转子-电磁轴承非线性系统时滞减振研究

电磁轴承具有与转子无接触、可施加主动控制等特性，越来越多地被应用于高速旋转机械的支撑与减振.为了研究转子-电磁轴承系统中时滞的减振作用，在主共振情况下推导了八极电磁轴承支撑的转子非线性振动方程.应用多尺度法获得了振动方程的近似解，并利用Lyapunov方法对解的稳定性进行判定.结果表明，时滞的某些取值会使转子在x和y方向上的振幅相对于无时滞时减小，称之为时滞的“减振区域”,并且x和y方向上“减振区域”不同；通过计算不同比例系数与微分系数下的时滞-振幅曲线，发现比例系数对“减振区域”的范围影响更大；同一时滞量参数不能保证所有转速下均减振，当时滞量选取不合适时，会造成系统失稳；通过计算偏心率-振幅曲线，发现时滞控制能有效降低由于转子不平衡所产生的振幅，并且消除了非线性现象如多值、突跳等，系统稳定性增加.数值模拟验证了解析结果的正确性.

Vibration Suppression of Time Delay in Rotor Magnetic Bearing Nonlinear System

Active magnetic bearing (AMB) has the characteristics of no contact with the rotor and can be applied to active control. It is more and more used in the support and vibration reduction of high-speed rotating machinery. In order to study the vibration suppression of the time delay in the rotor-magnetic bearing system, the nonlinear vibration equation of the rotor supported by the eight-pole legs magnetic bearing is derived based on the primary resonance. The method of multiple scales is applied to obtain the approximate solution of the vibration equation and the stability of the solution is also analyzed by Lya-punov principle. The 'vibration suppression area' of the time delay is defined as the range in which the stable vibration amplitude is less than the amplitude when the time delay is zero. The study found that proportional gain has a greater impact on the 'vibration suppression area' of the time delay relative to derivative gain by the time delay-amplitude curves at different proportional gains and derivative gains. The same time delay cannot guarantee suppressing vibration at all speeds, and if the time delay is not selected properly, it will cause system instability. By calculating the eccentricity-amplitude curves, it is found that the time delay control can effectively reduce the amplitude due to rotor unbalance and eliminate the nonlinear phenomena such as multiple values and jumping, and the system stability increases. Numerical simulations verify the correctness of the analytical results. © 2023 Journal of Dynamics and Control. All rights reserved.