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A mesh stiffness model with the asperity contact for spur gear in mixed elastohydrodynamic lubrication

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Abstract

The gear time-varying mesh stiffness (TVMS) calculation is the basis for analyzing gear dynamics, which has considerable effects on the optimal design of gear parameters. Gear drives generally operate in mixed elastohydrodynamic lubrication (EHL), and it is significant to investigate the time-varying mesh stiffness for spur gear pairs in mixed EHL. In this work, a novel TVMS model for spur gear in mixed EHL is presented in consideration of asperity contact stiffness and oil film stiffness. The influences of gear geometric and operation parameters on TVMS are analyzed. The TVMS of spur gear pair in mixed EHL is found to be larger than that in dry contact. Results show that TVMS reduces with the increased module but increases with the large pressure angle. When tooth number of pinion is closer to that of gear, the gear TVMS becomes large. Moreover, the fluctuations of velocity and torque have a negligible effect on the TVMS of the spur gear in mixed EHL.

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Abbreviations

A n :

Nominal contact area (mm2)

A a :

Asperity contact area (mm2)

a H :

Half contact width (mm)

B :

Tooth width (mm)

d :

Separation based on asperity heights (mm)

d 0 :

Initial separation (mm)

d c :

Iteration step (mm)

E eq :

Equivalent elastic modulus (Pa)

F a :

Total asperity contact load (N)

F at :

Asperity contact load (N)

F n :

Normal load (N)

G :

Dimensionless elasticity modulus

H :

Surface hardness (Gpa)

H c :

Dimensionless central film thickness

h c :

Central film thickness (mm)

L a :

Asperity contact ratio (%)

k a :

Axial compressive stiffness (N/mm)

k ac :

Asperity contact stiffness (N/mm)

k b :

Tooth bending stiffness (N/mm)

k c :

Contact stiffness (N/mm)

k t :

Tooth stiffness (N/mm)

k f :

Tooth bending stiffness (N/mm)

k m :

Mesh stiffness of gear pair (N/mm)

k o :

Oil film stiffness (N/mm)

k s :

Shear stiffness (N/mm)

p :

Contact pressure (Pa)

p h :

Oil film pressure (Pa)

R c :

Curvature radius (mm)

R a :

Surface roughness (μm)

R Ra :

Asperity radius (mm)

U :

Dimensionless rolling speed

u r :

Rolling velocity of contact position (mm/s)

V :

Dimensionless surface hardness

W :

Dimensionless load

z :

Asperity height (mm)

α :

Pressure-viscosity coefficient (Pa−1)

μ 0 :

Lubricating oil viscosity (Pa·s)

δ :

Asperity deformation (mm)

ν :

Poisson ratio of gear material

λ :

Correction coefficient of kf

p,g :

Driving gear, driven gear

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grants Nos. 52005051 and 52075153), the Key Research and Development Program of Hunan Province (Grants No. 2020WK2032) and the Natural Science Foundation of Hunan Province (Grant No. 2021JJ40580).

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Authors and Affiliations

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

    Changjiang Zhou & Mingcai Xing

  2. Hunan Provincial Key Laboratory of Intelligent Manufacturing Technology for High-Performance Mechanical Equipment, Changsha University of Science and Technology, Changsha, 410114, People’s Republic of China

    Bo Hu

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  1. Changjiang Zhou
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Correspondence to Bo Hu.

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Zhou, C., Xing, M. & Hu, B. A mesh stiffness model with the asperity contact for spur gear in mixed elastohydrodynamic lubrication. J Braz. Soc. Mech. Sci. Eng. 44, 466 (2022). https://doi.org/10.1007/s40430-022-03748-9

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