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Research Papers

# Effect of the Inhomogeneity in Races on the Dynamic Behavior of Rolling Bearing

[+] Author and Article Information
Wen-zhong Wang

School of Mechanical Engineering,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: wangwzhong@bit.edu.cn

Sheng-guang Zhang, Zi-qiang Zhao, Si-yuan Ai

School of Mechanical Engineering,
Beijing Institute of Technology,
Beijing 100081, China

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 9, 2014; final manuscript received June 3, 2015; published online October 6, 2015. Assoc. Editor: John Yu.

J. Vib. Acoust 137(6), 061015 (Oct 06, 2015) (19 pages) Paper No: VIB-14-1464; doi: 10.1115/1.4031410 History: Received December 09, 2014; Revised June 03, 2015

## Abstract

This paper develops an analytical model to investigate the effect of inhomogeneity in races on the dynamic behaviors of rolling bearing. The governing differential equations are obtained based on the Hertz contact theory and bearing kinematic equations with the centrifugal force and frictions considered. The surface disturbed displacement caused by inhomogeneities is obtained by the semi-analytical method (SAM) and treated as local surface defect in equations of motion through load–deformation relation. For the first time, the effect of material inhomogeneity on dynamics of rolling bearing is explored. The result shows that the inhomogeneity can make the system motion more complicated. The inhomogeneity in the inner race has a greater influence than in the outer race.

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## Figures

Fig. 1

The displacement of the inner ring under a radial force

Fig. 2

Schematic diagram of defects on race induced by inhomogeneity

Fig. 3

The flowchart of the solving process

Fig. 4

The load of a ball in one period

Fig. 5

The surface disturbed displacement with a 100 μm inhomogeneity at different loads

Fig. 6

Simplified calculation of the surface disturbed displacement: (a) the real case and (b) the simplified case

Fig. 8

Bifurcation diagrams of displacement in y direction changing with different loads: (a) without inhomogeneities and (b) with a cubic inhomogeneity in the inner race

Fig. 9

The bifurcation diagram of displacement in y direction under the load W = 10 N: (a) without inhomogeneities and (b) with a cubic inhomogeneity in the inner race

Fig. 10

The Poincaré maps, phase trajectories, trajectory maps, and spectrums for ni = 400 rpm and Fr = 10 N: (a) without inhomogeneities and (b) with a cubic inhomogeneity in the inner race

Fig. 11

Poincaré maps, phase trajectories, trajectory maps, and spectrums for ni = 1150 rpm and Fr = 10 N: (a) without inhomogeneities and (b) with a cubic inhomogeneity in the inner race

Fig. 12

Poincaré maps, phase trajectories, trajectory maps, and spectrums for ni = 6500 rpm and Fr = 10 N: (a) without inhomogeneities and (b) with a cubic inhomogeneity in the inner race

Fig. 13

Poincaré maps, phase trajectories, trajectory maps, and spectrums for ni = 14,050 rpm and Fr = 10 N: (a) without inhomogeneities and (b) with a cubic inhomogeneity in the inner race

Fig. 14

Bifurcation diagrams of displacement in y direction: (a) no inhomogeneities and (b) the inhomogeneity in the outer race

Fig. 15

The influence of an inhomogeneity in the outer races: (a) 400 rpm; (b) 1150 rpm; (c) 6500 rpm; and (d) 14,050 rpm

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