Investigation of relation between singular points and number of limit cycles for a rotor–AMBs system

The relation between singular points and the number of limit cycles is investigated for a rotor-active magnetic bearings system with time-varying stiffness and single-degree-of-freedom. The averaged equation of the system is a perturbed polynomial Hamiltonian system of degree 5. The dynamic characteristics of the unperturbed system are first analyzed for a certain parameter group. The number of limit cycles and their configurations of the perturbed system under eight different parametric groups are obtained and the influence of eight control conditions on the number of limit cycles is studied. The results obtained here will play an important leading role in the study of the properties of nonlinear dynamics and control of the rotor-active magnetic bearings system with time-varying stiffness.