Nonlinear dynamics near resonances of a rotor-active magnetic bearings system with 16-pole legs and time varying stiffness

In this paper, we analyze the complicated nonlinear dynamics of rotor-active magnetic bearings (rotor-AMB) with 16-pole legs and the time varying stiffness. The magnetic force with 16-pole legs is obtained by applying the electromagnetic theory. The governing equation of motion for rotor-active magnetic bearings is derived by using the Newton's second law. The resulting dimensionless equation of motion for the rotor-AMB system is expressed as a two-degree-of-freedom nonlinear system including the parametric excitation, quadratic and cubic nonlinearities. The averaged equation of the rotor-AMB system is obtained by using the method of multiple scales when the primary parametric resonance and 1/2 subharmonic resonance are taken into account. From the frequency-response curves, it is found that there exist the phenomena of the soft-spring type nonlinearity and the hardening-spring type nonlinearity in the rotor-AMB system. The effects of different parameters on the nonlinear dynamic behaviors of the rotor-AMB system are investigated. The numerical results indicate that the periodic, quasi-periodic and chaotic motions occur alternately in the rotor-AMB system.