Nonlinear vibration of a rotor-active magnetic bearing system with 16-pole legs

In this paper, the nonlinear dynamics of a rotor-active magnetic bearing system with 16-pole legs and the time varying stiffness is investigated. The magnetic forces are obtained through an electromagnetic theory. The motion governing equation is derived by using Newton law. The resulting dimensionless equation of motion for the rotor-AMB system with 16-pole legs and the time varying stiffness is presented with the two-degree-of-freedom system including parametric excitation, the quadratic and cubic nonlinearities. The averaged equations of the rotor-AMB system are obtained by using the method of multiple scales under the case of the primary parametric resonance and 1/2 sub-harmonic resonance. The numerical results show that there exist the periodic, quasi-periodic and chaotic motions in the rotor-active magnetic bearing system. Since the weight of the rotor effect the system, it is also found that there are the different shapes of motion on the two directions of the rotor-AMB system. The parametric excitation, or the time-varying stiffness produced by the PD controller has great impact on the system. Thus, the complicated dynamical response in the rotor-AMB system can be controlled through adjusting the parametric excitation.