磁悬浮轴承-转子系统的分岔与混沌特性

Bifurcations and Chaos of an Active Magnetic Bearing-rotor System

研究磁悬浮轴承-转子系统主共振情形时的非线性动力学行为。由Taylor级数展开得到非线性电磁力的表达式。用Lung-Kutta法计算系统的运动响应。借助Poincare影射和Lyapunov指数对系统的运动形态进行分析。结果发现了在主共振情形下系统中由环面破裂产生的混沌现象及之后的由倍周期分岔导致的混沌现象。

The nonlinear dynamical behaviours of an active magnetic bearing-rotor system were investigated by numerical simulation. Using a Taylor series, the moving differential equations of above system were simplified into simple forms only with lower nonlinear terms. The response was obtained by Lung-Kutta method. To analyze the moving charaters of the system, some Poincare maps were given, and several Lyapunov index numbers were calculated. The results show that there exists chaos induced by both ring crack and double-period bifurcation;the complicatied behaviors in primary resonance may be avoid by adjusting some structural parameters.