# Patent

## Title
Methods for designing lobe-type rotors

## Abstract

The present invention provides a method for designing lobe-type rotors which enables a defined rotor and a conjugate rotor with three or more than three lobes intermeshing and conjugating to each other; by setting suitable parameters to generate a curve portion of a single lobe of the defined rotor as a pattern including a curve E, an arc A, an arc B, a straight line Y, an arc C and an arc F, then imaging (N-1) copy of the curve portion in which N represents number of lobes and is bigger than or equal to three, and then respectively rotating each curve portion in sequence from an appropriate degree computed by 360/N to a terminal degree computed by (N-1)*360/N; whereby to integrately form the defined rotor with three or more than three lobes.

## Background
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 lobe-type rotor. By setting suitable parameters, the method can profile a defined rotor and a conjugate rotor with three or more than three 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 lobe-type rotor mechanism are already known that generally include a defined rotor and a conjugate rotor with a single-lobe type, double-lobe type or three-lobe type, and the defined rotor and the conjugate rotor intermesh and conjugate to each other. 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 disclose relevant rotors. The rotors of the prior arts have drawbacks that curves of each lobe of the rotors are not continuously and smoothly contacted at the joint between each segment; such drawbacks 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, abnormal situations such as noise and vibration may be arisen in working chamber enclosed by the 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 a method for designing lobe-type rotors which is able to generate a defined rotor and a conjugate rotor with three or more than three lobes intermeshing and conjugating to each other by different parameters. Moreover, the method, 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 reduce noise and vibration.
To achieve the above-mentioned objects, the method for designing a defined rotor and a conjugate rotor with three or more than three lobes of the present invention includes: a curve portion of a single lobe of the defined rotor as a pattern having a curve E, an arc A, an arc B, a straight line Y, an arc C and an arc F, then imaging N minus one copy (Hereinafter referred to as N-1 copy in which N represents the number of lobes and is bigger than or equal to three )and respectively rotating each curve portion in sequence from an appropriate degree computed by 360/N to a terminal degree computed by (N-1)*360/N whereby to integrately form the defined rotor with three or more than three lobes. Moreover, by way of said curve portions of the defined rotor to generate conjugate curve portions for forming the conjugate rotor, wherein the main feature of the present invention is that a fourth center t4 of the arc F is located at an angle of Δθ=360°/N towards a first center t1 of the defined rotor and is spaced a distance of 2 Rp from the first center t1. The fourth center t4 has a radius rF which equals to the maximum radius R. A third line h3 is defined by straight connecting the fourth center t4 and the first center t1, and then designating a fourth point P4 thereon; the arc F is defined by drawing around the fourth center t4 with a radius rF from the fourth point P4 to a fifth point P5, wherein the fifth point P5 is determined by a central angle β.
Furthermore, a fourth line h4 is defined by straight connecting the fourth center t4 and the fifth point P5; whereby a fifth center t5 of the arc C is located in line with the fourth line h4 through the fifth point P5, and has a radius rC; the radius rC is defined by following equation:



  
    
      
        r
        C
      
      +
      
        
          (
          
            R
            +
            
              r
              C
            
          
          )
        
        ⁢
        sin
        ⁢
        
          
        
        ⁢
        β
      
    
    =
    
      D
      2
    
  




  
    
      r
      C
    
    =
    
      
        
          D
          /
          2
        
        -
        
          R
          ⁢
          
            
          
          ⁢
          sin
          ⁢
          
            
          
          ⁢
          β
        
      
      
        1
        +
        
          sin
          ⁢
          
            
          
          ⁢
          β
        
      
    
  



(wherein R and D respectively represents the maximum radius and the width of the defined rotor)




BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic view of forming a tip conjugate curve by a method for designing lobe-type rotors of the present invention;
FIG. 2 is a schematic view of forming a three-lobe profile of a defined rotor by the method of the present invention;
FIG. 3 is a schematic view of forming a three-lobe profile of a conjugate rotor by the method of the present invention;
FIGS. 4 to 6 are embodiments of four lobes, five lobes, and six lobes of the defined rotor and conjugate rotor of the present invention.
FIG. 7 is a schematic view of various combinations of the three-lobe defined rotor and conjugate rotor, wherein a width D thereof is 55, 60, 65, 70, 75, 80 mm and a central angle α is 6°, a central angle β is 6°.



DESCRIPTION OF THE PREFERRED EMBODIMENTS
A three-lobe or more than three-lobe rotor design process in accordance with the present invention is adapted for designing curve portions of a defined rotor 1 by suitable parameters, and then get the curve portions of a conjugate rotor 2 with conjugate theory. Referring to FIGS. 1 to 3, designing process for forming the curve portions of the 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 t1 of the defined rotor 1 and a second center t2 of the conjugate rotor 2, wherein R=60 mm, D=65 mm, Rp=40 mm, the pitch circle radius Rp is smaller than radius R, and R and Rp are in appropriate ratio R=3 Rp/2.
    2. Referring to FIG. 1, define a reference horizontal line h1 by straight connecting the first center t1 and the second center t2, a base point P0 located on the reference horizontal line h1 and being offset from the first center t1 with a length of the radius R, a conjugate curve E′ generated as the base point P0 rotating around the first center t1, a curve E generated by symmetrically imaging the conjugate curve E′ against a tangent point P7 of the two pitch circles of the defined and the conjugate rotor 1, 2, and a first point P1 located in an intersection of the curve E and the horizontal line h1.
    3. Referring to FIG. 2, designate a second point P2 which is located by drawing around the first center t1 with the radius R from the point P0 at a central angle α (α is 6°), whereby an arc A is generated between the point P0 and P2 and is smoothly connected to the curve E.
    4. Define a second line h2 by straight connecting the first center t1 and the second point P2 and further designating a third center t3 thereon, the third center t3 has a radius rB which 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 is the maximum radius of the defined rotor 1, that is, a length between the first center t1 and the second point P2)

    5. defining an arc B by drawing around the third center t3 with the radius rB from the second point P2 to a third point P3, wherein the third point P3 is located above the third center t3;
    6. designate a fourth center t4 being located at an angle of 120° towards the first center t1 of the defined rotor 1 and being spaced a distance of 2 Rp from the first center t1, having a radius rF which equals to the maximum radius R;
    7. define a third line h3 by straight connecting the fourth center t4 and the first center t1, and then designate a fourth point P4 thereon; the fourth point P4 is spaced a distance of the radius rF from the fourth center t4;
    8. define an arc F by drawing around the fourth center t4 with a radius rF from the fourth point P4 to a fifth point P5 at a degree of β (β=6°), and then define a fourth line h4 by straight connecting the fourth center t4 and the fifth point P5;
    9. designate a fifth center t5 being located in line with the fourth line h4 through the fifth point P5, and having a radius rC defined by following equation:





  
    
      
        r
        C
      
      +
      
        
          (
          
            R
            +
            
              r
              C
            
          
          )
        
        ⁢
        sin
        ⁢
        
          
        
        ⁢
        β
      
    
    =
    
      D
      2
    
  




  
    
      r
      C
    
    =
    
      
        
          D
          /
          2
        
        -
        
          R
          ⁢
          
            
          
          ⁢
          sin
          ⁢
          
            
          
          ⁢
          β
        
      
      
        1
        +
        
          sin
          ⁢
          
            
          
          ⁢
          β
        
      
    
  



(wherein R and D respectively represents the maximum radius and the width of the defined rotor)

    10. define an arc C by drawing around the center t5 with the radius rC from the fifth point P5 to a sixth point P6 wherein the sixth point P6 is the external tangent point to a line Y;
    11. define the straight line Y by taking an external common tangent line of the arc C and arc B, wherein two end points of the straight line Y respectively connected to the sixth point P6 of the arc C and the third point P3 of the arc B;

whereby the curve portion of the single lobe of the defined rotor 1 is generated by linking the curve E, the arc A, the arc B, the straight line Y, the arc C and the arc F; further image two copies of the curve portion and respectively rotating the copied curve portion at 120°(which is computed by 360/3, 3 is the number of lobes) and 240°(which is computed by (3−1)*360/b, 3 is the number of lobes) in sequence to integrately form the defined rotor 1 with three lobes.



Moreover, likewise, follow the above-described steps, the conjugate rotor 2 is formed by conjugate curves profiled respectively from each arc and curve of the three-lobe of the defined rotor 1.
Further referring to FIG. 7, which is a schematic view of various combinations of the three-lobe defined rotor and conjugate rotor, wherein the maximum radius R is 60 mm, the pitch circle radius Rp is 40 mm, the width D is 55, 60, 65, 70, 75, 80 mm, the central angle α is 6°, and the central angle β is 6°; as general characteristics of conjugate intermeshing between two rotors, the defined rotor 1 (S1) of the minimum the width D corresponds to the conjugate rotor 2 (L1) 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.
Further referring to FIGS. 4 to 6, which are embodiments of four lobes, five lobes, and six lobes of the defined rotor 1′, 1′′, 1′′′ and the conjugate rotor 2′, 2′′, 2′′′; the designing process for theses embodiments are same as aforesaid steps. However, the degree of Δθ used in the these embodiments is different than used in the three-lobe rotor; the Δθ is an angle value and which is computed by 360°/N (N is the number of a lobe), the Δθ as shown in FIG. 4 is 90° (computed by 360°/4) as applied to four lobes rotor, the Δθ shown in FIG. 5 is 72° (computed by 360°/5) for five lobes rotor, and the Δθ shown in FIG. 6 is 36° (computed by 360°/10) for ten lobes rotor.
By setting suitable parameters, the method can generate a three lobes or more than three lobes of the defined rotor 1 and the conjugate rotor 2 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.
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.

## Claims

1. A method for designing lobe-type rotors adapted for generating a defined rotor and a conjugate rotor both having three or more than three lobes by setting suitable parameters into equations to generate a curve portion of a single lobe of the defined rotor as a pattern comprising an curve E, an arc A, an arc B, a straight line Y, an arc C, and an arc F, then imaging (N−1) copy of the curve portion in which N represents the number of lobes and is bigger than or equal to three, and then respectively rotating each curve portion in sequence from an appropriate degree computed by 360/N to a terminal degree computed by (N−1)*360/N, whereby to integrately form the defined rotor with three or more than three lobes; likewise, by way of the curve portions of the defined rotor to generate a conjugate curve portion for forming the conjugate rotor; thus the defined and the conjugate rotor intermesh and conjugate to each other; the method for designing a single lobe curve portion of the defined rotor comprising:
designating a maximum radius R of the defined rotor and a width D of the defined rotor, a pitch circle radius Rp of the defined rotor and the conjugate rotor, a first center t1 of the defined rotor and a second center t2 of the conjugate rotor, wherein a distance between the first center t1 and the second center t2 is 2Rp, the pitch circle radius Rp is smaller than radius R, and R and Rp are in appropriate ratio in length;
defining a reference horizontal line h1 by straight connecting the first center t1 and the second center t2, a base point P0 located on the reference horizontal line h1 and being offset from the first center t1 with a length of the radius R, a conjugate curve E′ generated as the base point P0 rotating around the first center t1, a curve E generated by symmetrically imaging the conjugate curve E′ against a tangent point P7 of the two pitch circles of the defined rotor and the conjugate rotor; therefore, a first point P1 is located in an intersection of the curve E and the horizontal line h1;
designating a second point P2 by drawing around the first center t1 with the radius R from the point P0 at an central angle α, thereby an arc A generated by connecting the base point P0 and the second point P2 and smoothly connected to the curve E;
defining a second line h2 by straight connecting the first center t1 and the second point P2, and then designating a third center t3 thereon and a radius rB of the third center t3, the radius rB being defined by following equation:




  
    
      
        r
        B
      
      +
      
        
          (
          
            R
            -
            
              r
              B
            
          
          )
        
        ⁢
        sin
        ⁢
        
          
        
        ⁢
        α
      
    
    =
    
      D
      2
    
  




  
    
      r
      B
    
    =
    
      
        
          D
          /
          2
        
        -
        
          R
          ⁢
          
            
          
          ⁢
          sin
          ⁢
          
            
          
          ⁢
          α
        
      
      
        1
        -
        
          sin
          ⁢
          
            
          
          ⁢
          α
        
      
    
  


defining an arc B by drawing around the third center t3 with the radius rB from the second point P2 to a third point P3 wherein the third point P3 is located above the third center t3;
designating a fourth center t4 being located at an angle of Δθ=360°/N towards the first center t1 of the defined rotor and being spaced a distance of 2 Rp from the first center t1, having a radius rF which equals to the maximum radius R;
defining a third line h3 by straight connecting the fourth center t4 and the first center t1, and then designating a fourth point P4 thereon; the fourth point P4 is spaced a distance of the radius rF from the fourth center t4;
defining an arc F by drawing around the fourth center t4 with a radius rFfrom the fourth point P4 to a fifth point P5 at a degree of β, and then defining a fourth line h4 by straight connecting the fourth center t4 and the fifth point P5;
designating a fifth center t5 being located in line with the fourth line h4 through the fifth point P5, and having a radius rC defined by following equation:




  
    
      
        r
        C
      
      +
      
        
          (
          
            R
            +
            
              r
              C
            
          
          )
        
        ⁢
        sin
        ⁢
        
          
        
        ⁢
        β
      
    
    =
    
      D
      2
    
  




  
    
      r
      C
    
    =
    
      
        
          D
          /
          2
        
        -
        
          R
          ⁢
          
            
          
          ⁢
          sin
          ⁢
          
            
          
          ⁢
          β
        
      
      
        1
        +
        
          sin
          ⁢
          
            
          
          ⁢
          β
        
      
    
  



(wherein R and D respectively represents the maximum radius and the width of the defined rotor)
defining an arc C by drawing around the center t5 with the radius rc from the fifth point P5 to a sixth point P6 wherein the sixth point P6 is the external tangent point to a line Y;
defining the straight line Y by taking an external common tangent line of the arc C and arc B, wherein two end points of the straight line Y respectively connected to the sixth point P6 of the arc C and the third point P3 of the arc B;
generating the curve portion of the single lobe of the defined rotor by linking the curve E, the arc A, the arc B, the straight line Y, the arc C and the arc F.

2. The method for designing lobe-type rotors as claimed in claim 1, wherein the maximum radius R of the defined rotor and the pitch circle radius Rp are in a ratio R=3Rp/2.