非线性转子系统碰摩的分岔与混沌研究

以线性项和立方项之和来表示转轴材料的物理非线性因素,建立了具有非线性刚度轴支撑的转子系统局部碰摩的动力学模型,利用数值积分和Poincaré映射方法,对转子系统由于局部碰摩故障导致的非线性动力学行为进行了研究,给出了系统响应随转子转动频率比和偏心量变化的分岔图和最大Lyapunov指数图,以及一些典型的Poincaré截面图、相平面图、轴心轨迹和幅值谱图等,从中发现此类非线性振动系统具有周期、拟周期和混沌等复杂的动力学行为,研究结果为此类系统的安全运行和有效识别转子故障提供了理论参考。

Study on Bifurcation and Chaos Behaviors of Nonlinear Rigidity Rotor System with Rubbing Fault

The dynamic model of the nonlinear rigidity rotor system with rubbing fault was set up, taking the linearity and cube item as the nonlinear physical factors. The nonlinear dynamic behaviors of the vibration system caused by rubbing fault were studied, using the numerical value integral and Poincaré mapping methods. The bifurcation diagram and maximal Lyapunov exponent curves of the response to the changing of frequency ratio were given. Some typical Poincaré maps, phase plane portraits, time history, trajectory of journal centers and amplitude spectra etc. were also given, which indicated that there are doubling periods, approximate periods and chaos behaviors in the rotor system. The conclusions provide theoretic reference for safety run and for identifying the rubbing fault in rotor efficiently.