Transient and steady nonlinear responses for a rotor-active magnetic bearings system with time-varying stiffness

In this paper, we investigate transient and steady nonlinear dynamics in rotor-active magnetic bearings (AMBs) system with 8-pole legs and the time-varying stiffness. The model of parametrically excited two-degree-of-freedom nonlinear system with the quadratic and cubic nonlinearities is established to explore the periodic and quasiperiodic motions as well as the bifurcations and chaotic dynamics of the system. The method of multiple scales is used to obtain the averaged equations in the case of primary parameter resonance and 1/2 subharmonic resonance. Numerical approach is applied to the averaged equations to find the periodic, quasiperiodic solutions and local bifurcations. It is found that there exist 2-period, 3-period, 4-period, 5-period, multi-period and quasiperiodic solutions in the rotor-AMBs system with 8-pole legs and the time-varying stiffness. The catastrophic phenomena for the amplitude of transient nonlinear oscillations are first observed in the rotor-AMBs system with 8-pole legs and the time-varying stiffness. The procedures of motion from the transient state chaotic motion to the steady state periodic and quasiperiodic motions are also found. The results obtained here show that there exists the ability of auto-controlling transient state chaos to the steady state periodic and quasiperiodic motions in the rotor-AMBs system with 8-pole legs and the time-varying stiffness.