Patent Publication Number: US-7594323-B2

Title: Methods for designing single-lobe and double-lobe rotors

Description:
REFERENCE TO RELATED APPLICATIONS 
   This application is a continuation-in-part application of U.S. patent application Ser. No. 11/214,876 filed Aug. 31, 2005, now U.S. Pat. No. 7,255,545 the entire contents of the above mentioned application being incorporated herein by reference. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to methods for designing single-lobe and double-lobe rotors. By parameterized sets, the methods can profile a defined rotor and a conjugate rotor with single lobe or double lobes which intermesh and conjugate to each other, and effectively evaluate optimum performance in intermeshing and conjugating, whereby to provide higher compression ratio and larger discharge capacity, secure a smooth process while working chamber undergoing compression and expansion, and reduce leakage, thus can reduce noise and vibration while operation of the rotors. 
   2. Related Art 
   A large variety of related rotor mechanism are already known, see for example U.S. Pat. Nos. 1,426,820, 4,138,848, 4,224,016, 4,324,538, 4,406,601, 4,430,050 and 5,149,256. Rotors of the prior arts have drawbacks that curves thereof are discontinuity and not smoothly at the joint between each segment and which cause tips of the rotors do not mesh completely with other rotor when they are rotating. Consequently, in applying to machines working as periodical expansion and compression operation, the abnormal situations such as noise and vibration take place in working chamber enclosed by defined rotor, conjugate rotor and inner walls of cylinder. Moreover, inappropriate intermeshing between the rotors increases wear and therefore reduces the durability of operation. 
   In view of aforesaid disadvantages, U.S. patent application Ser. No. 11/214,876 has disclosed a defined rotor and a conjugate rotor designed by variety of parameters. Such rotors can reduce noise and vibration as operation. 
   SUMMARY OF THE INVENTION 
   Accordingly, an object of the present invention is to provide methods for designing single-lobe and double-lobe rotors which is able to generate a defined rotor and a conjugate rotor intermeshing and conjugating to each other by different parameters. Moreover, the methods, as apply to machines working as periodical expansion and compression operation can provide higher compression ratio and larger discharge capacity, secure a smooth process while working chamber undergoing compression and expansion and which reduce leakage as well lessen noise and vibration while operation of the rotors. 
   To achieve the above-mentioned objects, the methods for designing single-lobe and double-lobe rotors of the present invention comprise: curve portions of half two lobes of the defined rotor including a curve E, an arc A, an arc B, an arc F, an arc C, an arc G and a line Y, wherein the center of the arc C is located in a straight extension direction of the line connected the center of the defined rotor and an end point of an arc F, and a radius of the arc C is defined by following equation: 
               r   C     =       x   +     r   F       =           ⁢           x   ⁢           ⁢   sin   ⁢           ⁢   β     +     D   2       ⁢     
     ⇒   x     =         (     D   /   2     )     -     r   F         1   -     sin   ⁢           ⁢   β               ;           ⁢       r   C     =           (     D   /   2     )     -     r   F         1   -     sin   ⁢           ⁢   β         +     r   F               
(in which r C  is a radius of the arc C, x is a length between the center of the defined rotor and the center of the arc C, r F  is a radius of the arc F, D is a width of the defined rotor)
 
   By the above-mentioned methods, the curve portions of half two lobes of the defined rotor are formed and further symmetrically imaging the curve portions to form a defined rotor with two lobes. 
   In the manner of generating the curve portions of half two lobes of the defined rotor  1 , further designating a symmetry point P 8  which is symmetrical to the fourth point P 4  against the first center t 1 , and which is located in an extension direction of a third line h 3 . A fourth center t 4 ′ located on the third line h 3  and being symmetrical to the fourth center t 4  against the first center t 1 , and defining an arc C′ by drawing around the fourth center t 4 ′ with the radius r C  from the symmetry point P 8  to the sixth point P 6 ; therefore the sixth point P 6  of the arc C′ is tangent to the horizontal line Y; further defining an arc G by drawing around the first center t 1  with the radius r F  from the fourth point P 4  to the symmetry point P 8 , whereby the arc C′ is smoothly linked with the horizontal line Y and the arc G; consequently, the single-lobe defined rotor is profiled by linking the curve E, the arc A, the arc B, the arc F, the arc C′, the arc G and the horizontal line Y. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic view of forming a tip conjugate curve by methods for designing single-lobe and double-lobe rotors of the present invention; 
       FIG. 2  is a schematic view of forming a double-lobe profile of a defined rotor by the methods of the present invention; 
       FIG. 3  is a schematic view of forming a double-lobe profile of a conjugate rotor by the methods of the present invention; 
       FIG. 4  is a schematic view of various combinations of the double-lobe defined rotor and conjugate rotor, wherein a width D thereof is 55, 60 . . . 80 mm, a central angle α is 5° and a central angel β is 5°. 
       FIG. 5  is a schematic view of forming a single-lobe profile of a defined rotor by the methods of the present invention. 
       FIG. 6  is a schematic view of forming a single-lobe profile of a conjugate rotor by the methods of the present invention. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   A double-lobe rotor design process in accordance with the present invention designs the curve portions of a defined rotor  1  by suitable parameters, and then get the curve portions of conjugate rotor  2  with conjugate theory. Referring to  FIGS. 1 to 3 , designing process for forming the curve portions of defined rotor  1  comprises the following steps:
     1. Designate a maximum radius R and a width D of the defined rotor  1 , a pitch circle radius Rp of the defined and the conjugate rotor  1 ,  2 , a first center t 1  of the defined rotor  1  and a second center t 2  of the conjugate rotor  2 , wherein a distance between the first center t 1  and the second center t 2  is 2 Rp, the pitch circle radius Rp is smaller than radius R, and R and Rp are in appropriate ratio R=4 Rp/3.   2. Referring to  FIG. 1 , define a reference horizontal line h 1  by straight connecting the first center t 1  and the second center t 2 , a base point P 0  located on the reference horizontal line h 1  and being offset from the first center t 1  in a length same as the radius R, a conjugate curve E′ generated as the base point P 0  rotating around the first center t 1 , a curve E generated by symmetrically imaging the conjugate curve E′ against a tangent point P 7  of the two pitch circles of the defined and the conjugate rotor, and a first point P 1  located in an intersection of the curve E and the horizontal line h 1 .   3. Referring to  FIG. 2 , designate a second point P 2  which is formed by drawing around the first center t 1  with the radius R from the point P 0  in an central angle α (α is 5°), whereby an arc A is generated between the point P 0  and P 2 , and is smoothly connected to the curve E.   4. Define a second line h 2  by straight connecting the first center t 1  and the second point P 2  and further designating a third center t 3  thereon, of which a radius is r B .   5. The radius r B  is defined by following equation:   

   
     
       
         
           
             
               r 
               B 
             
             + 
             
               
                 ( 
                 
                   R 
                   - 
                   
                     r 
                     B 
                   
                 
                 ) 
               
               ⁢ 
               sin 
               ⁢ 
               
                   
               
               ⁢ 
               α 
             
           
           = 
           
             D 
             2 
           
         
       
     
     
       
         
           
             r 
             B 
           
           = 
           
             
               
                 D 
                 / 
                 2 
               
               - 
               
                 R 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 sin 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 α 
               
             
             
               1 
               - 
               
                 sin 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 α 
               
             
           
         
       
     
       
       
         
           (wherein R=the maximum radius of the defined rotor  1 , that is, a length between the first center t 1  and the second point P 2 ) 
         
       
       6. Define an arc B by drawing around the third center t 3  with the radius r B  from the second point P 2  to a third point P 3 , wherein the third point P 3  is vertically located above the third center t 3 . 
       7. Define an arc F by drawing around the first center t 1  with a radius r F  from a first point P 1  to a fourth point P 4  wherein the fourth point P 4  is designated by an central angle β (β is 15°) measured downward from the first point P 1  according to the first center t 1 , and the radius r F  is defined by following equation r F =2 Rp−R. 
       8. Prior to generating an arc C, define a third line h 3  which is an extension line with the direction of straight connecting the fourth point P 4  and the first center t 1 , and further designate a fourth center t 4  being located in the third line h 3 . 
       9. Defining an arc C by drawing around the fourth center t 4  with a radius r C  from the fourth point P 4  to a fifth point P 5 , wherein the fifth point P 5  is vertically located under the fourth center t 4 , and the radius r C  is defined by following equation: 
     
  
   
     
       
         
           
             
               r 
               C 
             
             = 
             
               
                 x 
                 + 
                 
                   r 
                   F 
                 
               
               = 
               
                   
               
               ⁢ 
               
                 
                   
                     
                       x 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       β 
                     
                     + 
                     
                       D 
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⇒ 
                   x 
                 
                 = 
                 
                   
                     
                       ( 
                       
                         D 
                         / 
                         2 
                       
                       ) 
                     
                     - 
                     
                       r 
                       F 
                     
                   
                   
                     1 
                     - 
                     
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       β 
                     
                   
                 
               
             
           
           ; 
           
               
           
           ⁢ 
           
             
               r 
               C 
             
             = 
             
               
                 
                   
                     ( 
                     
                       D 
                       / 
                       2 
                     
                     ) 
                   
                   - 
                   
                     r 
                     F 
                   
                 
                 
                   1 
                   - 
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     β 
                   
                 
               
               + 
               
                 r 
                 F 
               
             
           
         
       
     
       
       
         
           in which r F =2 Rp−R. 
         
       
       10. Define a horizontal line Y by connecting the third point P 3  and a sixth point P 6  which is symmetrical to the fifth point P 5 ; whereby curve portions of half two lobes of the defined rotor  1  are generated by smooth linking the curve E, the arc A, arc B, arc F, arc C, and the horizontal line Y. And further symmetrically imaging each arc and curve of half two lobes of the defined rotor  1  to form the complete defined rotor  1  with doublelobes. 
       11. Furthermore, the conjugate rotor  2  is formed by way of aforesaid curve portions of the defined rotor  1  and through a conjugate curve profiled respectively from each arc and curve of the double-lobe of the defined rotor  1  by the above-described steps, the double-lobe defined rotor  1  and the conjugate rotor  2  are formed accordingly. 
     
  
   Further referring to  FIG. 4 , which is a schematic view of various combinations of the double-lobe defined rotor and conjugate rotor, wherein a width D thereof is 55, 60 . . . 80 mm, a central angle α is 5° and a central angel β is 5°; as general characteristics of conjugate intermeshing between two rotors, the defined rotor  1  (S 1 ) of the minimum width D corresponds to the conjugate rotor  2  (L 1 ) of the maximum value. Accordingly, depending on practical applications, an appropriate size of the defined rotor  1  and the conjugate rotor  2  can be determined by analogy with aforesaid characteristics. 
   Moreover, referring to  FIG. 5  for methods for generating curve portions of the single-lobe defined rotor  1 ′; in the manner of generating the curve portions of half two lobes of the defined rotor  1 , that is, bold parts shown in  FIG. 2 . Further designating a symmetry point P 8  which is symmetrical to the fourth point P 4  against the first center t 1 , and which is located in an extension direction of a third line h 3 . A fourth center t 4 ′ located on the third line h 3  and being symmetrical to the fourth center t 4  against the first center t 1 , and defining an arc C′ by drawing around the fourth center t 4 ′ with the radius r C  from the symmetry point P 8  to the sixth point P 6 ; therefore the sixth point P 6  of the arc C′ is tangent to the horizontal line Y; further defining an arc G by drawing around the first center t 1  with the radius r F  from the fourth point P 4  to the symmetry point P 8 , whereby the arc C′ is smoothly linked with the horizontal line Y and the arc G; consequently, the single-lobe defined rotor  1 ′ is profiled by linking the curve E, arc A, arc B, arc F, arc C′, arc G and horizontal line Y 
   The single-lobe conjugate rotor  2 ′ is formed (shown in  FIG. 6 ) by way of aforesaid curve portions and through the conjugate curve profiled respectively from each arc and curve of the single-lobe of the defined rotor  1  by the above-described steps. 
   By parameterized sets, the methods can profile a single-lobe or double-lobe of a defined rotor and a conjugate rotor which intermesh and conjugate to each other, and effectively evaluate optimum performance in intermeshing and conjugating, whereby to provide higher compression ratio and larger discharge capacity, secure a smooth process while working chamber undergoing compression and expansion, and which reduce leakage, thus lessen noise and vibration while operation of the rotors. Besides, the conjugate curve portions of the conjugate rotor  2  relatively profiled through the arc F and arc G of the defined rotor  1  are still arcs, could effectively enhance the sealing ability further. 
   It is understood that the invention may be embodied in other forms without departing from the spirit thereof. Thus, the present examples and embodiments are to be considered in all respects as illustrative and not restrictive, and the invention is not to be limited to the details given herein.