AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Friction Article
PDF (31.7 MB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Dynamics of lubricated spiral bevel gears under different contact paths

Wei CAO1,2, Tao HE3, Wei PU4( ), Ke XIAO5
School of Construction Machinery, Chang'an University, Xi’an 710064, China
Shantui Construction Machinery Co., Ltd., Jining 272073, China
Department of Mechanical Engineering, Northwestern University, Evanston, IL60208, USA
School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China
College of Mechanical Engineering, Chongqing University, Chongqing 400044, China
Show Author Information

Abstract

To assess the meshing quality of spiral bevel gears, the static meshing characteristics are usually checked under different contact paths to simulate the deviation in the footprint from the design point to the heel or toe of the gear flank caused by the assembly error of two gear axes. However, the effect of the contact path on gear dynamics under lubricated conditions has not been reported. In addition, most studies regarding spiral bevel gears disregard the lubricated condition because of the complicated solutions of mixed elastohydrodynamic lubrication (EHL). Hence, an analytical friction model with a highly efficient solution, whose friction coefficient and film thickness predictions agree well with the results from a well-validated mixed EHL model for spiral bevel gears, is established in the present study to facilitate the study of the dynamics of lubricated spiral bevel gears. The obtained results reveal the significant effect of the contact path on the dynamic response and meshing efficiency of gear systems. Finally, a comparison of the numerical transmission efficiency under different contact paths with experimental measurements indicates good agreement.

Keywords

frictionmeshing efficiencydynamic responsespiral bevel gearscontact path

References

[1]
Goldfarb V, Barmina N. Theory and Practice of Gearing and Transmissions. Cham: Springer International Publishing, 2016.
Crossref
[2]
Kahraman A, Singh R. Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system. J Sound Vib 146(1): 135-156 (1991)
Crossref Google Scholar
[3]
Shen Y J, Yang S P, Liu X D. Nonlinear dynamics of a spur gear pair with time-varying stiffness and backlash based on incremental harmonic balance method. Int J Mech Sci 48(11): 1256-1263 (2006)
Crossref Google Scholar
[4]
Khabou M T, Bouchaala N, Chaari F, Fakhfakh T, Haddar M. Study of a spur gear dynamic behavior in transient regime. Mech Syst Signal Process 25(8): 3089-3101 (2011)
Crossref Google Scholar
[5]
Li S, Anisetti A. On the flash temperature of gear contacts under the tribo-dynamic condition. Tribol Int 97: 6-13 (2016).
Crossref Google Scholar
[6]
Özgüven H N. A non-linear mathematical model for dynamic analysis of spur gears including shaft and bearing dynamics. J Sound Vib 145(2): 239-260 (1991)
Crossref Google Scholar
[7]
Maliha R, Doğruer C U, ÖZgüVen H N. Nonlinear dynamic modeling of gear shaft-disk-bearing systems using finite elements and describing functions. J Mech Design 126(3): 534-541 (2004).
Crossref Google Scholar
[8]
Andhare A B, Verma M K. Modeling and dynamic force simulation for detection of profile error in spur gear pair. In Vibration Engineering and Technology of Machinery. Sinha J, Ed. Cham: Springer International Publishing, 2014: 1091-1100.
Crossref
[9]
Ben Amar M, Maatar M, Maalej A. Experimental and numerical analysis of the effect of gear center distance variation and misalignment error on the dynamic behavior of narrow-faced spur gear drives. Mécanique Ind 7(1): 71-78 (2006)
Crossref Google Scholar
[10]
Donley, M, Lim T, Steyer G. Dynamic analysis of automotive gearing systems. sae transactions, 101(6): 958-968 (1992).
Crossref Google Scholar
[11]
Wang J, Lim T C, Li M F. Dynamics of a hypoid gear pair considering the effects of time-varying mesh parameters and backlash nonlinearity. J Sound Vib 308(1-2): 302-329 (2007)
Crossref Google Scholar
[12]
Yang J Y, Peng T, Lim T C. An enhanced multi-term harmonic balance solution for nonlinear period-one dynamic motions in right-angle gear pairs. Nonlinear Dyn 67(2): 1053-1065 (2012)
Crossref Google Scholar
[13]
Wang J, Lim T C. Effect of tooth mesh stiffness asymmetric nonlinearity for drive and Coast sides on hypoid gear dynamics. J Sound Vib 319(3-5): 885-903 (2009)
Crossref Google Scholar
[14]
Yang J Y, Lim T. Dynamics of coupled nonlinear hypoid gear mesh and time-varying bearing stiffness systems. SAE Int J Passeng Cars - Mech Syst 4(2): 1039-1049 (2011)
Crossref Google Scholar
[15]
Lim T C, Wang J. Effects of assembly errors on hypoid gear mesh and dynamic response. In ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Cincinnati, USA, 2005: 801-806.
Crossref
[16]
Wang Y W, Lim T C, Yang J Y. Multi-point mesh modeling and nonlinear multi-body dynamics of hypoid geared system. SAE Int J Passeng Cars-Mech Syst 6(2): 1127-1132 (2013)
Crossref Google Scholar
[17]
Karagiannis I, Theodossiades S, Rahnejat H. On the dynamics of lubricated hypoid gears. Mech Mach Theory 48: 94-120 (2012)
Crossref Google Scholar
[18]
Mohammadpour M, Theodossiades S, Rahnejat H. Multiphysics investigations on the dynamics of differential hypoid gears. J Vib Acoust 136(4): 041007 (2014)
Crossref Google Scholar
[19]
Mohammadpour M, Theodossiades S, Rahnejat H, Kelly P. Transmission efficiency and noise, vibration and harshness refinement of differential hypoid gear pairs. Proc Inst Mech Eng Part K: J Multi-body Dynamics 228(1): 19-33 (2014)
Crossref Google Scholar
[20]
Mohammadpour M, Theodossiades S, Rahnejat H. Tribo- dynamics of differential hypoid gears. In ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Portlan, USA, 2014: 340-350.
Crossref
[21]
Mohammadpour M, Johns-Rahnejat P M, Theodossiades S, Rahnejat H. Effect of tapered roller bearing supports on the dynamic behaviour of hypoid gear pair differentials. Proc Inst Mech Eng Part D: J Automob Eng 230(8): 1090-1104 (2016)
Crossref Google Scholar
[22]
Yavuz S D, Saribay Z B, Cigeroglu E. Nonlinear time- varying dynamic analysis of a spiral bevel geared system. Nonlinear Dyn 92(4): 1901-1919 (2018)
Crossref Google Scholar
[23]
Alves J T, Wang J, Guingand M, de Vaujany J P, Velex P. Static and dynamic models for spiral bevel gears. Mech Ind 13(5): 325-335 (2012)
Crossref Google Scholar
[24]
Simon V. Influence of position errors on EHD lubrication in spiral bevel gears. In Proceedings of the STLE/ASME 2010 International Joint Tribology Conference, California, USA, 2010: 179-181.
Crossref
[25]
Cao W, Pu W, Wang J, et al. Effect of contact path on the mixed lubrication performance, friction and contact fatigue in spiral bevel gears. Tribol Int 123: 359-371 (2018).
Crossref Google Scholar
[26]
Litvin F L, Fuentes A, Hayasaka K. Design, manufacture, stress analysis, and experimental tests of low-noise high endurance spiral bevel gears. Mech Mach Theory 41(1): 83-118 (2006)
Crossref Google Scholar
[27]
Goldfarb V, Barmina N. Theory and Practice of Gearing and Transmissions. Cham: Springer International Publishing, 2016.
Crossref
[28]
Fan Q. Enhanced algorithms of contact simulation for hypoid gear drives produced by face-milling and face-hobbing processes. J Mech Des 129(1): 31-37 (2007)
Crossref Google Scholar
[29]
Fujii M, Nagasaki Y, Nohara M. Differences in dynamic behavior between straight and skew bevel gears. Trans Jpn Soc Mech Eng Ser C 63(613): 3229-3234 (1997)
Crossref Google Scholar
[30]
Gosselin C. Computation and measurement of the kinematical motion error of actual hypoid gears under load. In 4th World Congress on Gearing and Power Transmission, Paris, France: 1999:1935-1946.
[31]
Gosselin C, Cloutier L, Nguyen Q D. A general formulation for the calculation of the load sharing and transmission error under load of spiral bevel and hypoid gears. Mech Mach Theory 30(3): 433-450 (1995)
Crossref Google Scholar
[32]
de Vaujany J P, Guingand M, Remond D, Icard Y. Numerical and experimental study of the loaded transmission error of a spiral bevel gear. J Mech Des 129(2): 195-200 (2007)
Crossref Google Scholar
[33]
Kolivand M, Kahraman A. A load distribution model for hypoid gears using ease-off topography and shell theory. Mech Mach Theory 44(10): 1848-1865 (2009)
Crossref Google Scholar
[34]
Sheveleva G I, Volkov A E, Medvedev V I. Algorithms for analysis of meshing and contact of spiral bevel gears. Mech Mach Theory 42(2): 198-215 (2007)
Crossref Google Scholar
[35]
Houpert L. Rolling bearing load distribution and load zone factor. In Encyclopedia of Tribology. Wang Q J, Chung Y W, Eds. Boston: Springer, 2013: 2839-2847.
Crossref
[36]
Cao W, Pu W, Wang J X. Tribo-dynamic model and fatigue life analysis of spiral bevel gears. Eur J Mech A-Solid 74: 124-138 (2019)
Crossref Google Scholar
[37]
Greenwood J A, Tripp J H. The contact of two nominally flat rough surfaces. Proc Inst Mech Eng 185(1): 625-633 (1970)
Crossref Google Scholar
[38]
Chittenden R J, Dowson D, Dunn J F, Taylor C M. A theoretical analysis of the isothermal elastohydrodynamic lubrication of concentrated contacts. II. General case, with lubricant entrainment along either principal axis of the Hertzian contact ellipse or at some intermediate angle. Proc R Soc Lond A 397(1813): 271-294 (1985)
Crossref Google Scholar
[39]
Paouris L, Rahmani R, Theodossiades S, Rahnejat H, Hunt G, Barton W. Inefficiency predictions in a hypoid gear pair through tribodynamics analysis. Tribol Int 119: 631-644 (2018)
Crossref Google Scholar
[40]
Wang J, Qu S Y, Yang P R. Simplified multigrid technique for the numerical solution to the steady-state and transient EHL line contacts and the arbitrary entrainment EHL point contacts. Tribol Int 34(3): 191-202 (2001)
Crossref Google Scholar
[41]
Jalali-Vahid D, Rahnejat H, Gohar R, Jin Z M. Prediction of oil-film thickness and shape in elliptical point contacts under combined rolling and sliding motion. Proc Inst Mech Eng Part J: J Eng Tribol 214(5): 427-437 (2000)
Crossref Google Scholar
[42]
Bair S, Winer W O. A rheological model for elastohydrodynamic contacts based on primary laboratory data. J Lubr Technol 101(3): 258-264 (1979)
Crossref Google Scholar
[43]
He T, Zhu D, Wang J X, Jane Wang Q. Experimental and numerical investigations of the stribeck curves for lubricated counterformal contacts. J Tribol 139(2): 021505 (2017)
Crossref Google Scholar
[44]
Zhu D, Hu Y Z. A computer program package for the prediction of EHL and mixed lubrication characteristics, friction, subsurface stresses and flash temperatures based on measured 3-D surface roughness. Tribol Trans 44(3): 383-390 (2001)
Crossref Google Scholar
[45]
Olver A V, Spikes H A. Prediction of traction in elastohydrodynamic lubrication. Proc Inst Mech Eng Part J: J Eng Tribol 212(5): 321-332 (1998)
Crossref Google Scholar
[46]
Xu H, Kahraman A. Prediction of friction-related power losses of hypoid gear pairs. Proc Inst Mech Eng Part K: J Multi - Body Dyn 221(3): 387-400 (2007)
Crossref Google Scholar
[47]
Kolivand M, Li S, Kahraman A. Prediction of mechanical gear mesh efficiency of hypoid gear pairs. Mech Mach Theory 45(11): 1568-1582 (2010)
Crossref Google Scholar
[48]
Li S, Kahraman A. Micro-pitting fatigue lives of lubricated point contacts: Experiments and model validation. Int J Fatigue 48: 9-18 (2013)
Crossref Google Scholar
[49]
Li S, Anisetti A. A tribo-dynamic contact fatigue model for spur gear pairs. Int J Fatigue 98: 81-91 (2017)
Crossref Google Scholar
[50]
Pu W, Wang J X, Zhang Y, Zhu D. A theoretical analysis of the mixed elastohydrodynamic lubrication in elliptical contacts with an arbitrary entrainment angle. J Tribol 136(4): 041505 (2014)
Crossref Google Scholar
[51]
Mohammadpour M, Theodossiades S, Rahnejat H, Saunders T. Non-Newtonian mixed elastohydrodynamics of differential hypoid gears at high loads. Meccanica 49(5): 1115-1138 (2014)
Crossref Google Scholar
[52]
Mohammadpour M, Theodossiades S, Rahnejat H, Dowson D. Non-Newtonian mixed thermo-elastohydrodynamics of hypoid gear pairs. Proc Inst Mech Eng Part J: J Eng Tribol 232(9): 1105-1125 (2018)
Crossref Google Scholar
Friction
Volume 10 Issue 2,
February 2022
Pages 247-267
DOI: 10.1007/s40544-020-0477-x
Cite this article:
CAO W, HE T, PU W, et al. Dynamics of lubricated spiral bevel gears under different contact paths. Friction, 2022, 10(2): 247-267. https://doi.org/10.1007/s40544-020-0477-x

735

Views

23

Downloads

6

Crossref

7

Web of Science

11

Scopus

2

CSCD

Altmetrics
Received: 25 July 2020
Revised: 09 October 2020
Accepted: 23 November 2020
Published: 24 March 2021
© The author(s) 2020
Return