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Time-varying mesh stiffness model of a modified gear–rack drive with tooth friction and wear

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Abstract

A time-varying mesh stiffness (TVMS) model of a modified gear–rack drive with tooth friction and wear is proposed in this work. The model considers the direction variation of the tooth friction and wear influence on single gear–rack tooth pair mesh stiffness and TVMS. The TVMS of the modified gear–rack drive is calculated using the generating method and the potential energy principle and verified using the finite element method based on an engineering application of the Three Gorges ship lift. Then, TVMS models of the gear–rack drive with tooth surface friction and wear are presented based on the engagement theory of gear–rack and Archard’s wear equation. Results show that the TVMS of the gear–rack drive decreases with the increase in the tooth friction and wear. The effects of the modification coefficient and the pressure angle on the TVMS of the gear–rack drive under constant center distance are further investigated. The results indicate that the bearing capacity and dynamic performance of the gear–rack drive can be enhanced by optimizing the modification coefficient and the pressure angle.

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Abbreviations

a H :

Half-width of Hertzian contact (m)

B e :

Effective tooth width (mm)

E i :

Young’s modulus (GPa)

E ij :

Tooth profile error of jth gear–rack pair (m)

E is :

Normal tooth pitch error (m)

F :

Total normal force (N)

F ix :

Axial tooth force (N)

F iy :

Bending tooth force (N)

F f :

Friction force (N)

f :

Friction coefficient

G i :

Shear modulus (GPa)

H :

Hardness of the softer material (GPa)

h i :

Wear depth (m)

k a :

Axial compressive stiffness (N/m)

k b i :

Bending stiffness (N/m)

k f i :

Fillet foundation stiffness (N/m)

k h i :

Hertzian contact stiffness (N/m)

k s i :

Shear stiffness (N/m)

k :

Single gear–rack tooth pair mesh stiffness (N/m)

K :

Total TVMS of the gear–rack pair (N/m)

K w :

Dimensionless wear coefficient

k w :

Dimensional wear coefficient (GPa−1)

M i :

Torque associated with Fix and Fiy (N·m)

p P :

Mean Hertzian contact pressure (Pa)

r :

Reference circle of the gear blank (mm)

r ʹ :

Distance of reference line and Y axis (mm)

s :

Relative sliding distance (m)

U a i :

Axial compressive deformation energy (N·m)

U b i :

Bending deformation energy (N·m)

U f i :

Fillet foundation deformation energy (N·m)

U s i :

Shear deformation energy (N·m)

U h i :

Hertzian contact deformation energy (N·m)

v i :

Tangential velocity (m/s)

V :

Wear volume (m3)

β i :

Angle of total normal force F and Y1 axis (°)

μ i :

Poisson’s ratio

θ :

Rolling angle of the rack cutter (°)

FE:

Finite Element

TVMS:

Time-varying mesh stiffness

2D:

Two dimensional

HPSTC:

Highest point of the single point contact

LPSTC:

Lowest point of the single tooth contact

3D:

Three dimensional

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Acknowledgements

The authors gratefully acknowledge the support by the National Natural Science Foundation of China (NSFC) through Grant Nos. 52075153, 51775516, and Key Basic Research Plan of Hunan Province 2020WK2032, and Natural Science Foundation of Hunan Province 2019JJ40020.

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Authors and Affiliations

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

    Changjiang Zhou, Xiaojie Dong & Hongbing Wang

  2. Zhengzhou Research Institute of Mechanical Engineering Co., Ltd., Zhengzhou, 450052, People’s Republic of China

    Zhongming Liu

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  1. Changjiang Zhou
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Correspondence to Hongbing Wang.

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Zhou, C., Dong, X., Wang, H. et al. Time-varying mesh stiffness model of a modified gear–rack drive with tooth friction and wear. J Braz. Soc. Mech. Sci. Eng. 44, 213 (2022). https://doi.org/10.1007/s40430-022-03517-8

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