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Research Papers: Applications

A New Model for the Relationship Between Vibration Characteristics Caused by the Time-Varying Contact Stiffness of a Deep Groove Ball Bearing and Defect Sizes

[+] Author and Article Information
Jing Liu

State Key Laboratory
of Mechanical Transmission;
College of Mechanical Engineering,
Chongqing University,
Chongqing 400044, China

Yimin Shao

State Key Laboratory
of Mechanical Transmission,
Chongqing University,
Chongqing 400044, China
e-mail: ymshao@cqu.edu.cn

W. D. Zhu

Department of Mechanical Engineering,
University of Maryland,
Baltimore County,
Baltimore, MD 21250

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 26, 2014; final manuscript received December 19, 2014; published online March 13, 2015. Assoc. Editor: Zhong Min Jin.

J. Tribol 137(3), 031101 (Jul 01, 2015) (15 pages) Paper No: TRIB-14-1187; doi: 10.1115/1.4029461 History: Received July 26, 2014; Revised December 19, 2014; Online March 13, 2015

Vibration characteristics of a deep groove ball bearing caused by a localized surface defect are greatly affected by defect sizes, such as the length, width, and depth. However, effects of the defect depth, the time-varying contact stiffness between the ball and defect, and the relationship between the time-varying contact stiffness and defect sizes have not been considered in previous defect models. In this work, a new defect model considering a new force–deflection relationship is presented to replace the Hertzian force–deflection relationship to describe the ball-line contact between the ball and defect edge. Both the time-varying displacement impulse and time-varying contact stiffness are considered. The relationship between the time-varying contact stiffness and defect sizes is obtained. Effects of defect sizes on the vibrations of the deep groove ball bearing, especially the defect depth that cannot be described by previous defect models, are investigated. The simulation results are compared with those from the previous defect models. The results show that the model developed can predict a more realistic impulse caused by a localized surface defect for dynamic simulation of the deep groove ball bearing. An experimental investigation is also presented to validate the proposed model.

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Figures

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Fig. 3

A lumped spring-mass model of a ball bearing

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Fig. 4

Flow chart of the solution process

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Fig. 5

(a) Contact FE model of the ball and outer race; (b) the center cross section of the FE model in (a); (c) the FE model of the outer race in defect case 7; (d) the FE model of the outer race in defect case 2; and (e) the FE model of the outer race in defect case 15

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Fig. 2

(a) Contact between a ball and normal race and (b) that between a ball and an edge of a defect

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Fig. 1

Schematic diagrams of localized surface defects on races and their effects on the deflections of a ball: (a) a defect on the inner race and (b) a defect on the outer race

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Fig. 10

(a) Experimental setup and (b) the test ball bearing with a defect on the outer race

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Fig. 11

Comparison of the frequency spectra of the accelerations in the Y direction from the simulation and experiment: (a) simulation result of the normal ball bearing, (b) experimental result of the normal ball bearing, (c) simulation result of the abnormal ball bearing, and (d) experimental result of the abnormal ball bearing

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Fig. 6

Accelerations of the inner race of the bearing in the Y direction for different defect cases from the time-varying displacement impulse models in Ref. [49] (- - -) and Ref. [52] (-•-•-), and the proposed model with (—) and without (…) a defect: (a) defect case 1 (A1 and B1 are the beginning and ending edges of the acceleration response curve from the three models when the ball passes over the defect); (b) defect case 6 (A2 and B2 are the beginning and ending edges of the acceleration response curve from the three models when the ball passes over the defect); and (c) defect case 11 (A3E3F3B3 is the acceleration response curve of the proposed model when the ball passes over the defect, a3b3c3d3 is that of the model in Ref. [49], and a3e3f3d3 is that of the model in Ref. [52] when the ball passes over the defect

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Fig. 7

Spectra of the displacements of the inner race of the bearing in the Y direction for different defect cases from the time-invariant displacement impulse model in Ref. [49] (- - -), the time-varying displacement impulse model in Ref. [52] (-•-•-), and the proposed model with (—) and without (…) a defect: (a) defect case 1; (b) defect case 6; and (c) defect case 11

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Fig. 8

Comparison of evolutions of statistical parameters of accelerations of the inner race of the bearing in the Y direction from the three defect models: (a) RMS values for defect cases 1, 2, and 3; (b) RMS values for defect cases 6, 7, and 8; (c) RMS values for defect cases 11, 12, and 13; (d) the kurtosis for defect cases 1, 2, and 3; (e) the kurtosis for defect cases 6, 7, and 8; and (f) the kurtosis for defect cases 11, 12, and 13. - - -○- - -, the model in Ref. [49]; —□—, the model in Ref. [52]; and —△—, the proposed model

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Fig. 9

Effect of the defect depth on evolutions of statistical parameters of accelerations of the inner race of the bearing in the Y direction for the proposed model: (a) RMS values for defect cases 4, 5, and 2; (b) RMS values for defect cases 9, 10, and 7; (c) RMS values for defect cases 17, 18, and 12; (d) the kurtosis for defect cases 4, 5, and 2; (e) the kurtosis for defect cases 9, 10, and 7; and (f) the kurtosis for defect cases 17, 18, and 12. - - -○- - -, the model in Ref. [49]; —□—, the model in Ref. [52]; and —△—, the proposed model

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