Abstract:
A system and method are presented for improved performance of gerotor compressors and expanders. Certain aspects of the disclosure reduce porting losses in a gerotor system. Other aspects of the disclosure provide for reduced deflection in lobes of an outer rotor of a gerotor system. Still other aspects of the disclosure provide for reduced leakage through tight gaps between components of a gerotor system.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application is related to U.S. Provisional Patent Application No. 61/940,293, which was filed on Feb. 14, 2014, and is entitled “Features that Improve the Performance of Gerotor Compressors and Expanders.” Provisional Patent No. 61/940,293 is hereby incorporated by reference into the present application as if fully set forth herein. The present application hereby claims priority under 35 U.S.C. §119(e) to U.S. Provisional Patent No. 61/940,293. 
     
    
     TECHNICAL FIELD 
       [0002]    The present disclosure is directed, in general, to gerotor compressors and expanders, and more specifically, to features that improve the performance of gerotor compressors and expanders. 
       BACKGROUND 
       [0003]    A gerotor operates using inner and outer rotors that rotate about their respective axes within a housing. A drive mechanism synchronizes the rotors so that they do not touch. As the rotors rotate, teeth of the inner rotor and lobes of the outer rotor move relative to each other to create voids between the teeth of the inner rotor and the lobes of the outer rotor that open, reach a maximum volume, and then close. Fluid enters and leaves the voids through gaps (referred to as ports) between the lobes of the outer rotor. 
         [0004]    The housing comprises four regions. A first of the four regions forms an inlet duct for the gerotor system. A second of the four regions forms an outlet duct for the gerotor system. The third and fourth of the four regions are located between the inlet duct region and the outlet duct region and have small clearances between inner and outer rotors and the housing. These two regions operate to prevent fluid flow around the outside of the outer rotor between the inlet duct and the outlet duct. 
         [0005]    For a gerotor system operating as a compressor, input power to the drive mechanism drives the rotors. A fluid enters from the inlet duct of the housing through one or more intake ports as the void opens. Once the fluid is captured, the void volume decreases, causing the pressure of the fluid to increase. After a desired pressure (generated by the geometries of the two rotors) is achieved, the fluid exits through one or more outlet ports into the outlet duct of the housing. 
         [0006]    For a gerotor system operating as an expander, high-pressure fluid enters from the inlet duct of the housing through one or more intake ports into a small void in the gerotor. The fluid is captured, and the fluid pressure operates on the rotors to cause the void volume to increase as the fluid pressure decreases. The expanding fluid causes the rotors to turn. After a desired pressure is achieved, the fluid exits through one or more outlet ports into the outlet duct of the housing. The rotation of the rotors produces output power from the gerotor drive mechanism. 
         [0007]    Gerotor compressors and expanders have several advantages that apply to both gerotor compressors and expanders, such as the following: 
         [0008]    No valves; 
         [0009]    Low vibration; 
         [0010]    Compact; 
         [0011]    Efficient; 
         [0012]    Tolerant of liquid; 
         [0013]    Low manufacturing cost; 
         [0014]    High pressure ratio per stage; 
         [0015]    Rotational speed matches conventional engines, motors, and generators; 
         [0016]    Low parts count; 
         [0017]    Oil-free operation; and 
         [0018]    Operates efficiently at varying speeds 
       SUMMARY OF THE DISCLOSURE 
       [0019]    According to a first embodiment of the present disclosure, a gerotor system includes an inner rotor, an outer rotor having a plurality of ports, and a housing. The plurality of ports includes an inlet subset of ports and an outlet subset of ports. Fluid flows into the gerotor system through the inlet subset of ports and out of the gerotor system through the outlet subset of ports. The housing includes an inlet duct fluidly coupled with the inlet subset of ports and an outlet duct fluidly coupled with the outlet subset of ports. The inlet duct includes an input pipe and the outlet duct includes an outlet pipe. The inlet pipe is located on the inlet duct based upon a location of an inlet port in the inlet subset of ports having a highest inlet fluid velocity through the inlet port. The outlet pipe is located on the outlet duct based upon a location of an outlet port in the outlet subset of ports having a highest outlet fluid velocity through the outlet port. 
         [0020]    According to a second embodiment of the present disclosure, a gerotor system includes an inner rotor, an outer rotor having a plurality of ports, and a housing. The plurality of ports includes an inlet subset of ports and an outlet subset of ports. Fluid flows into the gerotor system through the inlet subset of ports and out of the gerotor system through the outlet subset of ports. The housing further includes an inlet duct fluidly coupled with the inlet subset of ports and an outlet duct fluidly coupled with the outlet subset of ports. 
         [0021]    The inlet duct includes a plurality of inlet channel vanes that extend from an entrance end to a rotor end of the inlet duct. The inlet channel vanes form a plurality of inlet channels, which alter substantially identical velocities of fluid entering the inlet channels to a velocity at the rotor end that substantially matches a velocity of fluid through one or more corresponding inlet ports. 
         [0022]    The outlet duct includes a plurality of outlet channel vanes extending from a rotor end to an exit end of the outlet duct. The outlet channel vanes form a plurality of outlet channels, each outlet channel configured to alter a velocity of fluid at the rotor end of the outlet channel that is determined by a velocity of fluid through one or more corresponding outlet ports to substantially identical velocities of fluid exiting the outlet channels. 
         [0023]    According to a third embodiment of the present disclosure, a gerotor system includes an inner rotor, an outer rotor having a plurality of ports, and a housing. The plurality of ports includes an inlet subset of ports and an outlet subset of ports. Fluid flows into the gerotor system through the inlet subset of ports and out of the gerotor system through the outlet subset of ports. The housing further includes an inlet duct fluidly coupled with the inlet subset of ports and an outlet duct fluidly coupled with the outlet subset of ports. The inlet duct includes an input pipe located at a first end of the inlet duct and the outlet duct includes an outlet pipe located at a first end of the outlet duct. A profile of a circumferential portion of the inlet duct varies from the first end to a second end of the inlet duct to alter fluid velocity vectors in the inlet duct to more closely match fluid velocity vectors passing through corresponding inlet ports. A profile of a circumferential portion of the outlet duct varies from the first end to a second end of the outlet duct to alter fluid velocity vectors passing through one or more outlet ports to substantially the same fluid velocity in the outlet pipe. 
         [0024]    According to a fourth embodiment of the present disclosure, a gerotor system includes an inner rotor, an outer rotor having a plurality of ports, and a housing. The outer rotor includes a plurality of lobe portions and at least one disk portion. The outer rotor further includes a feature on an inner surface of the outer rotor, where the feature is configured to reduce stress concentration in the bases of the lobe portions. 
         [0025]    According to a fifth embodiment of the present disclosure, a gerotor system includes an inner rotor, an outer rotor having a plurality of ports, and a housing. The outer rotor includes a plurality of lobe components and a plurality of disk components. Each lobe component is mounted to the disk components by at least one pin passing through at least one disk component into the lobe component. 
         [0026]    According to a sixth embodiment of the present disclosure, a gerotor system includes an inner rotor, an outer rotor having a plurality of ports, and a housing. The outer rotor includes a plurality of lobe components and a plurality of disk components, wherein the lobe components are hollow. 
         [0027]    According to a seventh embodiment of the present disclosure, a gerotor system includes an inner rotor, an outer rotor having a plurality of ports, and a housing. The outer rotor includes a plurality of lobe components and a plurality of disk components. An outer portion of each lobe component includes a first material and an inner portion of each lobe component includes a second material. The second material is a lighter material than the first material. 
         [0028]    According to an eighth embodiment of the present disclosure, a gerotor system includes an inner rotor, an outer rotor having a plurality of ports, and a housing. The outer rotor includes an outer surface having a region in proximity to a corresponding region of an inner surface of the housing. Either the outer rotor region or the housing region includes a labyrinth seal that is configured to reduce fluid leakage through a gap between the outer rotor region and the housing region. 
         [0029]    According to a ninth embodiment of the present disclosure, a gerotor system includes an inner rotor, an outer rotor having a plurality of ports, and a housing. The inner rotor includes an outer face in proximity to a corresponding inner face of the housing. Either the inner rotor face or the housing face includes a labyrinth seal that is configured to reduce fluid leakage through a gap between the inner rotor face and the housing face. 
         [0030]    Before undertaking the DETAILED DESCRIPTION below, it may be advantageous to set forth definitions of certain words and phrases used throughout this patent document: the terms “include” and “comprise,” as well as derivatives thereof, mean inclusion without limitation; the term “or,” is inclusive, meaning and/or; the phrases “associated with” and “associated therewith,” as well as derivatives thereof, may mean to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, or the like. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0031]    For a more complete understanding of the present disclosure and its advantages, reference is now made to the following description taken in conjunction with the accompanying drawings, in which like reference numerals represent like parts: 
           [0032]      FIG. 1  shows radial velocity vectors through ports at an inlet and an outlet of a gerotor compressor; 
           [0033]      FIGS. 2A and 2B  show ducting geometries according to the disclosure that reduce mismatches in fluid velocities and directions for a compressor having a low rotation rate ( FIG. 2A ) and a compressor having a high rotation rate ( FIG. 2B ); 
           [0034]      FIG. 3  shows turning vanes according to the disclosure added to ducts to help turn fluid circumferential flow to and from radial flow, in order to enter and exit ports, respectively; 
           [0035]      FIG. 4  shows a gerotor system according to the disclosure having a converging section in an inlet pipe and a diverging section in an outlet pipe; 
           [0036]      FIG. 5  shows a gerotor system according to the disclosure having “tuning” sections in each of an inlet duct and an outlet duct; 
           [0037]      FIG. 6  shows a gerotor system according to the disclosure having two tuning sections in each of an inlet duct and an outlet duct; 
           [0038]      FIG. 7  shows an alternative duct geometry according to the disclosure that incorporates numerous channels that segment fluid flow; 
           [0039]      FIGS. 8A and 8B  show circumferential ducting according to the disclosure with varying cross-sectional area for a gerotor compressor ( FIG. 8A ) and a gerotor expander ( FIG. 8B ); 
           [0040]      FIGS. 9A and 9B  show circumferential ducting according to the disclosure having a converging section in an inlet duct and a diverging section in an outlet duct for a gerotor compressor ( FIG. 9A ) and a gerotor expander ( FIG. 9B ); 
           [0041]      FIGS. 10A-10D  show a gerotor system ( FIG. 10A ) having cutting edges located on an inner rotor ( FIG. 10D ) and an outer rotor ( FIGS. 10B AND 10C ) according to the disclosure; 
           [0042]      FIGS. 11A-11E  show an outer rotor having fillets according to the disclosure ( FIG. 11A ), first and second sections through the outer rotor ( FIGS. 11B and 11C ), an inner rotor for use with the outer rotor ( FIG. 11D ), and a section through the inner rotor ( FIG. 11E ); 
           [0043]      FIGS. 12A-12E  show undercuts in an outer rotor according to the disclosure ( FIG. 12A ), first and second sections through the outer rotor ( FIGS. 12B and 12C ), an inner rotor for use with the outer rotor ( FIG. 12D ), and a section through the inner rotor ( FIG. 12E ); 
           [0044]      FIGS. 13A-13C  show an outer rotor ( FIG. 13A ) and first and second sections through the outer rotor ( FIGS. 13B and 13C ) according to the disclosure, where lobes in an outer rotor are separate components from two discs that define axial ends of the outer rotor; 
           [0045]      FIGS. 14A-14C  show another outer rotor ( FIG. 14A ) and first and second sections through the outer rotor ( FIGS. 14B and 14C ) according to the disclosure, where lobes of the outer rotor are secured with bolts that bridge the discs; 
           [0046]      FIGS. 15A-15D  show yet another outer rotor ( FIG. 15A ), first and second sections of the outer rotor ( FIGS. 15B and 15C ), and a section through an alternative embodiment of the outer rotor ( FIG. 15D ) according to the disclosure where lobes of the outer rotor fit into pockets on the discs; 
           [0047]      FIGS. 16A-16D  shows still another outer rotor ( FIG. 16A ), first and second sections of the outer rotor ( FIGS. 16B and 16C ), and a section through an alternative embodiment of the outer rotor ( FIG. 16D ) according to the disclosure where lobes of the outer rotor fit into rounded pockets on the discs; 
           [0048]      FIG. 17  shows a cross-section view through hollow lobes of an outer rotor according to the disclosure; 
           [0049]      FIG. 18  shows a cross-section view through lobes of an outer rotor according to the disclosure wherein an outer portion of the lobes comprises a first material and an inner portion of the lobes comprises a second material; 
           [0050]      FIGS. 19A-19C  and  20 A- 20 C show gerotor systems ( FIGS. 19A and 20A ) having labyrinth seals according to the disclosure on a circumference of an outer rotor ( FIGS. 19B and 19C ) and a housing ( FIGS. 20B and 20C ); 
           [0051]      FIG. 21  shows exemplary labyrinth seals according to the disclosure; 
           [0052]      FIGS. 22A and 22B  show gerotor systems having exemplary labyrinth seals according to the disclosure on a housing ( FIG. 22A ) and on an outer rotor ( FIG. 22B ); and 
           [0053]      FIG. 23  shows labyrinth seals according to the disclosure on a face of an inner rotor. 
       
    
    
     DETAILED DESCRIPTION 
       [0054]    It should be understood at the outset that, although example embodiments are illustrated below, the present invention may be implemented using any number of techniques, whether currently known or not. The present invention should in no way be limited to the example implementations, drawings, and techniques illustrated below. Additionally, the drawings are not necessarily drawn to scale. 
         [0055]    For simplicity, this disclosure will focus on compressors; however, it should be understood that the disclosure applies equally as well to expanders. Further, it should be understood that a compressor and expander may be combined to form an engine, so the discussions below apply to engines as well. 
         [0056]    While this disclosure discusses fluid flow into, within, and out of gerotors according to the disclosure, it will be understood that such fluids may comprise vapor or gas or a mixture of gas and fluid. Indeed, in gerotor operating as a compressor, a gas may enter the gerotor and be liquefied through compression. 
         [0057]    The performance of gerotor compressors can be enhanced by incorporating features that accomplish the following: 
         [0058]    reduce porting losses; 
         [0059]    cut abradable coatings; 
         [0060]    reduce deflection of outer-rotor lobes; and 
         [0061]    reduce leakage through tight gaps. 
         [0000]    Each feature will be discussed in more detail. 
       Reduce Porting Losses 
       [0062]    In gerotor compressors, fluid enters through ports during an intake portion of a cycle and exits through other ports during a discharge portion of the cycle. Compared to the size of the ducts that carry fluid to and from the compressors, the size of the ports is relatively small; therefore, the fluid must accelerate to flow through the ports. The acceleration and subsequent deceleration may cause turbulence near the ports, which can reduce efficiency. Incorporating features that reduce turbulence can reduce porting losses. 
         [0063]      FIG. 1  shows radial velocity vectors through ports at an inlet and an outlet of a gerotor compressor  100 .  FIG. 1  presents a cutaway view of the compressor  100 . The compressor  100  includes an inner rotor  102 , an outer rotor  104  and a housing  106 . Radial velocity vectors  108  indicate fluid velocity through inlet ports  107   a ,  107   b , and  107   c  of the outer rotor  104 . Radial velocity vectors  110  indicate fluid velocity through outlet ports  109   a  and  109   b  of the outer rotor  104 . 
         [0064]    The radial velocity vectors  108  and  110  through the ports are directly related to the rate of change of the rotating void volume. It should be noted that in addition to the radial velocity vector, there is also a circumferential velocity vector (not shown) that results from the rotation of the rotors. The circumferential velocity vector depends upon rotation rate of the inner rotor and outer rotor. 
         [0065]    At the compressor inlet, the volume change is small at the 7 and 11 o&#39;clock positions and is largest at the 9 o&#39;clock position. The actual lengths of the radial velocity vectors shown in  FIG. 1  depends on the specific geometry of the rotors; here, the vectors are illustrative and not quantitative. 
         [0066]    At the compressor outlet, the volume change is small at the 1 o&#39;clock position and is largest at the 3 o&#39;clock position. The actual lengths of the radial velocity vectors shown in  FIG. 1  depends on the specific geometry of the rotors; here, the vectors are illustrative and not quantitative. 
         [0067]      FIG. 1  is also representative of the radial velocity vectors for an expander; however, for an expander the direction of the arrows would be reversed. 
         [0068]    To improve efficiency, fluid velocity through a port should more closely match the velocity in a duct external to the port. When there is a mismatch in fluid velocities, turbulence is generated, which converts kinetic energy into thermal energy and reduces efficiency. In addition, efficiency is improved when the direction of the velocity through the port matches that through ducts carrying fluid to or from the gerotor. The flow through a duct may be substantially radial; however, it should be noted that there is a circumferential component to the velocity vector, which reflects that fact that the inner rotor and outer rotor are rotating. 
         [0069]      FIG. 2  shows ducting geometries according to the disclosure that reduce mismatches in fluid velocities and directions for a compressor  200  having a low rotation rate ( FIG. 2   a ) and a compressor  250  having a high rotation rate ( FIG. 2   b ). The compressor  200  of  FIG. 2   a  includes an inlet duct  212  and an outlet duct  214 . The compressor  250  of  FIG. 2   b  includes an inlet duct  252  and an outlet duct  254 . 
         [0070]    Because the port velocities are highest in the 3 and 9 o&#39;clock positions, the compressor outlet and inlet pipes are located generally at the 3 and 9 o&#39;clock positions, respectively. It should be noted that for a compressor having a compression ratio higher than the compressors shown in  FIG. 2 , a trailing edge of a circumferential seal between the outer rotor and the housing would be placed in a more advanced position, for example the 2 o&#39;clock position. In such an embodiment, the compressor outlet pipe would move to the 2 o&#39;clock position so as to match the position with the greatest flow. On the other hand, for a compressor have a compression ratio less than the compressors shown in  FIG. 2 , the trailing edge of the circumferential seal would move to a less advanced position, for example the 4 o&#39;clock position. In such an embodiment, the compressor outlet pipe would stay in the 3 o&#39;clock position so as to match the position with the greatest flow. 
         [0071]    To reduce losses, it is desirable that fluid direction in a duct more closely match a direction of fluid flow through the port. To satisfy this condition, an axis of the inlet and outlet pipes may be substantially aligned with dominant velocity vectors emanating from the outer rotor. As noted previously, the velocity vectors through the ports are not purely radial and have a circumferential component that results from rotor rotation. To improve efficiency, the axis of the inlet and outlet pipes may be aligned with the dominant velocity vectors through the ports, which includes both a radial and circumferential component.  FIG. 2  shows two cases.  FIG. 2   a  shows desirable axes of inlet pipe  212  and outlet pipe  214  for a gerotor  200  that rotates slowly.  FIG. 2   b  shows desirable axes of inlet pipe  252  and outlet pipe  254  for a gerotor  250  that rotates rapidly. 
         [0072]    To service the entire circumference of the fluid inlet, an inlet duct should extend from the 6 to the 12 o&#39;clock positions. As a result, some of the fluid entering the compressor must flow in the circumferential direction. The gap between the outer rotor and the duct is defined by ensuring that at any angular position, the velocity of the fluid through the port (as illustrated in  FIG. 1 ) matches the velocity in the circumferential direction. Similar considerations are employed when specifying the gap for the compressor outlet. 
         [0073]    Although  FIG. 2  only shows two cases, in other configurations, the inlet pipe and outlet pipe in particular configurations may be movable to compensate for dynamic variations within the gerotor. As a non-limiting example, for certain rotation speeds, a first direction may be set for the inlet and/or outlet. For other rotations speeds, a second direction may be utilized for the inlet and/or outlet. Any suitable device may be used to dynamically change the direction of the inlet/outlet including, but not limited to, inlet/outlet pipes connected to a crank. In certain configurations, one or more sensors may detect changing conditions (e.g., dominant velocity, increased rotational speed, and/or flow rate) and automatically change the direction of the inlet and/or outlet pipe to maximize the efficiency. 
         [0074]      FIG. 3  shows turning vanes  316  according to the disclosure that are added to ducts to help turn fluid circumferential flow to and from radial flow, in order to enter and exit ports, respectively. A gerotor system  300  includes an outer rotor  304 , an inlet duct  312  having turning vanes  316 , and an outlet duct  314  having turning vanes  318 . As noted previously, the fluid flow through ports of the outer rotor  304  is not purely radial and has a circumferential component. Profiles of turning vanes  316  are designed to alter radial and circumferential velocity vector components of fluid in regions of the inlet duct  312  to more closely match fluid velocity vectors passing into corresponding ones of the inlet ports of the outer rotor  304 . Profiles of turning vanes  318  are designed to alter radial and circumferential velocity vector components of fluid passing through outlet ports in the outer rotor  304  to more closely match fluid velocity vectors in corresponding regions of the outlet duct  314 . 
         [0075]    Similar to the inlet and outlet pipes described with reference to  FIGS. 2   a  and  2   b , the turning vanes in particular configurations may also be designed to dynamically move based on changing conditions of the fluid flow through the gerotor system. In other configurations, the turning vanes may be fixed. 
         [0076]      FIG. 4  shows a gerotor system  400  according to the disclosure having a converging section  420  added to inlet pipe  412 . The converging section  420  pre-accelerates fluid flow to velocities that match the port velocities. The gerotor system  400  also includes a diverging section  422  in outlet pipe  414 . The diverging section  422  decelerates fluid flow to match a final fluid velocity exiting the system  400 . The system  400  also includes turning vanes  416  and  418 , however, it will be understood that other embodiments may not include turning vanes. 
         [0077]    Typically, fluid flow entering and exiting the compressor is not completely smooth and has pulses. The pulse frequency is N times the rotational rate of the outer rotor, where N is the number of ports in the outer rotor.  FIG. 5  shows a gerotor system  500  according to the disclosure, having a “tuning” section  524  in the inlet duct  512  and a tuning section  528  in the outlet duct  514 . The lengths of the tuning sections  524  and  528  are adjusted so that the resonant frequencies of the tuning sections  524  and  528  match the pulse frequency related to the pulse frequency of outer rotor  504 . The resonant frequencies in the tuning sections  524  and  528  are also dependent upon the mass of the fluid in the inlet duct  512  and the outlet duct  514 . 
         [0078]    There are many ways to construct a resonant tuning section according to the disclosure.  FIG. 5  shows an embodiment in which an end cap  526 , which is mechanically fixed in a larger section of the inlet duct  512 , defines a length of the tuning section  524 . Similarly, an end cap  530  that is mechanically fixed in a larger section of the outlet duct  514  and defines a length of the tuning section  528 . 
         [0079]    The gerotor system  500  includes a converging section  520  and turning vanes  516 . Additionally, the system  500  includes a diverging section  522  and turning vanes  518 . 
         [0080]      FIG. 6  shows a gerotor system  600  according to the disclosure having two tuning sections in each of the inlet and outlet ducts. The gerotor system  600  includes a first input tuning section  624 , defined by an end cap  626 . The system  600  also includes a second input tuning section  632 , defined by an end cap  634 . Additionally, the system  600  includes a first outlet tuning section  628 , defined by an end cap  630 , and a second outlet tuning section  636 , defined by an end cap  638 . 
         [0081]      FIG. 7  shows an alternative duct geometry according to the disclosure that incorporates numerous channels that segment the flow. A gerotor system  700  includes an inlet duct  712  and an outlet duct  714 . The inlet duct  712  includes inlet channel vanes  716  extending from an entrance end of the inlet duct  712  to a rotor end of the inlet duct  712 . The inlet channel vanes  716  form inlet channels (indicated generally as  740 ) between adjacent inlet channel vanes  716 , as well as between the walls of the inlet duct  712  and the outermost inlet channel vanes  716 . Similarly, the outlet duct  714  includes outlet channel vanes  718  extending from a rotor end of the outlet duct  714  to an exit end of the outlet duct  714 . The outlet channel vanes  718  form outlet channels (indicated generally as  742 ) between the adjacent outlet channel vanes  718 , as well as between the walls of the outlet duct  714  and the outermost outlet channel vanes  718 . Each inlet channel  740  and each outlet channel  742  has a profile, defining a width of the channel. 
         [0082]    The inlet channels  740  and the outlet channels  742  are designed with the following considerations. At the entrance to the inlet duct  712 , all fluid velocity vectors into the inlet duct  712  are substantially identical. As fluid flows along the inlet channels  740 , the widths of the channels change so that, at the rotor end of the channels, magnitudes of the fluid velocities in the inlet channels  740  substantially match magnitudes of the fluid velocity through corresponding ports of outer rotor  704  (as explained above with reference to  FIG. 1 ). Similarly, fluid flowing out of the outer rotor  704  has differing velocities, depending upon a current position of a port of the outer rotor  704  through which the fluid is flowing. As fluid flows along the outlet channels  742 , the widths of the channels change so that, at the exit end of the outlet duct  714 , magnitudes of the fluid velocities in each channel are substantially identical. 
         [0083]    Additionally, angles of the channels  740  in the inlet duct  712  vary so as to introduce circumferential components in the velocity of the incoming fluid that accommodate a rotational speed of the rotor  702  (as discussed with reference to  FIGS. 2 and 3 ). Similarly, angles of the channels  742  in the outlet duct  714  vary so as to remove circumferential components in the velocity of the fluid exiting the outlet duct  714 . 
         [0084]      FIGS. 8A and 8B  show circumferential ducting according to the disclosure with varying cross-sectional area.  FIG. 8A  depicts a gerotor compressor  800 A having an inlet duct  812 A and an outlet duct  814 A. A profile of a circumferential portion  844 A of the inlet duct  812 A is varied so that a velocity of incoming fluid in the inlet duct  812 A is varied by differing amounts in the circumferential portion  844 A to substantially match the velocities through the inlet ports of an outer rotor  804 A, as described above with reference to  FIG. 1 . Similarly, a profile of a circumferential portion  846 A of the outlet duct  814 A is varied so that the differing velocities of outgoing fluid at the outlet ports of the outer rotor  804 A are reduced by corresponding amounts to substantially the same velocity in the outlet duct  814 A. 
         [0085]      FIG. 8B  depicts a gerotor expander  800 B having an inlet duct  812 B and an outlet duct  814 B. A profile of a circumferential portion  844 B of the inlet duct  812 B is varied so that a velocity of incoming fluid in the inlet duct  812 B is varied by differing amounts in the circumferential portion  844 B to substantially match the velocities through the inlet ports of an outer rotor  804 B. Similarly, a profile of a circumferential portion  846 B of the outlet duct  814 B is varied so that the differing velocities of outgoing fluid at the outlet ports of the outer rotor  804 B are reduced by corresponding amounts to substantially the same velocity in the outlet duct  814 B. 
         [0086]      FIGS. 9A and 9B  show inlet ducts according to the disclosure in which a converging section pre-accelerates fluid velocity in an inlet duct to match a velocity in a circumferential duct.  FIG. 9A  depicts a gerotor compressor  900 A having an inlet duct  912 A and an outlet duct  914 A. A converging section  920 A pre-accelerates fluid flow in the inlet duct  912 A from a lower incoming velocity to a higher velocity entering a circumferential portion  944 A of the inlet duct  912 A. Similarly, a diverging section  922 A decelerates fluid flow leaving a circumferential portion  946 A of the outlet duct  914 A to a desired discharge velocity. 
         [0087]      FIG. 9B  depicts a gerotor expander  900 B having an inlet duct  912 B and an outlet duct  914 B. A converging section  920 B pre-accelerates fluid flow in the inlet duct  912 B from a lower incoming velocity to a higher velocity entering a circumferential portion  944 B of the inlet duct  912 B. Similarly, a diverging section  922 B decelerates fluid flow leaving a circumferential portion  946 B of the outlet duct  914 B to a desired discharge velocity. 
         [0088]    Inlet ducts  912 A and  912 B in this embodiment have rapidly converging profiles, while outlet ducts  914 A and  914 B have gradually diverging (e.g., conical) profiles. In other embodiments, an inlet duct may have a gradually converging profile and/or an outlet duct may have a rapidly diverging profile. To prevent flow separation, an angle less than about 7 degrees is preferred in such converging and diverging profiles. 
       Cut Abradable Coatings 
       [0089]    To reduce leakage losses, a gerotor system should have small clearances between inner and outer rotors and the gerotor housing. During operation, the rotors are subjected to temperatures that cause the rotors to thermally expand. Should the rotors touch each other or the housing, damage can occur to the rotors and/or the housing. 
         [0090]    To avoid damage when such contact occurs, it is desirable for one contacting element to have a hard surface, while the other contacting element has an abradable coating, such as molybdenum disulfide, polymers (e.g., porous epoxy), or soft metal (e.g., babbitt, brass, or copper). A particularly effective coating is nickel/graphite, which is applied via thermal spray. The nickel is porous with graphite-filled voids. If there is a large interference, the hard surface contacts the nickel/graphite coating and causes a portion of the coating to be removed. If there is a small interference, the hard surface contacts the nickel/graphite coating and pushes the nickel into the voids, thus displacing graphite. 
         [0091]    When there is contact between the hard surface and the abradable coating, it is preferred that the hard surface be rough, such as can be obtained via sand blasting. The roughened surface accomplishes two objectives: (1) it acts like sand paper and helps remove the abradable coating, and (2) the resulting gap is roughened, which causes turbulence and thereby reduces flow through the gap. 
         [0092]    The roughened surface works particularly well with softer coatings; however, with harder coatings (e.g., nickel/graphite), galling can occur. To avoid galling, the hard surface may incorporate cutting edges. Such cutting edges may include roughened edges, configured to leave the abradable coating roughened. 
         [0093]      FIG. 10  shows cutting edges located on an inner rotor and an outer rotor according to the disclosure. A gerotor system  1000  includes an inner rotor  1002 , an outer rotor  1004 , and a housing  1006 . As may be seen in  FIG. 10D , the inner rotor  1002  includes cutting edges  1062  on upper and lower edges of the inner rotor  1002 , forming cutting edges on an top surface, a bottom surface, and an outer surface of the inner rotor  1002 . As may be seen in  FIGS. 10B and 10C , the outer rotor  1004  includes cutting edges  1060  on an outer surface of each lobe of the outer rotor  1004 . The cutting edges  1060  and  1062  may be formed from Stellite or other very hard metal. 
         [0094]    The cutting edges  1062  on the inner rotor  1002  may come into contact with mating surfaces on the outer rotor  1004  and/or the housing  1006 . The mating surfaces have an abradable coating, as discussed above. The cutting edges  1062  are raised sufficiently high (preferably about 0.002 inch) from the upper and lower surfaces of the inner rotor  1002  that debris from the abradable coatings can be discharged, but not so high that significant dead volume is created between the inner rotor  1002  and the housing  1006 . 
         [0095]    The cutting edges  1060  on the outer rotor  1004  are located on the edges of the lobes. The mating surface of the housing  1006  has an abradable coating, as discussed above. The cutting edges are raised sufficiently high (preferably about 0.002 inch) from the surface of the outer rotor  1004  that debris from the abradable coatings can be discharged, but not so high that significant dead volume is created between the outer rotor  1004  and the housing  1006 . A rake angle of the cutting edges  1060  is adjusted so that the cutting edge  1060  cuts the abradable coating, rather than smearing it, thereby reducing or preventing galling. Also, an open pocket  1064  is formed in the outer rotor  1004  in front of the cutting edge  1060 , to collect debris generated from the abradable coating, which also reduces or prevents galling. 
       Reduce Deflection of Outer Rotor Lobes 
       [0096]    The lobes of the outer rotor of a gerotor system bridge two discs that define the axial ends of the outer rotor. As the outer rotor spins, centrifugal forces act to deform it. Because the two discs are well supported in the radial direction, they do not undergo much deformation from centrifugal forces. In contrast, the lobes are not well supported in the radial direction and can deform significantly from centrifugal forces, particularly if the lobes bridge a long distance between the two discs. 
         [0097]    If the disc and lobe are made from a single piece of material, then there are significant stress concentrations at the root of the lobe (the interface between the disc and lobe) as centrifugal forces are applied. If not addressed, such stress concentrations may cause cracks to form in the lobes of the outer rotor, which may lead to catastrophic failure. The chances of such failure can be reduced or eliminated by lowering the rotation rate of the outer rotor, however this solution may adversely affect compressor capacity. 
         [0098]    To address stresses in the roots of the lobes of the outer rotor, a number of strategies may be deployed, as described below. 
         [0099]      FIG. 11A  shows an outer rotor  1104  according to the disclosure. The outer rotor  1104  demonstrates a first strategy to reduce stresses in the roots of the lobes of the outer rotor  1104 .  FIG. 11B  is a first section through the outer rotor  1104 , along line A-A.  FIG. 11C  is a second section through the outer rotor  1104 , along line B-B. The outer rotor  1104  has fillets  1170 , which are features on an inner surface of the outer rotor  1104  that reduce stress concentrations at the roots—or bases—of lobes  1168  in the outer rotor  1104 . 
         [0100]    The outer rotor  1104  comprises components  1104 A and  1104 B that are joined like a “clam shell.” The component  1104 A comprises disk/shoulder portion  1166 A, fillet  1170 A, and lobe portion  1168 A. The component  1104 B comprises disk/shoulder portion  1166 B, fillet  1170 B, and lobe portion  1168 B. While components  1104 A and  1104 B are shown in  FIG. 11B  as separated by a gap, it will be understood that in operation, components  1104 A and  1104 B are mechanically coupled to each other to form a contiguous rotor. While the outer rotor  1104  is shown in  FIGS. 11B and 11C  as comprising two components, it will be understood that in other embodiments the outer rotor  1104  may be fabricated as a single component or from three or more components. 
         [0101]      FIG. 11D  depicts an inner rotor  1102  for use with the outer rotor  1104 . The inner rotor  1102  is placed in an interior formed by joining components  1104 A and  1104 B.  FIG. 11E  presents a section through the inner rotor  1102  along the line C-C. The inner rotor  1102  comprises components  1102 A and  1102 B. While components  1102 A and  1102 B are shown in  FIG. 11E  as separated by a gap, it will be understood that in operation, components  1102 A and  1102 B are mechanically coupled to each other to form a contiguous rotor. While the inner rotor  1102  is shown in  FIG. 11E  as comprising two components, it will be understood that in other embodiments the inner rotor  1102  may be fabricated as a single component or from three or more components. 
         [0102]    As may be seen in  FIG. 11E , the upper and lower edges of the inner rotor  1102  are rounded to match a profile of the fillets  1170 A and  1170 B of the outer rotor  1104 . Were the outer rotor  1104  to be entirely flat in the port regions (as outer rotor  1204  is, shown in  FIG. 12C ), the rounded edges of the inner rotor  1102  might introduce dead volume near the ports, which could adversely affect efficiency. 
         [0103]    To reduce or eliminate this effect, the fillets continue to the port region, as shown in View B. Components  1102 A and  1102 B are fabricated with the shoulder portions  1166 A and  1166 B in the port regions. The shoulder portions  1166 A and  1166 B continue the fillets  1170 A and  1170 B into the port regions of the outer rotor  1104 , to mate with the rounded upper and lower edges of the inner rotor  1102 , in order to reduce dead volume near the ports and improver the efficiency of a gerotor system utilizing the outer rotor  1104  and the inner rotor  1102 . 
         [0104]      FIG. 12A  shows an outer rotor  1204  according to the disclosure. The outer rotor  1204  demonstrates a second strategy to reduce stresses in the roots of the lobes of the outer rotor  1204 .  FIG. 12B  is a first section through the outer rotor  1204 , along line A-A.  FIG. 12C  is a second section through the outer rotor  1204 , along line B-B. The outer rotor  2104  has undercuts  1272 , which are features on an inner surface of the outer rotor  1204  configured to reduce stress concentrations at the roots of lobes  1268  in the outer rotor  1204 . As may be seen in  FIG. 12C , the outer rotor  1204  is flat in its port regions. 
         [0105]    The outer rotor  1204  comprises components  1204 A and  1204 B that are mechanically coupled to each other to form the contiguous outer rotor  1204 . The component  1204 A comprises undercut  1272 A and lobe portion  1268 A. The component  1204 B comprises undercut  1272 A and lobe portion  1268 A. While the outer rotor  1204  is shown in  FIGS. 12B and 12C  as comprising two components, it will be understood that in other embodiments the outer rotor  1204  may be fabricated as a single component or from three or more components. 
         [0106]      FIG. 12D  depicts an inner rotor  1202  for use with the outer rotor  1204 .  FIG. 12E  presents a section through the inner rotor  1202  along the line C-C. The inner rotor  1202  comprises components  1202 A and  1202 B, which are mechanically coupled to each other to form the inner rotor  1202 . While the inner rotor  1202  is shown in  FIG. 12E  as comprising two components, it will be understood that in other embodiments the inner rotor  1202  may be fabricated as a single component or from three or more components. 
         [0107]      FIGS. 13A-13C  show an outer rotor  1304  comprising disks  1374 A and  1374 B and lobes  1376 . The lobes  1376  are joined to the disks  1374 A and  1374 B by pins  1378 A and  1378 B, respectively.  FIG. 13B  is a first section through the outer rotor  1304 , along line A-A.  FIG. 13C  is a second section through the outer rotor  1304 , along line B-B. As may be seen in  FIG. 13C , the outer rotor  1304  is flat in its port regions. 
         [0108]    The outer rotor  1304  eliminates stresses in its lobes by forming the lobes  1376  as separate components from the disks  1374 A and  1374 B. Instead, because of centrifugal forces on the lobes  1376 , the pins  1378 A and  1378 B are subjected to shear forces. To reduce centrifugal forces, the lobes  1376  may be constructed from lightweight materials, such as titanium whereas the discs  1374 A and  1374 B may be made from less expensive materials, such as steel. In a preferred embodiment, the lobes  1376  are constructed from materials that are both lightweight and stiff, such as carbon fiber composites or silicon carbide. To reduce the impact of centrifugal forces on the lobes of the outer rotor, the material property of interest for the lobes is the specific modulus, also known as the stiffness to weight ratio or specific stiffness. 
         [0109]      FIGS. 14A-14C  show an outer rotor  1404  comprising disks  1474 A and  1474 B and lobes  1479 . The lobes  1479  are joined to the disks  1474 A and  1474 B by bolts  1480 .  FIG. 14B  is a first section through the outer rotor  1404 , along line A-A.  FIG. 14C  is a second section through the outer rotor  1404 , along line B-B. As may be seen in  FIG. 14C , the outer rotor  1404  is flat in its port regions. 
         [0110]    The bolts  1480  pass completely through the disk  1474 A, the lobe  1479 , and the disk  1474 B. As described for outer rotor  1304 , shown in  FIG. 13 , the outer rotor  1404  eliminates stresses in its lobes by forming the lobes  1479  as separate components from the disks  1474 A and  1474 B, subjecting the bolts  1480  to shear forces due to centrifugal forces on the lobes  1479 . Additionally, friction between mating surfaces of the lobes  1479  and the disks  1474 A and  1474 B, created by clamping forces from the bolts  1480 , reduces shear forces on the bolts  1480  and helps secure the lobes  1479  in place. A pin (not shown) can be used in addition to the bolts  1480  to ensure that the lobes  1479  are properly located on the discs  1474 A and  1474 B. Elements of alternative embodiments as described with reference to  FIGS. 13A-13C  may also be used with the embodiment shown in  FIGS. 14A-14C . 
         [0111]      FIGS. 15A-15D  show an outer rotor  1504  comprising disks  1582 A and  1582 B and lobes  1576  (in  FIG. 15B ) and lobes  1584  (in  FIG. 15D ).  FIG. 15B  is a section through the outer rotor  1504 , along line A-A, and shows the lobes  1576  joined to the disks  1582 A and  1582 B by short bolts  1578 .  FIG. 15C  is a section through the outer rotor  1504 , along line B-B. As may be seen in  FIG. 15C , the outer rotor  1504  is flat in its port regions.  FIG. 15D  is a section through the outer rotor  1504 , along line A-A, and shows the lobes  1584  joined to the disks  1582 A and  1582 B by through-bolts  1580 . 
         [0112]    The lobes  1576  and  1584  fit into pockets or recesses  1577  in the disks  1574 A and  1574 B. This design reduces stress on the bolts  1578  and  1580  by allowing some of the centrifugal force experienced by the lobes  1576  and  1584  to be resisted by forces on the sidewalls of the pockets  1577 , in addition to forces on the bolts  1578  and  1580 . Benefits and suitable elements of alternative embodiments as described with reference to  FIGS. 13A-13C  and  14 A- 14 C may also be used with the embodiment shown in  FIGS. 15A-15D . 
         [0113]      FIGS. 16A-16D  show an outer rotor  1604  comprising disks  1686 A and  1686 B and lobes  1688  (in  FIG. 16B ) and lobes  1690  (in  FIG. 16D ).  FIG. 16B  is a section through the outer rotor  1604 , along line A-A, and shows the lobes  1688  joined to the disks  1686 A and  1686 B by short bolts  1678 A and  1678 B.  FIG. 16C  is a section through the outer rotor  1604 , along line B-B. As may be seen in  FIG. 16C , the outer rotor  1604  is flat in its port regions.  FIG. 16D  is a section through the outer rotor  1604 , along line A-A, and shows the lobes  1690  joined to the disks  1686 A and  1686 B by through-bolts  1680 . 
         [0114]    The lobes  1688  and  1690  are rounded and fit into rounded pockets or recesses  1687  in the disks  1686 A and  1686 B. A rounding profile of the recesses  1687  corresponds to a rounding profile of the lobes  1688  and  1690 . As with the outer rotor  1504  described with reference to  FIGS. 15A-15D , the design of outer rotor  1604  reduces stress on the bolts  1678  and  1680  by allowing some of the centrifugal force experienced by the lobes  1688  and  1690  to be resisted by forces on the sidewalls of the pockets  1687 , in addition to forces on the bolts  1678  and  1680 . Additionally, this design element of outer rotor  1604  further reduces stresses on elements of the outer rotor  1604  by allowing the lobes  1688  and  1690  to rotate within the recesses  1687  when the center portions of the lobes  1688  and  1690  bow out relative to the end portions, due to centrifugal forces on the lobes  1688  and  1690 . Benefits and suitable elements of alternative embodiments as described with reference to  FIGS. 13A-13C ,  14 A- 14 C, and  15 A- 15 D may also be used with the embodiment shown in  FIGS. 16A-16D . 
         [0115]      FIG. 17  shows a cross-section view through hollow lobes  1792  of an outer rotor  1704  according to the disclosure. Fabricating a lobe of an outer rotor as a hollow element reduces the mass of the lobe and thereby its deflection from centrifugal force, while maintaining the strength of the lobe. The hollow lobes  1792  may be used with any of the outer rotor embodiments having separate disk and lobe elements, as were described with reference to  FIGS. 13A-13C ,  14 A- 14 C,  15 A- 15 D, and  16 A- 16 D. 
         [0116]      FIG. 18  shows a cross-section view through lobes  1894  of an outer rotor  1804  according to the disclosure wherein an outer portion of the lobes comprises a first material  1896  and an inner portion of the lobes comprises a second material  1898 . The second material  1898  may be a foamed metal, which reduces weight while supplying stiffness. In other embodiments, the second material  1898  may be a material that is light and stiff, such as carbon fiber composite or ceramic. The filled lobes  1894  may be used with any of the outer rotor embodiments having separate disk and lobe elements, as were described with reference to  FIGS. 13A-13C ,  14 A- 14 C,  15 A- 15 D, and  16 A- 16 D. 
       Reduce Leakage Through Tight Gaps 
       [0117]      FIGS. 19A-19C  show labyrinth seals according to the disclosure on a circumference of an outer rotor. As may be seen in  FIG. 19A , a gerotor system  1900  according to the disclosure includes an outer rotor  1904  and a housing  1906 .  FIG. 19B  is a first section through the outer rotor  1904  and housing  1906 , along line A-A.  FIG. 19C  is a second section through the outer rotor  1904  and housing  1906 , along line B-B. 
         [0118]    As may be seen in  FIG. 19B , the outer rotor  1904  comprises components  1904 A and  1904 B that are joined like a clam shell. The components  1904 A and  1904 B each has an outer surface region that is in proximity to a corresponding inner surface region of the housing  1906 . These outer surface regions are fabricated with labyrinth seals  1903  that create a tortuous path to reduce fluid leakage through the gaps between the outer surface regions of the components  1904 A and  1904 B and the corresponding inner surface regions of the housing  1906 . Exemplary labyrinth seals are discussed in greater detail with reference to  FIG. 21 . 
         [0119]      FIGS. 20A-20C  show a gerotor system  2000  having a similar system of labyrinth seals  2003  between an outer rotor  2004  and a housing  2006 . As may be seen in  FIGS. 20B and 20C , the labyrinth seals  2003  are fabricated in inner surface regions of the housing  2006  that are in proximity to outer surface regions of the outer rotor  2004 . 
         [0120]      FIG. 21  shows exemplary labyrinth seals according to the disclosure. As may be seen, many configurations are possible for labyrinth seals according to the disclosure. As depicted in  FIG. 21 , the upper side of the labyrinths seals are farthest from the outer rotor lobes, while the lower side of the labyrinth seals are closest to the outer rotor lobes. The slots closest to the outer rotor lobes are discontinuous, which prevents “short circuiting” of gas from high-pressure regions of the circumference to low-pressure regions. 
         [0121]    In the embodiments shown in  FIG. 21 , the slot farthest from the lobes is continuous, which allows the pressure to equalize along the circumference. The pressure in this farthest slot is intermediate between inlet and outlet pressure of the compressor, but closer to the inlet pressure. For example, if the inlet pressure of the compressor is 20 psia and the outlet is 50 psia, the pressure in the furthest slot would be approximately 25 psia. 
         [0122]    The outer faces of the outer rotor are coupled to bearings and gears, all of which are lubricated with oil that ultimately drains to a sump. Typically, the pressure in the oil sump is referenced to the compressor inlet (20 psia in this example), which is the lowest continuous pressure in the system. This strategy ensures that oil flows from the bearings and gears back to the sump. Temporarily, while a given void space is expanding and drawing gas into it, the pressure in the void space will drop below the compressor inlet pressure (for example 18 psia). During this temporary suction event, the void space could draw oil through the gaps into the void space. Generally, there is a desire to prevent the gas from being contaminated with oil, so this is an undesirable outcome. By ensuring that the farthest slot always has a slight pressure above the sump pressure, it ensures that gas leakage is always outward from the compression space and therefore oil cannot enter the compression space. 
         [0123]      FIGS. 22A and 22B  show top views of a gerotor system  2200  including an outer rotor  2204  and a housing  2206 . The gerotor system  2200  has labyrinth seals  2203  in the circumferential gaps between the housing and lobes of the outer rotor. In  FIG. 24A , the labyrinth seals  2203  are fabricated in a region of an inner surface of the housing  2206  in proximity to a region of an outer surface of the outer rotor  2204 . In  FIG. 22B , the labyrinth seals  2203  are fabricated in a region of an outer surface of the outer rotor  2204  that is in proximity to a region of an inner surface of the housing  2206 . The slots  2203  can be continuous or discontinuous in the axial direction. 
         [0124]      FIG. 23  shows a gerotor system  2300  that includes an inner rotor  2302  and a housing  2306 . The inner rotor  2302  includes labyrinth seals on an upper face and a lower face (not shown) of the inner rotor  2302 . The labyrinth seals of  FIG. 23  reduce fluid leakage along gaps between the faces of the inner rotor  2302  and inner faces of portions (not shown) of the housing  2306 . In  FIG. 23 , the labyrinth seal is represented as shallow rectangular depressions in a staggered, brick-like pattern. Other patterns are possible, for example, arrays of hexagons and circles or discontinuous slots. 
         [0125]    While the labyrinth seal is shown in  FIG. 23  on the face of the inner rotor, it will be understood that in other embodiments the labyrinth seal may be on the inner face of the housing. 
         [0126]    Modifications, additions, or omissions may be made to the systems, apparatuses, and methods described herein without departing from the scope of the invention. The components of the systems and apparatuses may be integrated or separated. Moreover, the operations of the systems and apparatuses may be performed by more, fewer, or other components. The methods may include more, fewer, or other steps. Additionally, steps may be performed in any suitable order. As used in this document, “each” refers to each member of a set or each member of a subset of a set. 
         [0127]    To aid the Patent Office, and any readers of any patent issued on this application in interpreting the claims appended hereto, applicants wish to note that they do not intend any of the appended claims or claim elements to invoke paragraph  6  of 35 U.S.C. Section 112 as it exists on the date of filing hereof unless the words “means for” or “step for” are explicitly used in the particular claim.