Helical trochoidal rotary machines
Rotary positive displacement machines with trochoidal geometry that comprise a helical rotor that undergoes planetary motion within a helical stator are described. The rotor can have a hypotrochoidal cross-section, with the corresponding stator cavity profile being the outer envelope of the rotor as it undergoes planetary motion, or the stator cavity can have an epitrochoidal cross-section with the corresponding rotor profile being the inner envelope of the trochoid as it undergoes planetary motion. In some multi-stage embodiments, the rotor-stator geometry remains substantially constant along the axis of the rotary machine. In other multi-stage embodiments, the rotor-stator geometry varies along the axis of the rotary machine.
1. A rotary machine comprising:
a stator having a stator length and a stator axis, and
a rotor having a rotor length and a rotor axis, said rotor disposed within said stator,
said rotor, along at least a portion of said rotor length, having a rotor helical profile, and a hypotrochoidal shape at any cross-section transverse to said rotor axis,
said stator, along at least a portion of said stator length, having a stator helical profile, and a stator shape at any cross-section transverse to said stator axis that is an outer envelope formed when said hypotrochoidal shape of said rotor undergoes planetary motion,
wherein said rotor is configured to undergo planetary motion within said stator.
2. The rotary machine of claim 1 wherein:
said hypotrochoidal shape of said rotor has n lobes, where n is an integer;
the stator shape has (n−1) lobes;
said rotor has a rotor pitch and a rotor lead;
said stator has a stator pitch and a stator lead;
said rotor pitch is the same as said stator pitch; and
a ratio of said rotor lead to said stator lead is n:(n−1).
3. The rotary machine of claim 2 wherein said hypotrochoidal shape is an ellipse and n=2.
4. The rotary machine of claim 3 wherein the rotary machine is a multi-stage machine having a plurality of chambers between cooperating surfaces of said rotor and said stator.
5. The rotary machine of claim 4 wherein each of said plurality of chambers has approximately the same dimensions and shape.
6. The rotary machine of claim 4 wherein at least one of said plurality of chambers has dimensions that are different from another of said plurality of chambers.
7. The rotary machine of claim 6 wherein each of said plurality of chambers has a different volume.
8. The rotary machine of claim 7 wherein said rotor pitch varies along at least a portion of said rotor length, and said stator pitch varies along at least a portion of said stator length.
9. The rotary machine of claim 7 wherein said hypotrochoidal shape is an ellipse and the aspect ratio of said ellipse varies along at least a portion of said rotor length.
10. The rotary machine of claim 7 wherein said rotor axis is inclined relative to said stator axis.
11. The rotary machine of claim 1 wherein said rotary machine is a pump.
12. The rotary machine of claim 7 wherein said rotary machine is a compressor or an expander.
13. A rotary machine comprising:
a stator having a stator length and a stator axis, and
a rotor having a rotor length and a rotor axis, said rotor disposed within said stator,
said stator, along at least a portion of said stator length, having a stator helical profile, and an epitrochoidal stator shape at any cross-section transverse to said stator axis,
said rotor, along at least a portion of said rotor length, having a rotor helical profile, and a rotor shape at any cross-section transverse to
said rotor axis that is an inner envelope formed when said epitrochoidal stator shape undergoes planetary motion,
wherein said rotor is configured to undergo planetary motion within said stator.
14. The rotary machine of claim 13 wherein:
the epitrochoidal stator shape has n- 1 lobes, where n is an integer;
said rotor shape has n lobes;
said rotor has a rotor pitch and a rotor lead;
said stator has a stator pitch and a stator lead;
said rotor pitch is the same as said stator pitch; and
a ratio of said rotor lead to said stator lead is n:(n−1).
15. The rotary machine of claim 14 wherein n=2.
16. The rotary machine of claim 15 wherein the rotary machine is a multi-stage machine having a plurality of chambers between cooperating surfaces of said rotor and said stator, and each of said plurality of chambers has approximately the same dimensions and shape.
17. The rotary machine of claim 15 wherein the rotary machine is a multi-stage machine having a plurality of chambers between cooperating surfaces of said rotor and said stator, and at least one of said plurality of chambers has dimensions that are different from another of said plurality of chambers.
18. The rotary machine of claim 17 wherein each of said plurality of chambers has a different volume.
19. The rotary machine of claim 18 wherein said rotor pitch varies along at least a portion of said rotor length, and
wherein said stator pitch varies along at least a portion of said stator length.
20. The rotary machine of claim 18 wherein said rotor axis is inclined relative to said stator axis.