非线性径向主动电磁轴承-转子系统的耦合动力学特性及稳定性

研究径向主动电磁轴承支承的不对称转子系统的动力行为及稳定性。转子模型中考虑了陀螺效应，结合分散PID(pmponional integral differential)控制器方程和转子运动方程，形成系统方程。将预估—校正机理和Newton-Raphson方法相结合，给出一种径向主动电磁轴承—转子系统线性失稳转速即Hopf分岔点所对应转速的计算方法。基于打靶法及将预估—校正机理和打靶法相结合形成的一种轨迹预测追踪的延续算法，研究系统非线性不平衡周期响应及稳定性边界。结合Floquet分岔理论研究随系统控制参数改变径向主动电磁轴承—转子系统周期运动的局部稳定性和分岔行为。

STABILITY AND COUPLING DYNAMIC BEHAVIORS OF NONLINEAR JOURNAL ACTIVE ELECTROMAGNETIC BEARING-ROTOR SYSTEM

Stability and coupling dynamic behaviors of a journal active electromagnetic bearing rotor system are analyzed. The effects of gyroscope can be taken into consideration in the model of the rotor. The system equations are formulated by combining the equations of the motion of the rotor and the equations of the decentralized PID(proportional integral differential) controllers. A method consisting of a predictor corrector mechanism and Netwon Raphson method is presented to calculate critical speed corresponding to Hopf bifurcation point of the system. A continuation of periodic motions method,combining a predictor corrector mechanism to shooting method, is presented. The nonlinear unbalanced periodic motions and their stability margins are obtained by shooting method and the established continuation of periodic motions method. The local stability and bifurcation behaviors of the system with the change of control parameters are obtained by the Floquet theory. The numerical examples show that the schemes of this study not only save computing efforts greatly but also have good precision.