Patent Publication Number: US-11644034-B2

Title: Complex screw rotors

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation under 35 U.S.C. § 120 of U.S. patent application Ser. No. 15/760,086, filed Mar. 14, 2018, and titled “COMPLEX SCREW ROTORS,” which in turn is a U.S. national stage entry of International Patent Application No. PCT/US2016/059613, filed on Oct. 29, 2016, which claims priority to United States Patent Application Nos. 62/248,785, 62/248,811, 62/248,832 and 62/248,858, filed on Oct. 30, 2015, the entire contents of all of which are fully incorporated herein by reference. 
    
    
     FIELD 
     Various exemplary embodiments relate to screw compressor rotors used to compress fluids. 
     BACKGROUND 
     Rotary screw compressors typically include two or more intermeshing rotors positioned in a housing. A male rotor includes one or more lobes that mate with grooves of a female rotor. The housing defines a chamber in which the male and female rotors are positioned. The chamber is dimensioned closely with the outer diameters of the male and female rotor, generally shaped as a pair of cylinders that are parallel and intersecting. An inlet is provided for the introduction of fluid to the rotors and an outlet is provided for discharging the compressed fluid. 
     The rotors include a driving mechanism, for example gears, that drive and synchronize the movement of the male and female rotors. During rotation, the intermeshing male and female rotors form cells of varying sizes to first receive the inlet fluid and then compress, thus increasing the pressure of, the fluid as it moves toward the outlet. Dry compressors can utilize one or more gears connected to a shaft to drive and synchronize rotation of the rotors. Wet compressors can utilize a fluid, for example oil, to space and driver the rotors. 
     The profiles of the male and female rotors can be generated a number of ways. One way is to define one of the two rotors and then derive the other profile using conjugation. Another method includes defining a rack curve for the rotors, and using the rack curve to define the male and female rotors. This method is described, for example in: U.S. Pat. No. 4,643,654; WO 97/43550; and GB 2,418,455. Another method of defining male and female rotor profiles by enveloping a rack curve is described in U.S. Pat. No. 8,702,409, the disclosure of which is hereby incorporated by reference in its entirety. 
     SUMMARY 
     Various exemplary embodiments relate to a screw compressor or expander having a female rotor including a first section having a right-hand first groove and a second section having a left-hand second groove. The first groove has a first variable helix, the second groove has a second variable helix, and the female rotor has a first variable profile and a first variable outer diameter. A male rotor includes a third section having a left-hand first lobe and a fourth section having a right-hand second lobe. The first lobe has a third variable helix, the second lobe has a fourth variable helix, and the male rotor has a second variable profile and a second variable outer diameter. 
     Various exemplary embodiments relate to a screw compressor or expander having a female rotor including a first section, a second section, and a first central section. The first section having a set of right-hand first grooves, the second section having a set of left-hand second grooves corresponding to the set of first grooves. The first grooves have a first variable helix, the second grooves have a second variable helix, and the female rotor has a first variable profile. A male rotor includes a third section, a fourth section, and a second central section positioned between the third and fourth sections. The third section having a set of left-hand first lobes and the fourth section having a set of right-hand second lobes corresponding to the set of first lobes. The first lobes have a third variable helix, the second lobes have a fourth variable helix, and the male rotor has a second variable profile. The female rotor transitions to a substantially circular cross section at the first central section and the male rotor transitions to a substantially circular cross section at the second central section. 
     Various exemplary embodiments relate to a screw compressor or expander having a female rotor including a first section having a first groove with a right-hand first variable helical profile and a second section having a second groove with a left-hand second variable helical profile, A male rotor including a third section having a first lobe with a right-hand third variable helical profile and a fourth section having a second lobe with a left-hand fourth variable helical profile. 
     Various exemplary embodiments relate to a screw compressor or expander including a male rotor having a first axial length extending from an inlet portion to an outlet portion and a set of lobes with a variable profile extending along the first axial length. A female rotor having a second axial length extending from the inlet portion to the outlet portion and a set of grooves with a variable profile extending along the second axial length. The set of grooves mating with the set of lobes. At least a portion of the male rotor and the female rotor each have a non-cylindrical configuration with a non-constant outer diameter. 
     Various exemplary embodiments relate to a screw compressor or expander including a male rotor having a first axial length extending from an inlet portion to an outlet portion and a set of lobes with a variable profile extending along at least a portion of the first axial length. A female rotor having a second axial length extending from the inlet portion to the outlet portion and a set of grooves with a variable profile extending along at least a portion of the second axial length, the set of grooves mating with the set of lobes. The male rotor and the female rotor transition to a substantially circular cross section near the outlet portion. 
     Various exemplary embodiments relate to a screw compressor or expander including a male rotor having a first axial length extending from an inlet portion to an outlet portion and a set of lobes extending along at least a portion of the first axial length. A female rotor having a second axial length extending from the inlet portion to the outlet portion and a set of grooves extending along at least a portion of the second axial length, the set of grooves mating with the set of lobes. The male rotor and the female rotor have a first section with a first profile defined by a first rack having a first set of X and Y coordinates and a second section with a second profile defined by a second rack different than the first rack having a second set of X and Y coordinates. 
     Various exemplary embodiments relate to a method of designing a set of screw compressor or expander rotors. A first rack is established for a male and female rotor. The first rack having at least one curved segment with a first crest having a first set of X and Y coordinates. The first rack is scaled in the X and Y directions to create a second rack having at least one curved segment with a second crest having a second set of X and Y coordinates. The X coordinate of the second crest is spaced from the X coordinate of the first crest. 
     Various exemplary embodiments relate to a method of designing a set of screw compressor or expander rotors. A first rack is established for a male and female rotor. The first rack having at least one curved segment with a first crest having a first set of a X and Y coordinates. A second rack is established for a male and female rotor. The second rack having at least one curved segment with a second crest having a second set of a X and Y coordinates, wherein the X coordinate of the second crest is spaced from the X coordinate of the first crest. 
     Various exemplary embodiments relate to a screw compressor or expander including a male rotor having a first axial length and a set of lobes with a first helical profile extending along the first axial length. A female rotor having a second axial length and a set of grooves with a second helical profile extending along the second axial length. The set of grooves mating with the set of lobes. The first helical profile is non-continuously variable over the first axial length. 
     Various exemplary embodiments relate to a screw compressor or expander including a male rotor having a lobe with a first helical profile extending between a first position proximate to an inlet portion and a second position proximate an outlet portion. A female rotor having a groove with a second helical profile extending between a third position proximate an inlet portion and a fourth position proximate an outlet portion, the groove mating with the lobes. A wrap-angle curve of the male rotor lobe includes a convex portion. 
     Various exemplary embodiments relate to a screw compressor or expander including a female rotor including a first section having a first groove with a right-hand helical profile, a second section having a second groove with a left-hand helical profile, and a first central section having a first curved transition connecting the first and second groove. A male rotor including a third section having a first lobe with a right-hand helical profile, a fourth section having a second lobe with a left-hand helical profile, and a second central section having a second curved transition connecting the first and second lobes. 
     Various exemplary embodiments relate to a screw compressor or expander including a female rotor including a first section having a first groove with a right-hand helical profile, a second section having a second groove with a left-hand helical profile, and a first central section. A male rotor including a third section having a first lobe with a right-hand helical profile, a fourth section having a second lobe with a left-hand helical profile, and a second central section. One of the first and second central sections includes a pocket. 
     Various exemplary embodiments relate to a screw compressor or expander including a housing having an inlet port, a discharge port, and a body at least partially defining a compression chamber having a first portion and a second portion. A female rotor rotatably positioned in the first portion of the compression chamber, the female rotor including a first section having a first groove with a right-hand helical profile, a second section having a second groove with a left-hand helical profile, and a first central section having a first curved transition connecting the first and second groove. A male rotor rotatably positioned in the first portion of the compression chamber, the male rotor including a third section having a first lobe with a right-hand helical profile, a fourth section having a second lobe with a left-hand helical profile, and a second central section having a second curved transition connecting the first and second lobes. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The aspects and features of various exemplary embodiments will be more apparent from the description of those exemplary embodiments taken with reference to the accompanying drawings, in which: 
         FIG.  1    is a top view of traditional set of rotors for a screw compressor; 
         FIG.  2    is a cross sectional view of the rotors of  FIG.  1   ; 
         FIG.  3    is a top view of an exemplary set of variable rotors for a screw compressor; 
         FIG.  4    is a graph representing the outer diameter of the male and female rotors of  FIG.  3   ; 
         FIGS.  5 A- 5 E  are cross sectional views of the rotors of  FIG.  3    taken at the positions indicated in  FIG.  3   ; 
         FIG.  6    is a top view of another exemplary set of variable rotors for a screw compressor; 
         FIG.  7    is a graph representing the outer diameter of the male and female rotors of  FIG.  6   ; 
         FIGS.  8 A- 8 E  are cross sectional views of the rotors of  FIG.  6    taken at the positions indicated in  FIG.  6   ; 
         FIG.  9    is a chart showing a set of curves representing different embodiments of variable male rotors; 
         FIG.  10    is a chart showing volume vs male rotation angle for the male rotors of  FIGS.  1 ,  3 , and  6   ; 
         FIG.  11    is a chart showing compression vs male rotation angle for the male rotors of  FIGS.  1 ,  3 , and  6   ; 
         FIG.  12    is three sets of rack curves used to create a variable profile rotor; 
         FIG.  13    is set of variable profile rotors showing the tip widening do to the rack scaling in the X and Y direction; 
         FIG.  14    shows a set of rack curves created through scaling a rack in the X and Y direction; and 
         FIG.  15    shows a s set rack curves used to create a linearly variable rotor and a set of rack curves used to create a non-linearly variable rotor; 
         FIG.  16    is a perspective view of a continuously variable male and female rotor; 
         FIG.  17    is a top view of  FIG.  16   ; 
         FIG.  18    is a graph showing the wrap-angle curve of the male rotors of  FIG.  16    and  FIG.  17   ; 
         FIG.  19    is top view of a Fast Slow Fast helix male and female rotor; 
         FIG.  20    is a graph showing the wrap-angle curve of the male rotors of  FIG.  1   ,  FIG.  16   , and  FIG.  19   ; 
         FIG.  21    is top view of a Faster Slower Faster helix male and female rotor; 
         FIG.  22    is a graph showing the wrap-angle curve of the male rotors of  FIG.  1   ,  FIG.  16   , and  FIG.  21   ; 
         FIG.  23    is a graph showing the wrap-angle curve of the male rotors of  FIG.  1   ,  FIG.  16   , and a Slow Fast Slow helix male rotor; 
         FIG.  24    is a graph showing the wrap-angle curve of the male rotors of  FIG.  1   ,  FIG.  16   , and a Fast Slow helix male rotor; 
         FIG.  25    is a graph showing volume vs male rotation angle; 
         FIG.  26    is a graph showing compression vs male rotation angle; 
         FIG.  27    shows a top view of an exemplary double helix rotor; 
         FIG.  28    shows a side view of an exemplary compressor or expander housing; 
         FIG.  29    shows a top view of an exemplary set of double helix rotors with a curved transition; 
         FIG.  30    shows a perspective view of  FIG.  29   ; 
         FIG.  31    shows a top view of an exemplary set of double helix rotors with a curved transition and a pocket; 
         FIG.  32    is an enlarged view of the pocket area of  FIG.  31   ; 
         FIG.  33    is a side cross section of the rotors of  FIG.  31    in a first position; 
         FIG.  34    is a side cross section of the rotors of  FIG.  31    in a second position; 
         FIG.  35    is a top view of an exemplary set of variable double helix rotors; 
         FIG.  36    is perspective view of an exemplary set of double helix, variable profile rotors; 
         FIG.  37    is a top view of  FIG.  36   ; 
         FIG.  38    is a top view of an exemplary set of double helix variable profile rotors where the lobes and grooves are offset; 
         FIG.  38 A  is a left side view of  FIG.  38   ; 
         FIG.  38 B  is a right side view of  FIG.  38   ; 
         FIG.  39    shows an example of a set of rotors having a fixed double helix and a conical rotor profile; 
         FIG.  40    shows an example of a set of rotors having a fixed double helix and a rounded or ogive rotor profile; 
         FIG.  41    shows an example of a set of rotors having a variable double helix and a conical rotor profile where both sides of the helix are a continuously variable helix having a concave wrap-angle curve; 
         FIG.  42    shows an example of a set of rotors having a variable double helix and a conical rotor profile where both sides of the helix are a Fast Slow variable helix having a convex wrap-angle curve; 
         FIG.  43    shows an example of a set of rotors having a conical rotor profile where both sides of the helix are a Slow Fast Slow non-continuously variable helix; 
         FIG.  44    shows an example of a set of rotors having an ogive rotor profile where both sides of the helix are a Slow Fast Slow non-continuously variable helix; 
         FIG.  45    shows an example of a set of rotors having a conical rotor profile where both sides of the helix are a Fast Slow Fast non-continuously variable helix; and 
         FIG.  46    shows an example of a set of rotors having an ogive rotor profile where both sides of the helix are a Fast Slow Fast non-continuously variable helix. 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       FIG.  1    shows an exemplary embodiment of a typical compressor design that includes a male rotor  10  having one or more lobes  12  and a female rotor  14  having one or more grooves or gates  16 . The male rotor  10  is mounted on a first shaft  18  and the female rotor  14  is mounted on a second shaft  20 . The male rotor  10  is positioned in a first section of a chamber and the female rotor  14  is positioned in a second section of the chamber. Fluid enters the chamber at an inlet  22 , and when the rotors are driven, the lobes  12  of the male rotor  10  fit into the grooves  16  of the female rotor  14 , causing compression and movement of the fluid towards an outlet or discharge end  24  where the compressed fluid is discharged. The male and female rotors  10 ,  14  have a constant lead or pitch extending along the length of the rotor, a constant profile, and a constant outer diameter. Accordingly the chamber is defined by a pair of intersecting cylinders that have parallel longitudinal axes. 
     As best shown in  FIG.  2   , the male rotor  10  rotates around a first axis A 10  of rotation whereas the female rotor  14  rotates around a second axis A 14  of rotation. In particular, the first axis A 10  is located at a distance D 1  (commonly known by the term “center distance”) from the second axis A 14  of rotation. The first axis A 10  and second axis A 14  are mutually parallel, so that D 1  is constant over the axial length of the rotor. 
     The male rotor  10  includes a pitch circumference Cp 10 . The radius Rp 10  of the pitch circumference Cp 10  is proportional to the number of lobes  12  of the male rotor  10 . Each lobe  12  of the male rotor  10  extends prevalently outside the corresponding pitch circumference Cp 10  until reaching an outer circumference Ce 10  of the male rotor  10 . The remaining part of the lobe  12  of the male rotor  10  extends inside the corresponding pitch circumference Cp 10  until reaching a root circumference Cf 10  of the male rotor  10 . The radius Rf 10  of the root circumference Cf 10  is smaller than the radius Rpm of the pitch circumference Cp 10 , which is in turn smaller than the radius Rem of the outer circumference Ce 10  of the male rotor  10 . The distance between the pitch circumference Cp 10  and the outer circumference Ce 10  of the male rotor  10  is defined as the addendum of the male rotor  10 . The male addendum corresponds to the difference between the value of the radius Rem of the outer circumference Ce 10  and the value of the radius Rpm of the pitch circumference Cp 10  of the male rotor  10 . Each lobe  12  of the male rotor  10  has a first thickness Tito measured on the respective pitch circumference Cp 10  that extends from a first mid-point between two lobes to an adjacent midpoint between two lobes, or the pith circumference Cp 10  divided by the number of lobes, in this case 120° of the pitch circumference Cp 10 . 
     The female rotor  14  includes a pitch circumference Cp 14 . The measure of the radius Rp 14  of the circumference Cp 14  of the female rotor  14  is proportional to the number of grooves  16  of the female rotor. Each groove  16  extends prevalently inside the corresponding pitch circumference Cp 14  until reaching a root circumference Cf 1 . 4  of the female rotor  14 . The remaining part of the groove  16  of the female rotor  14  extends outside the corresponding pitch circumference Cp 14  until reaching an outer circumference Ce 14  of the female rotor  14 . The radius Rf 14  of the root circumference Cf 14  is smaller than the radius Rp 14  of the pitch circumference Cp 14 , which is in turn smaller than the radius Re 14  of the outer circumference Ce 14  of the female rotor  14 . The distance between the pitch circumference Cp 14  and the outer circumference Ce 14  of the female rotor  14  is defined as the addendum of the female rotor  14 . The female addendum corresponds to the difference between the value of the radius Re 14  of the outer circumference Ce 14  and the value of the radius Rp 14  of the pitch circumference Cp 14  of the female rotor  14 . The space between each groove  16  of the female rotor  14  has a second thickness T 14  measured on the respective pitch circumference Cp 14  that extends from a first mid-point between two grooves to an adjacent midpoint between two grooves, or the pith circumference Cp 14  divided by the number of grooves  16 , in this case 72° of the pitch circumference Cp 14 . 
     Variable Profile 
     Various exemplary embodiments are directed to a rotor combination where at least one of the rotors has a varied profile and/or outer diameter.  FIG.  3    shows an exemplary embodiment of a compressor design that includes a male rotor  110  having one or more lobes  112  and a female rotor  114  having one or more grooves  116 . The rotors  110 ,  114  have an inlet side  118  and an outlet side  120 , with the rotors  110 ,  114  extending an axial length there between. The profile of the lobes  112  and grooves  116  varies between the inlet side  118  and the outlet side  120 , as does the outer diameter of the male rotor  110  and the female rotor  112 . 
       FIG.  4    shows a chart representing the outer diameter of the male rotor  110  and the female rotor  114  vs the axial position. As shown in  FIG.  4   , the outer diameter of the male rotor  110  and the female rotor  114  decrease in a substantially linear fashion. The outer diameter of the male and female rotor  110 ,  114  decreases toward the pitch diameter which remains constant, and in some embodiments the final outer diameter of both the male and female rotors  110 ,  114  substantially equals the respective pitch diameter. Because of this, the axis of rotation of the male and female rotors  110 ,  114  remains substantially parallel. Because the male has a larger beginning addendum, the outer diameter of the male rotor  110  will decrease more proportional to the outer diameter of the female rotor  114 , Moreover, the male rotor portion and the female rotor portion of the compression chamber will have a diameter that decreases in conjunction with the outer diameter of the rotors  110 ,  114 . This results in rotors  110 .  114  and the respective compressor chamber portions having a substantially frusto-conical configuration. 
       FIGS.  5 A- 5 E  shows the change in profile of the male rotor  110  and the female rotor  114  from the inlet side  118  to the outlet side  120 , respectively. As shown, the male and female rotors  110 ,  114  transition from a form resembling a more traditional lobe and groove profile to a substantially cylindrical profile. The male and female addendum decrease with the value of the outer radii moving toward the respective pitch radii. In certain exemplary embodiment, the male outer radius can substantially equal the male pitch radius and the female outer radius can substantially equal the female pitch radius at the outlet side  120 , resulting in an addendum of approximately zero. The tip width and the root diameter of the male and female rotor  110 ,  114  increase toward the outlet side  120 . 
       FIG.  6    shows an exemplary embodiment of a compressor design that includes a male rotor  210  having one or more lobes  212  and a female rotor  214  having one or more grooves  216 . The rotors  210 ,  214  have an inlet side  218  and an outlet side  220 , with the rotors  210 ,  214  extending an axial length therebetween. The profile of the lobes  212  and grooves  216  varies between the inlet side  218  and the outlet side  220 . The profile of the lobes  212  and grooves  216  varies between the inlet side  218  and the outlet side  220 , as does the outer diameter of the male rotor  210  and the female rotor  212 . 
       FIG.  7    shows a chart representing the outer diameter of the male rotor  210  and the female rotor  214  vs the axial position. As shown in  FIG.  7   , the outer diameter of the male rotor  210  and the female rotor  214  decrease in a non-linear fashion. As shown in this example, the outer diameter holds substantially constant for a first portion and then decreases at a rate that forms a curved portion that has an arc. Similar to the male and female rotors  110 ,  114  in  FIG.  3   , the outer diameter of the male and female rotor  110 ,  114  decreases toward the respective pitch diameter, allowing the axis of rotation of the male and female rotors  210 ,  214  to remain substantially parallel. Moreover, the male rotor portion and the female rotor portion of the compression chamber will have a diameter that decreases in conjunction with the outer diameter of the rotors  110 ,  114 . This results in rotors  110 .  114  and the respective compressor chamber portions having a substantially frusto-ogive configuration. 
       FIGS.  8 A- 8 E  shows the change in profile of the male rotor  210  and the female rotor  214  from the inlet side  218  to the outlet side  220 , respectively. As shown, the male and female rotors  210 ,  214  transition from a form resembling a more traditional lobe and groove profile to a substantially cylindrical profile. The male and female addendum decrease with the value of the outer radii moving toward the respective pitch radii. In certain exemplary embodiment, the male outer radius can substantially equal the male pitch radius and the female outer radius can substantially equal the female pitch radius at the outlet side  220 , resulting in an addendum of approximately zero. The tip width and the root diameter of the male and female rotor  210 ,  214  increase toward the outlet side  220 . 
     When comparing  FIGS.  5 A- 5 E  and  FIGS.  8 A- 8 E , it is shown that the transition steps are substantially constant for the rotor sections shown in  FIGS.  5 A- 5 E , while the transition is much more significant toward the outlet side of the rotors in  FIGS.  8 A- 8 E . 
     The rotors  110 ,  114  shown in  FIG.  3    are just one example of a linear transition and the rotors  210 ,  214  shown in  FIG.  6    are just one example of a curved transition in the outer diameter of the male rotor.  FIG.  9    shows different curves of the male rotor outer diameter vs the rotor length. The curves include various portions having a fast transition (larger or more pronounced) or a slow transition (smaller or less pronounced). Other changes in the outer diameter of the male and female rotors can be used, including various linear and curved combinations, and more complex curves have a non-constant arch or different sections with different radii of curvature. 
     The variable profile can result in lower radial leakage and short sealing lines in a compressor. In certain embodiments, the profile can be varied to eliminate the blow hole on the discharge end. A compressor can also be created with little or no discharge end clearance and no trap pocket. The varied profile can also result in a large discharge port. Some exemplary advantages of using the variable profile configuration can include faster compression, lower leakage, and higher performance. The variable profile configuration can also result in higher efficiency, higher speeds, decreased port losses at maximum speeds, and higher internal pressure ratios from a single stage. 
     FIG. in shows the volume of the fluid vs the rotation angle of the male rotors  10 ,  110 ,  210 . The inlet volume increases faster for the variable profile rotors  110 ,  210  and reduces faster once the inlet is closed at the maximum volume and the fluid begins to compress.  FIG.  11    shows the internal compression vs the rotation angle of the male rotors  10 ,  110 ,  210 . The compression rate for the variable profile rotors  110 ,  210  is greater than the traditional rotor  10  at any given rotation angle. 
     Rack Scaling 
     Various exemplary embodiments are directed to designing and creating a rotor with a variable profile. In one exemplary method, a rack curve is created that is used to create the male lobes and female grooves for a given rotor section. A rack is substantially equal to the lobe thickness T 10  and groove thickness T 14  shown in  FIG.  2   . A first rack is created that can define the lobes and grooves at a first section. In an exemplary embodiment, the first section can be the very beginning or inlet end of the rotors. One or more additional racks are then created to correspond to different section along the rotors axial length. The racks are created to have different curves, for example with different crests. The profile of the rotors can then be created based on this set of racks. The sections between the racks can be determined using different methods, including linear interpolation or different curve fitting techniques. 
     One exemplary embodiment includes creating a variable profile rotor by scaling the X and Y coordinates of a rack.  FIG.  12    shows a series of rack curves R 1 , R 2 , and R 3 . A rack is substantially equal to the lobe thickness Trio and groove thickness T 14  show in  FIG.  2   . An initial rack curve R 1 A is determined based on the operating characteristics of a compressor, having a top endpoint and a bottom endpoint. In an exemplary embodiment, the remaining rack curves R 1 B, R 1 C, R 1 D, R 1 E are then scaled in the X and Y directions down to a certain level, for example down to the single point R 1 E which represents a completely vertical rack line, and therefore a cylindrical surface. Scaling in the X and Y direction results in a decreased height in the Y direction, which moves the top and bottom endpoint of each intermediate curve R 1 B-R 1 D in towards the final point R 1 E. In certain embodiments, it is necessary to maintain the original rack height to maintain a constant ditch diameter down the rotor length. As shown in the second set of rack curves R 2 , the non-initial rack curves R 2 B-R 2 E are separated at a certain point and spaced apart forming open sections between a first and second inner point as shown in the thinner line segments of the intermediate second rack curves R 2 B-R 2 D. The curves can be separated at a crest or peak of the respective curve in the X direction. The first and second inner points can then be connected and the top and bottom end points can be extended to the original top and bottom Y values as shown in the third set of rack curves. As best shown in  FIG.  13   , when the rack curves are spaced to maintain a consistent Y height, the male rotor tips  250  are widened as the male rotor  252  and the female rotor  254  travel from the inlet side  256  to the outlet side  258 . This can help reduce the tip leakage rate of the compressor. The amount of scaling and the amount of steps chosen can be varied to create different types and amount of transitions as discussed above. Although this process describes choosing an initial rack curve R 1  that is toward an inlet side, the initial rack curve can be selected at any point, and then scaled up or down appropriately. 
     In certain embodiments, only discrete points along the rack curve will be known, and different methods of interpolation and/or curve fitting can be used to determine the connections between these points. For example, linear interpolation, polynomial interpolation, and spline interpolation can be used to determine the rack curves. 
       FIG.  14    shows an exemplary series of scaled rack curves A-J and their position along the axial length of a rotor.  FIG.  15    shows the set of rack curves R 110  that are linearly variable, for example used to create a male rotor having a substantially conical configuration similar to the rotor  110  shown in  FIG.  3    and a set of rack curves R 210  that are non linearly variable, for example used to create a male rotor having a substantially ogive configuration similar to the rotor  210  shown in  FIG.  6   . As can be seen in  FIG.  15   , the first set of curves R 110  has substantially even scaling, while the second set of curves R 210  has varied scaling, with the initial curves scaled by smaller amounts and the later curves scaled by larger amounts. 
     Variable Helix 
     Other exemplary embodiments are directed to set of rotors having a variable helix.  FIG.  1    shows an exemplary embodiment of a compressor design that includes a male rotor  10  having one or more lobes  12  and a female rotor  14  having one or more grooves or gates  16 . The male rotor  10  is mounted on a first shaft  18  and the female rotor  14  is mounted on a second shaft  20 . Fluid enters at an inlet portion  22 , and when the rotors are driven, the lobes  12  of the male rotor  10  fit into the grooves  16  of the female rotor  14 , causing compression and movement of the fluid towards an outlet or discharge portion  24  where the compressed fluid is discharged. The male and female rotors  10 ,  14  have a constant lead or pitch extending along the length of the rotor. 
       FIGS.  16  and  17    show an exemplary embodiment of a male rotor  310  and a female rotor  314  having a helical profile that has a continuously variable lead, meaning that the helical lead varies at a substantially constant rate. The male rotor  310  includes a plurality of lobes  312 . The female rotor  314  includes a plurality of grooves  316 . The rotation of the lobes  312  and grooves  316  increases at a substantially continuous rate from the inlet portion  322  to the outlet portion  324 , allowing the rotors  310 ,  314  to mesh more at the outlet portion  324 . 
       FIG.  18    shows a graph of the wrap angle curve—profile rotation vs axial location—of the male constant helical rotor C 10  and the wrap angle curve of the male continuously variable helical rotors C 310 . As shown, the warp angle curve C 10  for the constant lead is a line having a substantially constant slope. With the continuously variable helical profile, the wrap angle curve C 310  forms a concave curve where the tangent line of the points on the curve has a slope that slowly increases at a constant rate, that is the increase in the change in the slope occurs at a substantially constant rate along the length of the rotor. The change in the slope for theses rotors  310 ,  314  is always positive as the wrap angle curve moves from the inlet portion to the outlet portion. The female rotor curves will have different values, but follow similar trends. 
       FIG.  19    shows an exemplary embodiment of a male rotor  410  and a female rotor  414  having a helical profile that has a non-continuously variable lead, meaning that the helical lead varies at different rates over the length of the rotors. The male rotor  410  includes a plurality of lobes  412  and the female rotor  414  includes a plurality of grooves  416 . In this exemplary embodiment, the spacing of the lobes  412  and grooves  4   l  changes at a Fast-Slow-Fast (FSF) rate from the inlet portion  422  to the outlet portion  424 , meaning that the rate of change is less in the interior portion of the rotors  410 ,  414  than toward the inlet and discharge ends. 
       FIG.  20    shows a graph of the wrap angle of the male constant helical rotor C 10 , the wrap angle curve of the male continuously variable helical rotors C 310 , and the wrap angle curve of the FSF male non-continuously variable helical rotor C 410 . As shown the FSF curve C 410  includes an initial convex portion that transitions to a concave portion. Accordingly, the change in the slope is initially negative and then transitions to a positive change in the slope. As discussed above, the change in slope toward the beginning and end for the FSF curve C 410  is greater than the middle portion. 
       FIG.  21    shows another exemplary embodiment of a male rotor  510  and a female rotor  514  having a helical profile that has a non-continuously variable lead, meaning that the helical lead varies at different rates over the length of the rotors. The male rotor  510  includes a plurality of lobes  512  and the female rotor  514  includes a plurality of grooves  516 . In this exemplary embodiment, the spacing of the lobes  512  and grooves  516  changes at a Faster-Slower-Faster (FrSrFr) rate from the inlet portion  522  to the outlet portion  524 , meaning that the rate of change is less in the interior portion of the rotors  510 ,  514  than toward the inlet and discharge ends, and that the rate of change is faster than the FSF rotors  510 ,  514 . 
       FIG.  22    shows a graph of the wrap angle of the male constant helical rotor C 10 , the wrap angle curve of the male continuously variable helical rotors C 310 , and the wrap angle curve of the FrSrFr male non-continuously variable helical rotor C 510 . As shown the FrSrFr curve C 510  includes an initial convex portion that transitions to a concave portion. Accordingly, the change in the slope is initially negative and then transitions to a positive change in the slope. As discussed above, the change in slope toward the beginning and end for the FrSrF curve C 510  is greater than the middle portion. 
       FIG.  23    shows a graph of the wrap angle of the male constant helical rotor C 10 , the wrap angle curve of the male continuously variable helical rotors C 310 , and the wrap angle curve of a male non-continuously variable Slow-Fast-Slow (SFS) helical rotor C 530 . As shown the SFS curve C 530  includes an initial convex portion that transitions to a concave portion. Accordingly, the change in the slope is initially negative and then transitions to a positive change in the slope. The change in slope toward the beginning and end for the SFS curve C 530  is slower than the middle portion. 
       FIG.  24    shows a graph of the wrap angle of the male constant helical rotor C 10 , the wrap angle curve of the male continuously variable helical rotors Cam, and the wrap angle curve of a Fast Slow (FS) variable helical rotor C 540 . As shown the FS curve C 540  has a convex curve that slowly decreases toward a horizontal line. The FS variable helical rotor accordingly has a negative change in slope along the length of the curve C 540 . The rate of the change in the slope can vary at a constant rate or a non-constant rate. 
     Varying the helical pattern of the rotors as discussed above can provide a number of advantages over the constant helical rotor or a continuously variable helical rotor.  FIG.  25    shows the volume of the fluid vs the rotation angle of the male rotors for the constant helix  10 , the FSF helix.  410 , and the FrSrFr helix  510 . The inlet volume increases faster for the variable profile rotors  410 ,  510  and reduces faster after the maximum volume and the fluid begins to compress.  FIG.  26    shows the internal compression vs the rotation angle of the male rotors of the constant helix  10 , the continuously, variable helix  310 , and the FSF helix  410 . The FSF helix  410  has less pressure when the cells are within the inlet end clearance, resulting in lower leakage. The FSF helix  510  also keeps the cell pressure lower for a given rotation angle lowering leakage.  FIG.  26    also shows that the discharge pressure can be reached sooner than the constant helix  10 . 
     Other advantages can include decreased leakage due to a reduction in the sealing line length. The sealing line of a rotor is considered the line of closest proximity between intermeshed lobes and grooves. Because the rotors are not in direct contact with one another, the sealing line represents the closed point of contact and is determinative of the amount of leakage that will occur between intermesh rotors. The variable helical profile has a decreasing sealing line length from the inlet end of the compressor to the discharge end. For the same rotation angle of the groove, the sealing line for a given cell is shorter in the variable helix rotor than in the fixed helix rotor, resulting in less leakage. The reduction of the sealing line length is in a position where greater pressure is developed and gas leakage is most critical. Other advantages of the rotors include increased discharge port area and improved high speed performance. 
     Double Helix 
     Other exemplary embodiments are directed to a set of rotors having a double helix configuration.  FIG.  27    shows an exemplary embodiment of a compressor design that includes a male rotor  610  having one or more lobes  612  and a female rotor  614  having one or more grooves or gates  616 . The male and female rotors  610 ,  614  can be mounted on shafts that are rotatably positioned in a housing  620  that at least partially defines a compression chamber. The male rotor  610  is positioned in a first section of the compression chamber and the female rotor  614  is positioned in a second section of the compression chamber. 
     The male and female rotors  610 ,  614  each have a double helix configuration. The male rotor  610  includes a first section  610 A having a left-hand helical profile and a second section  610 B having a right-hand helical profile. The first and second sections  610 A,  610 B of the male rotor  610  meet at a central section  610 C. Similarly, the female rotor  614  includes a first section  614 A having a right-hand helical profile and a second section  614 B having a left-hand helical profile, with the first and second sections  614 A,  6 : 14 B meeting at a central section  614 C. Inlet portions  622  are provided at both ends of the rotors  610 ,  614  and a discharge portion  624  is positioned in the central sections  6100 ,  614 C of the rotors  610 ,  614 . 
       FIG.  28    shows an exemplary embodiment of a housing  620  that can be used with a double helix rotor. The housing  620  includes a pair of inlet ports  626  positioned near each end and a discharge port  628  positioned in a central region, for example aligned with the discharge portion  624  of the male and female rotors  610 ,  614 . Fluid enters the chamber at the inlet ports  626  and when the rotors are driven, the lobes  612  of the male rotor  610  fit into the grooves  616  of the female rotor  614 , causing compression and movement of the fluid towards the outlet or discharge portion  624  where the compressed fluid is discharged through the discharge port  628 . The male and female rotors  61   o ,  614  have a constant lead or pitch extending along the length of the rotor, a constant profile, and a constant outer diameter. Accordingly the chamber is defined by a pair of intersecting cylinders that have parallel longitudinal axes. 
       FIGS.  29  and  30    show a double helix design where the male rotor  710  includes a first section  710 A having a left-hand helical profile and a second section  710 B having a right-hand helical profile. The first and second sections  710 A,  710 B of the male rotor  710  meet at a central section  7100 . Similarly, the female rotor  714  includes a first section  714 A having a right-hand helical profile and a second section  714 B having a left-hand helical profile, with the first and second sections  714 A,  714 B meeting at a central section  714 C. The male rotor central section  710 C includes a set of curved transitions  718  between the first section  710 A and the second section  710 B and the female rotor  714  includes a set of curved transitions  720  between the first section  714 A and the second section  714 B, The curved transitions  718 ,  720  can have a circular or U-shaped configuration depending on the helical profile of the rotors  710 ,  714 . This is in contrast to the double helix design  610  shown in  FIG.  28   , where the central section of the male and female rotors  610 C,  614 C is essentially a line where the two sections meet, providing a sharp transition between the first sections  610 A,  614 A, and the second sections  610 B,  614 B. 
       FIGS.  31 - 34    show a double helix design where the male rotor  810  includes a first section  810 A having a left hand-helical profile and a second section  810 B having a right-hand helical profile. The first and second sections  810 A,  810 B of the male rotor  810  meet at a central section  810 C. Similarly, the female rotor  814  includes a first section  814 A having a right hand helical profile and a second section  8143  having a left hand helical profile, with the first and second sections  814 A,  814 B meeting at a central section  814 C. The male rotor central section  810 C includes a set of curved transitions  818  between the first section  810 A and the second section  810 B and the female rotor  814  includes a set of curved transitions  820  between the first section  814 A and the second section  814 B. According to various exemplary embodiments, at least one of the curved transitions  818 ,  820  can include a pocket that provides trapped air relief.  FIGS.  31 - 34    show an example where the central section  814 C of the female rotor  814  includes a set of curved transitions  820  each having a pocket  822 , As fluid is compressed by the male and female rotors  810 ,  814 , a portion of the fluid can become trapped, causing torque spikes and high pressure and temperature areas. The pocket  822  allows fluid to be directed to the discharge, helping to reduce or prevent trapped air from disrupting operation. The pocket  822  can be formed in only a portion of each groove  816  for example in the upper or trailing half of the groove  816  as best shown in  FIGS.  33  and  34   . 
     Using a double helix as shown above can provide a number of advantages. Larger displacement can be achieved for a given rotor center distance. Positioning the air inlet on both sides of the compressor with a single, central discharge point can eliminate the need for a discharge end clearance which can reduce leakage and increase performance. The double helix configuration can reduce or eliminate the axial load on the rotors, which typically results from the compressed air pressing in a single direction. The air inlet on both sides can also cool the bearings and simplify the sealing at the ends of the rotors due to the reduced heat and pressure. In various exemplary embodiments, a herringbone gear is used to maintain no axial load, for example with a dry compressor or blower. The housing can also be simplified as both ends can mirror each other and the axial bearing can be eliminated. The rotors can be driven from either end. In various embodiments, a single intake port can deliver fluid to both ends. 
     Advantages of using the double helix configuration can include lower leakage and higher performance. The double helix configuration can also result in higher efficiency, cost reduction, for example due to the simplified assembly, and easier maintenance. 
     Combination Rotors 
     Various exemplary embodiments are directed to combining one or more of the rotor features discussed above. For example, a combination of the variable helix features discussed with respect to  FIGS.  16 - 26    and the double helix features discussed with respect to  FIGS.  27 - 34    can be combined to create a rotor combination that has a variable double helix.  FIG.  35    shows an exemplary embodiment of a variable double helix design where the male rotor  910  includes a first section  910 A having a right-hand helical profile and a second section  910 B having a left-hand helical profile. The first and second sections  910 A,  910 B of the male rotor  910  meet at a central section  910 C. Similarly, the female rotor  914  includes a first section  914 A having a left-hand helical profile and a second section  914 B having a right-hand helical profile, with the first and second sections  914 A,  914 B meeting at a central section  914 G. The male rotor central section  910 C includes a set of curved transitions  918  between the first section  910 A and the second section  910 B and the female rotor  914  includes a set of curved transitions  920  between the first section  914 A and the second section  914 B. The curved transitions  918 ,  920  can have a circular or U-shaped configuration. The right hand helix sections  910 A,  914 A and the left hand helix sections  910 B,  914 B can have any of the variable helix profiles discussed above or other helical profiles that can be developed from the teachings herein. 
     In other embodiments, the variable profile features discussed with respect to  FIGS.  1 - 45    and the double helix features discussed with respect to  FIGS.  27 - 34    can be combined to create a rotor combination that has a double helix with a variable profile.  FIGS.  36  and  37    show an exemplary embodiment of a double helix rotor combination with a variable profile, where the male rotor  1010  includes a first section  1010 A having a left-hand helical profile and a second section  1010 B having a right-hand helical profile. The first and second sections  1010 A,  1010 B of the male rotor  1010  meet at a central section  1010 G. Similarly, the female rotor  14  includes a first section  1014 A having a right-hand helical profile and a second section  1014 B having a left-hand helical profile, with the first and second sections  1014 A,  1014 B meeting at a central section  1014 G. The male rotor loin is mounted on a first shaft  1018  and the female rotor  1014  is mounted on a second shaft  1020 . The rotors have a first and second inlet portions  1022  and an outlet portion  1024  in the central sections  10100 ,  1014 G. 
     The profile of lobes  1012  and grooves  1016  varies between the first and second inlet portions  1022  and the outlet portion  1024 , as does the outer diameter of the male rotor  1010  and the female rotor  1012 , while the rotation axis of the two rotors is maintained substantially parallel. The outer diameter of the male and female rotors can be decreased in a conical configuration, an ogive configuration, a complex curve configuration, or any other type of configuration according to the teachings herein. 
     In an exemplary embodiment, the male rotor  1010  profile is varied down to a substantially cylindrical portion  1026  and the female rotor is varied down to a substantially cylindrical portion  1028 . In some exemplary embodiments, the addendum of the male and female rotors  1010 ,  1014  is reduced to substantially zero, with the outer diameter substantially equaling the pitch diameter. The male and female cylindrical portions  1026 ,  1028  can be used as a bearing surface for a journal bearing support in a housing. 
       FIG.  38    shows another exemplary embodiment of a double helix rotor combination with a variable profile, where the male rotor  1110  includes a first section  1110 A having a left-hand helical profile and a second section  1110 B having a right-hand helical profile. The first and second sections  1110 A,  1110 B of the male rotor  1110  meet at a central section  1110 G. Similarly, the female rotor  1114  includes a first section  1114 A having a right hand helical profile and a second section  1114 B having a left hand helical profile, with the first and second sections  1114 A,  1114 B meeting at a central section  1114 G. 
     The profile of lobes  1112  and grooves  1116  varies between the first and second inlet portions  1122  and the outlet portion  1124 , as does the outer diameter of the male rotor  1110  and the female rotor  1112 , while the rotation axis of the two rotors is maintained substantially parallel. The male rotor  1110  profile is varied down to a substantially cylindrical portion  1126  and the female rotor  1114  is varied down to a substantially cylindrical portion  1128 . In this embodiment, the lobes  1112  and grooves  1116  on the right hand portions of the rotors  1110 A,  1114 A are offset from the corresponding lobes  1112  and grooves  1816  on the left hand portions of the rotors  1110 B,  1114 B. For example, the male rotor first and second sections  1110 A,  1110 B can each include five equally spaced lobes  1112 . In the configuration shown in  FIGS.  36  and  37    the lobes  1012  in the first section  1010 A and the lobes in the second section  1010 B start and end at equivalent angular positions. In  FIG.  38   , however, the lobes  1112  in the first section  1110 A and the lobes  1112  in the second section  1110 B end in offset angular positions. In some embodiments the lobes  1112  can also start in offset angular positions, as best shown in  FIGS.  38 A and  38 B .  FIG.  38 A  shows a first end of the rotors  1110 ,  1114  while  FIG.  38 B  shows the second end of the rotors  1110 ,  1114 , with the rotors in the same relative position as shown in  FIG.  38   . In an exemplary embodiment, the offset is a by approximately half the lobe as shown in  FIG.  38   , although other degrees or amounts of offset can also be used. This offset can help reduce or eliminate pressure and velocity pulses that can generate unwanted noise. 
       FIG.  39    shows an example of a set of rotors  1200  having a fixed double helix and a conical rotor profile.  FIG.  40    shows an example of a set of rotors  1300  having a fixed double helix and a rounded or ogive rotor profile. In other embodiments, the variable profile features discussed with respect to  FIGS.  1 - 15    the variable helix features discussed with respect to  FIGS.  16 - 26   , and the double helix features discussed with respect to  FIGS.  27 - 34    can be combined to create a rotor combination that has a variable double helix with a variable profile.  FIG.  41    shows an example of a set of rotors  1400  having a variable double helix and a conical rotor profile where both sides of the helix are a continuously variable helix having a concave wrap-angle curve.  FIG.  42    shows an example of a set of rotors  1500  having a variable double helix and a conical rotor profile where both sides of the helix are a FS variable helix having a convex wrap-angle curve.  FIG.  43    shows an example of a set of rotors  1600  having a conical rotor profile where both sides of the helix are a SFS non-continuously variable helix.  FIG.  44    shows an example of a set of rotors  1700  having an ogive rotor profile where both sides of the helix are a SFS non-continuously variable helix.  FIG.  45    shows an example of a set of rotors  1800  having a conical rotor profile where both sides of the helix are a FSF non-continuously variable helix.  FIG.  46    shows an example of a set of rotors  1900  having an ogive rotor profile where both sides of the helix are a FSF non-continuously variable helix. 
     The combination rotors shown in  FIGS.  35 - 46    can provide all or some of the advantages described above with respect to each individual rotor. Additionally, the variable profile and helix angle allow the discharge port to be properly sized for a dual helix compressor. 
     Although some combinations of the exemplary embodiments are specifically shown and described, applicant understands that other combinations of the exemplary embodiments can also be made. 
     The foregoing detailed description of the certain exemplary embodiments has been provided for the purpose of explaining the principles of the application and examples of practical implementation, thereby enabling others skilled in the art to understand the disclosure for various embodiments and with various modifications as are suited to the particular use contemplated. This description is not necessarily intended to be exhaustive or to limit the application to the exemplary embodiments disclosed. Any of the embodiments and/or elements disclosed herein may be combined with one another to form various additional embodiments not specifically disclosed. Accordingly, additional embodiments are possible and are intended to be encompassed within this specification and the scope of the appended claims. The specification describes specific examples to accomplish a more general goal that may be accomplished in another way. 
     As used in this application, the terms “front,” “rear,” “upper,” “lower,” “upwardly,” “downwardly,” and other orientational descriptors are intended to facilitate the description of the exemplary embodiments of the present application, and are not intended to limit the structure of the exemplary embodiments to any particular position or orientation. Terms of degree, such as “substantially” or “approximately” are understood by those of ordinary skill to refer to reasonable ranges outside of the given value, for example, general tolerances associated with manufacturing, assembly, and use of the described embodiments. 
     Various exemplary embodiments relate to a screw compressor or expander comprising: a female rotor including a first section having a right-hand first groove and a second section having a left-hand second groove, wherein the first groove has a first variable helix, the second groove has a second variable helix, and the female rotor has a first variable profile and a first variable outer diameter; and a male rotor including a third section having a left-hand first lobe and a fourth section having a right-hand second lobe, wherein the first lobe has a third variable helix, the second lobe has a fourth variable helix, and the male rotor has a second variable profile and a second variable outer diameter. 
     The screw compressor or expander, wherein the first and third variable helix each include a fast-slow-fast transition. The screw compressor or expander, wherein the first and third variable helix each include a slow-fast-slow transition. The screw compressor or expander, wherein a wrap-angle curve of the first section includes a convex portion and a concave portion. The screw compressor or expander, wherein the female rotor includes a first central section positioned between the first section and the second section and the male rotor includes a second central section positioned between the third section and the fourth section. The screw compressor or expander, wherein the first and second section of the female rotor and the third and fourth section of the male rotor each have a conical configuration in which the outer diameters of the female and male rotors each decrease in a linear fashion toward the first and second central sections respectively. The screw compressor or expander, wherein the first and second section of the female rotor and the third and fourth section of the male rotor each have a curvilinear configuration in which the outer diameter of the female and male rotors each decrease in a curved fashion toward the first and second central sections, respectively. The screw compressor or expander, wherein the outer diameter of the male rotor equals a male rotor pitch diameter at the second central section. The screw compressor or expander of claim  5 , wherein the female rotor transitions to a substantially circular cross section at the first central section and the male rotor transitions to a substantially circular cross section at the second central section. The screw compressor or expander, wherein the female rotor has a first axis of rotation and the male rotor has a second axis of rotation that is parallel to the first axis of rotation. The screw compressor or expander, wherein the first and second lobes are corresponding lobes and the first lobe is angularly offset from the second lobe. 
     Various exemplary embodiments relate to a screw compressor or expander comprising: a female rotor including a first section, a second section, and a first central section, the first section having a set of right-hand first grooves, the second section having a set of left-hand second grooves corresponding to the set of first grooves, wherein the first grooves have a first variable helix, the second grooves have a second variable helix, and the female rotor has a first variable profile; and a male rotor including a third section, a fourth section, and a second central section positioned between the third and fourth sections, the third section having a set of left-hand first lobes and the fourth section having a set of right-hand second lobes corresponding to the set of first lobes, wherein the first lobes have a third variable helix, the second lobes have a fourth variable helix, and the male rotor has a second variable profile, wherein the female rotor transitions to a substantially circular cross section at the first central section and the male rotor transitions to a substantially circular cross section at the second central section. 
     The screw compressor or expander, wherein the lobes of the first set of lobes corresponding to the lobes of the second set of lobes are angularly offset. The screw compressor or expander, wherein the lobes of the first set of lobes corresponding to the lobes of the second set of lobes are offset by a half a lobe rotation. The screw compressor or expander, further comprising a housing having a journal bearing engaging at least the first center section. 
     Various exemplary embodiments relate to a screw compressor or expander comprising: a female rotor including a first section having a first groove with a right-hand first variable helical profile and a second section having a second groove with a left-hand second variable helical profile; and a male rotor including a third section having a first lobe with a right-hand third variable helical profile and a fourth section having a second lobe with a left-hand fourth variable helical profile. 
     The screw compressor or expander, wherein the female rotor includes a first curved transition connecting the first and second groove in a first central section and the male rotor includes a second curved transition connecting the first and second lobes in a second central section. The screw compressor or expander, wherein the first, second, third and fourth variable helical profiles are each non-continuously variable. The screw compressor or expander, wherein the first, second, third and fourth variable helical profiles are each continuously variable. 
     Various exemplary embodiments relate to a screw compressor or expander comprising: a male rotor having a first axial length extending from an inlet portion to an outlet portion and a set of lobes with a variable profile extending along the first axial length; and a female rotor having a second axial length extending from the inlet portion to the outlet portion and a set of grooves with a variable profile extending along the second axial length, the set of grooves mating with the set of lobes, wherein at least a portion of the male rotor and the female rotor each have a non-cylindrical configuration with a non-constant outer diameter. 
     The screw compressor or expander of, wherein the male rotor and the female rotor each have a conical configuration in which the outer diameters of the female and male rotors each decrease in a linear fashion along at least a portion of the respective axial length from the inlet portion to the outlet portion. The screw compressor or expander, wherein the male rotor and the female rotor have an ogive configuration where the outer diameter of the rotor decreases in an arc along at least a portion of the respective axial length from the inlet portion to the outlet portion. The screw compressor or expander, wherein the male rotor and the female rotor each have a complex curve configuration in which the outer diameter of the rotor decreases in a curve having at least two different radii of curvature along at least a portion of the respective axial length from the inlet portion to the outlet portion. The screw compressor or expander, wherein the addendum of the male rotor and of the female rotor decreases along the first axial length. The screw compressor or expander, wherein the outer diameter of the male rotor equals a male rotor pitch diameter at the outlet portion. The screw compressor or expander, wherein a tip width of the male lobes widens along at least a portion of the axial length from the inlet portion to the outlet portion. The screw compressor or expander, further comprising a compression chamber having a non-cylindrical first portion and a non-cylindrical second portion. The screw compressor, wherein the non-cylindrical second portion has a substantially conical configuration. The screw compressor, wherein the non-cylindrical second portion has a substantially ogive configuration. The screw compressor or expander, wherein a rotation axis of the male rotor and a rotation axis of the female rotor are parallel. 
     Various exemplary embodiments relate to a screw compressor or expander comprising: a male rotor having a first axial length extending from an inlet portion to an outlet portion and a set of lobes with a variable profile extending along at least a portion of the first axial length; and a female rotor having a second axial length extending from the inlet portion to the outlet portion and a set of grooves with a variable profile extending along at least a portion of the second axial length, the set of grooves mating with the set of lobes, wherein the male rotor and the female rotor transition to a substantially circular cross section near the outlet portion. 
     The screw compressor or expander, wherein the male rotor has a first outer diameter and a first pitch diameter less than the first outer diameter near the inlet portion and a second outer diameter substantially equal to the first pitch diameter at the outlet portion. The screw compressor or expander, wherein the male rotor has a non-constant outer diameter. The screw compressor or expander, wherein the male rotor has a conical configuration where the outer diameter of the rotor decreases in a linear fashion along at least a portion of the first axial length. The screw compressor or expander, wherein the male rotor has a curved configuration where the outer diameter of the rotor decreases in a curved fashion along at least a portion of the first axial length. The screw compressor or expander, wherein a rotation axis of the male rotor and a rotation axis of the female rotor are parallel. 
     Various exemplary embodiments relate to a screw compressor or expander comprising: a male rotor having a first axial length extending from an inlet portion to an outlet portion and a set of lobes extending along at least a portion of the first axial length; and a female rotor having a second axial length extending from the inlet portion to the outlet portion and a set of grooves extending along at least a portion of the second axial length, the set of grooves mating with the set of lobes, wherein the male rotor and the female rotor have a first section with a first profile defined by a first rack having a first set of X and Y coordinates and a second section with a second profile defined by a second rack different than the first rack having a second set of X and Y coordinates. 
     The screw compressor or expander, wherein the second rack is scaled from the first rack in the X and Y direction. 
     Various exemplary embodiments relate to a method of designing a set of screw compressor or expander rotors comprising: establishing a first rack for a male and female rotor, the first rack having at least one curved segment with a first crest having a first set of X and coordinates; and scaling the first rack in the X and Y directions to create a second rack having at least one curved segment with a second crest having a second set of X and coordinates, wherein the X coordinate of the second crest is spaced from the X coordinate of the first crest. 
     The method above, further comprising separating the second rack at a portion along the curved segment and offsetting the second rack in the Y direction to create a first inner point, a second inner point, a first end point, and a second end point. The method above, further comprising connecting the first inner point and the second inner point and extending a first end point and the second end point to extend the Y height of the second rack to substantially equal the Y height of the first rack. The method above, further comprising using an interpolation method to connect points on the rack to create the second rack curve. The method above, further comprising scaling the first or second rack in both the X and Y directions to create a third rack having an X coordinate of substantially zero. 
     Various exemplary embodiments relate to a method of designing a set of screw compressor or expander rotors comprising: establishing a first rack for a male and female rotor, the first rack having at least one curved segment with a first crest having a first set of a X and Y coordinates; and establishing a second rack for a male and female rotor, the second rack having at least one curved segment with a second crest having a second set of a X and Y coordinates, wherein the X coordinate of the second crest is spaced from the X coordinate of the first crest. 
     The method above, wherein the first rack has a first height in the Y direction and the second rack has a second height in the Y direction equal to the first height. The method above, further comprising using interpolation to define the male and female rotor between the first rack and the second rack. 
     Various exemplary embodiments relate to a screw compressor or expander comprising: a male rotor having a first axial length and a set of lobes with a first helical profile extending along the first axial length; and a female rotor having a second axial length and a set of grooves with a second helical profile extending along the second axial length, the set of grooves mating with the set of lobes, wherein the first helical profile is non-continuously variable over the first axial length. 
     The screw compressor or expander, wherein the first helical profile includes a fast-slow-fast transition. The screw compressor or expander, wherein the first helical profile includes a slow-fast-slow transition. The screw compressor or expander, wherein a wrap-angle curve of the male rotor includes a convex portion and a concave portion. The screw compressor or expander, wherein the male rotor has an inlet portion and an outlet portion defining the first axial length. The screw compressor or expander, wherein a wrap-angle curve of the male rotor includes a first point positioned between the inlet portion and the outlet portion and a second point positioned between the first point and the outlet portion, and wherein the slope of a line tangent to the first point is less than the slope of a line tangent to the second point. The screw compressor or expander, wherein the male rotor and the female rotor are rotatably positioned in a housing having an inlet port and an outlet port. 
     Various exemplary embodiments relate to a screw compressor or expander comprising: a male rotor having a lobe with a first helical profile extending between a first position proximate to an inlet portion and a second position proximate an outlet portion; and a female rotor having a groove with a second helical profile extending between a third position proximate an inlet portion and a fourth position proximate an outlet portion, the groove mating with the lobes, wherein a wrap-angle curve of the male rotor lobe includes a convex portion. 
     The screw compressor or expander, wherein the wrap-angle includes a first point positioned between the first position and the second position and a second point positioned between the first point and the second position, and wherein the slope of a line tangent to the second point is less than the slope of a line tangent: to the first point. The screw compressor or expander, wherein the slope of the lines tangential to each point on the wrap angle curve decreases from the first position to the second position. The screw compressor or expander, wherein the first helical profile includes a slow-fast transition. The screw compressor or expander, wherein the wrap-angle curve further comprises a third point and a fourth point, and the slope of a line tangent to the third point is greater than the slope of a line tangent to the second point. The screw compressor or expander, wherein the third point is positioned between the second point and the second position and the fourth point is positioned between the third point and the second position. The screw compressor or expander, wherein the first helical profile includes a fast-slow-fast transition. The screw compressor or expander, wherein the first helical profile includes a slow-fast-slow transition. 
     Various exemplary embodiments relate to a screw compressor or expander comprising: a female rotor including a first section having a first groove with a right-hand helical profile, a second section having a second groove with a left-hand helical profile, and a first central section having a first curved transition connecting the first and second groove; and a male rotor including a third section having a first lobe with a right-hand helical profile, a fourth section having a second lobe with a left-hand helical profile, and a second central section having a second curved transition connecting the first and second lobes. The screw compressor or expander, wherein the first and second curved transitions each have a substantially U-shaped configuration. 
     The screw compressor or expander, wherein the first and second curved transitions each have a substantially rounded configuration. The screw compressor or expander, wherein at least one of the first and second curved transitions includes a pocket. The screw compressor or expander, wherein the pocket is formed in a surface of the first curved transition. The screw compressor or expander, wherein the male rotor includes a first inlet portion, a second inlet portion, and a discharge portion. The screw compressor or expander, further comprising a housing at least partially defining a compression chamber for receiving the male rotor and the female rotor. The screw compressor or expander, wherein the housing includes a first inlet port, a second inlet port, and a discharge port. 
     Various exemplary embodiments relate to a screw compressor or expander comprising: a female rotor including a first section having a first groove with a right-hand helical profile, a second section having a second groove with a left-hand helical profile, and a first central section; and a male rotor including a third section having a first lobe with a right-hand helical profile, a fourth section having a second lobe with a left-hand helical profile, and a second central section, wherein one of the first and second central sections includes a pocket. 
     The screw compressor Or expander, wherein the first central section includes a first curved transition connecting the first and second groove. The screw compressor or expander, wherein the pocket is formed in the first curved transition. The screw compressor or expander, wherein the second central section includes a second curved transition connecting the first and second lobes. The screw compressor or expander, wherein the male rotor includes a first inlet portion, a second inlet portion, and a discharge portion. The screw compressor or expander, further comprising a housing at least partially defining a compression chamber for receiving the male rotor and the female rotor. The screw compressor or expander, wherein the housing includes a first inlet port, a second inlet port, and a discharge port. 
     Various exemplary embodiments relate to a screw compressor or expander comprising: a housing having an inlet port, a discharge port, and a body at least partially defining a compression chamber having a first portion and a second portion; a female rotor rotatably positioned in the first portion of the compression chamber, the female rotor including a first section having a first groove with a right-hand helical profile, a second section having a second groove with a left-hand helical profile, and a first central section having a first curved transition connecting the first and second groove; and a male rotor rotatably positioned in the first portion of the compression chamber, the male rotor including a third section having a first lobe with a right-hand helical profile, a fourth section having a second lobe with a left-hand helical profile, and a second central section having a second curved transition connecting the first and second lobes. 
     The screw compressor or expander, wherein at least one of the first and second curved transitions includes a pocket. The screw compressor or expander, wherein the pocket is formed in the first curved transition. The screw compressor or expander, wherein the first and second curved transitions have a substantially U-shaped configuration. The screw compressor or expander, wherein the housing includes a second inlet port.