滚动轴承转子系统不对中-碰摩耦合故障非线性动力学分析

为了获取转子系统不对中-碰摩耦合故障下的动力学特性,通过拉格朗日待定乘子法建立了在完整约束下滚动轴承转子系统非线性动力学微分方程,采用龙格库塔数值法研究了不对中-碰摩耦合故障下系统的动力学响应,采用时域图、轴心轨迹图、分叉图、Poincare截面图和FFT谱图分析了不对中度、碰摩刚度和碰摩间隙对转子振动响应的影响。分析结果表明:不对中度的增大会使系统1倍频振动响应增大,也会产生2倍、4倍等偶数倍频,同时出现与VC(Varying Compliance)频率之间的组合频率响应。在低转速下,碰摩刚度和碰摩间隙对转子系统的影响较小;在高转速下,较小的碰摩刚度和较大的碰摩间隙会缓解系统的非线性行为。

Nonlinear dynamics of a rotor-ball bearing system with misalignment-rubbing coupled faults

In order to obtain the dynamic characteristics of rotor system under misalignment-rubbing coupling fault, the nonlinear dynamic differential equation of rolling bearing rotor system under holonomic constraints was established by Lagrangian undetermined multiplier method. The dynamic response of the system under misalignment-rubbing coupling fault was studied by Runge-Kutta numerical method. Time domain diagram, axis orbit diagram, bifurcation diagram, Poincare section diagram and FFT spectrum were used to analyze the effects of misalignment, rubbing stiffness and clearance on the vibration response of the rotor. The analysis results show that the misalignment increase will increase the vibration response of the system with 1-octave,and produce even-octave such as 2-fold and 4-fold, and the combined frequency response with VC (varying compliance) frequency at the same time. At low speed, the rubbing stiffness and clearance have little influence on the rotor system; at high speed,smaller rubbing stiffness and larger rubbing clearance would alleviate the nonlinear behavior of the system.