基础摆动条件下主动电磁轴承-柔性转子系统的稳定性

与基础平动不同，基础摆动不仅会给转子系统产生额外的激励力，而且还会改变转子系统的阻尼及刚度特性，对系统的稳定性产生影响。以电磁轴承支承的柔性转子系统为例，研究了基础摆动条件下转子系统的稳定性。首先，用有限元法建立了基础摆动条件下电磁轴承–柔性转子系统的动力学模型，然后基于Routh-Hurwitz准则推导了基础恒定摆动条件下转子系统的稳定性条件，并用特征根轨迹进行分析。之后，基于Floquet理论研究了基础正弦摆动对电磁轴承柔性转子系统稳定性的影响，得到了系统的稳定性边界，并利用转子系统响应进行了验证。最后，研究了PID控制器参数对基础摆动条件下电磁轴承–柔性转子系统稳定性的影响，针对基础正弦摆动，提出了使用相位补偿器补偿转子系统稳定性的方法。研究结果表明，基础恒定摆动条件下，主动柔性转子系统的稳定性与摆动的幅值有关；基础正弦摆动条件下，转子系统的稳定性与摆动的幅值和频率有关。合理地选择PID控制器的参数能够改善转子系统的稳定性。PID控制器串联相位补偿器，对于基础正弦摆动条件下电磁轴承–柔性转子系统的稳定性具有良好的补偿效果。

Stability of Active Magnetic Bearing Flexible Rotor System under Base Swing Condition

Different from the base translational motion, the base swing motion not only generates additional load in a rotor system, but also changes its damping and stiffness, thereby affecting its stability. Taking the flexible rotor system supported by active magnetic bearings as an example, the stability of the rotor system under the base swing motion was studied. The dynamic model was firstly established by the finite element method. Then the stability of the rotor system under constant swing base motion was derived with Routh-Hurwitz and analyzed using the root locus. After that, based on Floquet theory, the influence of sinusoidal swing base motion on the system stability was studied, and the stability boundary was obtained, which was verified by the response of the rotor system. Finally, the effect of the PID controller parameters on the system stability under the base swing motion was studied. For the sinusoidal swing motion condition, the phase compensator was proposed to compensate the system stability. The results show that the system stability is related to the motion amplitude under the constant swing base motion, and related to both the amplitude and frequency under the sinusoidal swing motion. Reasonable selecting the parameters of the PID controller will improve the system stability. The phase compensator has a good effect on the system stability under the sinusoidal base swing motion.