Non-undercutting region and property evaluation of epitrochoidal gerotor geometry

Abstract

The gerotor pump is widely used for industrial applications. In this paper, the inner rotor profile is an equidistant epitrochoidal curve, and the outer rotor is generated by the inner rotor profile. This paper discusses an undercutting analysis of the rotor profile, in which the undercutting equations are derived by the theory of gearing. The non-undercutting region is determined by the undercutting curves of the inner and the outer rotors. Numerical examples show that the non-undercutting region on the gerotor profiles only needs to consider the lower part of the undercutting curve of the inner rotor. Besides, the curvature equations of the outer and inner rotors are derived for evaluating the rotor profile properties such as assessing the sealing property and the Hertz stress forecast. The theoretical stress and software simulations proved the stress forecast. The results obtained are important for using the gerotor profile in optimum design.

Keywords

gerotor undercutting curvature stress

Get full access to this article

View all access options for this article.

References

Tsay

C. B.

C. Y.

, ‘The mathematical model of gerotor pump applicable to its characteristic study’ J. Chin. Soc. Mech. Engrs 11 4 (1990): 385–391.

Beard

J. E.

Hall

A. S.

Soedel

, ‘Comparison of hypotrochoidal and epitrochoidal gerotors’ Trans. ASME, J. Mech. Des. 113 (1991): 133–141.

Beard

J. E.

Yannietll

D. W.

Pennock

G. R.

, ‘The effects of the generating pin size and placement on the curvature and displacement of epitrochoidal gerotors’ Mech. Mach. Theory 27 4 (1992): 373–389.

Shung

J. B.

Pennock

G. R.

, ‘Geometry for trochoidal-type machines with conjugate envelopes’ Mech. Mach. Theory 29 1 (1994): 25–42.

Mimmi

G. C.

Pennacchi

P. E.

, ‘Non-undercutting conditions in internal gears’ Mech. Mach. Theory 35 (2000): 477–490.

Vecchiato

Demenego

Argyris

Litvin

F. L.

, ‘Geometry of a cycloidal pump’ Comput. Methods Appl. Mech. Eng. 190 (2001): 2309–2330.

Demenego

Vecchiato

Litvin

F. L.

Nervegna

Manco

, ‘Design and simulation of meshing of a cycloidal pump’ Mech. Mach. Theory 37 3 (2002): 311–332.

Paffoni

, ‘Pressure and film thickness in a trochoidal hydrostatic gear pump’ Proc. IMechE, Part G: J. Aerospace Engineering 217 G4 (2003): 179–187 DOI: 10.1243/095441003769700744.

Paffoni

Progri

Gras

, ‘Teeth clearance effects upon pressure and film thickness in a trochoidal hydrostatic gear pump’ Proc. IMechE, Part G: J. Aerospace Engineering 218 G4 (2004): 247–256 DOI: 10.1243/0954410041872799.

10.

Hwang

Y. W.

Hsieh

C. F.

, ‘Determination of surface singularities of a cycloidal gear drive with inner meshing’ Math. Comput. Model. 45 4 (2007): 340–354.

11.

Yan

Yang

D. C. H.

Tong

S. H.

, ‘A new gerotor design method with switch angle assignability’ Trans. ASME, J. Mech. Des. 131 1 (2009): 11–006.

12.

Colbourne

J. R.

, ‘Reduction of the contact stress in internal gear pumps’ ASME J. Eng. Ind. (1976): 296–300.

13.

Gamez-Montero

P. J.

Castilla

Khamashta

Codina

, ‘Contact problems of a trochoidal-gear pump’ Int. J. Mech. Sci. 48 12 (2006): 1471–1480.

14.

Gamez-Montero

P. J.

Codina

, ‘Contact stress in a gerotor pump’ In Proceedings of the ASME 2003 International Mechanical Engineering Congress and Exposition, Washington, DC, USA, 15–21 November 2003, pp. 65–71.

15.

Litvin

F. L.

, Gear geometry and applied theory (New York: Prentice Hall 1994).