Patent Publication Number: US-10316434-B2

Title: Method and device of dynamically configuring linear density and blending ratio of yarn by five-ingredient asynchronous/synchronous drafting

Description:
TECHNICAL FIELD 
     The invention relates to a ring spinning field of a textile industry, and particularly relates to a method and device of dynamically configuring linear density and blending ratio of yarn by five-ingredient asynchronous/synchronous drafting. 
     BACKGROUND 
     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. 
     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 dotted yarn, etc.; 
     (3) yarn with a variable linear density and blending ratio, such as segmented a color slub yarn, a segmented color dotted yarn, etc.; 
     (4) blended yarn or mixed color yarn mixed at any rate, with a constant linear density and blending ratio. 
     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: 
     (1) yarn with a constant linear density and a variable blending ratio (color blending ratio) 
     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. 
     (2) yarn with a constant blending ratio and variable linear density 
     The yarn with a constant blending ratio and variable linear density, can be such as a slub yarn, a dotted 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” (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 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 dotted yarn, a slub 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. 
     (3) yarn with a variable linear density and blending ratio 
     No existing patent application relates to this type of yarn. 
     (4) blended yarn or mixed color yarn mixed at any rate, with a constant linear density and blending ratio 
     The blended yarn or mixed color yarn mixed/blended at any rate can be produced with a constant linear density and blending ratio. 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. 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 
     To solve the above problems, the objective of this invention is to disclose a process of providing five-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 freely/flexibly. 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 online. 
     To achieve the above objectives, the invention discloses a method of dynamically configuring a linear density and a blending ratio of a yarn by five-ingredient asynchronous drafting, comprising:
         1) An actuating mechanism mainly includes a five-ingredient asynchronous/synchronous two-stage drafting mechanism, a twisting mechanism and a winding mechanism. The five-ingredient asynchronous/synchronous two-stage drafting mechanism includes a first stage asynchronous drafting unit and a successive second stage synchronous drafting unit;   2) The first stage asynchronous drafting unit includes a combination of back rollers and a middle roller. The combination of back rollers has five rotational degrees of freedom and includes a first back roller, a second back roller, a third back roller, a fourth back roller and a fifth back roller, which are set abreast on a same back roller shaft. The first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller move at the speeds V h1 , V h2 , V h3 , V h4  and V h5  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 .       

     Assuming the linear densities of a first roving yarn ingredient, a second roving yarn ingredient, a third roving yarn ingredient, a fourth roving yarn ingredient and a fifth roving yarn ingredient drafted by the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller are respectively ρ 1 , ρ 2 , ρ 3 , ρ 4  and ρ 5 , the linear density of the yarn Y drafted and twisted by the front roller is ρ y . 
     
       
         
           
             
               
                 
                   
                     ρ 
                     y 
                   
                   = 
                   
                     
                       1 
                       
                         V 
                         q 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           * 
                           
                             ρ 
                             1 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           * 
                           
                             ρ 
                             2 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               3 
                             
                           
                           * 
                           
                             ρ 
                             3 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               4 
                             
                           
                           * 
                           
                             ρ 
                             4 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               5 
                             
                           
                           * 
                           
                             ρ 
                             5 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     The blending ratios of the first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient, the fourth roving yarn ingredient and the fifth roving yarn ingredient are respectively k 1 , k 2 , k 3 , k 4  and k 5 . 
     
       
         
           
             
               k 
               1 
             
             = 
             
               
                 
                   ρ 
                   1 
                 
                 * 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
               
               
                 
                   
                     ρ 
                     1 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     2 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     3 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     4 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     5 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               2 
             
             = 
             
               
                 
                   ρ 
                   2 
                 
                 * 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
               
               
                 
                   
                     ρ 
                     1 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     2 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     3 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     4 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     5 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               3 
             
             = 
             
               
                 
                   ρ 
                   3 
                 
                 * 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
               
               
                 
                   
                     ρ 
                     1 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     2 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     3 
                   
                   * 
                   
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     ++ 
                   
                   ⁢ 
                   
                     ρ 
                     4 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     5 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               4 
             
             = 
             
               
                 
                   ρ 
                   4 
                 
                 * 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
               
               
                 
                   
                     ρ 
                     1 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     2 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     3 
                   
                   * 
                   
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     ++ 
                   
                   ⁢ 
                   
                     ρ 
                     4 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     5 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               5 
             
             = 
             
               
                 
                   ρ 
                   5 
                 
                 * 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
               
               
                 
                   
                     ρ 
                     1 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     2 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     3 
                   
                   * 
                   
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     ++ 
                   
                   ⁢ 
                   
                     ρ 
                     4 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                 
                 + 
                 
                   
                     ρ 
                     5 
                   
                   * 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
             
           
         
       
         
         
           
             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; 
             4) The linear density of yarn Y or/and blending ratio can be dynamically adjusted online, by adjusting the rotation rates of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller. 
           
         
       
    
     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 the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller are derived. The blending ratios of the first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient, the fourth roving yarn ingredient and the fifth roving yarn ingredient are set respectively as k 1 , k 2 , k 3 , k 4  and k 5 . The ratios of blending ratios of the yarn Y are respectively K 1 , K 2 , K 3  and K 4 . 
     
       
         
           
             
               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 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               K 
               3 
             
             = 
             
               
                 
                   k 
                   1 
                 
                 
                   k 
                   4 
                 
               
               = 
               
                 
                   
                     ρ 
                     1 
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
                 
                   
                     ρ 
                     4 
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               K 
               4 
             
             = 
             
               
                 
                   k 
                   1 
                 
                 
                   k 
                   5 
                 
               
               = 
               
                 
                   
                     ρ 
                     1 
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
                 
                   
                     ρ 
                     5 
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
             
           
         
       
     
     Then a surface linear speed of the back roller  1 : 
     
       
         
           
             
               V 
               
                 h 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 1 
               
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 ⁢ 
                 
                   V 
                   q 
                 
               
               
                 
                   ρ 
                   1 
                 
                 ⁡ 
                 
                   ( 
                   
                     1 
                     + 
                     
                       1 
                       
                         K 
                         1 
                       
                     
                     + 
                     
                       1 
                       
                         K 
                         2 
                       
                     
                     + 
                     
                       1 
                       
                         K 
                         3 
                       
                     
                     + 
                     
                       1 
                       
                         K 
                         4 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     a surface linear speed of the back roller  2 : 
     
       
         
           
             
               V 
               
                 h 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 2 
               
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 ⁢ 
                 
                   V 
                   q 
                 
               
               
                 
                   ρ 
                   2 
                 
                 ⁡ 
                 
                   ( 
                   
                     1 
                     + 
                     
                       K 
                       1 
                     
                     + 
                     
                       
                         K 
                         1 
                       
                       
                         K 
                         2 
                       
                     
                     + 
                     
                       
                         K 
                         1 
                       
                       
                         K 
                         3 
                       
                     
                     + 
                     
                       
                         K 
                         1 
                       
                       
                         K 
                         4 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     a surface linear speed of the back roller  3 : 
     
       
         
           
             
               V 
               
                 h 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 3 
               
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 ⁢ 
                 
                   V 
                   q 
                 
               
               
                 
                   ρ 
                   3 
                 
                 ⁡ 
                 
                   ( 
                   
                     1 
                     + 
                     
                       K 
                       2 
                     
                     + 
                     
                       
                         K 
                         2 
                       
                       
                         K 
                         1 
                       
                     
                     + 
                     
                       
                         K 
                         2 
                       
                       
                         K 
                         3 
                       
                     
                     + 
                     
                       
                         K 
                         2 
                       
                       
                         K 
                         4 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     a surface linear speed of the back roller  4 : 
     
       
         
           
             
               V 
               
                 h 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 4 
               
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 ⁢ 
                 
                   V 
                   q 
                 
               
               
                 
                   ρ 
                   4 
                 
                 ⁡ 
                 
                   ( 
                   
                     1 
                     + 
                     
                       K 
                       3 
                     
                     + 
                     
                       
                         K 
                         3 
                       
                       
                         K 
                         1 
                       
                     
                     + 
                     
                       
                         K 
                         3 
                       
                       
                         K 
                         2 
                       
                     
                     + 
                     
                       
                         K 
                         3 
                       
                       
                         K 
                         4 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     a surface linear speed of the back roller  5 : 
     
       
         
           
             
               V 
               
                 h 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 5 
               
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 ⁢ 
                 
                   V 
                   q 
                 
               
               
                 
                   ρ 
                   5 
                 
                 ⁡ 
                 
                   ( 
                   
                     1 
                     + 
                     
                       K 
                       4 
                     
                     + 
                     
                       
                         K 
                         4 
                       
                       
                         K 
                         1 
                       
                     
                     + 
                     
                       
                         K 
                         4 
                       
                       
                         K 
                         2 
                       
                     
                     + 
                     
                       
                         K 
                         4 
                       
                       
                         K 
                         3 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     wherein ρ 1 , ρ 2 , ρ 3 , ρ 4  and ρ 5  are constants, and K i  and ρ y  are functions changing with time t. 
     Further, let ρ 1 =ρ 2 =ρ 3 =ρ 4 =ρ 5 =ρ, then: 
     1) change the speed of any one of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and keep the speeds of the other four 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: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δρ 
                   y 
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   ( 
                   
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         4 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         5 
                       
                     
                     + 
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         i 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     wherein Δρ y  is a linear density change of the yarn, ΔV hi  is a speed change of the back roller i, i=1, 2, 3, 4, 5. 
     2) change the speeds of any two back rollers of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and keep the speeds of the other three 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: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δρ 
                   y 
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         5 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         hi 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hj 
                           
                         
                         + 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hk 
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
               
             
           
         
       
     
     wherein Δρ y  is a linear density change of the yarn, ΔV hj  and ΔV hk  are speed changes of the back rollers j and K, j≠k; j=1, 2, 3, 4, 5; k=1, 2, 3, 4, 5. 
     3) change the speeds of any three back rollers of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and keep the speeds of the other two backer rollers unchanged. 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: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δρ 
                   y 
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         5 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         hi 
                       
                     
                     + 
                     
                       ( 
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hj 
                           
                         
                         + 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hk 
                           
                         
                         + 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hm 
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
               
             
           
         
       
     
     wherein Δρ y  is a linear density change of yarns, ΔV hj , ΔV hk  and ΔV hm  are speed changes of the back rollers j, K and m, j≠k≠m; j=1, 2, 3, 4, 5; k=1, 2, 3, 4, 5; m=1, 2, 3, 4, 5. 
     4) change the speeds of any four back rollers of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and keep the speed of the remaining backer roller unchanged. The yarn ingredients of the yarn Y drafted by these four back rollers and the linear densities thereof change accordingly. The linear density ρ′ y  of yarn Y is adjusted as: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δρ 
                   y 
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       V 
                       hi 
                     
                     + 
                     
                       ( 
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hj 
                           
                         
                         + 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hk 
                           
                         
                         + 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hm 
                           
                         
                         + 
                         
                           V 
                           hn 
                         
                       
                       ) 
                     
                   
                   ] 
                 
               
             
           
         
       
     
     wherein Δρ y  is a linear density change of yarns, ΔV hj , ΔV hk , ΔV hm  and ΔV hn  are speed changes of the back rollers j, K, m and n, j≠k≠m≠n; j=1, 2, 3, 4, 5; k=1, 2, 3, 4, 5; m=1, 2, 3, 4, 5; n=1, 2, 3, 4, 5. 
     5) change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller simultaneously, and the sum of the speeds of the five back rollers is unequal to zero. The yarn ingredients of the yarn Y drafted by these five back rollers and the linear densities thereof change accordingly. The linear density ρ′ y  of the yarn Y is adjusted as: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δρ 
                   y 
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       5 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           V 
                           hi 
                         
                         + 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hi 
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
               
             
           
         
       
     
     6) change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speed of any of back rollers equal to zero, while the speeds of the other four 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 four yarn ingredients are continuous. The linear density ρ′ y  of yarn Y is adjusted as: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δρ 
                   y 
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     ( 
                     
                       
                         V 
                         hr 
                       
                       + 
                       
                         V 
                         hs 
                       
                       + 
                       
                         V 
                         hm 
                       
                       + 
                       
                         V 
                         hn 
                       
                       + 
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hj 
                           
                         
                       
                     
                     ) 
                   
                   ] 
                 
               
             
           
         
       
     
     wherein r≠s≠m≠n; r=1, 2, 3, 4, 5; s=1, 2, 3, 4, 5; m=1, 2, 3, 4, 5; n=1, 2, 3, 4, 5; 
     7) change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speeds of any two back rollers equal to zero, while the speeds of the other three 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 three yarn ingredients are continuous. The linear density ρ′ y  of the yarn Y is adjusted as: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δρ 
                   y 
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     ( 
                     
                       
                         V 
                         hr 
                       
                       + 
                       
                         V 
                         hs 
                       
                       + 
                       
                         V 
                         hm 
                       
                       + 
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hj 
                           
                         
                       
                     
                     ) 
                   
                   ] 
                 
               
             
           
         
       
     
     wherein r≠s≠m; r=1, 2, 3, 4, 5; s=1, 2, 3, 4, 5; m=1, 2, 3, 4, 5; 
     8) change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speeds of any three back rollers equal to zero, while the speeds of the other two backer rollers unequal to zero. The yarn ingredients of the yarn Y drafted by the any three back rollers are thus discontinuous, while the other two yarn ingredients are continuous. The linear density ρ′ y  of the yarn Y is adjusted as: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δρ 
                   y 
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     ( 
                     
                       
                         V 
                         hr 
                       
                       + 
                       
                         V 
                         hs 
                       
                       + 
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hj 
                           
                         
                       
                     
                     ) 
                   
                   ] 
                 
               
             
           
         
       
     
     wherein r≠s; r=1, 2, 3, 4, 5; s=1, 2, 3, 4, 5. 
     9) change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speeds of any four back rollers equal to zero, while the speed of the another backer roller unequal to zero. The yarn ingredients of the yarn Y drafted by the any four back rollers are thus discontinuous, while the another yarn ingredient is continuous. The linear density ρ′ y  of the yarn Y is adjusted as: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δρ 
                   y 
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       V 
                       hr 
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         5 
                       
                       ⁢ 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           hj 
                         
                       
                     
                   
                   ] 
                 
               
             
           
         
       
       
         
           
             ( 
             
               
                 r 
                 = 
                 1 
               
               , 
               2 
               , 
               3 
               , 
               4 
               , 
               5 
             
             ) 
           
         
       
     
     Further, change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speeds of any two back rollers equal to zero successively, while the speeds of the other three backer rollers unequal to zero. The yarn ingredients of the yarn Y drafted by the any two back rollers are thus discontinuous successively, while the other three yarn ingredients are continuous. The linear density ρ′ y  of yarn Y is adjusted as: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     ( 
                     
                       
                         V 
                         hr 
                       
                       + 
                       
                         V 
                         hs 
                       
                       + 
                       
                         V 
                         hm 
                       
                       + 
                       
                         V 
                         hn 
                       
                       + 
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hj 
                           
                         
                       
                     
                     ) 
                   
                   ] 
                 
                 ⁢ 
                 
                   ( 
                   
                     0 
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     ⌈ 
                     
                       ( 
                       
                         
                           V 
                           hr 
                         
                         + 
                         
                           V 
                           hs 
                         
                         + 
                         
                           V 
                           hm 
                         
                         + 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               V 
                               hj 
                             
                           
                         
                       
                       ) 
                     
                     ⌉ 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     wherein T 1 , and T 2  are time points, and t is a time variable. 
     Further, change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speeds of any three back rollers equal to zero successively, while the speeds of the other two backer rollers unequal to zero. The yarn ingredients of the yarn Y drafted by the any three back rollers are thus discontinuous successively, while the other two yarn ingredients are continuous. The linear density ρ′ y  of yarn Y is adjusted as: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     ( 
                     
                       
                         V 
                         hr 
                       
                       + 
                       
                         V 
                         hs 
                       
                       + 
                       
                         V 
                         hm 
                       
                       + 
                       
                         V 
                         hn 
                       
                       + 
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hj 
                           
                         
                       
                     
                     ) 
                   
                   ] 
                 
                 ⁢ 
                 
                   ( 
                   
                     0 
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           hr 
                         
                         + 
                         
                           V 
                           hs 
                         
                         + 
                         
                           V 
                           hm 
                         
                         + 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               V 
                               hj 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           hr 
                         
                         + 
                         
                           V 
                           hs 
                         
                         + 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               V 
                               hj 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     wherein T 1 , T 2  and T 3  are time points, and t is a time variable. 
     Further, change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speeds of any four back rollers equal to zero successively, while the speeds of another backer roller unequal to zero. The yarn ingredients of the yarn Y drafted by the any four back rollers are thus discontinuous successively, while the another yarn ingredient is continuous. The linear density ρ′ y  of the yarn Y is adjusted as: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     ( 
                     
                       
                         V 
                         hr 
                       
                       + 
                       
                         V 
                         hs 
                       
                       + 
                       
                         V 
                         hm 
                       
                       + 
                       
                         V 
                         hn 
                       
                       + 
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hj 
                           
                         
                       
                     
                     ) 
                   
                   ] 
                 
                 ⁢ 
                 
                   ( 
                   
                     0 
                     ≤ 
                     t 
                     ≤ 
                     
                       T 
                       1 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           hr 
                         
                         + 
                         
                           V 
                           hs 
                         
                         + 
                         
                           V 
                           hm 
                         
                         + 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               V 
                               hj 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         T 
                         1 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           hr 
                         
                         + 
                         
                           V 
                           hs 
                         
                         + 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               V 
                               hj 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         T 
                         2 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         3 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               
                 ρ 
                 y 
                 ′ 
               
               = 
               
                 
                   
                     ρ 
                     y 
                   
                   + 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ρ 
                       y 
                     
                   
                 
                 = 
                 
                   
                     ρ 
                     
                       V 
                       q 
                     
                   
                   * 
                   
                     [ 
                     
                       ( 
                       
                         
                           V 
                           hr 
                         
                         + 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               V 
                               hj 
                             
                           
                         
                       
                       ) 
                     
                     ] 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         T 
                         3 
                       
                       ≤ 
                       t 
                       ≤ 
                       
                         T 
                         4 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     wherein T 1 , T 2 , T 3 , and T 4  are time points, and t is a time variable; r≠s≠m≠n; r=1, 2, 3, 4, 5; s=1, 2, 3, 4, 5; m=1, 2, 3, 4, 5; n=1, 2, 3, 4, 5. 
     Further, change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and keep 
     V h1 *ρ 1 +V h2 *ρ 2 +V h3 *ρ 3 +V h4 *ρ 4 +V h5 *ρ 5  as a constant 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, the third yarn ingredient, the fourth yarn ingredient, and the fifth yarn ingredient are k 1 , k 2 , k 3 , k 4 , k 5 . 
     
       
         
           
             
               k 
               1 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         i 
                       
                     
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           i 
                         
                       
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               k 
               2 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         i 
                       
                     
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           i 
                         
                       
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               k 
               3 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         i 
                       
                     
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           i 
                         
                       
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               k 
               4 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         i 
                       
                     
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           i 
                         
                       
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               k 
               5 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       V 
                       
                         h 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         i 
                       
                     
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           i 
                         
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     Further, let ΔV h1 +ΔV h2 +ΔV h3 +ΔV h4 +ΔV h5 =0, then the blending ratios are respectively: 
     
       
         
           
             
               k 
               1 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     i 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               2 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     i 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               3 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     i 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               4 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     i 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               5 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     i 
                   
                 
               
             
           
         
       
     
     Further, let V h1 +V h2 +V h3 +V h4 +V h5 =V Z , i.e., the sum of the linear speeds of the five back rollers is equal to the linear speed of the middle roller, then: 
               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                         k   4     =         V     h   ⁢           ⁢   4         V   z       =     1     e     h   ⁢           ⁢   4                         k   5     =         V     h   ⁢           ⁢   5         V   z       =       1     e     h   ⁢           ⁢   5         ⁢     :               
i.e., the blending ratios of the five yarn ingredients ρ 1 , ρ 2 , ρ 3 , ρ 4 , ρ 5  of the yarn Y are equal to the inverses of their drafting ratios in the first stage drafting area,
 
     
       
         
           
             
               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 
                 
               
             
           
         
       
       
         
           
             
               e 
               
                 h 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 4 
               
             
             = 
             
               
                 
                   V 
                   z 
                 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
               
               = 
               
                 1 
                 
                   k 
                   4 
                 
               
             
           
         
       
       
         
           
             
               e 
               
                 h 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 5 
               
             
             = 
             
               
                 
                   V 
                   z 
                 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
               
               = 
               
                 1 
                 
                   k 
                   5 
                 
               
             
           
         
       
     
     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 the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller are V h1i , V h2i , V h3i , V h4i , V h5i , wherein i∈(1, 2, . . . , n); The first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient, the fourth roving yarn ingredient and the fifth 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 , k 3i , k 4i  and k 5i  thereof are expressed as below: 
                     k     1   ⁢           ⁢   i       =         ρ   1     *     V     h   ⁢           ⁢   1   ⁢   i             ∑     m   =   1     5     ⁢       ρ   i     *     V   hmi                   (   2   )                 k     2   ⁢           ⁢   i       =         ρ   2     *     V     h   ⁢           ⁢   2   ⁢   i             ∑     m   =   1     5     ⁢       ρ   i     *     V   hmi                   (   3   )                 k     3   ⁢           ⁢   i       =         ρ   3     *     V     h   ⁢           ⁢   3   ⁢   i             ∑     m   =   1     5     ⁢       ρ   i     *     V   hmi                   (   4   )                 k     4   ⁢           ⁢   i       =         ρ   4     *     V     h   ⁢           ⁢   4   ⁢   i             ∑     m   =   1     5     ⁢       ρ   i     *     V   hmi                   (   5   )                 k     5   ⁢           ⁢   i       =         ρ   5     *     V     h   ⁢           ⁢   5   ⁢   i             ∑     m   =   1     5     ⁢       ρ   i     *     V   hmi                   (   6   )               
the linear density of segment i of yarn Y is:
 
                           ρ   yi     =       ⁢         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       +         V     h   ⁢           ⁢   4   ⁢   i         V   z       ⁢     ρ   4       +         V     h   ⁢           ⁢   5   ⁢   i         V   z       ⁢     ρ   5         )                   =       ⁢       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       +         V     h   ⁢           ⁢   4   ⁢   i         V   z       ⁢     ρ   4       +         V     h   ⁢           ⁢   5   ⁢   i         V   z       ⁢     ρ   5         )                     (   7   )               
wherein
 
               e   q     =       V   q       V   z             
is the two-stage drafting ratio;
 
     (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, the fourth back roller and the fifth back roller for this segment are respectively V h10 , V h20 , V h30 , V h40  and V h50 ; and the reference blending ratios of the first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient, the fourth roving yarn ingredient, and the fifth roving yarn ingredient for this segment are respectively k 10 , k 20 , k 30 , k 40  and k 50 , 
     Keep the linear speed of the middle roller constant, and
 
 V   z   =V   h10   +V   h20   +V   h30   +V   h40   +V   h50   (8)
 
also keep two-stage drafting ratio
 
               e   q     =       V   q       V   z             
constant;
 
     wherein the reference linear speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller for this segment are respectively V h10 , V h20 , V h30 , V h40  and V h50 , which can be predetermined according to the material, reference linear density ρ 0  and reference blending ratios k 10 , k 20 , k 30 , k 40  and k 50  of the first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient, the fourth roving yarn ingredient, and the fifth roving yarn ingredient. 
     (2) 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 , k 4i  and k 5i , the linear speeds V h1i , V h2i , V h3i , V h4i  and V h5i  of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller are calculated according to Equations (2)-(8); 
     (3) Based on the reference linear speeds V h10 , V h20 , V h30 , V h40  and V h50  for the reference segment, increase or decrease the rotation rates of the first back roller, the second back roller, the third back roller, the fourth back roller or/and the fifth back roller to dynamically adjust the linear density or/and blending ratio for the segment i of the yarn Y. 
     Further, let ρ 1 =ρ 2 =ρ 3 =ρ 4 =ρ 5 =ρ 
     the Equation (7) can be simplified as 
     
       
         
           
             
               
                 
                   
                     ρ 
                     yi 
                   
                   = 
                   
                     
                       ρ 
                       
                         e 
                         q 
                       
                     
                     * 
                     
                       
                         
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                               ⁢ 
                               i 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                               ⁢ 
                               i 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               3 
                               ⁢ 
                               i 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               4 
                               ⁢ 
                               i 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               5 
                               ⁢ 
                               i 
                             
                           
                         
                         
                           V 
                           z 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     According to Equations (2)-(6) and (8)-(9), the linear speeds V h1i , V h2i , V h3i , V h4i , V h5i  of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller are calculated; based on the reference linear speeds V h10 , V h20 , V h30 , V h40  and V h50 , the rotation rates of the first back roller, the second back roller, the third back roller, the fourth back roller or/and the fifth back roller are increased or decreased to reach the preset linear density and blending ratio for the segment i of yarn Y. 
     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, the fourth back roller and the fifth back roller have corresponding increments on the basis of the reference linear speed, i.e., when (V h10 +V h20 +V h30 +V h40 +V h50 )→(V h10 +ΔV h1i +V h20 +ΔV h2i +V h30 +ΔV h3i +V h40 +ΔV h4i +V h50 +ΔV h5i ), the linear density increment of yarn Y is: 
               Δρ   yi     =       ρ       e   q     *     V   z         *     (       Δ   ⁢           ⁢     V     h   ⁢           ⁢   1   ⁢   i         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   2   ⁢   i         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   3   ⁢   i         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   4   ⁢   i         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   5   ⁢   i           )     ⁢     :             
Then the linear density ρ yi  of the yarn Y is expressed as
 
                     ρ   yi     =         ρ     y   ⁢           ⁢   0       +     Δ   ⁢           ⁢     ρ   yi         =       ρ     y   ⁢           ⁢   0       +           Δ   ⁢           ⁢     V     h   ⁢           ⁢   1   ⁢   i         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   2   ⁢   i         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   3   ⁢   i         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   4   ⁢   i         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   5   ⁢   i             V   z       *       ρ     e   q       .                   (   10   )               
Let ΔV i =ΔV h1i +ΔV h2i +ΔV h3i +ΔV h4i +ΔV h5i , then Equation (10) is simplified as:
 
     
       
         
           
             
               
                 
                   
                     ρ 
                     yi 
                   
                   = 
                   
                     
                       ρ 
                       
                         y 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                     
                     + 
                     
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             i 
                           
                         
                         
                           V 
                           z 
                         
                       
                       * 
                       
                         
                           ρ 
                           
                             e 
                             q 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     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, the fourth back roller and the fifth back roller. 
     Further, let ρ 1 =ρ 2 =ρ 3 =ρ 4 =ρ 5 =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)-(6) can be simplified as: 
     
       
         
           
             
               
                 
                   
                     k 
                     
                       1 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                             ⁢ 
                             i 
                           
                         
                       
                     
                     
                       
                         V 
                         z 
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       2 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                             ⁢ 
                             i 
                           
                         
                       
                     
                     
                       
                         V 
                         z 
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       3 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                             ⁢ 
                             i 
                           
                         
                       
                     
                     
                       
                         V 
                         z 
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       4 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           4 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                             ⁢ 
                             i 
                           
                         
                       
                     
                     
                       
                         V 
                         z 
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       5 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           5 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                             ⁢ 
                             i 
                           
                         
                       
                     
                     
                       
                         V 
                         z 
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     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, the fourth back roller and the fifth back roller; 
     wherein
 
Δ V   h1i   =k   1i *( V   Z   +ΔV   i )− V   h10  
 
Δ V   h2i   =k   2i *( V   Z   +ΔV   i )− V   h20  
 
Δ V   h3i   =k   3i *( V   Z   +ΔV   i )− V   h30  
 
Δ V   h4i   =k   4i *( V   Z   +ΔV   i )− V   h40  
 
Δ V   h5i   =k   5i *( V   Z   +ΔV   i )− V   h50  
 
     Further, let V h1i *ρ 1 +V h2i *ρ 2 +V h3i *ρ 3 +V h4i *ρ 4 +V h5i *ρ 5 =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. 
     Further, let any one to four of ΔV h1i , ΔV h2i , ΔV h3i , ΔV h4i  and ΔV h5i  be equal to zero, while the remaining ones are not zero, then the one to four roving yarn ingredients can be changed while the other roving yarn ingredients are unchanged. The adjusted blending ratio are: 
               k   ki     =         V     hk   ⁢           ⁢   0       +     ΔV   hki           V   z     +     Δ   ⁢           ⁢     V   i                         k   ji     =       V     hj   ⁢           ⁢   0           V   z     +     Δ   ⁢           ⁢     V   i                 
wherein k, j∈(1,2,3,4,5) and k≠j.
 
     Further, let none of ΔV h1i , ΔV h2i , ΔV h3i , ΔV h4i  and ΔV h5i  be equal to zero, then the proportion of the five roving yarn ingredients in the yarn Y may be changed. 
     Further, let any one to four of ΔV h1i , ΔV h2i , ΔV h3i , ΔV h4i  and ΔV h5i  be equal to zero, while the remaining ones are not zero, then the one to four roving yarn ingredients of the segment i of the yarn Y may be discontinuous. 
     Further, yellow, magenta, cyan, black, and white yarns are respectively drafted by the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller. The speed V q  of the front roller is kept constant and the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller are adjusted to regulate the colors of the yarns. When blending the colors, the color depth or the saturation of the colored spun yarn is adjusted by the black yarn, the concentration or brightness of the colored spun yarn is adjusted by the white yarn, and the hue is adjusted with the proportion of the black color and the white color. 
     By coupling and drafting, interactive discolor, gradient color matching, and blending and twisting from the ring spinning frame-drafting-twisting system, the yellow, magenta, cyan, black, and white fibers of the yellow, magenta, cyan, black, and white roving yarns, i.e., CMYKW five basic colors roving yarns can be blended in any proportion, and in turn the five basic colors matching is operated to get colored spun yarn with any color and make the developed color purer. 
     A device for configuring a linear density and a blending ratio of a yarn by five-ingredient asynchronous/synchronous drafting, comprises a control system and an actuating mechanism. The actuating mechanism includes five-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 five rotational degrees of freedom and includes a first back roller, a second back roller, a third back roller, a fourth back roller and a fifth back roller, which are set abreast on a same back roller shaft. The five back rollers are set adjacently and the driving mechanisms thereof are set on both sides of the five back rollers. The second stage drafting unit includes a front roller and the middle roller. 
     Further, the third back roller is fixedly set on the back roller shaft. The other four back rollers are respectively symmetrically set on both sides of the third back roller, and the five back rollers are independently rotatable with each other. The second back roller has a second sleeve connected to the driving mechanism thereof; the second sleeve is placed around the back roller shaft, and the first back roller is rotatably placed around the second sleeve. The fourth back roller has a fourth sleeve connected to the driving mechanism thereof; the fourth sleeve is placed around the back roller shaft, and the fifth back roller is rotatably placed around the fourth sleeve. 
     Further, the control system mainly includes a PLC programmable controller, a servo driver, a servo motor, etc. 
     Further, there is a bell mouth between the combination of back rollers and the middle roller, the speed of the middle roller is kept unchanged, and then the first stage drafting unit functions as a blended or color-mixing unit, and the second stage drafting unit functions as a pure liner density regulating unit. 
     The five back rollers are set abreast on a same back roller shaft, with the driving mechanisms set on both sides, which makes the mechanic structure more compact and the five types of roving yarn drafted by the five back rollers more close when blending, effectively preventing the yarn from interferences and pollutions when the driving mechanisms work. In addition, the five basic colors yarns go through the bell mouth with a smaller clamping angle, rendering the blending of the yarn more even and almost unbreakable. 
     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, the fourth back roller and the fifth back roller. 
     The dotted 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. 
     
       
         
           
               
             
               
                 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 
               
               
                   
               
            
           
         
       
     
     Therefore, the invention is very effective. 
     The method of the invention changes the traditional five-ingredient front and back areas synchronous drafting to five-ingredient separate asynchronous drafting (referred to as first stage asynchronous drafting) and five-ingredient integrated synchronous drafting (referred to as second stage synchronous drafting). The blending proportion of the five 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 five-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. 
     Calculations for the Processing Parameters of Five-Ingredient Separate/Integrated Asynchronous/Synchronous Two-Stage Drafting Coaxial Twisting Spinning System 
     According to the drafting theory, the drafting ratio of the first stage drafting is: 
                     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   3   ′                 (   3   )                 e     h   ⁢           ⁢   4       =         V   z       V     h   ⁢           ⁢   4         =       ρ   4       ρ   4   ′                 (   4   )                 e     h   ⁢           ⁢   5       =         V   z       V     h   ⁢           ⁢   5         =       ρ   5       ρ   5   ′                 (   5   )               
The equivalent drafting ratio of the first stage drafting is:
 
                       e   _     h     =           ρ   1     +     ρ   2     +     ρ   3     +     ρ   4     +     ρ   5           ρ   1   ′     +     ρ   2   ′     +     ρ   3   ′     +     ρ   4   ′     +     ρ   5   ′         =         ∑     i   =   1     5     ⁢     ρ   i           ∑     i   =   1     5     ⁢     ρ   i   ′                   (   6   )               
The drafting ratio of the second stage drafting is:
 
                     e   q     =         V   q       V   z       =         ρ   1   ′       ρ   1   ″       =         ρ   2   ′       ρ   2   ″       =         ρ   3   ′       ρ   3   ″       =         ρ   4   ′       ρ   4   ″       =         ρ   5   ′       ρ   5   ″       =         ∑     i   =   1     n     ⁢     ρ   i   ′           ∑     i   =   1     n     ⁢     ρ   i   ″                             (   7   )               
The total equivalent drafting ratio ē is:
 
     
       
         
           
             
               
                 
                   
                     e 
                     _ 
                   
                   = 
                   
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                           ρ 
                           i 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           n 
                         
                         ⁢ 
                         
                           ρ 
                           i 
                           ″ 
                         
                       
                     
                     = 
                     
                       
                         
                           e 
                           _ 
                         
                         h 
                       
                       ⋆ 
                       
                         e 
                         q 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     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 five roving yarns 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 , k 4 , k 5  can be expressed as follows: 
     
       
         
           
             
               
                 
                   
                     k 
                     1 
                   
                   = 
                   
                     
                       
                         ρ 
                         1 
                         ″ 
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                           ρ 
                           i 
                           ″ 
                         
                       
                     
                     = 
                     
                       
                         
                           ρ 
                           1 
                           ′ 
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             ρ 
                             i 
                             ′ 
                           
                         
                       
                       = 
                       
                         
                           
                             ρ 
                             1 
                           
                           ⋆ 
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             n 
                           
                           ⁢ 
                           
                             
                               ρ 
                               i 
                             
                             ⋆ 
                             
                               V 
                               
                                 h 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 i 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     2 
                   
                   = 
                   
                     
                       
                         ρ 
                         2 
                         ″ 
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                           ρ 
                           i 
                           ″ 
                         
                       
                     
                     = 
                     
                       
                         
                           ρ 
                           2 
                           ′ 
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             ρ 
                             i 
                             ′ 
                           
                         
                       
                       = 
                       
                         
                           
                             ρ 
                             2 
                           
                           ⋆ 
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             n 
                           
                           ⁢ 
                           
                             
                               ρ 
                               i 
                             
                             ⋆ 
                             
                               V 
                               
                                 h 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 i 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     3 
                   
                   = 
                   
                     
                       
                         ρ 
                         3 
                         ″ 
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                           ρ 
                           i 
                           ″ 
                         
                       
                     
                     = 
                     
                       
                         
                           ρ 
                           3 
                           ′ 
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             ρ 
                             i 
                             ′ 
                           
                         
                       
                       = 
                       
                         
                           
                             ρ 
                             3 
                           
                           ⋆ 
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               3 
                             
                           
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             n 
                           
                           ⁢ 
                           
                             
                               ρ 
                               i 
                             
                             ⋆ 
                             
                               V 
                               
                                 h 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 i 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     4 
                   
                   = 
                   
                     
                       
                         ρ 
                         4 
                         ″ 
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                           ρ 
                           i 
                           ″ 
                         
                       
                     
                     = 
                     
                       
                         
                           ρ 
                           4 
                           ′ 
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             ρ 
                             i 
                             ′ 
                           
                         
                       
                       = 
                       
                         
                           
                             ρ 
                             4 
                           
                           ⋆ 
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               4 
                             
                           
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             n 
                           
                           ⁢ 
                           
                             
                               ρ 
                               i 
                             
                             ⋆ 
                             
                               V 
                               
                                 h 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 i 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     5 
                   
                   = 
                   
                     
                       
                         ρ 
                         5 
                         ″ 
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                           ρ 
                           i 
                           ″ 
                         
                       
                     
                     = 
                     
                       
                         
                           ρ 
                           5 
                           ′ 
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             ρ 
                             i 
                             ′ 
                           
                         
                       
                       = 
                       
                         
                           
                             ρ 
                             5 
                           
                           ⋆ 
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               5 
                             
                           
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             n 
                           
                           ⁢ 
                           
                             
                               ρ 
                               i 
                             
                             ⋆ 
                             
                               V 
                               
                                 h 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 i 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     As known from the Equations (9), (10), (11), (12), (13), the blending ratios of the five ingredients in the yarn is related to the surface rotation rates V h1 , V h2 , V h3 , V h4 , V h5  of the back rollers and the linear densities ρ 1 , ρ 2 , ρ 3 , ρ 4 , ρ 5  of the five roving yarns. Generally, ρ 1 , ρ 2 , ρ 3 , ρ 4 , ρ 5  are constant and irrelevant to the time, while V h1 , V h2 , V h3 , V h4 , V h5  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 , ρ 4 , ρ 5  of the roving yarns are constant, the blending ratios determined by Equations (8), (9), (10), (11) change due to the speed change of the main shaft, which results in the changes of V h1 , V h2 , V h3 , V h4 , V h5 , rendering the blending ratios uncertain. 
     In the same way, the five roving yarns are two-stage drafted, integrated and twisted to form a yarn with the following linear density: 
                       ρ   y     =         ∑     i   =   1     5     ⁢     ρ   i         e   _         ⁢     
     ⁢       ρ   y     =         V   z       V   q       ⋆       ∑     i   =   1     5     ⁢     ρ   i   ′           ⁢     
     ⁢     ρ   y     =         V   z       V   q       ⋆       ∑     i   =   1     5     ⁢         V   hi       V   z       *     ρ   i                   (   14   )               
and then the linear density of the yarn is:
 
     
       
         
           
             
               
                 
                   
                     ρ 
                     y 
                   
                   = 
                   
                     
                       1 
                       
                         V 
                         q 
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           0 
                         
                         5 
                       
                       ⁢ 
                       
                         
                           V 
                           hi 
                         
                         ⋆ 
                         
                           ρ 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     As known from Equation (15), the linear density of the yarn is related to the speed V h1 , V h2 , V h3 , V h4 , V h5  of the combination of back rollers and the linear densities ρ 1 , ρ 2 , ρ 3 , ρ 4 , ρ 5  of the five roving yarns. Generally, ρ 1 , ρ 2 , ρ 3 , ρ 4 , ρ 5  are constant and irrelevant to the time while V h1 , V h2 , V h3 , V h4 , V h5  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 , ρ 4 , ρ 5  of the five roving yarns remain unchanged, V h1 , V h2 , V h3 , V h4 , V h5  would change with the main shaft speed, rendering the linear density uncertain. 
     From Equation (1): 
     
       
         
           
             
               ρ 
               1 
               ′ 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 
                   V 
                   z 
                 
               
               ⋆ 
               
                 ρ 
                 1 
               
             
           
         
       
     
     From Equation (2): 
     
       
         
           
             
               ρ 
               2 
               ′ 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 
                   V 
                   z 
                 
               
               ⋆ 
               
                 ρ 
                 2 
               
             
           
         
       
     
     From Equation (3): 
               ρ   3   ′     =         V     h   ⁢           ⁢   3         V   z       ⋆     ρ   3             
From Equation (4):
 
               ρ   4   ′     =         V     h   ⁢           ⁢   4         V   z       ⋆     ρ   4             
From Equation (5):
 
     
       
         
           
             
               ρ 
               5 
               ′ 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
                 
                   V 
                   z 
                 
               
               ⋆ 
               
                 ρ 
                 5 
               
             
           
         
       
     
     
       
         
           
             
               
                 
                   
                     ∴ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ρ 
                         1 
                         ′ 
                       
                       + 
                       
                         ρ 
                         2 
                         ′ 
                       
                       + 
                       
                         ρ 
                         3 
                         ′ 
                       
                       + 
                       
                         ρ 
                         4 
                         ′ 
                       
                       + 
                       
                         ρ 
                         5 
                         ′ 
                       
                     
                   
                   = 
                   
                     
                       1 
                       
                         V 
                         z 
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           0 
                         
                         5 
                       
                       ⁢ 
                       
                         
                           V 
                           hi 
                         
                         ⋆ 
                         
                           ρ 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     Equation (16) is substituted in Equation (7) and then solved for the equivalent drafting ratio ē h : 
     
       
         
           
             
               
                 
                   
                     
                       e 
                       _ 
                     
                     h 
                   
                   = 
                   
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                           ρ 
                           i 
                         
                       
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           5 
                         
                         ⁢ 
                         
                           
                             V 
                             hi 
                           
                           ⋆ 
                           
                             ρ 
                             i 
                           
                         
                       
                     
                     ⋆ 
                     
                       V 
                       z 
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     Equation (17) is substituted in Equation (8) and then solved for the total equivalent drafting ratio ē: 
     
       
         
           
             
               
                 
                   
                     
                       e 
                       _ 
                     
                     = 
                     
                       
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             ρ 
                             i 
                           
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             
                               V 
                               hi 
                             
                             ⋆ 
                             
                               ρ 
                               i 
                             
                           
                         
                       
                       ⋆ 
                       
                         V 
                         z 
                       
                       ⋆ 
                       
                         
                           V 
                           q 
                         
                         
                           V 
                           z 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       e 
                       _ 
                     
                     = 
                     
                       
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             ρ 
                             i 
                           
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             
                               V 
                               hi 
                             
                             ⋆ 
                             
                               ρ 
                               i 
                             
                           
                         
                       
                       ⋆ 
                       
                         V 
                         q 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     To negate the changes caused by the different main shaft speeds, the limited condition is provided as follows:
 
ρ 1 =ρ 2 =ρ 3 =ρ 4 =ρ 5 =ρ  (19)
 
Equation (12) is substituted in Equation (9):
 
                       ρ   1   ′     +     ρ   2   ′     +     ρ   3   ′     +     ρ   4   ′     +     ρ   5   ′       =     ρ   ⋆         ∑     i   =   1     5     ⁢     V   hi         V   z                 (   20   )               
Equations (12), (13) are substituted in Equation (10):
 
                       e   _     h     =       V   z           ∑     i   =   1     5     ⁢     V   hi       5               (   21   )               
Equations (14) is substituted in Equation (8):
 
                     e   _     =           e   _     h     ⋆     e   q       =       5   ⋆     V   q           ∑     i   =   1     5     ⁢     V   hi                   (   22   )               
Equations (18), (19), (20) are substituted in Equations (9), (10), (11), (12), (13):
 
     
       
         
           
             
               
                 
                   
                     k 
                     1 
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                       
                     
                     = 
                     
                       
                         1 
                         
                           e 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                       ⋆ 
                       
                         
                           V 
                           z 
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             V 
                             hi 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     2 
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                       
                     
                     = 
                     
                       
                         1 
                         
                           e 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                       ⋆ 
                       
                         
                           V 
                           z 
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             V 
                             hi 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     3 
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                         
                       
                       
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                       
                     
                     = 
                     
                       
                         1 
                         
                           e 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                       
                       ⋆ 
                       
                         
                           V 
                           z 
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             V 
                             hi 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     4 
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           4 
                         
                       
                       
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                       
                     
                     = 
                     
                       
                         1 
                         
                           e 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                       
                       ⋆ 
                       
                         
                           V 
                           z 
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             V 
                             hi 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     5 
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           5 
                         
                       
                       
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                         + 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                       
                     
                     = 
                     
                       
                         1 
                         
                           e 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                       
                       ⋆ 
                       
                         
                           V 
                           z 
                         
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             5 
                           
                           ⁢ 
                           
                             V 
                             hi 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
     Assuming
 
ρ 1 =ρ 2 =ρ 3 =ρ 4 =ρ 5 =ρ
 
 V   h1   +V   h2   +V   h3   +V   h4   +V   h5   =V   z  
 
then the blending ratios k 10 , k 20 , k 30 , k 40  and k 50  are:
 
     
       
         
           
             
               k 
               10 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
               = 
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 
                   V 
                   z 
                 
               
             
           
         
       
       
         
           
             
               k 
               20 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
               = 
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 
                   V 
                   z 
                 
               
             
           
         
       
       
         
           
             
               k 
               30 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
               = 
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 
                   V 
                   z 
                 
               
             
           
         
       
       
         
           
             
               k 
               40 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
               = 
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 
                   V 
                   z 
                 
               
             
           
         
       
       
         
           
             
               k 
               50 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
                 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                   + 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
               = 
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
                 
                   V 
                   z 
                 
               
             
           
         
       
     
     It can be understand that blending ratios change on a basis of the reference blending ratios, when (V h1 +V h2 +V h3 +V h4 +V h5 )→(V h1 +ΔV h1 +V h2 +ΔV h2 +V h3 +ΔV h3 +V h4 +ΔV h4 +V h5 +ΔV h5 ), 
     the blending ratios are changed as: 
     
       
         
           
             
               k 
               1 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
               
               
                 
                   V 
                   z 
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   V 
                 
               
             
           
         
       
       
         
           
             
               k 
               2 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
               
               
                 
                   V 
                   z 
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   V 
                 
               
             
           
         
       
       
         
           
             
               k 
               3 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                 
               
               
                 
                   V 
                   z 
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   V 
                 
               
             
           
         
       
       
         
           
             
               k 
               4 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                 
               
               
                 
                   V 
                   z 
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   V 
                 
               
             
           
         
       
       
         
           
             
               k 
               5 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
               
                 
                   V 
                   z 
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   V 
                 
               
             
           
         
       
     
     As known from the five equations as above, the changes of the blending ratios all depend on the changes of (V h1 +ΔV h1 ), (V h2 +ΔV h2 ), (V h3 +ΔV h3 ), (V h4 +ΔV h4 ), (V h5 +ΔV h5 ), i.e., the changes of speeds of the five back rollers. 
     
       
         
           
             
               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 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           4 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           5 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               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 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           4 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           5 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               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 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           4 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           5 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               4 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                 
               
               
                 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                         
                       
                       + 
                     
                   
                 
                 
                   
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           4 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           5 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               5 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
               
                 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                         
                       
                       + 
                     
                   
                 
                 
                   
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           4 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                       
                       + 
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           5 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     In a special condition, ΔV h1 +ΔV h2 +ΔV h3 +ΔV h4 +ΔV h5 =0, then the above equation can be simplified as: 
     
       
         
           
             
               k 
               1 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
               
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               2 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
               
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               3 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                 
               
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               4 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                 
               
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               5 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 + 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
               
             
           
         
       
     
     Further in a special condition, V h1 +V h2 +V h3 +V h4 +V h5 =V Z , i.e., the sum of the speeds of the five back rollers is equal to the linear speed of the middle roller, then the above five equations can be further simplified as: 
     
       
         
           
             
               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 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               4 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 
                   V 
                   z 
                 
               
               = 
               
                 1 
                 
                   e 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
               
             
           
         
       
       
         
           
             
               k 
               5 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
                 
                   V 
                   z 
                 
               
               = 
               
                 1 
                 
                   e 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
               
             
           
         
       
     
     The blending ratios of the five ingredients ρ 1 , ρ 2 , ρ 3 , ρ 4 , ρ 5  in the yarn are equal to the inverses of their respective drafting ratios. 
     
       
         
           
             
               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 
                 
               
             
           
         
       
       
         
           
             
               e 
               
                 h 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 4 
               
             
             = 
             
               
                 
                   V 
                   z 
                 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
               
               = 
               
                 1 
                 
                   k 
                   4 
                 
               
             
           
         
       
       
         
           
             
               e 
               
                 h 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 5 
               
             
             = 
             
               
                 
                   V 
                   z 
                 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
               
               = 
               
                 1 
                 
                   k 
                   5 
                 
               
             
           
         
       
     
     Because k 1 +k 2 +k 3 +k 4 +k 5 =100% k 1 , k 2 , k 3 , k 4  and k 5  have numerous combinations. 
     The color mixing ratios can be configured by gradients to get different color schemes. Let k 1 , k 2 , k 3 , k 4  and k 5  change within the range of 0-100%. Under various color mixing schemes of the five basic colors, the color mixing ratio increases at least at the rate of 10%, the color mixing and matching schemes are provides as below: 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 color mixing and matching schemes 
               
            
           
           
               
               
               
            
               
                   
                   
                 Color 
               
               
                   
                 Color mixing mode 
                 numbers 
               
               
                   
                   
               
            
           
           
               
               
               
            
               
                 Single color mode 
                 A, B, C, D, E 
                 5 
               
               
                 Double-color mode 
                 AB, AC, AD, AE, BC, BD, 
                 9*10 = 90 
               
               
                   
                 BE, CD, CE, DE 
               
               
                 Three-color mode 
                 ABC, BCD, CDE, DEA, EAB 
                 36*5 = 180 
               
               
                 Four-color mode 
                 ABCD, BCDE, CDEA, DEAB, 
                 82*5 = 410 
               
               
                   
                 EABC 
               
               
                 Five-color mode 
                 ABCDE 
                 28*3 − 2 = 82 
               
               
                   
                 In total 
                 248 
               
               
                   
               
            
           
         
       
     
     The blended yarn with a certain blending ratio is produced by blending the materials or sliver in the current ring spinning process. The roving yarns with different materials or colors are blended in the spinning process in the invention to spin a blended yarn or a color mixing and matching yarn. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a principle schematic diagram of the two-stage drafting spinning device; 
         FIG. 2  is a structural schematic diagram of a combination of back rollers; 
         FIG. 3  is a structural side view of the two-stage drafting spinning device; 
         FIG. 4  is a yarn route of the two-stage drafting in an embodiment; 
         FIG. 5  is a structural schematic diagram of a control system. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The embodiments of the invention are described as below, in combination with the accompanying drawings. 
     Embodiment 1 
     A method of configuring a linear density and a blending ratio of a yarn by five-ingredient asynchronous/synchronous drafting is disclosed, comprising: 
     1) as shown in  FIGS. 1-4 , a drafting and twisting system includes a first stage drafting unit and a successive second stage drafting unit; 
     2) the first stage drafting unit includes a combination of back rollers and a middle roller; the combination of back rollers has five rotational degrees of freedom and includes a first back roller h 1 , a second back roller h 2 , a third back roller h 3 , a fourth back roller h 4  and a fifth back roller h 5 , which are set abreast on a same back roller shaft; the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller move at the speeds V h1 , V h2 , V h3 , V h4  and V h5  respectively; the middle roller rotates at the speed V z ; the second stage drafting unit includes a front roller and the middle roller; the front roller rotates at the surface linear speed V q . 
     Assuming the linear densities of a first roving yarn ingredient P 1 , a second roving yarn ingredient P 2 , a third roving yarn ingredient P 3 , a fourth roving yarn ingredient P 4  and a fifth roving yarn ingredient P 5  drafted by the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller are respectively ρ 1 , ρ 2 , ρ 3 , ρ 4  and ρ 5 , the linear density of the yarn Y drafted and twisted by the front roller is ρ y . 
     As shown in  FIG. 1 , the numerals  6 , 8 , 10 , 12 , 14  refer to five movable rollers of a combination, which is made up of nested sleeves, the numerals  5 ,  7 ,  9 , 11 ,  13  refer to the top rollers corresponding to each back roller, the numerals  3 , 4  refer to a middle roller and a top roller, and the numerals  1 , 2  refer to a front roller and an another top roller. The numerals  25 ,  26 ,  28  and  30  are bearings. 
       FIG. 2  shows a five-nested combination of back rollers with five rotational degrees of freedom. The five movable back rollers  6 , 8 , 10 , 12 , 14  are respectively driven by a core shaft  20  and pulleys  33 , 34 , 35 , 36 .  FIG. 3  shows a five-ingredient separate/integrated asynchronous/synchronous second-stage drafting device, O 1 , O′ 1 , O 2 ,O′ 2 , O 3 ,O′ 3 , respectively refer to axis centers of back rollers, the middle roller and the front roller. The first stage drafting is implemented by the middle roller and the back rollers and the second drafting is implemented by the front roller and the middle roller. 
     During the process of spinning, the five 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. As such, the five roving yarns respectively go through separate/integrate drafting, and asynchronous/synchronous drafting. 
     The surface linear speeds of the nested five back rollers are respectively V h1 , V h2 , V h3 , V h4  and V h5 , the surface linear speed of the middle roller is V z , and the surface linear speed of the front roller is V q . The five coaxial back rollers with the same diameters correspond with five coaxial top rollers with the same diameters. The roving yarns are held by the five pairs of parallel arranged upper aprons and corresponding lower aprons located in the back area. When spinning, the five roving yarns are located by a guide rod and a bell mouth in the process of drafting and twisting, to travel according to the route showed in  FIG. 4 . The five roving yarns ρ 1 , ρ 2 , ρ 3 , ρ 4 , ρ 5  are fed into the first stage drafting area via the jaws a 1 , a 2 , a 3 , a 4 , a 5  of the back rollers at different speeds V h1 , V h2 , V h3 , V h4  and V h5 , and travel in parallel to the holding points b 1 , b 2 , b 3 , b 4 , b 5  and output at the speed V z . The linear densities of the five strands are respectively ρ 1′ , ρ 2′ , ρ 3′ , ρ 4′ , ρ 5′  after asynchronously drafted with
 
 e   h1 =( V   Z   −V   h1 )/ V   h1  
 
 e   h2 =( V   Z   −V   h2 )/ V   h2  
 
 e   h3 =( V   Z   −V   h3 )/ V   h3  
 
 e   h4 =( V   Z   −V   h4 )/ V   h4  
 
 e   h5 =( V   Z   −V   h5 )/ V   h5  
 
     then the five strands enter into the second stage drafting area and integrate at the jaw c of the front roller. The linear densities of the five strands are changed to ρ 1″ , ρ 2″ , ρ 3″ , ρ 4″ , ρ 5″  after synchronously drafted by the front roller at the surface speed V q . The five strands are integrated at the jaw c of the front roller and then twisted together to form a yarn with a linear density of (ρ 1″ +ρ 2″ +ρ 3″ +ρ 4″ +ρ 5″ ) (the twist shrinkage is not considered). 
     The linear density ρ y  of the yarn Y after drafted and twisted by the front roller is provided as below: 
     
       
         
           
             
               
                 
                   
                     ρ 
                     y 
                   
                   = 
                   
                     
                       1 
                       
                         V 
                         q 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                           ⋆ 
                           
                             ρ 
                             1 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ⋆ 
                           
                             ρ 
                             2 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               3 
                             
                           
                           ⋆ 
                           
                             ρ 
                             3 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               4 
                             
                           
                           ⋆ 
                           
                             ρ 
                             4 
                           
                         
                         + 
                         
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               5 
                             
                           
                           ⋆ 
                           
                             ρ 
                             5 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     3) The second stage drafting unit includes the front roller and the middle roller; the front roller moves at the speed V q ; 
     4) The speed V q  of the front roller and the speed V z  of the middle roller are kept constant, and only the speeds of first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller are adjusted, and the linear density or/and the blending ratio of the yarn can be adjusted. 
     The Specific Adjusting Method for the Linear Density: 
     Assuming the linear densities of a first roving yarn ingredient, a second roving yarn ingredient, a third roving yarn ingredient, a fourth roving yarn ingredient and a fifth roving yarn ingredient drafted by the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller are respectively ρ 1 , ρ 2 , ρ 3 , ρ 4  and ρ 5 , the linear density of the yarn Y drafted and twisted by the front roller is ρ y . 
                     ρ   y     =       1     V   q       ⁢     (         V     h   ⁢           ⁢   1       ⋆     ρ   1       +       V     h   ⁢           ⁢   2       ⋆     ρ   2       +       V     h   ⁢           ⁢   3       ⋆     ρ   3       +       V     h   ⁢           ⁢   4       ⋆     ρ   4       +       V     h   ⁢           ⁢   5       ⋆     ρ   5         )                               
Let ρ 1 =ρ 2 =ρ 3 =ρ 4 =ρ 5 =ρ, then:
 
     1) change the speed of any of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and keep the speeds of the other four backer rollers unchanged, and then the yarn ingredient of the yarn Y drafted by this back roller and the linear density thereof change accordingly. The linear density ρ′ y  of the yarn Y is adjusted as: 
               ρ   y   ′     =         ρ   y     +     Δρ   y       =       ρ     V   q       ⋆     (       V     h   ⁢           ⁢   1       +     V     h   ⁢           ⁢   2       +     V     h   ⁢           ⁢   3       +     V     h   ⁢           ⁢   4       +     V     h   ⁢           ⁢   5       +     Δ   ⁢           ⁢     V   hi         )               
wherein Δρ y  is a linear density change of the yarn, ΔV hi  is a speed change of the back roller i=1, 2, 3, 4, 5;
 
     2) change the speeds of any two back rollers of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and keep the speeds of the other three 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 the yarn Y is adjusted as: 
               ρ   y   ′     =         ρ   y     +     Δρ   y       =       ρ     V   q       *     [         ∑     j   =   1     5     ⁢     V   hi       +     (       Δ   ⁢           ⁢     V   hj       +     Δ   ⁢           ⁢     V   hk         )       ]               
wherein Δρ y  is a linear density change of the yarn, ΔV hj  and ΔV hk  are speed changes of the back rollers j and K, j≠k; j=1, 2, 3, 4, 5; k=1, 2, 3, 4, 5;
 
     3) change the speeds of any three back rollers of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and keep the speeds of the other two backer rollers unchanged, 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 yarn Y is adjusted as: 
               ρ   y   ′     =         ρ   y     +     Δρ   y       =       ρ     V   q       *     [         ∑     i   =   1     5     ⁢     V   hi       +     (       Δ   ⁢           ⁢     V   hj       +     Δ   ⁢           ⁢     V   hk       +     Δ   ⁢           ⁢     V   hm         )       ]               
wherein Δρ y  is a linear density change of the yarn, ΔV hj , ΔV hk  and ΔV hm  are speed changes of the back rollers j, K and m, j≠k≠m; j=1, 2, 3, 4, 5; k=1, 2, 3, 4, 5; m=1, 2, 3, 4, 5;
 
     4) change the speeds of any four back rollers of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and keep the speed of the remaining backer roller unchanged, the yarn ingredients of the yarn Y drafted by these four back rollers and the linear densities thereof change accordingly. The linear density ρ′ y  of the yarn Y is adjusted as: 
               ρ   y   ′     =         ρ   y     +     Δρ   y       =       ρ     V   q       *     [       V   hi     +     (       Δ   ⁢           ⁢     V   hj       +     Δ   ⁢           ⁢     V   hk       +     Δ   ⁢           ⁢     V   hm       +     Δ   ⁢           ⁢     V   hn         )       ]               
wherein Δρ y  is a linear density change of the yarn, ΔV hj , ΔV hk , ΔV hm  and ΔV hn  are speed changes of the back rollers j, K, m and n, j≠k≠m≠n; j=1, 2, 3, 4, 5; k=1, 2, 3, 4, 5; m=1, 2, 3, 4, 5;
 
     n=1, 2, 3, 4, 5; 
     5) change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller simultaneously, and the sum of the speeds of the five back rollers is unequal to zero. The yarn ingredients of the yarn Y drafted by these five back rollers and the linear densities thereof change accordingly. The linear density ρ′ y  of the yarn Y is adjusted as: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       5 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           V 
                           hi 
                         
                         + 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             hi 
                           
                         
                       
                       ) 
                     
                   
                   ] 
                 
               
             
           
         
       
     
     6) change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speed of any of back rollers equal to zero, while the speeds of the other four 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 four yarn ingredients are continuous. The linear density ρ′ y  of the yarn Y is adjusted as: 
               ρ   y   ′     =         ρ   y     +     Δ   ⁢           ⁢     ρ   y         =       ρ     V   q       *     [     (       V   hr     +     V   hs     +     V   hm     +     V   hn     +       ∑     j   =   1     5     ⁢     Δ   ⁢           ⁢     V   hj           )     ]               
wherein r≠s≠m≠n; r=1, 2, 3, 4, 5; s=1, 2, 3, 4, 5; m=1, 2, 3, 4, 5; n=1, 2, 3, 4, 5;
 
     7) change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speeds of any two back rollers equal to zero, while the speeds of the other three 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 three yarn ingredients are continuous. The linear density ρ′ y  of the yarn Y is adjusted as: 
               ρ   y   ′     =         ρ   y     +     Δ   ⁢           ⁢     ρ   y         =       ρ     V   q       *     [     (       V   hr     +     V   hs     +     V   hm     +       ∑     j   =   1     5     ⁢     Δ   ⁢           ⁢     V   hj           )     ]               
wherein r≠s≠m; r=1, 2, 3, 4, 5; s=1, 2, 3, 4, 5; m=1, 2, 3, 4, 5;
 
     8) change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speeds of any three back rollers equal to zero, while the speeds of the other two backer rollers unequal to zero. The yarn ingredients of the yarn Y drafted by the any three back rollers are thus discontinuous, while the other two yarn ingredients are continuous. The linear density ρ′ y  of the yarn Y is adjusted as: 
               ρ   y   ′     =         ρ   y     +     Δ   ⁢           ⁢     ρ   y         =       ρ     V   q       *     [     (       V   hr     +     V   hs     +       ∑     j   =   1     5     ⁢     Δ   ⁢           ⁢     V   hj           )     ]               
wherein r≠s; r=1, 2, 3, 4, 5; s=1, 2, 3, 4, 5
 
     9) change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speeds of any four back rollers equal to zero, while the speed of the another backer roller unequal to zero. The yarn ingredients of the yarn Y drafted by the any four back rollers are thus discontinuous, while the another yarn ingredient is continuous. The linear density ρ′ y  of the yarn Y is adjusted as: 
     
       
         
           
             
               ρ 
               y 
               ′ 
             
             = 
             
               
                 
                   ρ 
                   y 
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ρ 
                     y 
                   
                 
               
               = 
               
                 
                   ρ 
                   
                     V 
                     q 
                   
                 
                 * 
                 
                   [ 
                   
                     
                       V 
                       hr 
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         5 
                       
                       ⁢ 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           hj 
                         
                       
                     
                   
                   ] 
                 
               
             
           
         
       
       
         
           
             ( 
             
               
                 r 
                 = 
                 1 
               
               , 
               2 
               , 
               3 
               , 
               4 
               , 
               5 
             
             ) 
           
         
       
     
     10) change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speeds of any two back rollers equal to zero successively, while the speeds of the other three backer rollers unequal to zero. The yarn ingredients of the yarn Y drafted by the any two back rollers are thus discontinuous successively, while the other three yarn ingredients are continuous. The linear density ρ′ y  of the yarn Y is adjusted as: 
               ρ   y   ′     =         ρ   y     +     Δ   ⁢           ⁢     ρ   y         =       ρ     V   q       *     [     (       V   hr     +     V   hs     +     V   hm     +     V   hn     +       ∑     j   =   1     5     ⁢     Δ   ⁢           ⁢     V   hj           )     ]     ⁢     (     0   ≤   t   ≤     T   1       )                             ⁢       ρ   y   ′     =         ρ   y     +     Δ   ⁢           ⁢     ρ   y         =       ρ     V   q       *     [     (       V   hr     +     V   hs     +     V   hm     +       ∑     j   =   1     5     ⁢     Δ   ⁢           ⁢     V   hj           )     ]     ⁢     (       T   1     ≤   t   ≤     T   2       )                 
wherein T 1 , and T 2  are time points, and t is a time variable.
 
     11) change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speeds of any three back rollers equal to zero successively, while the speeds of the other two backer rollers unequal to zero. The yarn ingredients of the yarn Y drafted by the any three back rollers are thus discontinuous successively, while the other two yarn ingredients are continuous. The linear density ρ′ y  of yarn Y is adjusted as: 
               ρ   y   ′     =         ρ   y     +     Δ   ⁢           ⁢     ρ   y         =       ρ     V   q       *     [     (       V   hr     +     V   hs     +     V   hm     +     V   hn     +       ∑     j   =   1     5     ⁢     Δ   ⁢           ⁢     V   hj           )     ]     ⁢     (     0   ≤   t   ≤     T   1       )                             ⁢       ρ   y   ′     =         ρ   y     +     Δ   ⁢           ⁢     ρ   y         =       ρ     V   q       *     [     (       V   hr     +     V   hs     +     V   hm     +       ∑     j   =   1     5     ⁢     Δ   ⁢           ⁢     V   hj           )     ]     ⁢     (       T   1     ≤   t   ≤     T   2       )                               ⁢       ρ   y   ′     =         ρ   y     +     Δ   ⁢           ⁢     ρ   y         =       ρ     V   q       *     [     (       V   hr     +     V   hs     +       ∑     j   =   1     5     ⁢     Δ   ⁢           ⁢     V   hj           )     ]     ⁢     (       T   2     ≤   t   ≤     T   3       )                 
wherein T 1 , T 2  and T 3  are time points, and t is a time variable.
 
     12) change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and make the speeds of any four back rollers equal to zero successively, while the speeds of another backer roller unequal to zero. The yarn ingredients of the yarn Y drafted by the any four back rollers are thus discontinuous successively, while the another yarn ingredient is continuous. The linear density ρ′ y  of yarn Y is adjusted as: 
               ρ   y   ′     =         ρ   y     +     Δ   ⁢           ⁢     ρ   y         =       ρ     V   q       *     [     (       V   hr     +     V   hs     +     V   hm     +     V   hn     +       ∑     j   =   1     5     ⁢     Δ   ⁢           ⁢     V   hj           )     ]     ⁢     (     0   ≤   t   ≤     T   1       )                             ⁢       ρ   y   ′     =         ρ   y     +     Δ   ⁢           ⁢     ρ   y         =       ρ     V   q       *     [     (       V   hr     +     V   hs     +     V   hm     +       ∑     j   =   1     5     ⁢     Δ   ⁢           ⁢     V   hj           )     ]     ⁢     (       T   1     ≤   t   ≤     T   2       )                               ⁢       ρ   y   ′     =         ρ   y     +     Δ   ⁢           ⁢     ρ   y         =       ρ     V   q       *     [     (       V   hr     +     V   hs     +       ∑     j   =   1     5     ⁢     Δ   ⁢           ⁢     V   hj           )     ]     ⁢     (       T   2     ≤   t   ≤     T   3       )                               ⁢       ρ   y   ′     =         ρ   y     +     Δ   ⁢           ⁢     ρ   y         =       ρ     V   q       *     [     (       V   hr     +       ∑     j   =   1     5     ⁢     Δ   ⁢           ⁢     V   hj           )     ]     ⁢     (       T   3     ≤   t   ≤     T   4       )                 
wherein T 1 , T 2 , T 3 , and T 4  are time points, and t is a time variable; r≠s≠m≠n; r=1, 2, 3, 4, 5; s=1, 2, 3, 4, 5; m=1, 2, 3, 4, 5; n=1, 2, 3, 4, 5.
 
The Specific Adjusting Method for Blending Ratio:
 
     change the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller, and keep V h1 *ρ 1 +V h2 *ρ 2 +V h3 *ρ 3 +V h4 *ρ 4 +V h5 *ρ 5  as a constant, then linear density of the yarn Y is thus fixed while the blending ratios of the ingredients thereof change; the blending ratios k 1 , k 2 , k 3 , k 4 , k 5  of the first yarn ingredient, the second yarn ingredient, the third yarn ingredient, the fourth yarn ingredient, and the fifth yarn ingredient are provided as below: 
     
       
         
           
             
               k 
               1 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       V 
                       hi 
                     
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         hi 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               k 
               2 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       V 
                       hi 
                     
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         hi 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               k 
               3 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       V 
                       hi 
                     
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         hi 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               k 
               4 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       V 
                       hi 
                     
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         hi 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               k 
               5 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       V 
                       hi 
                     
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         hi 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     Let ΔV h1 +ΔV h2 +ΔV h3 +ΔV h4 +ΔV h5 =0, then the blending ratios are respectively: 
     
       
         
           
             
               k 
               1 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   V 
                   hi 
                 
               
             
           
         
       
       
         
           
             
               k 
               2 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   V 
                   hi 
                 
               
             
           
         
       
       
         
           
             
               k 
               3 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   V 
                   hi 
                 
               
             
           
         
       
       
         
           
             
               k 
               4 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   V 
                   hi 
                 
               
             
           
         
       
       
         
           
             
               k 
               5 
             
             = 
             
               
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     V 
                     
                       h 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                   
                 
               
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   5 
                 
                 ⁢ 
                 
                   V 
                   hi 
                 
               
             
           
         
       
     
     Let V h1 +V h2 +V h3 +V h4 +V h5 =V Z , i.e., the sum of the linear speeds of the five back rollers is equal to the linear speed of the middle roller, then: 
               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                         k   4     =         V     h   ⁢           ⁢   4         V   z       =     1     e     h   ⁢           ⁢   4                           k   5     =         V     h   ⁢           ⁢   5         V   z       =     1     e     h   ⁢           ⁢   5             ;         
i.e., the blending ratios of the five yarn ingredients ρ 1 , ρ 2 , ρ 3 , ρ 4 , ρ 5  of the yarn Y are equal to the inverses of their drafting ratios in the first stage drafting area,
 
     
       
         
           
             
               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 
                 
               
             
           
         
       
       
         
           
             
               e 
               
                 h 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 4 
               
             
             = 
             
               
                 
                   V 
                   z 
                 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
               
               = 
               
                 1 
                 
                   k 
                   4 
                 
               
             
           
         
       
       
         
           
             
               e 
               
                 h 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 5 
               
             
             = 
             
               
                 
                   V 
                   z 
                 
                 
                   V 
                   
                     h 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                 
               
               = 
               
                 1 
                 
                   k 
                   5 
                 
               
             
           
         
       
     
     Wherein there is an integrator between the combination of back rollers and the middle roller, the speed of the middle roller is kept unchanged, and then the first stage drafting unit functions as a blended or color-mixing unit, and the second stage drafting unit functions as a pure liner density regulating unit. 
     By controlling the operating speed of the middle roller, without regard for the later linear density adjusting process, the yarn can be blended more even and thorough, preventing the influences on the blending process from the linear density adjusting process. 
     Embodiment 2 
     The method of this embodiment is substantially the same as Embodiment 1, and the differences are: 
     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 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, the fourth back roller and the fifth back roller are V h1i , V h2i , V h3i , V h4i , V h5i , wherein i∈(1, 2, . . . , n); the first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient, the fourth roving yarn ingredient and the fifth roving yarn ingredient are two-stage drafted and twisted to form segment i of yarn Y, and the blending ratios k 1i , k 2i , k 3i , k 4i  and k 5i  thereof are expressed as below: 
                     k     1   ⁢   i       =         ρ   1     ⋆     V     h   ⁢           ⁢   1   ⁢   i             ∑     m   =   1     5     ⁢       ρ   i     ⋆     V   hmi                   (   2   )                 k     2   ⁢   i       =         ρ   2     ⋆     V     h   ⁢           ⁢   2   ⁢   i             ∑     m   =   1     5     ⁢       ρ   i     ⋆     V   hmi                   (   3   )                 k     3   ⁢   i       =         ρ   3     ⋆     V     h   ⁢           ⁢   3   ⁢   i             ∑     m   =   1     5     ⁢       ρ   i     ⋆     V   hmi                   (   4   )                 k     4   ⁢   i       =         ρ   4     ⋆     V     h   ⁢           ⁢   4   ⁢   i             ∑     m   =   1     5     ⁢       ρ   i     ⋆     V   hmi                   (   5   )                 k     5   ⁢   i       =         ρ   5     ⋆     V     h   ⁢           ⁢   5   ⁢   i             ∑     m   =   1     5     ⁢       ρ   i     ⋆     V   hmi                   (   6   )               
the linear density of the segment i of yarn Y is:
 
                           ρ   yi     =       ⁢         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       +         V     h   ⁢           ⁢   4   ⁢   i         V   z       ⁢     ρ   4       +         V     h   ⁢           ⁢   5   ⁢   i         V   z       ⁢     ρ   5         )                   =       ⁢       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       +         V     h   ⁢           ⁢   4   ⁢   i         V   z       ⁢     ρ   4       +         V     h   ⁢           ⁢   5   ⁢   i         V   z       ⁢     ρ   5         )                     (   7   )               
wherein
 
               e   q     =       V   q       V   z             
is the two-stage drafting ratio;
 
     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, the fourth back roller and the fifth back roller for this segment are respectively V h10 , V h20 , V h30 , V h40  and V h50 ; and the reference blending ratios of the first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient, the fourth roving yarn ingredient, and the fifth roving yarn ingredient for this segment are respectively k 10 , k 20 , k 30 , k 40  and k 50 , 
     keep the linear speed of the middle roller constant, and
 
 V   z   =V   h10   +V   h20   +V   h30   +V   h40   +V   h50   (8);
 
also keep two-stage drafting ratio
 
               e   q     =       V   q       V   z             
constant;
 
     wherein the reference linear speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller for this segment are respectively V h10 , V h20 , V h30 , V h40  and V h50 , which can be predetermined according to the material, the reference linear density ρ 0  and the reference blending ratios k 10 , k 20 , k 30 , k 40  and k 50  of the first roving yarn ingredient, the second roving yarn ingredient, the third roving yarn ingredient, the fourth roving yarn ingredient, and the fifth roving yarn ingredient. 
     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 , k 4i  and k 5i , the linear speeds V h1i , V h2i , V h3i , V h4i  and V h5i  of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller are calculated according to Equations (2)-(8); 
     4) Based on the reference linear speeds V h10 , V h20 , V h30 , V h40  and V h50  for the reference segment, increase or decrease the rotation rates of the first back roller, the second back roller, the third back roller, the fourth back roller or/and the fifth back roller to dynamically adjust the linear density or/and blending ratio for the segment i of yarn Y. 
     5) Let ρ 1 =ρ 2 =ρ 3 =ρ 4 =ρ 5 =ρ 
     the Equation (7) can be simplified as 
     
       
         
           
             
               
                 
                   
                     ρ 
                     yi 
                   
                   = 
                   
                     
                       ρ 
                       
                         e 
                         q 
                       
                     
                     ⋆ 
                     
                       
                         
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                               ⁢ 
                               i 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                               ⁢ 
                               i 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               3 
                               ⁢ 
                               i 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               4 
                               ⁢ 
                               i 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               5 
                               ⁢ 
                               i 
                             
                           
                         
                         
                           V 
                           z 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     According to Equations (2)-(6) and (8)-(9), the linear speeds V h1i , V h2i , V h3i , V h4i , V h5i  of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller are calculated. Based on the reference linear speeds V h10 , V h20 , V h30 , V h40  and V h50 , the rotation rates of the first back roller, the second back roller, the third back roller, the fourth back roller or/and the fifth back roller are increased or decreased to reach the preset linear density and blending ratio for the segment i of the yarn Y. 
     6) 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 the reference linear density; and thus the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller have corresponding increments on the basis of the reference linear speed, i.e., when (V h10 +V h20  V h30  V h40  V h50 )→(V h10 +ΔV h1i +V h20 +ΔV h2i +V h30 +ΔV h3i +V h40 +ΔV h4i +V h50 +ΔV h5i ), the linear density increment of yarn Y is: 
               Δρ   yi     =       ρ       e   q     ⋆     V   z         ⋆       (       Δ   ⁢           ⁢     V     h   ⁢           ⁢   1   ⁢   i         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   2   ⁢   i         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   3   ⁢   i         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   4   ⁢   i         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   5   ⁢   i           )     ⁢     ;               
Then the linear density ρ yi  of the yarn Y is expressed as
 
                     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         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   4   ⁢   i         +     Δ   ⁢           ⁢     V     h   ⁢           ⁢   5   ⁢   i             V   z       ⋆       ρ     e   q       .                   (   10   )               
Let ΔV 1 =ΔV h1i +ΔV h2i +ΔV h3i +ΔV h4i +ΔV h5i , then Equation (10) is simplified as:
 
     
       
         
           
             
               
                 
                   
                     ρ 
                     yi 
                   
                   = 
                   
                     
                       ρ 
                       
                         y 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                     
                     + 
                     
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             i 
                           
                         
                         
                           V 
                           z 
                         
                       
                       ⋆ 
                       
                         
                           ρ 
                           
                             e 
                             q 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     The linear density of the 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, the fourth back roller and the fifth back roller. 
     7) let ρ 1 =ρ 2 =ρ 3 =ρ 4 =ρ 5 =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)-(6) can be simplified as: 
     
       
         
           
             
               
                 
                   
                     k 
                     
                       1 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           10 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                             ⁢ 
                             i 
                           
                         
                       
                     
                     
                       
                         V 
                         z 
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       2 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           20 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                             ⁢ 
                             i 
                           
                         
                       
                     
                     
                       
                         V 
                         z 
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       3 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           30 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                             ⁢ 
                             i 
                           
                         
                       
                     
                     
                       
                         V 
                         z 
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       4 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           40 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                             ⁢ 
                             i 
                           
                         
                       
                     
                     
                       
                         V 
                         z 
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   
                     k 
                     
                       5 
                       ⁢ 
                       i 
                     
                   
                   = 
                   
                     
                       
                         V 
                         
                           h 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           50 
                         
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           
                             h 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                             ⁢ 
                             i 
                           
                         
                       
                     
                     
                       
                         V 
                         z 
                       
                       + 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     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, the fourth back roller and the fifth back roller; 
     wherein
 
Δ V   h1i   =k   1i *( V   Z   +ΔV   i )− V   h10  
 
Δ V   h2i   =k   2i *( V   Z   +ΔV   i )− V   h20  
 
Δ V   h3i   =k   3i *( V   Z   +ΔV   i )− V   h30  
 
Δ V   h4i   =k   4i *( V   Z   +ΔV   i )− V   h40  
 
Δ V   h5i   =k   5i *( V   Z   +ΔV   i )− V   h50  
 
     8) Let V h1i *ρ 1 +V h2i *ρ 2 +V h3i *ρ 3 +V h4i *ρ 4 +V h5i *ρ 5 =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. 
     9) Let any one to four of ΔV h1i , ΔV h2i , ΔV h3i , ΔV h4i  and ΔV h5i  be equal to zero, while the remaining ones are not zero, then the one to four roving yarn ingredients can be changed while the other roving yarn ingredients are unchanged. The adjusted blending ratio are: 
               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, j∈(1,2,3,4,5) and k≠j.
 
     10) Let none of ΔV h1i , ΔV h2i , ΔV h3i , ΔV h4i  and ΔV h5i  be equal to zero, then the five roving yarn ingredients in the yarn Y may be changed. 
     11) Let any one to four of ΔV h1i , ΔV h2i , ΔV h3i , ΔV h4i  and ΔV h5i  be equal to zero, while the remaining ones are not zero, then the one to four roving yarn ingredients of the segment i of the yarn Y may be discontinuous. 
     Embodiment 3 
     The method of this embodiment is substantially the same as Embodiment 1, and the differences are: 
     The yellow, magenta, cyan, black, and white yarns are respectively drafted by the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller; the speed V q  of the front roller is kept constant and the speeds of the first back roller, the second back roller, the third back roller, the fourth back roller and the fifth back roller are adjusted to regulate the colors of the yarns; when blending the colors, the color depth or the saturation of the colored spun yarn is adjusted by the black yarn, the concentration or brightness of the colored spun yarn is adjusted by the white yarn, and the hue is adjusted with the proportion of the black color and the white color. 
     Embodiment 4 
     The method of dynamically configuring linear density and blending ratio of a yarn by five-ingredient asynchronous drafting disclosed in this embodiment is substantially the same as Embodiment 2, and the differences are: 
     Set the initial linear speeds of the first back roller, a second back roller, a third back roller, a fourth back roller and a fifth back roller as V h10 , V h20 , V h30 , V h40 , V h50 ; the initial linear speed of the middle roller
 
 V   Z0   =V   h10   +V   h20   +V   h30   +V   h40   +V   h50  
 
     In addition, set
 
 V   Zi   =V   h1(i-1)   +V   h2(i-1)   +V   h3(i-1)   +V   h4(i-1)   +V   h5(i-1) ,
 
and let the two-stage drafting ratio
 
               e   qi     =       V   qi       V   zi             
constantly be equal to the set value e q ;
 
     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 , k 4i , k 5i , the linear speeds V h1i , V h2i , V h3i , V h4i , V h5i  of a first back roller, a second back roller, a third back roller, a fourth back roller and a fifth back roller are calculated. 
     On the basis of the segment i−1, the rotation rates of the first back roller and/or the second back roller are adjusted to dynamically regulate the linear density or/and blending ratio of segment i of the yarn Y online. 
     In the method,
 
 V   Zi   =V   h1(i-1)   +V   h2(i-1)   +V   h3(i-1)   +V   h4(i-1)   +V   h5(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.
 
     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. 
     Embodiment 5 
     A device for spinning a multi-color slub yarn and dotted yarn by five-ingredient two-stage drafting, comprises a control system and an actuating mechanism. The actuating mechanism includes five-ingredient separate/integrated 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. 
     As shown in  FIGS. 1 and 2 , the first stage drafting unit includes combination  15  of back rollers and middle roller  3 ; combination  15  of back rollers has five rotational degrees of freedom and includes first back roller  6 , second back roller  8 , third back roller  10 , fourth back roller  12  and fifth back roller  14 , which are set abreast on a same back roller shaft  20 . The second stage drafting unit includes front roller  1  and middle roller  3 . The numeral  4  refers to a top roller corresponding to middle roller  3 , and the numerals  5 , 7 , 9 , 11  and  13  refer to five top rollers corresponding to the five back rollers. The numeral  2  refers to a top roller corresponding to front roller  1 . 
     As shown in  FIG. 2 , a five-nested combination of back rollers with five rotational degrees of freedom is provided. The five movable back rollers  6 , 8 , 10 , 12 , 14  are movably placed around the same core shaft  20  and respectively driven by pulleys  32 , 33 , 34 , 35 , 36 . The five back rollers are adjacently provided in sequence and the driving pulleys  32 , 33 , 34 , 35 , 36  are located on both sides of the five back rollers. The five back rollers are set abreast on a same back roller shaft, with the driving mechanisms set on both sides, which makes the mechanic structure more compact and the five types of roving yarns drafted by the five back rollers more close when blending, so as to effectively prevent the yarn from interferences and pollutions when the driving mechanisms work. In addition, the five basic colors yarns go through the bell mouth with a smaller clamping angle, rendering the blending of the yarn more even and almost unbreakable. 
     As shown in  FIG. 5 , the control system mainly includes a PLC programmable controller, a servo driver, a servo motor, Recommended Standard (RS) 232 serial port, RS 485 serial port, etc. The PLC programmable controller controls the motor by the servo driver, to drive the rollers, ring plates and spindles. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Parameter comparison between asynchronous drafting and synchronous drafting (taking 18.45tex cotton yarn as an example) 
               
            
           
           
               
               
               
            
               
                   
                 Synchronous 
                   
               
               
                   
                 drafting 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Synchronous 
                 for double 
                 Synchronous 
                   
               
               
                   
                 drafting 
                 ingredients 
                 drafting 
               
               
                   
                 for single 
                 spinning 
                 for double 
                 Asynchronous drafting for five ingredients spinning 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 ingredient 
                 Ingredient 
                 Ingredient 
                 ingredients 
                 Ingredient 
                 Ingredient 
                 Ingredient 
                 Ingredient 
                 Ingredient 
               
               
                   
                 spinning 
                 1 
                 2 
                 spinning 
                 1 
                 2 
                 3 
                 4 
                 5 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Roving 
                 5.0 
                 5.0 
                 5.0 
                 Roving 
                  5.0 
                  5.0 
                  5.0 
                  5.0 
                  5.0 
                  5.0 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 yarn 
                   
                   
                   
                   
                 yarn 
                   
                   
                   
                   
                   
                   
               
               
                 weight 
                   
                   
                   
                   
                 weight 
               
               
                 (g/5 m) 
                   
                   
                   
                   
                 (g/5 m) 
               
               
                 Back 
                 1.1-1.3 
                 1.1-1.3 
                 1.1-1.3 
                 Back 
                 1.1-1.3 
                 1.1-1.3 
                 5*(k1 + 
                 5*(k1 + 
                 5*(k1 + 
                 5*(k1 + 
                 5*(k1 + 
               
               
                 area 
                   
                   
                   
                 area 
                   
                   
                 k2 + k3 + 
                 k2 + k3 + 
                 k2 + k3 + 
                 k2 + k3 + 
                 k2 + k3 + 
               
               
                 drafting 
                   
                   
                   
                 drafting 
                   
                   
                 k4 + 
                 k4 + 
                 k4 + 
                 k4 + 
                 k4 + 
               
               
                 ratio 
                   
                   
                   
                 ratio 
                   
                   
                 k5)/k1 
                 k5)/k1 
                 k5)/k1 
                 k5)/k1 
                 k5)/k1 
               
               
                   
                   
                   
                   
                   
                   
                   
                 Changes 
                 Changes 
                 Changes 
                 Changes 
                 Changes 
               
               
                   
                   
                   
                   
                   
                   
                   
                 with the 
                 with the 
                 with the 
                 with the 
                 with the 
               
               
                   
                   
                   
                   
                   
                   
                   
                 blending 
                 blending 
                 blending 
                 blending 
                 blending 
               
               
                   
                   
                   
                   
                   
                   
                   
                 ratio 
                 ratio 
                 ratio 
                 ratio 
                 ratio 
               
               
                 Front 
                 24.6-20.8 
                 22.7  
                 49.2-41.6 
                 Front 
                 24.6-20.8 
                 22.7 
                 13.5 
                 13.5 
                 13.5 
                 13.5 
                 13.5 
               
               
                 area 
                   
                   
                   
                 area 
               
               
                 drafting 
                   
                   
                   
                 drafting 
               
               
                 ratio 
                   
                   
                   
                 ratio 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Back 
                 unchanged 
                 changed 
                 unchanged 
                 changed 
                   
                 Asyn- 
                 Asyn- 
                 Asyn- 
                 Asyn- 
                 Asyn- 
               
               
                 rollers 
                   
                   
                   
                   
                   
                 chronous 
                 chronous 
                 chronous 
                 chronous 
                 chronous 
               
               
                 speed 
                   
                   
                   
                   
                   
                 change 
                 change 
                 change 
                 change 
                 change 
               
            
           
           
               
               
               
               
               
               
            
               
                 Middle 
                 unchanged 
                 unchanged 
                 unchanged 
                 unchanged 
                 unchanged 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 roller 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 speed 
               
            
           
           
               
               
               
               
               
               
            
               
                 Front 
                 unchanged 
                 unchanged 
                 uachanged 
                 unchanged 
                 unchanged 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 roller 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 speed 
               
            
           
           
               
               
               
               
               
               
            
               
                 Average 
                 18.45 
                 18.45 
                 18.45 
                 18.45 
                 18.45 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 spinning 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 number 
               
               
                 (tex) 
               
            
           
           
               
               
               
               
               
               
            
               
                 Linear 
                 invariable 
                 Limitedly 
                 invariable 
                 Limitedly 
                 Variable, adjustable 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 speed 
                   
                 variable 
                   
                 variable 
                   
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 variable 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Blending 
                 invariable 
                 invariable 
                 invariable 
                 Limitedly 
                 Variable, adjustable 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 ratio 
                   
                   
                   
                 variable 
                   
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 variable 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Linear 
                 invariable 
                 invariable 
                 invariable 
                 Limitedly 
                 Variable, adjustable 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 speed 
                   
                   
                   
                 variable 
                   
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 and 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 blending 
               
               
                 ratio 
               
               
                 both 
               
               
                 variable 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Spinning 
                 Even 
                 Slub 
                 Even 
                 Limited 
                 Even 
                 Even 
                 Even 
                 Even 
               
               
                 effect 
                 yarn 
                 yarn 
                 yarn 
                 segmeated 
                 yarn 
                 yarn 
                 yarn 
                 yarn 
               
               
                   
                   
                   
                   
                 color 
                 Any 
                 Any 
                 Any 
                 Any 
               
               
                   
                   
                   
                   
                 Limited 
                 blending 
                 blending 
                 blending 
                 blending 
               
               
                   
                   
                   
                   
                 slub yarn 
                 ratio 
                 ratio 
                 ratio 
                 ratio 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Color- 
                 Segment- 
                 Segment- 
                 slub 
               
               
                   
                 blended 
                 color 
                 color 
                 yarn 
               
               
                   
                 yarn 
                 blended 
                 slub 
               
            
           
           
               
               
               
               
            
               
                   
                 yarn 
                 yarn 
               
               
                   
                   
               
            
           
         
       
     
     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.