Nonlinear dynamics and motion bifurcations of 12-pole variable stiffness rotor active magnetic bearings system under complex resonance

In this study, we analyze the nonlinear dynamic characteristics of a 12-pole variable stiffness rotor active magnetic bearings (rotor-AMBs) under intricate resonance conditions. Using the principles of electromagnetic bearings, a model for the 12-pole variable stiffness rotor-AMBs system is developed. Next, the dynamic equations for a two-degree-of-freedom 12-pole variable stiffness rotor-AMBs system are derived, incorporating both quadratic and cubic nonlinearities, through Newton's second law. Considering the primary parametric resonance, 1:1 internal resonance, and 1/2 subharmonic resonance, the multiple time scale perturbation method is applied to derive the average equation of the system. Based on these averaged equations, the characteristics and complex dynamics of the system are analyzed. Finally, MATLAB software is employed for numerical simulations of the 12-pole variable stiffness rotor-AMBs system. The simulation results indicate that the nonlinear control parameters can modify the system's softening and hardening spring behaviors. Varying the parametric excitation amplitude leads to diverse dynamic behaviors, including single-periodic motion, double-periodic motion, and chaotic vibrations.