Skip to main content
SpringerLink
Log in

Effects of oil film stiffness and damping on spur gear dynamics

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

An enhanced spur gear dynamic model considering the combined stiffness and damping of both gear tooth and oil film is established. To acquire the combined stiffness and damping involved in the modified dynamics equations, Ishikawa formulas are adopted to calculate the gear mesh stiffness, and given the viscous-elastic oil film in elastohydrodynamic lubrication line contact equivalent to massless spring and damping elements, the models of oil film stiffness and damping in normal and tangential directions are then developed. The combined stiffness is deduced from the stiffness of both the gear tooth and oil film, while the combined damping is derived from the damping of these parts. Effects of oil film stiffness and damping on the gear dynamics are investigated, and the dynamic response of the developed model is in contrast to that of the conventional model. The results show that by utilizing the enhanced dynamic model, the displacement fluctuation in transient stage fast decays and displacement response reaches steady state faster. The speed and acceleration fluctuations in the period converting from transient to steady stages are obviously reduced, and the response curves of speed and acceleration in steady stage are smoother. Moreover, the oil film normal damping plays large role in the gear periodic motion. This indicates that the oil film stiffness is prone to effectively alleviate impact and the oil film damping is inclined to substantially reduce vibration and frictional heat for a gear drive.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Litvin, F.L., Lian, Q., Kapelevich, A.L.: Asymmetric modified spur gear drives: reduction of noise, localization of contact, simulation of meshing and stress analysis. Comput. Methods Appl. Mech. Eng. 188, 363–390 (2000)

    Article  MATH  Google Scholar 

  2. Tamminana, V.K., Kahraman, A., Vijayakar, S.: A study of the relationship between the dynamic factors and the dynamic transmission error of spur gear pairs. J. Mech. Des. 129, 75–84 (2007)

    Article  Google Scholar 

  3. Grolet, A., Thouverez, F.: Computing multiple periodic solutions of nonlinear vibration problems using the harmonic balance method and Groebner bases. Mech. Syst. Signal Process. 52–53, 529–547 (2015)

    Article  Google Scholar 

  4. Li, Y., Chen, S.: Periodic solution and bifurcation of a suspension vibration system by incremental harmonic balance and continuation method. Nonlinear Dyn. 83, 941–950 (2016)

    Article  MathSciNet  Google Scholar 

  5. Ankouni, M., Lubrecht, A.A., Velex, P.: Modelling of damping in lubricated line contacts—applications to spur gear dynamic simulations. Proc. IMechE C J. Mech. Eng. Sci. 230, 1–11 (2016)

    Article  Google Scholar 

  6. Kahraman, A., Singh, R.: Non-linear dynamics of a spur gear pair. J. Sound Vib. 142, 49–75 (1990)

    Article  Google Scholar 

  7. Kahraman, A., Singh, R.: Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system. J. Sound Vib. 146, 135–156 (1991)

    Article  Google Scholar 

  8. Kahraman, A., Singh, R.: Non-linear dynamics of a geared rotor-bearing system with multiple clearances. J. Sound Vib. 144, 469–506 (1991)

    Article  Google Scholar 

  9. Baud, S., Velex, P.: Static and dynamic tooth loading in spur and helical geared systems-experiments and model validation. J. Mech. Des. 124, 334–346 (2002)

    Article  Google Scholar 

  10. Chen, S., Tang, J., Li, Y., Hu, Z.: Rotordynamics analysis of a double-helical gear transmission system. Meccanica 51, 251–268 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chen, S., Tang, J., Chen, W., Hu, Z., Cao, M.: Nonlinear dynamic characteristic of a face gear drive with effect of modification. Meccanica 49, 1023–1037 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Dowson, D., Higginson, G.R.: A numerical solution to the elasto-hydrodynamic problem. J. Mech. Eng. Sci. 1, 6–15 (1959)

    Article  MATH  Google Scholar 

  13. Larsson, R.: Transient non-Newtonian elastohydrodynamic lubrication analysis of an involute spur gear. Wear 207, 67–73 (1997)

    Article  Google Scholar 

  14. Raisin, J., Fillot, N., Dureisseix, D., Vergne, P., Lacour, V.: Characteristic times in transient thermal elastohydrodynamic line contacts. Tribol. Int. 82, 472–483 (2015)

    Article  Google Scholar 

  15. Kumar, P., Khonsari, M.M.: On the role of lubricant rheology and piezo-viscous properties in line and point contact EHL. Tribol. Int. 42, 1522–1530 (2009)

    Article  Google Scholar 

  16. Kumar, P., Khonsari, M.M.: Effect of starvation on traction and film thickness in thermo-EHL line contacts with shear-thinning lubricants. Tribol. Lett. 32, 171–177 (2008)

    Article  Google Scholar 

  17. Liu, H., Zhu, C., Sun, Z., Song, C.: Starved lubrication of a spur gear pair. Tribol. Int. 94, 52–60 (2016)

    Article  Google Scholar 

  18. Qin, W., Chao, J., Duan, L.: Study on stiffness of elastohydrodynamic line contact. Mech. Mach. Theory 86, 36–47 (2015)

    Article  Google Scholar 

  19. Zhang, Y., Liu, H., Zhu, C., Liu, M., Song, C.: Oil film stiffness and damping in an elastohydrodynamic lubrication line contact-vibration. J. Mech. Sci. Technol. 30, 3031–3039 (2016)

    Article  Google Scholar 

  20. Zhang, Y., Liu, H., Zhu, C., Song, C., Li, Z.: Influence of lubrication starvation and surface waviness on the oil film stiffness of elastohydrodynamic lubrication line contact. J. Vib. Control 24, 924–936 (2016)

    Article  Google Scholar 

  21. Lubrecht, A.A., Velex, P., Ankouni, M.: Numerical simulation of damping in EHL line contacts. In: International Gear Conference 2014, Lyon, pp. 1020–1028 (2014)

  22. Zhou, C., Xiao, Z., Chen, S., Han, X.: Normal and tangential oil film stiffness of modified spur gear with non-newtonian elastohydrodynamic lubrication. Tribol. Int. 109, 319–327 (2017)

    Article  Google Scholar 

  23. Xiao, Z., Li, Z., Shi, X., Zhou, C.: Oil film damping analysis in non-Newtonian transient thermal elastohydrodynamic lubrication for gear transmission. J. Appl. Mech. 85, 035001 (2018)

    Article  Google Scholar 

  24. Li, S., Kahraman, A.: A spur gear mesh interface damping model based on elastohydrodynamic contact behavior. Int. J. Power 1, 4–21 (2011)

    Article  Google Scholar 

  25. Li, S., Kahraman, A.: A tribo-dynamic model of a spur gear pair. J. Sound Vib. 332, 4963–4978 (2013)

    Article  Google Scholar 

  26. Guilbault, R., Lalonde, S., Thomas, M.: Nonlinear damping calculation in cylindrical gear dynamic modeling. J. Sound Vib. 331, 2110–2128 (2012)

    Article  Google Scholar 

  27. Wang, J., He, G., Zhang, J., Zhao, Y., Yao, Y.: Nonlinear dynamics analysis of the spur gear system for railway locomotive. Mech. Syst. Signal Process. 85, 41–55 (2017)

    Article  Google Scholar 

  28. Yang, P., Wen, S.: A generalized reynolds equation for non-Newtonian thermal elastohydrodynamic lubrication. J. Tribol. 112, 631–636 (1990)

    Article  Google Scholar 

  29. Roelands, C.J.A., Vlugter, J.C., Waterman, H.I.: The viscosity-temperature-pressure relationship of lubricating oils and its correlation with chemical constitution. J. Basic Eng. 85, 601–607 (1963)

    Article  Google Scholar 

  30. Dowson, D., Higginson, G.R.: Elastohydrodynamic Lubrication: The Fundamentals of Roller and Gear Lubrication. Pergamon Press, Oxford (1966)

    Google Scholar 

  31. Zhou, C., Xiao, Z.: Stiffness and damping models for the oil film in line contact elastohydrodynamic lubrication and applications in the gear drive. Appl. Math. Model. 61, 634–649 (2018)

    Article  MathSciNet  Google Scholar 

  32. Habchi, W.: A numerical model for the solution of thermal elastohydrodynamic lubrication in coated circular contacts. Tribol. Int. 73, 57–68 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (Grant No. 51675168), the Key Basic Research Plan of Hunan Province (2016JC2001), and the Open Research Fund of Key Laboratory of High Performance Complex Manufacturing, Central South University (Kfkt2017-10).

Author information

Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082, People’s Republic of China

    Zeliang Xiao & Changjiang Zhou

  2. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Zeliang Xiao & Zuodong Li

  3. State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha, 410083, People’s Republic of China

    Changjiang Zhou & Siyu Chen

Authors
  1. Zeliang Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Changjiang Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Siyu Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zuodong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Changjiang Zhou.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiao, Z., Zhou, C., Chen, S. et al. Effects of oil film stiffness and damping on spur gear dynamics. Nonlinear Dyn 96, 145–159 (2019). https://doi.org/10.1007/s11071-019-04780-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-019-04780-6

Keywords

Search

Navigation