转子－电磁轴承非线性系统时滞减振研究

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.