A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system

作     者：Yulin JIN Zhenyong LU Rui YANG Lei HOU Yushu CHEN 

作者机构：School of AstronauticsHarbin Institute of Technology School of Energy Science and EngineeringHarbin Institute of Technology 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2018年第39卷第3期

页      面：365-378页

核心收录：

学科分类：08[工学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0802[工学-机械工程] 0701[理学-数学] 080101[工学-一般力学与力学基础] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Project supported by the National Basic Research Program(973 Program)of China(No.2015CB057400) the National Natural Science Foundation of China(No.11602070) the China Postdoctoral Science Foundation(No.2016M590277) the Heilongjiang Postdoctoral Financial Assistance(No.LBH-Z16067) 

主　　题：rolling element bearing, Hertzian contact, fractional index cubic polyno-miali rotor ball bearing system 

摘      要：A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.