Effects of oil film stiffness and damping on spur gear dynamics

  • Zeliang Xiao
  • Changjiang ZhouEmail author
  • Siyu Chen
  • Zuodong Li
Original Paper


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.


Gear dynamics Elastohydrodynamic lubrication Oil film stiffness Oil film damping Transmission error 



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).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Advanced Design and Manufacture for Vehicle BodyHunan UniversityChangshaPeople’s Republic of China
  2. 2.School of Mechanical EngineeringShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China
  3. 3.State Key Laboratory of High Performance Complex ManufacturingCentral South UniversityChangshaPeople’s Republic of China

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