磁悬浮高速转子系统双频Bode图稳定性分析方法研究

 对于具有强陀螺效应的磁悬浮高速转子系统，转子进动和章动的稳定性是决定系统稳定性的首要因素。为了实现直观鲁棒的进动和章动稳定性设计，针对对称磁悬浮转子系统提出一种基于双频Bode图的进动与章动稳定性分析方法，通过复数变换将实系数双变量转子动力学模型等效为复系数单变量形式，绘制等效开环传递函数的负频和正频Bode图，采用推广的经典频率域稳定性判据进行稳定性判定和稳定裕度分析，为稳定性设计提供了重要基础。实验结果验证了该方法的有效性。

Stability Analysis Method of Magnetically Suspended High-Speed Rotor Based on Two-Frequency Bode Diagram

In magnetically suspended high-speed rotor, the strong gyroscopic effect causes radial rotations of the rotor coupled and leads to precession and nutation, which exhibits different stabilities at different rotor speeds and influences rotor system stability primarily. For direct-viewing and robust stability design, a new stability analysis method based on two-frequency Bode diagram is proposed to discriminate precession and nutation stability of magnetically suspended symmetric high-speed rotor. Complex transformation is introduced and two-variable rotor dynamics model with real-coefficient is converted to equivalent single variable form with complex-coefficient, thus the Bode diagrams of equivalent open-loop transfer function are plotted within both negative and positive frequency fields. Subsequently, classic frequency field stability criterion is generalized to two-frequency Bode diagram, and precession and nutation stability and its margins are analyzed, which provides important foundation for stability design. Relevant experiments verified the benefits of the above-mentioned method.