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Rough surface modeling and contact analysis based on micro-scale spherical roller bearing

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Abstract

Based on Gaussian random function, the micro-contact model of spherical roller bearing is established by reverse engineering, and the contact states of surfaces with different roughness are calculated. The contact characteristics of contact surface such as equivalent stress, contact stress, contact area ratio and relative fatigue life are studied. Then, the accuracy of finite element calculation is verified by rough surface contact experiment. The results show that with the increase of displacement load, the equivalent stress and contact stress of contact surface increase, and the contact area ratio of rough contact surface increases steadily. With the decrease of roughness, the fatigue life of contact surface increases slightly. When the contact surface is close to smooth, the fatigue life of the contact surface is significantly improved, and the equivalent stress is significantly reduced: as the roughness of the contact surface is close to the target surface, the contact stress of the contact surface is significantly reduced. The results show that the roughness surface Ra = 0.05 μm has good performance in the aspects of equivalent stress, contact area and fatigue life. The contact stress of the roughness surface Ra = 0.4 μm has a minimum value, which provides a reference for selecting the machining accuracy of the contact surface of spherical roller bearings.

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Abbreviations

Ra:

Contour arithmetic mean deviation

Rz:

Contour maximum height

A * :

The height data of rough surface

p :

The value of Ra of the reference contour

z :

Variance

M :

Matrix

X′, Y′, Z′:

The three-way coordinates of the rough surface

Rsm:

The spacing characteristic parameter

x′, y′, z′:

The three-way coordinates of the smooth surface

ρ :

Density

E :

Elastic modulus

μ :

Poisson’s ratio

Rm:

Tensile strength

σ s :

Yield strength

K :

The probability of survival

N :

The number of stress cycles

e :

The slope of Weibull distribution

V :

The volume obtained by integrating the stress

τ eq :

Von Mises stress

f :

The stress index

σ 1 :

The first principal stress

σ 2 :

The second principal stress

σ 3 :

The third principal stress

N 1 :

The stress cycles of smooth surface

N 2 :

The stress cycles of rough surface

L r :

The fatigue life

ΔS :

The displacement load

δ :

The contact area rate

a, b :

The value factors of the formula, corresponding to different roughness fitting formulas.

x :

The force response value

f(x) :

The equivalent stress value

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Acknowledgements

Ming Chen performed the data analyses and wrote the manuscript; Qiang Bian performed the experiment and data analyses; Guang Zeng contributed significantly to analysis and manuscript preparation; Chunjiang Zhao helped perform part of the finite element analysis. Lianyun Jiang contributed to the conception of the study; Xiangyun Zhang helped perform the analysis with constructive discussions; Bowen Jiao helped perform the chart.

Funding

This research work supported by National Natural Science Foundation of China (No.20201102003), Key Research and Development Projects in Shanxi province (grant number 201903D421031), National Natural Science Foundation of China (No. 51375325).

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Authors and Affiliations

  1. School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, 030024, China

    Ming Chen, Qiang Bian, Chunjiang Zhao, Lianyun Jiang, Xiangyun Zhang & Bowen Jiao

  2. School of Aerospace Engineering, Zhengzhou University of Aeronautics, Zhengzhou, 450015, China

    Guang Zeng

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  1. Ming Chen
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Correspondence to Chunjiang Zhao.

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Chen, M., Bian, Q., Zeng, G. et al. Rough surface modeling and contact analysis based on micro-scale spherical roller bearing. J Braz. Soc. Mech. Sci. Eng. 45, 616 (2023). https://doi.org/10.1007/s40430-023-04530-1

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