Study on Simplified Model and Numerical Solution of High-Speed Angular Contact Ball Bearing

Guang Zeng,Biao Sun,Chunjiang Zhao,Xiaokai Yu,Qiang Bian,Bingyang Liu,Zhigang Xiao,Anindya Ghoshal

doi:10.1155/2020/8843524

Guang Zeng, Biao Sun + Show 6 more

Open Access

https://doi.org/10.1155/2020/8843524

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Abstract

For the calculation model of high-speed angular contact bearing has many variables, the large root difference exists, and the Newton iterative method solving the convergence depends on the initial value problems; thus, the simplified calculation model is proposed and the algorithm is improved. Firstly, based on the nonlinear equations of variables recurrence method of the high-speed angular contact ball bearing calculation model, it is proved that the ultimate fundamental variables of calculation model are the actual inner and outer contact angles, the axial and radial deformations. According to this reason, the nonlinear equations are deformed and deduced, and the number of equations is reduced from 4Z + 2 to 2Z + 2 (Z represents the number of rolling bodies); a simplified calculation model is formed. Secondly, according to the small dependence of the artificial bee colony algorithm on the initial value, an improved artificial bee colony algorithm is proposed for the large root difference characteristics of high-speed ball bearings. The validity of the improved algorithm is verified by standard test function. The algorithm is used to solve the high-speed angular contact ball bearing calculation model. Finally, the deformations of high-speed angular contact ball bearings are compared and verified by experiments, and the results of improved algorithm show good agreement with the experiments results.

Highlights

The angular contact ball bearing has a simple structure, the internal force and motion relationship become complicated due to the gyroscopic moment and centrifugal force at high speed [1]
E J-H model consists of a series of deformed geometric equations, rolling element equilibrium equations, and inner ring equilibrium equations, which form a high-dimensional nonlinear equation [12]. e system consists of a total of 4Z + 2 nonlinear equations [1]
Kurvinen et al [15] studied the method of solving the dynamic characteristics of angular contact bearings without considering gyroscopic moment and centrifugal force

Summary

Introduction

The angular contact ball bearing has a simple structure, the internal force and motion relationship become complicated due to the gyroscopic moment and centrifugal force at high speed [1]. Wang et al [17] studied the modeling and dynamic characteristics of angular contact bearings under axial, radial, and moment loads simultaneously These methods effectively improve the convergence of the original J-H method, they do not fundamentally reduce the computational complexity of the model. Fang et al [18] simplified the calculation model by deriving the internal balance equation of the bearing, but the solution still uses the Newton-Raphson method These algorithms have proved to be effective in solving nonlinear systems of equations [1, 19], there are still some shortcomings such as high dependence on initial values, slow convergence speed, and being easy to fall into premature convergence and early convergence when solving nonlinear equations with large root differences [20].

Establishing a Simplified Calculation Model

Results and Discussion

43.5 Under static condition

Increase with speed

Conclusion