Resonance behavior of a rotor-active magnetic bearing with time-varying stiffness

The non-linear dynamic behavior of a rigid disc-rotor supported by active magnetic bearings (AMB) is investigated, without gyroscopic effects. The rotor-AMB system is subjected to a periodically time-varying stiffness. The simultaneous primary resonance case is considered and examined. The vibration of the rotor is modeled by a coupled second-order non-linear ordinary differential equations with quadratic and cubic non-linearities. Their approximate solutions are sought applying the method of multiple scales. The steady-state response and the stability of the system at the simultaneous primary resonance case for various parameters are studied numerically, applying the frequency response function method. It is found that different shapes of chaotic motion exist, which are determined using phase-plane method. It is also shown that the system parameters have different effects on the non-linear response of the rotor. For steady-state response, however, multiple-valued solutions, jump phenomenon, hardening and softening non-linearity occur. Results are compared to previously published work.