Elasto-Plastic Analysis for Static and Dynamic Performance of Rolling Element Bearings

doi:10.13438/j.cnki.jdzk.2019.05.007

Abstract

Abstract:

Aiming at the status quo of research in the elasto-plastic mechanical behavior of rolling bearings, taking deep groove ball bearings as an example, a semi-analytical model was established to study the elasto-plastic mechanical behavior of rolling bearings. By introducing a mixed strain hardening yield criterion which is related to spherical stress tensor, the model established an elasto-plastic incremental constitutive equation for mixed hardening materials. The model used Hertz contact theory to determine the relationship between the load exerted on the inner and outer rings. And from the symmetry between the inner and outer rings, the equilibrium equations, as well as the corresponding deterministic conditions for a quarter of the outer ring of the bearings were obtained in the orthogonal curvilinear coordinate system. And then the finite difference method, as well as Newmark-β approach, was applied comprehensively to find an iterative solution of related problems. The numerical results show that the elasto-plastic model can more accurately describe the mechanical properties of rolling bearings; the traditional elastic model might overestimate the stiffness of bearings; the load weight, bearing dimensions and plastic properties of materials are all important factors that should be considered in the design of bearings.

Key words: deep groove ball bearings, Hertz' contact theory, elasto-plastic, static and dynamic performance

BI Rengui, QIAN Ping, YAN Can, YANG Daiyun. Elasto-Plastic Analysis for Static and Dynamic Performance of Rolling Element Bearings[J]. Journal of Jishou University（Natural Sciences Edition), DOI: 10.13438/j.cnki.jdzk.2019.05.007.

References

[1] 刘泽九.滚动轴承应用手册[M].第3版.北京：机械工业出版社，2014.
[2] HARRIS TEDRIC A, KOTZALAS MICHAEL N. Rolling Bearing Analysis[M]. New York: John Wiley and Sons, 2001.
[3] JOHNSON K L. Contact Mechanics[M]. Cambridge: Cambridge University Press, 1987.
[4] JONES A B. A General Theory for Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions[J]. Journal of Basic Engineering, 1960, 82(2): 309-320.
[5] HARRIS TEDRIC A. An Analytical Method to Predict Skidding in High Speed Roller Bearings[J]. ASLE Transactions, 1966, 9(3): 229-241.
[6] RUMBARGER J H, FILETTI E G, GUBERNICK D. Gas Turbine Engine Mainshaft Roller Bearing-System Analysis[J].ASME Journal of Lubrication Technology, 1973, 95(4): 401-416.
[7] WALTERS C T. The Dynamics of Ball Bearings[J]. Journal of Lubrication Technology, 1971, 93(1): 1-10.
[8] HARSHA S P. Nonlinear Dynamic Analysis of Rolling Element Bearings Due to Cage Run-Out and Number of Balls[J]. Journal of Sound and Vibration, 2006, 289(1/2): 360-381.
[9] 汪久根,王庆九,章维明.滚动轴承动力学的研究[J].轴承,2007(3):40-45.
[10] 童宝宏,刘颖,苏荭.滚动轴承动态接触特性数值模拟中若干问题[J].机械工程学报,2012,48(21):116-123.
[11] 刘义亚,李可,陈鹏.基于同步压缩小波变换的滚动轴承故障诊断[J].中国机械工程,2018,29(5):585-590.
[12] SCHMIDT S, HEYNS P S, GRYLLIAS K C. A Discrepancy Analysis Methodology for Rolling Element Bearing Diagnostics Under Variable Speed Conditions[J]. Mechanical Systems and Signal Processing, 2019, 116: 40-61.
[13] KUMAR ANIL, KUMAR RAJESH. Role of Signal Processing, Modeling and Decision Making in the Diagnosis of Rolling Element Bearing Defect: A Review[J]. Journal of Nondestructive Evaluation, 2019, 38(1): 5.
[14] 梁华.滚动轴承的失效分析[J].理化检验-物理分册,2005,41(s1):99-103.
[15] BI Rengui, FU Yiming, TIAN Yanping, et al. Buckling and Postbuckling Analysis of Elasto-Plastic Fiber Metal Laminates[J]. Acta Mechanica Solida Sinica, 2014, 27(1): 73-84.