中文摘要：

振动分析是研究主动磁悬浮轴承（Active magnetic bearings,AMB）系统的一个重要部分,但是目前结合控制器以及动态不平衡响应建立的系统数学模型相对较少。通过对高速主动磁悬浮轴承转子系统受力分析,参考所使用的不完全微分PID控制器的频率特性对AMB广义动刚度的影响以及对转子动态不平衡激励响应的影响,建立径向子系统的力学振动方程。通过此振动方程的解,得出AMB系统存在的振动形式。一种是由于系统固有频率存在而产生的自由振动,另一种是由于不平衡响应存在而产生的简谐振动,并解释当两种振动频率相近时系统所产生的拍振现象。通过调节控制电流主动控制作用,可以改变磁悬浮轴承广义动刚度,进而改变系统固有频率,最终起到减弱拍振现象作用。仿真和试验能够验证拍振现象以及改变主动控制作用后的减振效果。此力学模型可为AMB系统不平衡振动补偿算法研究提供仿真平台。

英文摘要：

Vibration analysis plays an important role in the research of active magnetic bearing（AMB） system.However,the established system mathematical models which combine the controller with the dynamic response are relatively few.The vibration equations of radial AMB subsystems are built on the basis of the stress analysis of high speed rotor system,referring the influences of the frequency characteristics of adopted incomplete differential PID controller on the generalized magnetic bearing dynamic stiffness and rotor dynamic unbalance response.The vibration modes existing in AMB system can be obtained by solving the vibration equations.One is free vibration because of the inherent frequency,and the other is harmonic vibration due to unbalanced excitation response.And the produced beat vibration phenomenon is explained when the two kinds of vibration frequency are similar.Through adjusting the control current,the generalized dynamic stiffness of magnetic bearings and as well as the inherent frequency of the system can be changed,thus resulting in the weakening of beat vibration.Simulation and experimental results can verify the ＂beat vibration＂ phenomenon and the damping effect after changing the active control.The mechanical model can provide the simulation platform for the research of vibration compensation algorithm of AMB system.