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Mechanics and FEM estimation of gaps generated in star-ring active contacts of ORBIT motor during operation

  • Debanshu RoyEmail author
  • Rathindranath Maiti
  • Prasanta Kumar Das
Article
  • 33 Downloads

Abstract

We estimate deformations or gaps occurring at all the ideally form-closed contacts, that separate the chambers, in epitrochoid (cycloidal class) generated star-ring gears of ORBIT® motors. The direct measurement of these deformations and gaps is not an easy task as the contact positions are inaccessible for installing any measuring device. Therefore, we target the accurate theoretical estimation of these deformations and gaps for any pressure or torque load. The problem poses statically indeterminate, as there are multiple contacts. We use FEM in Ansys® environment to model the problem and its solution. We develop the model to its final stage with gradual improvement in assessing more accurate and realistic boundary conditions as well as loading patterns. We make an elaborate presentation of this process in this investigation report. Interestingly, in ORBIT motor momentary occurrence of gap at the transition active contact, i.e., the contact separating the two adjacent chambers with one in high pressure and the other in low pressure, is unavoidable. This occurs for a substantial period of a power cycle and sometimes in both transition contacts, that separate the overall high pressure zone and the low pressure zone. The inter-chamber leakages through these gaps are partially responsible for lowering the volumetric efficiency. The present investigation is limited to establishing a method of estimating deformation and gaps at the active contacts of such units. Our proposed method can be used for any such unit of any geometric design data and kinematic model.

Keywords

Epitrochoid star ORBIT motor Active and transition contacts Deformations and gaps Load sharing FEM 

List of symbols

‘−’

Super score indicate dimensionless form

\( A_{ 0} \)

(See Fig. 8) nominal arm length of star generating point in an epitrochoidal generation, also it is the pitch circle radius of the roller/lobe in the ring \( \bar{A}_{ 0} = A_{ 0} / \, R_{ 0} \)

\( b \)

Nominal width of the star-ring/Length of roller

\( C_{ 0} \)

Eccentricity or centre distance \( \frac{{C_{ 0} }}{{R_{ 0} }} = \frac{1}{Z} \)

\( E \)

Young’s modulus,\( E_{t} = E_{e} = E \), (t denotes trochoid and e denotes envelope)

\( L_{i} \)

Length of a line joining two transition contact points at any instant

\( F_{i} \)

Resultant instantaneous separating force due to fluid pressure acting on Li

\( F_{n} \)

Contact force in the normal direction

µ

Coefficient of friction at active contacts

\( f_{n} \)

Coefficient of friction (steel)

\( I_{ 0} \)

Instantaneous centre of rotation of the centrodes

\( M_{i} \)

Instantaneous torque (due to fluid pressure)

\( M_{n} \)

Reaction torque due to force \( F_{n} \)

\( p_{i} \)

Pressure at the inlet

\( p_{o} \)

Pressure at the outlet

\( \varDelta p_{i} \)

Differential pressure (\( p_{i} - p_{o} \))

\( R_{ 0} \)

Radius of outer centrode. Base circle radius of envelope/ring profile

\( r_{ 0} \)

Radius of inner centrode. Base circle radius of epitrochoid/star

\( r_{i} \)

Instantaneous torque arm (uniform inlet and outlet pressure)

\( r_{m} \)

Radius of ring lobe/Roller \( \overline{{r_{m} }} = \, r_{m} /R_{ 0} \)

\( \delta \)

The deviation of I0 from its ideal geometric position due to fluid pressure

\( \delta_{n} \)

Deformation at nth Contact (− means gap)

\( f_{m} \)

Material property factor

\( \psi \)

Angle of rotation of \( A_{ 0} \) with respect to the X-axis fixed on the inner centrode

\( \xi \)

Rotational angle of star about its own axis/Shaft rotational angle

\( \xi_{o} \)

Phase angle (with respect to \( \xi \)) for which chambers remain in the same phase = \( \pi /Z\left( {Z - 1} \right) \)

\( \phi \)

Leaning angle

\( \upsilon \)

Poisson’s ratio; \( \upsilon_{t} = \, \upsilon_{e} = \, \upsilon \), (t denotes trochoid and e denotes envelope)

\( Z \)

Number of chambers in HST unit (= the number of lobes/rollers in ring)

\( Q_{il} \)

Instantaneous inter-chamber leakage flow rate (m3/s)

\( \eta \)

Viscosity of hydraulic oil (Kg/m s)

Abbreviations

FEM

Finite element method

HPZ

High pressure zone

HST

Hydrostatic transmission

HSLT

High speed low torque

LPZ

Low pressure zone

LSHT

Low speed high torque

ROPIMA

Rotary piston machine

TEM

Trial and error method

Notes

Acknowledgements

This research work is an outcome of the general PhD program in the authors’ Institute, IIT Kharagpur, India. There is no specific financial grant for this investigation.

Compliance with ethical standards

Conflict of interest

The author(s) declare that they have no potential conflict of interest with respect to the research, authorship, and/or publication of this article.

References

  1. Ansdale, R.F.: The Wankel RC Engine: Design and Performance. Iliffe, London (1968)Google Scholar
  2. Bonandrini, G., Mimmi, G., Rottenbacher, C.: Theoretical analysis of internal epitrochoidal and hypotrochoidal machines. Proc IMechE Part C: J Mech Eng Sci 223(6), 1469–1480 (2009)CrossRefzbMATHGoogle Scholar
  3. Bonandrini, G., Mimmi, G., Rottenbacher, C.: Theoretical analysis of internal epitrochoidal and hypotrochoidal machines. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 223(6), 1469–1480 (2009)CrossRefzbMATHGoogle Scholar
  4. Colbourne, J.: Reduction of the contact stress in internal gear pumps. ASME J. Eng. Ind. 98(4), 1296–1300 (1976)CrossRefGoogle Scholar
  5. Gamez-Montero, P.J., Codina, E.: Flow characteristics of a trochoidal-gear pump using bond graphs and experimental measurement: part 2. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 221(3), 347–363 (2007)CrossRefGoogle Scholar
  6. Gamez-Montero, P.J., Castilla, R., Khamashta, M., Codina, E.: Contact problems of a trochoidal-gear pump. Int. J. Mech. Sci. 48(12), 1471–1480 (2006)CrossRefzbMATHGoogle Scholar
  7. Ivanovic, L., Devedzic, G., Miric, N., Cukovic, S.: Analysis of forces and moments in Gerotor pumps. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 224(10), 2257–2269 (2010a)CrossRefGoogle Scholar
  8. Ivanovic, L., Blagojević, M., Devedžić, G., Assoul, Y.: Analitycal and numerical analysis of load gerotor pumps. Sci. Tech. Rev. 60(1), 30–38 (2010b)Google Scholar
  9. Kwon, S.M., Kim, M.S., Shin, J.H.: Analytical wear model of a Gerotor pump without hydrodynamic effect. J. Adv. Mech. Des. Syst. 2(2), 230–237 (2008)CrossRefGoogle Scholar
  10. Maiti, R.: Studies on orbital rotory piston ‘LSHT’ hydrostatic motor- low speed performance and design. Doctoral dissertation, IIT, Kharagpur (1990)Google Scholar
  11. Maiti, R.: Active contact stresses at epitrochoid generated ROTOR-STATOR set of fixed axis or equivalent system ‘ROPIMA’ type hydrostatic units. ASME J. Eng. Ind. 113(4), 465–473 (1991)Google Scholar
  12. Maiti, R.: Distributor valve port sequences in epitrochoid generated rotary piston machine type hydrostatic units. Arch. Appl. Mech. 62(4), 223–229 (1992)CrossRefGoogle Scholar
  13. Maiti, R.: Active contact problems in epitrochoid generated ‘floating axis’ orbital rotary piston machines. ASME J. Eng. Ind. 115(3), 337–340 (1993)Google Scholar
  14. Maiti, R., Nagao, M.: Prediction of starting torque characteristics of epitrochoid generated orbital rotary piston hydraulic motors. JSME Int. J. C Mech. Syst. Mach. Elem. Manuf. 42(2), 416–426 (1999)CrossRefGoogle Scholar
  15. Maiti, R., Sinha, G.L.: Kinematics of active contact in modified epitrochoid generated rotary piston machines. Mech. Mach. Theory 23(1), 39–45 (1988–2013)CrossRefGoogle Scholar
  16. Maiti, R., Sinha, G.L.: Limits on modification of epitrochoid used in rotary piston machines and the effects of modification on geometric volume displacement and ripple. Ing. Arch. 60(3), 183–194 (1990)CrossRefGoogle Scholar
  17. Nag, A.: Analysis of active contacts in epitrochoid generated form-closed rotor-stator set with specific reference to Hydrostatic motor performance. Doctoral dissertation, IIT Kharagpur (2015)Google Scholar
  18. Nag, A., Maiti, R.: Unification of epitrochoid origin profile design approaches for external lobed star member used in hydrostatic and gear units. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 227(2), 299–310 (2013)CrossRefGoogle Scholar
  19. Pellegri, M., Vacca, A.: Numerical simulation of Gerotor pumps considering rotor micro-motions. Meccanica 52(8), 1851–1870 (2017)MathSciNetCrossRefGoogle Scholar
  20. Pellegri, M., Vacca, A., Frosina, E., Buono, D., Senatore, A.: Numerical analysis and experimental validation of Gerotor pumps: a comparison between a lumped parameter and a computational fluid dynamics-based approach. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 231(23), 4413–4430 (2017)CrossRefGoogle Scholar
  21. Roy, D., Kumar, A., Maiti, R., Das, P.K.: Effect of modification in flow distributor valve geometry on the pressure drop and chamber pressures, in numerical and analytical way, in ORBIT Motor HST unit.  https://doi.org/10.20944/preprints201809.0184.v1 (2018)
  22. Weber, R.L., Manning, K.V., White, M.W.: College physics, vol. 66. McGraw-Hill, New York (1965)Google Scholar
  23. White, G.: Epicyclic gears applied to early steam engines. Mech. Mach. Theory 23(1), 25–37 (1988)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentIndian Institute of TechnologyKharagpurIndia

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