Vibration Control of a Time-Delayed Rotor-Active Magnetic Bearing System by Time-Varying Stiffness

Active magnetic bearing (AMB) can actively control the vibration of the rotor, and its control law plays a key role. In this study, the vibration control of a rotor-AMB system with time delay is studied. The nonlinear vibration equation is derived based on the Newton law considering the time-varying stiffness (TVS) control. The method of multiple scales is applied to obtain the approximate solutions in the case of the primary parametric resonance and 1:1 internal resonance. The results show that the vibration amplitude and stable region are both periodic with respect to time delay. Their period is exactly equal to the rotating period of rotor. Additionally, the eccentricity-response curves are constructed to illustrate the vibration control of the time-varying stiffness. The results show that the time-varying stiffness control suppresses the vibration effectively. At the same time, it is also found that the time-varying stiffness control may cause an increase in vibration amplitude or even instability in small range of unbalance eccentricity. The influence of time delay on the time-varying stiffness control is investigated. It is found that the time-varying stiffness controller exhibits different performance depending on the time delay.