [0000]    is the two-stage drafting ratio; 
         [0047]    (1) Take the segment with the lowest density as a reference segment, whose reference linear density is ρ 0 . The reference linear speeds of the first back roller, the second back roller, the third back roller for this segment are respectively V h10 , V h20 , V h30 ; and the reference blending ratios of the first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient for this segment are respectively k 10 , k 20 , k 30 , 
         [0048]    Keep the linear speed of the middle roller constant, and 
         [0000]        V   z   =V   h10   +V   h20   +V   h30   (6);
 
         [0049]    (2) also keep two-stage drafting ratio 
         [0000]    
       
         
           
             
               e 
               q 
             
             = 
             
               
                 V 
                 q 
               
               
                 V 
                 z 
               
             
           
         
       
     
         [0000]    constant; wherein the reference linear speeds of the first back roller, the second back roller, the third back roller for this segment are respectively V h10 , V h20 , V h30 , which can be predetermined according to the material, reference linear density ρ 0  and reference blending ratios k 10 , k 20 , k 30  of the first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient. 
         [0050]    (3) When the segment i of the yarn Y is drafted and blended, on the premise of known set linear density ρ yi  and blending ratios k 1i , k 2i , k 3i , the linear speeds V h1i , V h2i , V h3i , of the first back roller, the second back roller, the third back roller are calculated according to Equations (2)-(6); 
         [0051]    (4) Based on the reference linear speeds V h10 , V h20 , V h30  for the reference segment, increase or decrease the rotation rates of the first back roller, the second back roller, the third back roller to dynamically adjust the linear density or/and blending ratio for the segment i of the yarn Y. 
         [0052]    Further, let ρ 1 =ρ 2 =ρ 3 =ρ, 
         [0053]    then Equation (5) can be simplified as 
         [0000]    
       
         
           
             
               
                 
                   
                     ρ 
                     yi 
                   
                   = 
                   
                     
                       ρ 
                       
                         e 
                         q 
                       
                     
                     * 
                     
                       
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                                
                               i 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                                
                               i 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                                
                               i 
                             
                           
                         
                         
                           V 
                           z 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0054]    According to Equations (2)-(4) and (6)-(7), the linear speeds V h1i , V h2i , V h3i  of the first back roller, the second back roller, the third back roller are calculated; based on the reference linear speeds V h10 , V h20 , V h30 , the rotation rates of the first back roller, the second back roller, the third back roller are increased or decreased to reach the preset linear density and blending ratio for the segment i of yarn Y. 
         [0055]    Further, at the moment of switching the segment i−1 to the segment i of yarn Y, let the linear density of the yarn Y increase by dynamic increment Δρ yi , i.e., thickness change Δρ yi . on the basis of reference linear density; and thus the first back roller, the second back roller, the third back roller have corresponding increments on the basis of the reference linear speed, i.e., when (V h10 +V h20 +V h30 )→(V h10 +ΔV h1i +V h20 +ΔV h2i +V h30 +ΔV h3i )|, the linear density increment of yarn Y is: 
         [0000]    
       
         
           
             
               Δρ 
               yi 
             
             = 
             
               
                 ρ 
                 
                   
                     e 
                     q 
                   
                   * 
                   
                     V 
                     z 
                   
                 
               
               * 
               
                 ( 
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                          
                         i 
                       
                     
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                          
                         i 
                       
                     
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                          
                         i 
                       
                     
                   
                 
                 ) 
               
                
               
                 : 
               
             
           
         
       
       
         
           
             Then the linear density ρ yi  of the yarn Y is expressed as 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     ρ 
                     yi 
                   
                   = 
                   
                     
                       
                         ρ 
                         
                           y 
                            
                           
                               
                           
                            
                           0 
                         
                       
                       + 
                       
                         Δρ 
                         yi 
                       
                     
                     = 
                     
                       
                         ρ 
                         
                           y 
                            
                           
                               
                           
                            
                           0 
                         
                       
                       + 
                       
                         
                           
                             
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   i 
                                 
                               
                             
                             + 
                             
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   i 
                                 
                               
                             
                             + 
                             
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   3 
                                    
                                   i 
                                 
                               
                             
                           
                           
                             V 
                             z 
                           
                         
                         * 
                         
                           
                             ρ 
                             
                               e 
                               q 
                             
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
       
         
           
             Let ΔV 1 =ΔV h1i +ΔV h2i +ΔV h3i , 
             then Equation (8) is simplified as: 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     ρ 
                     yi 
                   
                   = 
                   
                     
                       ρ 
                       
                         y 
                          
                         
                             
                         
                          
                         0 
                       
                     
                     + 
                     
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             1 
                           
                         
                         
                           V 
                           z 
                         
                       
                       * 
                       
                         
                           ρ 
                           
                             e 
                             q 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0059]    The linear density of yarn Y can be adjusted by controlling the sum of the linear speed increments ΔV i  of the first back roller, the second back roller, the third back roller. 
         [0060]    Further, let ‘ρ 1 =ρ 2 =ρ 3 =ρ’ at the moment of switching the segment i−1 to the segment i of the yarn Y, the blending ratios of the yarn Y in Equations (2)-(4) can be simplified as: 
         [0000]    
       
         
           
             
               
                 
                   
                     k 
                     
                       1 
                        
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           10 
                         
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                              
                             i 
                           
                         
                       
                     
                     
                       
                         V 
                         z 
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       2 
                        
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           20 
                         
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                              
                             i 
                           
                         
                       
                     
                     
                       
                         V 
                         z 
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       3 
                        
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           30 
                         
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                              
                             i 
                           
                         
                       
                     
                     
                       
                         V 
                         z 
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0061]    The blending ratios of the yarn Y can be adjusted by controlling the linear speed increments of the first back roller, the second back roller, the third back roller,
       wherein       
 
         [0000]      Δ V   h1i   =k   1i *( V   z   +ΔV   i )− V   h10  
 
         [0000]      Δ V   h2i   =k   2i *( V   z   +ΔV   i )− V   h20  
 
         [0000]      Δ V   h3i   =k   3i *( V   z   +ΔV   i )− V   h30 .
 
         [0063]    Further, let ‘V h1i *ρ 1 +V h2i *ρ 2 +V h3i *ρ 3 =H’ and H is a constant, then ΔV i  is constantly equal to zero, and thus the linear density is unchanged when the blending ratios of the yarn Y are adjusted. 
         [0064]    Further, let any one to two of ΔV h1i , ΔV h2i , ΔV h3i  be equal to zero, while the remaining ones are not zero, then the one to two roving yarn ingredients can be changed while the other roving yarn ingredients are unchanged. The adjusted blending ratios are: 
         [0000]    
       
         
           
             
               k 
               ki 
             
             = 
             
               
                 
                   V 
                   
                     hk 
                      
                     
                         
                     
                      
                     0 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     hki 
                   
                 
               
               
                 
                   V 
                   z 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     i 
                   
                 
               
             
           
         
       
       
         
           
             
               K 
               ji 
             
             = 
             
               
                 V 
                 
                   hj 
                    
                   
                       
                   
                    
                   0 
                 
               
               
                 
                   V 
                   z 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     i 
                   
                 
               
             
           
         
       
       
         
           
             wherein k, jε(1, 2, 3), and k≠j. 
           
         
       
     
         [0066]    Further, let none of ΔV h1i , ΔV h2i , ΔV h3i  be equal to zero, then the proportion of the three roving yarn ingredients in the yarn Y may be changed. 
         [0067]    Further, let any one to two of ΔV h1i , ΔV h2i , ΔV h3i  be equal to zero, while the remaining ones are not zero, then the one to two roving yarn ingredients of the segment i of the yarn Y may be discontinuous. 
         [0068]    A device for configuring a linear density and a blending ratio of a yarn by three-ingredient asynchronous/synchronous drafted, comprises a control system and an actuating mechanism. The actuating mechanism includes three-ingredient asynchronous/synchronous two-stage drafting mechanism, a twisting mechanism and a winding mechanism. The two-stage drafting mechanism includes a first stage drafting unit and a second stage drafting unit; the first stage drafting unit includes a combination of back rollers and a middle roller. The combination of back rollers has three rotational degrees of freedom and includes a first back roller, a second back roller, a third back roller, which are set abreast on a same back roller shaft. The three back rollers are set adjacently and the driving mechanisms thereof are set on both sides of the three back rollers. The second stage drafting unit includes a front roller and the middle roller. 
         [0069]    Further, the control system mainly includes a PLC programmable controller, a servo driver, a servo motor, etc. 
         [0070]    Further, any of the three back rollers is fixedly set on the back roller shaft. The other two back rollers are respectively set on the back roller shaft, and independently rotatable with each other. 
         [0071]    Further, during the process of drafting, the speed of the middle roller is fixed and no more than the sum of the speeds of the first back roller, the second back roller, the third back roller. 
         [0072]    The dot yarn and slub yarn produced by the method and device of the invention are more even and accurate in color mixing. Further, the rotation rate of the middle roller is constant, ensuring the stable blending effect. The color difference of the yarn from different batches is not obvious. The contrast about technical effects between the invention and the prior art is showed in the following table. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 The contrast about technical effects between 
               
               
                 the invention and the prior art 
               
             
          
           
               
                   
                 Dot yarn 
                 Slub yarn 
                 Linear 
                   
               
               
                   
                 pattern 
                 linear density 
                 density 
                 Color- 
               
               
                   
                 errors 
                 adjustment 
                 adjustment 
                 blending 
               
               
                   
                 (/100 m) 
                 error rate 
                 error rate 
                 evenness 
               
               
                   
                   
               
             
          
           
               
                 prior art 
                 7-8 
                 10-12% 
                 11-13% 
                 level 2-3 
               
               
                 the invention 
                 1-2 
                  1-3% 
                  1-3% 
                 level 1 
               
               
                   
               
             
          
         
       
     
         [0073]    Therefore, the invention is very effective. 
         [0074]    The method of the invention changes the traditional three-ingredient front and back areas synchronous drafting to three-ingredient separate asynchronous drafting (referred to as first stage asynchronous drafting) and three-ingredient integrated synchronous drafting (referred to as second stage synchronous drafting). The blending proportion of the three ingredients and linear density of the yarn are dynamically adjusted by the first stage separate asynchronous drafting, and the reference linear density of the yarn is adjusted by the second stage synchronous drafting. The linear density and the blending ratio of the yarn can be dynamically adjusted online by the three-ingredient separate/integrated asynchronous/synchronous two-stage drafting, combined with the spinning device and process of the twisting, which breaks through the three bottlenecks existing in the slub yarn spinning process of the prior art. The three bottlenecks are: 1. only the linear density can be adjusted while the blending ratio (color change) cannot be adjusted; 2. monotonous pattern of the slub yarn; 3. poor reproducibility of the slub yarn pattern. 
         [0075]    Calculations for the Processing Parameters of Three-Ingredient Separate/Integrated Asynchronous/Synchronous Two-Stage Drafting Coaxial Twisting Spinning System 
         [0076]    According to the drafting theory, the drafting ratio of the first stage drafting is: 
         [0000]    
       
         
           
             
               
                 
                   
                     e 
                     
                       h 
                        
                       
                           
                       
                        
                       1 
                     
                   
                   = 
                   
                     
                       
                         V 
                         z 
                       
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                     = 
                     
                       
                         ρ 
                         1 
                       
                       
                         ρ 
                         1 
                         ′ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     e 
                     
                       h 
                        
                       
                           
                       
                        
                       2 
                     
                   
                   = 
                   
                     
                       
                         V 
                         z 
                       
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           2 
                         
                       
                     
                     = 
                     
                       
                         ρ 
                         2 
                       
                       
                         ρ 
                         2 
                         ′ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     e 
                     
                       h 
                        
                       
                           
                       
                        
                       3 
                     
                   
                   = 
                   
                     
                       
                         V 
                         z 
                       
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           3 
                         
                       
                     
                     = 
                     
                       
                         ρ 
                         3 
                       
                       
                         ρ 
                         2 
                         ′ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
       
         
           
             The equivalent drafting ratio of the first stage drafting is: 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     
                       e 
                       _ 
                     
                     h 
                   
                   = 
                   
                     
                       
                         
                           ρ 
                           
                             1 
                             + 
                           
                         
                          
                         
                           ρ 
                           2 
                         
                       
                       + 
                       
                         ρ 
                         3 
                       
                     
                     
                       
                         ρ 
                         1 
                         ′ 
                       
                       + 
                       
                         ρ 
                         2 
                         ′ 
                       
                       + 
                       
                         ρ 
                         3 
                         ′ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
       
         
           
             The drafting ratio of the second stage drafting is: 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     e 
                     q 
                   
                   = 
                   
                     
                       
                         V 
                         q 
                       
                       
                         V 
                         z 
                       
                     
                     = 
                     
                       
                         
                           ρ 
                           1 
                           ′ 
                         
                         
                           ρ 
                           1 
                           ″ 
                         
                       
                       = 
                       
                         
                           
                             ρ 
                             2 
                             ′ 
                           
                           
                             ρ 
                             2 
                             ″ 
                           
                         
                         = 
                         
                           
                             
                               ρ 
                               3 
                               ′ 
                             
                             
                               ρ 
                               3 
                               ″ 
                             
                           
                           = 
                           
                             
                               
                                 ρ 
                                 1 
                                 ′ 
                               
                               + 
                               
                                 ρ 
                                 2 
                                 ′ 
                               
                               + 
                               
                                 ρ 
                                 3 
                                 ′ 
                               
                             
                             
                               
                                 ρ 
                                 1 
                                 ″ 
                               
                               + 
                               
                                 ρ 
                                 2 
                                 ″ 
                               
                               + 
                               
                                 ρ 
                                 3 
                                 ″ 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
       
         
           
             The total equivalent drafting ratio e is: 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     e 
                     _ 
                   
                   = 
                   
                     
                       
                         
                           ρ 
                           1 
                         
                         + 
                         
                           ρ 
                           2 
                         
                         + 
                         
                           ρ 
                           3 
                         
                       
                       
                         
                           ρ 
                           1 
                           ″ 
                         
                         + 
                         
                           ρ 
                           2 
                           ″ 
                         
                         + 
                         
                           ρ 
                           3 
                           ″ 
                         
                       
                     
                     = 
                     
                       
                         
                           e 
                           _ 
                         
                         h 
                       
                       * 
                       
                         e 
                         q 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0080]    The total equivalent drafting ratio ē is a significant parameter in the spinning process, which is the product of front area drafting ratio and back area drafting ratio. According to the established spinning model of the invention, the three roving yarns ρ 1 , ρ 2 , and ρ 3  are asynchronously drafted in the back area and synchronously drafted in the front area and then are integrated and twisted to form a yarn, the blending ratios thereof k 1 , k 2 , k 3  can be expressed as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     k 
                     1 
                   
                   = 
                   
                     
                       
                         ρ 
                         1 
                         ″ 
                       
                       
                         
                           ρ 
                           1 
                           ″ 
                         
                         + 
                         
                           ρ 
                           2 
                           ″ 
                         
                         + 
                         
                           ρ 
                           3 
                           ″ 
                         
                       
                     
                     = 
                     
                       
                         
                           ρ 
                           1 
                           ′ 
                         
                         
                           
                             ρ 
                             1 
                             ′ 
                           
                           + 
                           
                             ρ 
                             2 
                             ′ 
                           
                           + 
                           
                             ρ 
                             3 
                             ′ 
                           
                         
                       
                       = 
                       
                         
                           
                             ρ 
                             1 
                           
                           * 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         
                           
                             
                               ρ 
                               1 
                             
                             * 
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                           + 
                           
                             
                               ρ 
                               2 
                             
                             * 
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                           
                           + 
                           
                             
                               ρ 
                               3 
                             
                             * 
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     2 
                   
                   = 
                   
                     
                       
                         ρ 
                         2 
                         ″ 
                       
                       
                         
                           ρ 
                           1 
                           ″ 
                         
                         + 
                         
                           ρ 
                           2 
                           ″ 
                         
                         + 
                         
                           ρ 
                           3 
                           ″ 
                         
                       
                     
                     = 
                     
                       
                         
                           ρ 
                           2 
                           ′ 
                         
                         
                           
                             ρ 
                             1 
                             ′ 
                           
                           + 
                           
                             ρ 
                             2 
                             ′ 
                           
                           + 
                           
                             ρ 
                             3 
                             ′ 
                           
                         
                       
                       = 
                       
                         
                           
                             ρ 
                             2 
                           
                           * 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                         
                           
                             
                               ρ 
                               1 
                             
                             * 
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                           + 
                           
                             
                               ρ 
                               2 
                             
                             * 
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                           
                           + 
                           
                             
                               ρ 
                               3 
                             
                             * 
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     3 
                   
                   = 
                   
                     
                       
                         ρ 
                         2 
                         ″ 
                       
                       
                         
                           ρ 
                           1 
                           ″ 
                         
                         + 
                         
                           ρ 
                           2 
                           ″ 
                         
                         + 
                         
                           ρ 
                           3 
                           ″ 
                         
                       
                     
                     = 
                     
                       
                         
                           ρ 
                           2 
                           ′ 
                         
                         
                           
                             ρ 
                             1 
                             ′ 
                           
                           + 
                           
                             ρ 
                             2 
                             ′ 
                           
                           + 
                           
                             ρ 
                             3 
                             ′ 
                           
                         
                       
                       = 
                       
                         
                           
                             ρ 
                             3 
                           
                           * 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                         
                           
                             
                               ρ 
                               1 
                             
                             * 
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                           + 
                           
                             
                               ρ 
                               2 
                             
                             * 
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                           
                           + 
                           
                             
                               ρ 
                               3 
                             
                             * 
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0081]    As known from the Equations (7), (8), (9) the blending ratios of the three ingredients in the yarn is related to the surface rotation rates V h1 , V h2 , V h3  of the back rollers and the linear densities ρ 1 , ρ 2 , ρ 3  of the three roving yarns. Generally, ρ 1 , ρ 2 , ρ 3  are constant and irrelevant to the time, while V h1 , V h2 , V h3  are related to the speed of the main shaft. Because the main shaft speed has a bearing on the spinner production, different main shaft speeds are adopted for different materials and product specifications in different enterprises. As such, even though ρ 1 , ρ 2 , ρ 3  of the roving yarns are constant, the blending ratios determined by Equations (6), (7) change due to the speed change of the main shaft, which results in the changes of V h1 , V h2 , V h3  rendering the blending ratios uncertain. 
         [0082]    In the same way, the three roving yarns are two-stage drafted, integrated and twisted to form a yarn with the following linear density: 
         [0000]    
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
               
               = 
               
                 
                   
                     
                       ρ 
                       1 
                     
                     + 
                     
                       ρ 
                       2 
                     
                     + 
                     
                       ρ 
                       3 
                     
                   
                   
                     e 
                     _ 
                   
                 
                 = 
                 
                   
                     ρ 
                     1 
                     ″ 
                   
                   + 
                   
                     ρ 
                     2 
                     ″ 
                   
                   + 
                   
                     ρ 
                     3 
                     ″ 
                   
                 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
             
             = 
             
               
                 
                   
                     
                       V 
                       z 
                     
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     ρ 
                     1 
                     ′ 
                   
                 
                 + 
                 
                   
                     
                       V 
                       z 
                     
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     ρ 
                     2 
                     ′ 
                   
                 
                 + 
                 
                   
                     
                       V 
                       z 
                     
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     ρ 
                     3 
                     ′ 
                   
                 
               
               = 
               
                 
                   
                     
                       V 
                       z 
                     
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     
                       V 
                       
                         
                           h 
                            
                           
                               
                           
                            
                           1 
                         
                          
                         
                             
                         
                       
                     
                     
                       V 
                       z 
                     
                   
                   * 
                   
                     ρ 
                     1 
                   
                 
                 + 
                 
                   
                     
                       V 
                       2 
                     
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     
                       V 
                       z 
                     
                   
                    
                   
                     ρ 
                     2 
                   
                 
                 + 
                 
                   
                     
                       V 
                       2 
                     
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                     
                       V 
                       z 
                     
                   
                    
                   
                     ρ 
                     3 
                   
                 
               
             
           
         
       
       
         
           
             and then the linear density of the yarn is: 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     ρ 
                     y 
                   
                   = 
                   
                     
                       1 
                       
                         V 
                         q 
                       
                     
                      
                     
                       ( 
                       
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           * 
                           
                             ρ 
                             1 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           * 
                           
                             ρ 
                             2 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                           * 
                           
                             ρ 
                             3 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0084]    As known from Equation (10), the linear density of the yarn is related to the speed V h1 , V h2 , V h3  of the combination of back rollers and the linear densities ρ 1 , ρ 2 , ρ 3  of the three roving yarns. Generally, ρ 1 , ρ 2 , ρ 3  are constant and irrelevant to the time while V h1 , V h2 , V h3  are related to the main shaft speed set by the spinning machine. Because the main shaft speed has a bearing on the production of the spinning machine, different main shaft speeds would be adopted when spinning the different materials with different product specifications in different enterprises. As such, for the linear density determined by Equation (8), even though ρ 1 , ρ 2 , ρ 3  of the three roving yarns remain unchanged, V h1 , V h3 , V h3  would change with the main shaft speed, rendering the linear density uncertain.
       From Equation (1):       
 
         [0000]    
       
         
           
             
               ρ 
               1 
               ′ 
             
             = 
             
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 
                   V 
                   2 
                 
               
               * 
               
                 ρ 
                 1 
               
             
           
         
       
       
         
           
             From Equation (2): 
           
         
       
     
         [0000]    
       
         
           
             
               ρ 
               2 
               ′ 
             
             = 
             
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 
                   V 
                   2 
                 
               
               * 
               
                 ρ 
                 2 
               
             
           
         
       
       
         
           
             From Equation (3): 
           
         
       
     
         [0000]    
       
         
           
             
               ρ 
               3 
               ′ 
             
             = 
             
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 
                   V 
                   2 
                 
               
               * 
               
                 ρ 
                 3 
               
             
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     ∴ 
                     
                       
                         ρ 
                         1 
                         ′ 
                       
                       + 
                       
                         ρ 
                         2 
                         ′ 
                       
                       + 
                       
                         ρ 
                         3 
                         ′ 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         * 
                         
                           ρ 
                           1 
                         
                       
                       + 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         * 
                         
                           ρ 
                           2 
                         
                       
                       + 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         * 
                         
                           ρ 
                           3 
                         
                       
                     
                     
                       V 
                       z 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0088]    Equation (9) is substituted in Equation (3) and then solved for the equivalent drafting ratio ē h : 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       e 
                       _ 
                     
                     h 
                   
                   = 
                   
                     
                       
                         
                           ρ 
                           1 
                         
                         + 
                         
                           ρ 
                           2 
                         
                         + 
                         
                           ρ 
                           3 
                         
                       
                       
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           * 
                           
                             ρ 
                             1 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           * 
                           
                             ρ 
                             2 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                           * 
                           
                             ρ 
                             3 
                           
                         
                       
                     
                     * 
                     
                       V 
                       z 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0089]    Equation (10) is substituted in Equation (5) and then solved for the total equivalent drafting ratio ē: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       e 
                       _ 
                     
                     = 
                     
                       
                         
                           
                             ρ 
                             1 
                           
                           + 
                           
                             ρ 
                             2 
                           
                           + 
                           
                             ρ 
                             3 
                           
                         
                         
                           
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                             * 
                             
                               ρ 
                               1 
                             
                           
                           + 
                           
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                             * 
                             
                               ρ 
                               3 
                             
                           
                           + 
                           
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                             * 
                             
                               ρ 
                               3 
                             
                           
                         
                       
                       * 
                       
                         V 
                         z 
                       
                       * 
                       
                         
                           V 
                           q 
                         
                         
                           V 
                           z 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       e 
                       _ 
                     
                     = 
                     
                       
                         
                           
                             ρ 
                             1 
                           
                           + 
                           
                             ρ 
                             2 
                           
                           + 
                           
                             ρ 
                             3 
                           
                         
                         
                           
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                             * 
                             
                               ρ 
                               1 
                             
                           
                           + 
                           
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                             * 
                             
                               ρ 
                               2 
                             
                           
                           + 
                           
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                             * 
                             
                               ρ 
                               3 
                             
                           
                         
                       
                       * 
                       
                         V 
                         q 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0090]    To negate the changes caused by the different main shaft speeds, the limited condition is provided as follows: 
         [0000]      ρ 1 =ρ 2 =ρ 3 =ρ  (14)
       Equation (14) is substituted in Equation (9):       
 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ρ 
                       1 
                       ′ 
                     
                     + 
                     
                       ρ 
                       2 
                       ′ 
                     
                     + 
                     
                       ρ 
                       3 
                       ′ 
                     
                   
                   = 
                   
                     ρ 
                     * 
                     
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                         ) 
                       
                       
                         V 
                         z 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
       
         
           
             Equations (12), (13) are substituted in Equation (10): 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     
                       e 
                       _ 
                     
                     h 
                   
                   = 
                   
                     
                       V 
                       z 
                     
                     
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                         ) 
                       
                       3 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
       
         
           
             Equation (14) is substituted in Equation (5): 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     e 
                     _ 
                   
                   = 
                   
                     
                       
                         
                           e 
                           _ 
                         
                         h 
                       
                       * 
                       
                         e 
                         q 
                       
                     
                     = 
                     
                       
                         V 
                         q 
                       
                       
                         
                           ( 
                           
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                             + 
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                             + 
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                           ) 
                         
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
       
         
           
             Equations (15), (16), (17) are substituted in Equations (7), (8), (9): 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     k 
                     1 
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           1 
                         
                       
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           V 
                           z 
                         
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       * 
                       
                         1 
                         
                           e 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     2 
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           V 
                           z 
                         
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       * 
                       
                         1 
                         
                           e 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     3 
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           3 
                         
                       
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                       
                     
                     = 
                     
                       
                         
                           V 
                           z 
                         
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       * 
                       
                         1 
                         
                           e 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
         [0095]    Assuming ρ 1 =ρ 2 =ρ 3 =π, and adjusting the speeds of the first back roller, the second back roller and the third back roller making sure that V h1 +V h2 +V h3 =V z , then
       Equations (18), (19), (20) are changed as:       
 
         [0000]    
       
         
           
             
               k 
               1 
             
             = 
             
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     1 
                   
                 
                 
                   V 
                   z 
                 
               
               = 
               
                 1 
                 
                   e 
                   
                     h 
                      
                     
                         
                     
                      
                     1 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               2 
             
             = 
             
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 
                   V 
                   z 
                 
               
               = 
               
                 1 
                 
                   e 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               3 
             
             = 
             
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     3 
                   
                 
                 
                   V 
                   z 
                 
               
               = 
               
                 1 
                 
                   e 
                   
                     h 
                      
                     
                         
                     
                      
                     3 
                   
                 
               
             
           
         
       
     
         [0097]    The blending ratios of the three ingredients ρ 1 , ρ 2 , ρ 3  in the yarn are equal to the inverses of their respective drafting ratios. 
         [0000]    
       
         
           
             
               e 
               
                 h 
                  
                 
                     
                 
                  
                 1 
               
             
             = 
             
               
                 
                   V 
                   z 
                 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     1 
                   
                 
               
               = 
               
                 1 
                 
                   k 
                   1 
                 
               
             
           
         
       
       
         
           
             
               e 
               
                 h 
                  
                 
                     
                 
                  
                 2 
               
             
             = 
             
               
                 
                   V 
                   z 
                 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
               
               = 
               
                 1 
                 
                   k 
                   2 
                 
               
             
           
         
       
       
         
           
             
               e 
               
                 h 
                  
                 
                     
                 
                  
                 3 
               
             
             = 
             
               
                 
                   V 
                   z 
                 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     3 
                   
                 
               
               = 
               
                 1 
                 
                   k 
                   3 
                 
               
             
           
         
       
     
         [0098]    For example, assuming: 
         [0099]    k 1 =0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1 
         [0100]    k 2 =0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0, 0.1, 0.1, 0 
         [0101]    k 3 =0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.1, 0, 0 
         [0102]    Then e h1 , e h2  and e h3  can be calculated respectively, as showed in Table 2. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Blend ratio and first-stage drafting ratio 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 k 1   
                 0   
                 0.1 
                 0.2 
                 0.3 
                 0.4 
                 0.5 
                 0.6 
                 0.7 
                 0.8 
                 0.9 
                 1 
               
               
                 e h1   
                 X 
                 10   
                 5   
                 10/3 
                 10/4 
                 10/5 
                 10/6 
                 10/7 
                 10/8 
                 10/9 
                 1 
               
               
                 k 2   
                 0.7 
                 0.6 
                 0.5 
                 0.4 
                 0.3 
                 0.2 
                 0.1 
                 0   
                 0.1 
                 0.1 
                 0 
               
               
                 e h2   
                 10/7 
                 10/6 
                 10/5 
                 10/4 
                 10/3 
                 5   
                 10   
                 X 
                 10   
                 10   
                 X 
               
               
                 k 3   
                 0.3 
                 0.3 
                 0.3 
                 0.3 
                 0.3 
                 0.3 
                 0.3 
                 0.3 
                 0.1 
                 0   
                 0 
               
               
                 e h3   
                 10/3 
                 10/3 
                 10/3 
                 10/3 
                 10/3 
                 10/3 
                 10/3 
                 10/3 
                 10   
                 X 
                 X 
               
               
                   
               
             
          
         
       
     
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0103]      FIG. 1  is a principle schematic diagram of the two-stage drafting spinning device; 
           [0104]      FIG. 2  is a structural schematic diagram of a combination of back rollers; 
           [0105]      FIG. 3  is a structural side view of the two-stage drafting spinning device; 
           [0106]      FIG. 4  is a yarn route of the two-stage drafting in an embodiment; 
           [0107]      FIG. 5  is a structural schematic diagram of a control system. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0108]    The embodiments of the invention are described as below, in combination with the accompanying drawings. 
       Embodiment 1 
       [0109]    As demonstrated by  FIG. 1-5 , a method of dynamically configuring linear density and blending ratio of yarn by three-ingredient asynchronous/synchronous drafting is disclosed, comprising: 
         [0110]    1) a drafting and twisting system includes a first stage drafting unit and a successive second stage drafting unit; 
         [0111]    2) the first stage drafting unit includes a combination of back rollers  11  and a middle roller  3 ; The combination of back rollers has three rotational degrees of freedom and includes a first back roller  5 , a second back roller  7 , a third back roller  9 , which are set abreast on a same back roller shaft. The second stage synchronous drafting unit includes a front roller  1  and the middle roller  3 .  4  is the top roller of middle roller  3 .  6 ,  8 ,  10  are the top rollers of three back rollers respectively.  2  is the top roller of front roller  1 .  13  and  14  are the winding device and guider roller respectively.  15  is the yarn Y. 
         [0112]    The first back roller, the second back roller, the third back roller move at the speeds V h1 , V h2 , and V h3  respectively. The middle roller rotates at the speed V z . The second stage synchronous drafting unit includes a front roller and the middle roller. The front roller rotates at the surface linear speed V q . 
         [0113]      FIG. 2  shows a three-nested combination of back rollers with three rotational degrees of freedom. The three movable back rollers  5 ,  7 ,  9  are respectively driven by a core shaft and pulleys  16 ,  22  and  17 . 
         [0114]      FIG. 4  illustrates the yarn route of the two-stage drafting. During the process of spinning, the three roving yarns are fed in parallel into the corresponding independently driven first stage drafting mechanism to be asynchronously drafted, and synchronously drafted and integrated by the second stage drafting mechanism, and then twisted to form a yarn Y. Dynamical change of blend ratio and yarn density can be controlled exactly by the first-stage asynchronous drafting. The yarn density can be controlled by the second-stage drafting. Thus the yarn can be produces with much fine mixing and low breaking ration. 
         [0115]    As figured out by  FIG. 5  the control system mainly includes a PLC programmable controller, a servo driver, a servo motor, etc. PLC programmable controller controls rollers, ring rails and spindles by servo motor which is controlled by servo driver. Assuming the linear densities of a first roving yarn ingredient, a second roving yarn ingredient, a third roving yarn ingredient drafted by the first back roller, the second back roller, the third back roller are respectively ρ 1 , ρ 2 , and ρ 3 , the linear density of the yarn Y drafted and twisted by the front roller is ρ y . 
         [0000]      ρ y =1/ V   o ( V   h1 *ρ 1   +V   h2 *ρ 2   +V   h3 *ρ 3 )  (1)
 
         [0116]    The blending ratios of the first roving yarn ingredient, the second roving yarn ingredient, and the third roving yarn ingredient are respectively k 1 , k 2 , and k 3 . 
         [0000]    
       
         
           
             
               k 
               1 
             
             = 
             
               
                 
                   ρ 
                   1 
                   ″ 
                 
                 
                   
                     ρ 
                     1 
                     ″ 
                   
                   + 
                   
                     ρ 
                     2 
                     ″ 
                   
                   + 
                   
                     ρ 
                     3 
                     ″ 
                   
                 
               
               = 
               
                 
                   
                     ρ 
                     1 
                     ′ 
                   
                   
                     
                       ρ 
                       1 
                       ′ 
                     
                     + 
                     
                       ρ 
                       2 
                       ′ 
                     
                     + 
                     
                       ρ 
                       3 
                       ′ 
                     
                   
                 
                 = 
                 
                   
                     
                       ρ 
                       1 
                     
                     * 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                   
                     
                       
                         ρ 
                         1 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                     + 
                     
                       
                         ρ 
                         2 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           2 
                         
                       
                     
                     + 
                     
                       
                         ρ 
                         3 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           3 
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               2 
             
             = 
             
               
                 
                   ρ 
                   2 
                   ″ 
                 
                 
                   
                     ρ 
                     1 
                     ″ 
                   
                   + 
                   
                     ρ 
                     2 
                     ″ 
                   
                   + 
                   
                     ρ 
                     3 
                     ″ 
                   
                 
               
               = 
               
                 
                   
                     ρ 
                     2 
                     ′ 
                   
                   
                     
                       ρ 
                       1 
                       ′ 
                     
                     + 
                     
                       ρ 
                       2 
                       ′ 
                     
                     + 
                     
                       ρ 
                       3 
                       ′ 
                     
                   
                 
                 = 
                 
                   
                     
                       ρ 
                       2 
                     
                     * 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                   
                   
                     
                       
                         ρ 
                         1 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                     + 
                     
                       
                         ρ 
                         2 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           2 
                         
                       
                     
                     + 
                     
                       
                         ρ 
                         3 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           3 
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               3 
             
             = 
             
               
                 
                   ρ 
                   3 
                   ″ 
                 
                 
                   
                     ρ 
                     1 
                     ″ 
                   
                   + 
                   
                     ρ 
                     2 
                     ″ 
                   
                   + 
                   
                     ρ 
                     3 
                     ″ 
                   
                 
               
               = 
               
                 
                   
                     ρ 
                     3 
                     ′ 
                   
                   
                     
                       ρ 
                       1 
                       ′ 
                     
                     + 
                     
                       ρ 
                       2 
                       ′ 
                     
                     + 
                     
                       ρ 
                       3 
                       ′ 
                     
                   
                 
                 = 
                 
                   
                     
                       ρ 
                       3 
                     
                     * 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                   
                   
                     
                       
                         ρ 
                         1 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                     + 
                     
                       
                         ρ 
                         2 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           2 
                         
                       
                     
                     + 
                     
                       
                         ρ 
                         3 
                       
                       * 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           3 
                         
                       
                     
                   
                 
               
             
           
         
       
     
         [0117]    3) Keeping the ratio of linear speeds of the front roller and the middle roller V q /V z  constant, the speeds of the front roller and the middle roller depend on reference linear density of the yarn; 
         [0000]    4) The linear density of yarn Y or/and blending ratio can be dynamically adjusted on line, by adjusting the rotation rates of the first back roller, the second back roller, the third back roller.
 
5) Further, the blending ratios of the first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient are set respectively as k 1 , k 2 , and k 3 . The ratios of blending ratios of the yarn Y are respectively K 1 , and K 2 .
 
         [0000]    
       
         
           
             
               
                 K 
                 1 
               
               = 
               
                 
                   
                     k 
                     1 
                   
                   
                     k 
                     2 
                   
                 
                 = 
                 
                   
                     
                       ρ 
                       1 
                     
                      
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                   
                     
                       ρ 
                       2 
                     
                      
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                   
                 
               
             
             , 
             
               
 
             
              
             
               
                 K 
                 2 
               
               = 
               
                 
                   
                     k 
                     1 
                   
                   
                     k 
                     3 
                   
                 
                 = 
                 
                   
                     
                       ρ 
                       1 
                     
                      
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                   
                     
                       ρ 
                       3 
                     
                      
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                   
                 
               
             
           
         
       
     
         [0118]    Linear density of yarn Y is 
         [0000]    
       
         
           
             
               ρ 
               y 
             
             = 
             
               
                 
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       1 
                     
                   
                   * 
                   
                     ρ 
                     1 
                   
                 
                 + 
                 
                   
                     V 
                     h2 
                   
                   * 
                   
                     ρ 
                     2 
                   
                 
                 + 
                 
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       3 
                     
                   
                   * 
                   
                     ρ 
                     3 
                   
                 
               
               
                 V 
                 q 
               
             
           
         
       
     
         [0119]    then a surface linear speed of the back roller  1 : 
         [0000]    
       
         
           
             
               V 
               
                 h 
                  
                 
                     
                 
                  
                 1 
               
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                  
                 
                   V 
                   q 
                 
               
               
                 
                   ρ 
                   1 
                 
                  
                 
                   ( 
                   
                     1 
                     + 
                     
                       1 
                       
                         K 
                         1 
                       
                     
                     + 
                     
                       1 
                       
                         K 
                         2 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
         [0120]    a surface linear speed of the back roller  2 : 
         [0000]    
       
         
           
             
               V 
               
                 h 
                  
                 
                     
                 
                  
                 2 
               
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                  
                 
                   V 
                   q 
                 
               
               
                 
                   ρ 
                   2 
                 
                  
                 
                   ( 
                   
                     1 
                     + 
                     
                       K 
                       1 
                     
                     + 
                     
                       
                         K 
                         1 
                       
                       
                         K 
                         2 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
         [0121]    a surface linear speed of the back roller  3 : 
         [0000]    
       
         
           
             
               V 
               
                 h 
                  
                 
                     
                 
                  
                 3 
               
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                  
                 
                   V 
                   q 
                 
               
               
                 
                   ρ 
                   3 
                 
                  
                 
                   ( 
                   
                     1 
                     + 
                     
                       K 
                       2 
                     
                     + 
                     
                       
                         K 
                         2 
                       
                       
                         K 
                         1 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
         [0122]    wherein ρ 1 , ρ 2 , and ρ 3  are constants, and K i  and ρ y  are functions changing with time t. 
         [0123]    6) Further, let ρ 1 =ρ 2 =ρ 3 =ρ, then:
       (1) change the speed of any one of the first back roller, the second back roller, and the third back roller, and keep the speeds of the other two backer rollers unchanged. The yarn ingredient and the linear density thereof of the yarn Y drafted by this back roller change accordingly. The linear density ρ′ y  of the yarn Y is adjusted as:       
 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   ( 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                     + 
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           3 
                         
                       
                     
                   
                   ) 
                 
                  
                 
                     
                 
                  
                 or 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   ( 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                     + 
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           2 
                         
                       
                     
                   
                   ) 
                 
                  
                 
                     
                 
                  
                 or 
               
             
           
         
       
       
         
           
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     ( 
                     
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           1 
                         
                       
                       + 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       + 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           3 
                         
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                     
                     ) 
                   
                 
               
             
              
             
                 
             
           
         
       
     
         [0125]    wherein Δρ y  is a linear density change of the yarn, ΔV h1 , ΔV h2  and ΔV h3  is a speed change of the first back roller, the second back roller, and the third back roller respectively.
       (2) change the speeds of any two back rollers of the first back roller, the second back roller, and the third back roller, and keep the speeds of the other backer roller unchanged. The yarn ingredients of the yarn Y drafted by these any two back rollers and the linear densities thereof change accordingly. The linear density ρ′ y  of yarn Y is adjusted as:       
 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 or 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 or 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                          
                         
                             
                         
                          
                         3 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
               
             
           
         
       
       
         
           
             (3) change the speeds of three back rollers of the first back roller, the second back roller, and the third back roller simultaneously. The yarn ingredients of the yarn Y drafted by these three back rollers and the linear densities thereof change accordingly. 
           
         
       
     
         [0128]    The linear density ρ′ y  of the yarn Y is adjusted as: 
         [0000]    
       
         
           
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           1 
                         
                       
                       + 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       + 
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           3 
                         
                       
                       + 
                       
                         ( 
                         
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                         ) 
                       
                     
                     ] 
                   
                 
               
             
              
             
                 
             
           
         
       
     
         [0129]    7) Further, change the speeds of the first back roller, the second back roller, and the third back roller, and make the speed of any of back rollers equal to zero, while the speeds of the other two backer rollers unequal to zero. The yarn ingredient of the yarn Y drafted by the any one of back rollers is thus discontinuous, while the other two yarn ingredients are continuous. The linear density ρ′ y  of yarn Y is adjusted as: 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     0 
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     
                       T 
                       1 
                     
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       2 
                     
                   
                   ) 
                 
                  
                 
                     
                 
                  
                 or 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     
                       T 
                       1 
                     
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       2 
                     
                   
                   ) 
                 
                  
                 
                     
                 
                  
                 or 
               
             
           
         
       
       
         
           
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                         ) 
                       
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
              
             
                 
             
           
         
       
     
         [0130]    wherein T 1  and T 2  are time points, and t is a time variable. 
         [0131]    8) Further, change the speeds of the first back roller, the second back roller, and the third back roller, make the speeds of any two back rollers equal to zero successively, while the speeds of the other one backer rollers unequal to zero. The yarn ingredients of the yarn Y drafted by the any two back rollers are thus discontinuous, while the other yarn ingredients are continuous. The linear density ρ′ y  of the yarn Y is adjusted as: 
         [0132]    (1) When the first back roller is unequal to zero 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     0 
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     
                       T 
                       1 
                     
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       2 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                    
                   
                       
                   
                    
                   or 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                         ) 
                       
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
              
             
                 
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0133]    wherein T 3  is time points, and T 1 ≦T 2 ≦T 3    
         [0134]    (2) When the second back roller is unequal to zero 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     0 
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     
                       T 
                       1 
                     
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       2 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                    
                   
                       
                   
                    
                   or 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                         ) 
                       
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0135]    (3) When the third back roller is unequal to zero 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     0 
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     
                       T 
                       1 
                     
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       2 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                    
                   
                       
                   
                    
                   or 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               V 
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 3 
                               
                             
                           
                         
                         ) 
                       
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         
                           T 
                           1 
                         
                         ≤ 
                         t 
                       
                       | 
                       
                         ≤ 
                         
                           T 
                           2 
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0136]    9) further change the speeds of the first back roller, the second back roller, and the third back roller, make the speeds of any two back rollers equal to zero simultaneously, while the speeds of the other one backer rollers unequal to zero. The yarn ingredients of the yarn Y drafted by the any two back rollers are thus discontinuous, while the other one yarn ingredients are continuous. The linear density ρ′ y  of the yarn Y is adjusted as: 
         [0000]    
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     0 
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                    
                   
                       
                   
                    
                   or 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                    
                   
                       
                   
                    
                   or 
                 
               
             
           
         
       
       
         
           
             
                 
             
              
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             3 
                           
                         
                         + 
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             
                               h 
                                
                               
                                   
                               
                                
                               3 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0137]    10) Further, change the speeds of the first back roller, the second back roller, and the third back roller, and keep 
         [0000]        V   h1 *ρ 1   +V   h2 *ρ 2   +V   h3 *ρ 3 =constant
 
         [0000]      and ‘ρ 1 =ρ 2 =ρ 3 =ρ’
 
         [0138]    then the linear density of the yarn Y is thus fixed while the blending ratios of the ingredients thereof change; the blending ratios of the first yarn ingredient, the second yarn ingredient, and the third yarn ingredient are k 1 , k 2 , k 3 . 
         [0000]    
       
         
           
             
               k 
               1 
             
             = 
             
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     1 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       1 
                     
                   
                 
               
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     1 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       1 
                     
                   
                 
                 + 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     h2 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     3 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       3 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               2 
             
             = 
             
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       2 
                     
                   
                 
               
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     1 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       1 
                     
                   
                 
                 + 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     h2 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     3 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       3 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               3 
             
             = 
             
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     3 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       3 
                     
                   
                 
               
               
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     1 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       1 
                     
                   
                 
                 + 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     2 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     h2 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                      
                     
                         
                     
                      
                     3 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     
                       h 
                        
                       
                           
                       
                        
                       3 
                     
                   
                 
               
             
           
         
       
     
       Embodiment 2 
       [0139]    The method of this embodiment is substantially the same as Embodiment 1, and the differences are: 
         [0140]    1) according to the set blending ratio and/or linear density, divide the yarn Y into n segments. The linear density and blending ratio of each segment of the yarn Y are the same, while the linear densities and blending ratios of the adjacent segments are different. When drafting the segment i of the yarn Y, the linear speeds of the first back roller, the second back roller, the third back roller are V h1i , V h2i , V h3i , wherein iε(1, 2, . . . , n); The first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient are two-stage drafted and twisted to form segment i of the yarn Y, and the blending ratios k 1i , k 2i  and k 3i  thereof are expressed as below: 
         [0000]    
       
         
           
             
               
                 
                   
                     k 
                     11 
                   
                   = 
                   
                     
                       
                         ρ 
                         1 
                       
                       * 
                       Δ 
                        
                       
                           
                       
                        
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           11 
                         
                       
                     
                     
                       
                         
                           ρ 
                           1 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             11 
                           
                         
                       
                       + 
                       
                         
                           ρ 
                           2 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             21 
                           
                         
                       
                       + 
                       
                         
                           ρ 
                           3 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             31 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     21 
                   
                   = 
                   
                     
                       
                         ρ 
                         2 
                       
                       * 
                       Δ 
                        
                       
                           
                       
                        
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           21 
                         
                       
                     
                     
                       
                         
                           ρ 
                           1 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             11 
                           
                         
                       
                       + 
                       
                         
                           ρ 
                           2 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             21 
                           
                         
                       
                       + 
                       
                         
                           ρ 
                           3 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             31 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     31 
                   
                   = 
                   
                     
                       
                         ρ 
                         3 
                       
                       * 
                       Δ 
                        
                       
                           
                       
                        
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           31 
                         
                       
                     
                     
                       
                         
                           ρ 
                           1 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             11 
                           
                         
                       
                       + 
                       
                         
                           ρ 
                           2 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             21 
                           
                         
                       
                       + 
                       
                         
                           ρ 
                           3 
                         
                         * 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             31 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
       
         
           
             the linear density of segment i of yarn Y is: 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     ρ 
                     yi 
                   
                   = 
                   
                     
                       
                         
                           V 
                           z 
                         
                         
                           V 
                           q 
                         
                       
                       × 
                       
                         ( 
                         
                           
                             
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   11 
                                 
                               
                               
                                 V 
                                 x 
                               
                             
                             * 
                             
                               ρ 
                               1 
                             
                           
                           + 
                           
                             
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   21 
                                 
                               
                               
                                 V 
                                 □ 
                               
                             
                              
                             
                               ρ 
                               2 
                             
                           
                           + 
                           
                             
                               
                                 V 
                                 □ 
                               
                               
                                 V 
                                 x 
                               
                             
                              
                             
                               ρ 
                               3 
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         1 
                         
                           e 
                           q 
                         
                       
                       * 
                       
                         ( 
                         
                           
                             
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   11 
                                 
                               
                               
                                 V 
                                 x 
                               
                             
                             * 
                             
                               ρ 
                               1 
                             
                           
                           + 
                           
                             
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   21 
                                 
                               
                               
                                 V 
                                 x 
                               
                             
                              
                             
                               ρ 
                               2 
                             
                           
                           + 
                           
                             
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   31 
                                 
                               
                               
                                 V 
                                 x 
                               
                             
                              
                             
                               ρ 
                               3 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
       
         
           
             wherein 
           
         
       
     
         [0000]    
       
         
           
             
               e 
               q 
             
             = 
             
               
                 V 
                 q 
               
               
                 V 
                 z 
               
             
           
         
       
     
         [0000]    is the two-stage drafting ratio; 
         [0143]    2) Take the segment with the lowest density as a reference segment, whose reference linear density is ρ 0 . The reference linear speeds of the first back roller, the second back roller, the third back roller for this segment are respectively V h10 , V h20 , V h30 ; and the reference blending ratios of the first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient for this segment are respectively k 10 , k 20 , k 30 , 
         [0144]    Keep the linear speed of the middle roller constant, and 
         [0000]        V   z   =V   h10   +V   h20   +V   h30   (6);
 
         [0145]    also keep two-stage drafting ratio 
         [0000]    
       
         
           
             
               e 
               q 
             
             = 
             
               
                 V 
                 q 
               
               
                 V 
                 z 
               
             
           
         
       
     
         [0000]    constant; 
         [0146]    wherein the reference linear speeds of the first back roller, the second back roller, the third back roller for this segment are respectively V h10 , V h20 , V h30 , which can be predetermined according to the material, reference linear density ρ 0  and reference blending ratios k 10 , k 20 , k 30  of the first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient. 
         [0147]    3) When the segment i of the yarn Y is drafted and blended, on the premise of known set linear density ρ yi  and blending ratios k 1i , k 2i , k 3i , the linear speeds V h1i , V h2i , V h3i , of the first back roller, the second back roller, the third back roller are calculated according to Equations (2)-(6); 
         [0148]    4) Based on the reference linear speeds V h10 , V h20 , V h30  for the reference segment, increase or decrease the rotation rates of the first back roller, the second back roller, the third back roller to dynamically adjust the linear density or/and blending ratio for the segment i of the yarn Y. 
         [0149]    5) Further, let ρ 1 =ρ 2 =ρ 3 =ρ,
       then Equation (5) can be simplified as       
 
         [0000]    
       
         
           
             
               
                 
                   
                     ρ 
                     yi 
                   
                   = 
                   
                     
                       ρ 
                       
                         e 
                         q 
                       
                     
                     * 
                     
                       
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             11 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             21 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             31 
                           
                         
                       
                       
                         V 
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0151]    According to Equations (2)-(4) and (6)-(7), the linear speeds V h1i , V h2i , V h3i  of the first back roller, the second back roller, the third back roller are calculated; based on the reference linear speeds V h10 , V h20 , V h30 , the rotation rates of the first back roller, the second back roller, the third back roller are increased or decreased to reach the preset linear density and blending ratio for the segment i of yarn Y. 
         [0152]    6) Further, at the moment of switching the segment i−1 to the segment i of yarn Y, let the linear density of the yarn Y increase by dynamic increment Δρ yi , i.e., thickness change Δρ yi , on the basis of reference linear density; and thus the first back roller, the second back roller, the third back roller have corresponding increments on the basis of the reference linear speed, i.e., when (V h10 +V h20 +V h30 )→(V h10 +ΔV h1i +V h20 +ΔV h2i +V h30 +ΔV h3i )|, the linear density increment of yarn Y is: 
         [0000]    
       
         
           
             
               Δ 
                
               
                   
               
                
               
                 ρ 
                 yi 
               
             
             = 
             
               
                 ρ 
                 
                   
                     e 
                     q 
                   
                   × 
                   
                     V 
                     z 
                   
                 
               
               * 
               
                 
                   ( 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           11 
                         
                       
                     
                     + 
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           21 
                         
                       
                     
                     + 
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           31 
                         
                       
                     
                   
                   ) 
                 
                 . 
               
             
           
         
       
       
         
           
             Then the linear density ρ yi  of the yarn Y is expressed as 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     ρ 
                     
                       y 
                        
                       
                           
                       
                        
                       1 
                     
                   
                   = 
                   
                     
                       
                         ρ 
                         
                           y 
                            
                           
                               
                           
                            
                           0 
                         
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           ρ 
                           
                             y 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                     
                     = 
                     
                       
                         ρ 
                         
                           y 
                            
                           
                               
                           
                            
                           0 
                         
                       
                       + 
                       
                         
                           
                             
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   i 
                                 
                               
                             
                             + 
                             
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   i 
                                 
                               
                             
                             + 
                             
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 V 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   3 
                                    
                                   
                                       
                                   
                                    
                                   i 
                                 
                               
                             
                           
                           
                             V 
                             z 
                           
                         
                         * 
                         
                           
                             ρ 
                             
                               e 
                               q 
                             
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
       
         
           
             Let ΔV i =ΔV h1i +ΔV h2i +ΔV h3i , 
             then Equation (8) is simplified as: 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     ρ 
                     
                       y 
                        
                       
                           
                       
                        
                       1 
                     
                   
                   = 
                   
                     
                       ρ 
                       
                         y 
                          
                         
                             
                         
                          
                         0 
                       
                     
                     + 
                     
                       
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             V 
                             i 
                           
                         
                         
                           V 
                           z 
                         
                       
                       * 
                       
                         
                           ρ 
                           
                             e 
                             q 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0156]    The linear density of yarn Y can be adjusted by controlling the sum of the linear speed increments ΔV i  of the first back roller, the second back roller, the third back roller. 
         [0157]    7) Further, let ρ 1 =ρ 2 =ρ 3 =ρ,
       at the moment of switching the segment i−1 to the segment i of the yarn Y, the blending ratios of the yarn Y in Equations (2)-(3) can be simplified as:       
 
         [0000]    
       
         
           
             
               
                 
                   
                     k 
                     
                       1 
                        
                       
                           
                       
                        
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           10 
                         
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             11 
                           
                         
                       
                     
                     
                       
                         V 
                         1 
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           1 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       2 
                        
                       
                           
                       
                        
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           20 
                         
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             21 
                           
                         
                       
                     
                     
                       
                         V 
                         1 
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           1 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       3 
                        
                       
                           
                       
                        
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                            
                           
                               
                           
                            
                           30 
                         
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           
                             h 
                              
                             
                                 
                             
                              
                             31 
                           
                         
                       
                     
                     
                       
                         V 
                         1 
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           V 
                           1 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0159]    The blending ratios of the yarn Y can be adjusted by controlling the linear speed increments of the first back roller, the second back roller, the third back roller;
       wherein       
 
         [0000]      Δ V   h1i   =k   1i *( V   z   +ΔV   i )− V   h10  
 
         [0000]      Δ V   h2i   =k   2i *( V   z   +ΔV   i )− V   h20  
 
         [0000]      Δ V   h3i   =k   3i *( V   z   +ΔV   i )− V   h30 .
 
         [0161]    8) Further, let ‘V h1i *ρ 1 +V h2i *ρ 2 +V h3i *ρ 3 =H’ and H is a constant, then ΔV i  is constantly equal to zero, and thus the linear density is unchanged when the blending ratios of the yarn Y are adjusted. 
         [0162]    9) Further, let any one to two of ΔV h1i , ΔV h2i , ΔV h3i  be equal to zero, while the remaining ones are not zero, then the one to two roving yarn ingredients can be changed while the other roving yarn ingredients are unchanged. The adjusted blending ratio are: 
         [0000]    
       
         
           
             
               k 
               ki 
             
             = 
             
               
                 
                   V 
                   
                     hk 
                      
                     
                         
                     
                      
                     0 
                   
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     hki 
                   
                 
               
               
                 
                   V 
                   z 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     i 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               ji 
             
             = 
             
               
                 V 
                 
                   hj 
                    
                   
                       
                   
                    
                   0 
                 
               
               
                 
                   V 
                   z 
                 
                 + 
                 
                   Δ 
                    
                   
                       
                   
                    
                   
                     V 
                     i 
                   
                 
               
             
           
         
       
       
         
           
             wherein k, jε(1, 2, 3), and k≠j. 
           
         
       
     
         [0164]    10) Further, let none of ΔV h1i , ΔV h2i , ΔV h3i  be equal to zero, then the proportion of the three roving yarn ingredients in the yarn Y may be changed. 
         [0165]    11) Further, let any one to two of ΔV h1i , ΔV h2i , ΔV h3i  be equal to zero, while the remaining ones are not zero, then the one to two roving yarn ingredients of the segment i of the yarn Y may be discontinuous. 
       Embodiment 3 
       [0166]    The method of dynamically configuring linear density and blending ratio of a yarn by three-ingredient asynchronous drafting disclosed in this embodiment is substantially the same as Embodiment 2, and the differences are: 
         [0167]    Set the initial linear speeds of the first back roller, a second back roller, a third back roller as V h10 , V h20 , V h30 ; the initial linear speed of the middle roller V x0 =V h10 +V h20 +V h30  In addition, set V zi =V h1(i-1) +V h2(i-1) +V h3(i-1) , and let the two-stage drafting ratio 
         [0000]    
       
         
           
             
               e 
               qi 
             
             = 
             
               
                 v 
                 qi 
               
               
                 v 
                 zi 
               
             
           
         
       
     
         [0000]    constantly be equal to the set value e q ; 
         [0168]    When drafting and blending the segment i of the yarn Y, take the linear density and the blending ratio of the segment i−1 as a reference linear density and a reference blending ratio of segment i. On the premise of the known set linear density ρ yi  and blending ratios k 1i , k 2i , k 3i , the linear speeds V h1i , V h2i , V h3i  of a first back roller, a second back roller, a third back roller are calculated. 
         [0169]    On the basis of the segment i−1, the rotation rates of the first back roller the second back roller and the third back roller are adjusted to dynamically regulate the linear density or/and blending ratio of segment i of the yarn Y on line. 
         [0170]    In the method, V zi =V h1(i-1) +V h2(i-1) +V h3(i-1)  and the two-stage drafting ratio is constant, and thus the speeds of the middle roller and the front roller are continually adjusted with the speeds of the back rollers, to avoid a substantial change of the drafting ratio of the yarn resulted from untimely adjusted speeds of the middle roller and the front roller as opposed to a relatively large speed adjustment of the combination of the back rollers, and effectively prevent yarn breakage. 
         [0171]    In addition, the operating speed of each roller is recorded in real time by a computer or other intellectual control unit, and thus the speeds of the middle roller and the front roller in the next step can be automatically calculated if the current speeds of the back rollers are known. The speed increments/decrements of the combination of the back rollers are calculated quickly with the above equations and models, to adjust the set blending ratio and linear density more easily and accurately. 
         [0000]    
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Parameter comparison between asynchronous drafting and synchronous drafting (taking 18.45tex cotton yarn as an example) 
               
             
          
           
               
                   
                 Synchronous drafting 
                 Synchronous drafting 
                 Asynchronous drafting 
               
               
                   
                 for double ingredients 
                 for double ingredients 
                 for three ingredients 
               
             
          
           
               
                   
                 Synchronous drafting 
                 spinning 
                 spinning 
                 spinning 
               
             
          
           
               
                   
                 for single ingredient 
                 Ingredi- 
                 Ingredi- 
                 Ingredi- 
                 Ingredi- 
                 Ingredi- 
                 Ingredi- 
                 Ingredi- 
               
               
                   
                 spinning 
                 ent 1 
                 ent 2 
                 ent 1 
                 ent 2 
                 ent 1 
                 ent 2 
                 ent 3 
               
               
                   
                   
               
             
          
           
               
                 Roving yarn 
                 5.0 
                 5.0 
                 5.0 
                 5.0 
                 5.0 
                 5.0 
                 5.0 
                 5.0 
               
               
                 weight 
               
               
                 (g/5 in) 
               
             
          
           
               
                 Back area 
                 1.1-1.3 
                 1.1-1.3 
                 1.1-1.3 
                 1.1-1.3 
                 1.1-1.3 
                 1.1-1.3 
                 3°(k1 + 
                 3°(k1 + 
                 3°(k1 + 
               
               
                 drafting 
                   
                   
                   
                   
                   
                   
                 k2 + 3)/k1 
                 k2 + k3)/k2 
                 k2 + k3)/k3 
               
               
                 ratio 
                   
                   
                   
                   
                   
                   
                 Changes with 
                 Changes with 
                 Changes with 
               
               
                   
                   
                   
                   
                   
                   
                   
                 the blending 
                 the blending 
                 the blending 
               
               
                   
                   
                   
                   
                   
                   
                   
                 ratio 
                 ratio 
                 ratio 
               
               
                 Front area 
                 24.6-20.8 
                 32.7 
                 49.2-41.6 
                 49.2-41.6 
                 45.4 
                 45.4 
                 81.6 
                 81.6 
                 81.6 
               
               
                 drafting 
               
               
                 ratio 
               
             
          
           
               
                 Back roller 
                 unchanged 
                 changed 
                 unchanged 
                 changed 
                   
                 Asynchronous 
                 Asynchronous 
                 Asynchronous 
               
               
                 speed 
                   
                   
                   
                   
                   
                 change 
                 change 
                 change 
               
             
          
           
               
                 Middle roller 
                 unchanged 
                 unchanged 
                 unchanged 
                 unchanged 
                 unchanged 
               
               
                 speed 
               
               
                 Front roller 
                 unchanged 
                 unchanged 
                 unchanged 
                 unchanged 
                 unchanged 
               
               
                 speed 
               
               
                 Average 
                 18.45 
                 18.45 
                 18.45 
                 18.45 
                 18.45 
               
               
                 spinning 
               
               
                 number 
               
               
                 (tex) 
               
               
                 Linear speed 
                 invariable 
                 Limitedly 
                 invariable 
                 Limitedly 
                 Variable, adjustable 
               
               
                 variable 
                   
                 variable 
                   
                 variable 
               
               
                 Blending 
                 invariable 
                 invariable 
                 invariable 
                 Limitedly 
                 Variable, adjustable 
               
               
                 ratio 
                   
                   
                   
                 variable 
               
               
                 variable 
               
               
                 Linear speed 
                 invariable 
                 invariable 
                 invariable 
                 Limitedly 
                 Variable, adjustable 
               
               
                 and blending 
                   
                   
                   
                 variable 
               
               
                 ratio both 
               
               
                 variable 
               
             
          
           
               
                 Spinning 
                 Even yarn 
                 Slub yarn 
                 Even yarn 
                 Limited 
                 Even yarn 
                 Even yarn 
                 Even yarn 
                 Even yarn 
               
               
                 effect 
                   
                   
                   
                 segmented 
                 Any 
                 Any 
                 Any 
                 Any 
               
               
                   
                   
                   
                   
                 color 
                 blending 
                 blending 
                 blending 
                 blending 
               
               
                   
                   
                   
                   
                 Limited 
                 ratio 
                 ratio 
                 ratio 
                 ratio 
               
               
                   
                   
                   
                   
                 slub yarn 
                 Color- 
                 Segment- 
                 Segment- 
                 slub yarn 
               
               
                   
                   
                   
                   
                   
                 blended 
                 color 
                 color 
               
               
                   
                   
                   
                   
                   
                 yarn 
                 blended 
                 blended 
               
               
                   
                   
                   
                   
                   
                   
                 yarn 
                 yarn 
               
               
                   
               
             
          
         
       
     
         [0172]    Several preferable embodiments are described, in combination with the accompanying drawings. However, the invention is not intended to be limited herein. Any improvements and/or modifications by the skilled in the art, without departing from the spirit of the invention, would fall within protection scope of the invention.