滚动轴承-转子系统有限元离散建模非线性动力学数值分析

Nonlinear Dynamics Numerical Analysis of Rolling Bearing-rotor System based on Finite Element Modeling

在滚动轴承和转子动力学的基础上,考虑滚动轴承滚动体与内外圈滚道的Hertz弹性接触模型,采用Newmark数值方法对其求解,利用分岔图、Poincaré映射图、频谱图、相图和轴心轨迹图,分析了滚动轴承-转子系统在转速和游隙等参数下的非线性动力响应行为。结果表明,转子系统呈现周期和非周期(拟周期或混沌)响应形式,在倍周期响应区域内有明显的跳变现象,经过混沌区后,转子系统经倍周期分岔进入混沌,后经过阵发性分岔离开混沌;故合理选择转子的工作转速和游隙,降低非线性轴承力引起的非周期振动,可提高系统运行的稳定性。分析结果为定量和定性分析该双转子的稳定性提供了参考依据。

Based on the bearing dynamics and rotor dynamics,considering the nonlinear factors such asHertz elastic contact force and radial clearance between rolling element and inner and outer raceway of rollingbearing. According to Timoshenko beam-axis theory,the finite element discretization model of the bearing-rotorsystem is established and the Newmark numerical method is used to solve the problem. Meanwhile the nonlineardynamic behaviors of the system are illustrated by means of bifurcation diagrams,Poincaré maps,frequencyspectrum diagrams,phase diagrams and orbit plots. The results shows that,the rotor system presents periodicand aperiodic(quasi periodic or chaos) responses. After passing through the chaotic region,the rotor system en-ters into chaos through period doubling bifurcation,and then leaves chaos through paroxysmal bifurcation. Rea-sonable selection of rotor speed and clearance can reduce the non periodic vibration caused by nonlinear bearingforce,which can improve the stability of the system. The analytic results will provide a referenced gist for the dy-namic stability of dual-rotor-rolling-bearing by the quantitative and qualitative analysis.