Studies On Nonlinear Dynamics Of Rotor-Active Magnetic Bearings With Time-Varying Stiffness

Active Magnetic Bearings (AMB) have been widely used in the engineering field, Since most of the components in the AMB system are of nonlinear characteristics, the dynamics in the rotor-AMB system is very complicated. The nonlinear electromagnetic force may cause the large oscillations of the rotor in some parameter regions. Thus, the study on the properties of nonlinear dynamics and the stability for the rotor-AMB system plays an important role in the engineering. In this dissertation, we investigate the nonlinear dynamics in the rotor-AMB system with eight pole legs and sixteen pole legs. We establish the model, and obtain the averaged equations, then apply the numerical approach to acquire the results in these two systems. The major results obtained in this dissertation are as follows. First, a rigid model with two-degree-of-freedom is established after the rotor weight is considered. The formulation on the electromagnetic force results that the equations of motion includes the quadratic and cubic nonlinearities and parametric excitation. Due to the effect of the rotor weight, the equations of motion in the horizontal and vertical directions and the nonlinear properties are different. Then, in order to analyze the nonlinear systems including the quadratic and cubic nonlinearities conveniently, we investigate the nonlinear dynamics of the rotor-active magnetic bearings system in the case of primary parametric resonance-1/2 subharmonic resonances. We use the asymptotic perturbation method to investigate nonlinear oscillations and acquire the averaged equations of a rotor-active magnetic bearings system with 8-pole legs with the time-varying stiffness. Based on the averaged equations, the numerical simulations are utilized to obtain the amplitude-frequency response curve of the rotor-AMB system with 8-pole legs. Numerical approach through a computer software Dynamics is utilized to explore the existence of the periodic and chaotic motions in the rotor-AMB system with the time-varying stiffness. It is found that there exist period-3, period-4, period-6, period-7, period-8, quasiperiodic and chaotic modulated amplitude oscillations in the rotor-AMB system with 8-pole legs with the time-varying stiffness. It is seen from numerical results that there are the phenomena of the multiple solutions and the soft-spring type and the hardening-spring type in nonlinear frequency-response curves for the rotor-AMB system with 8-pole legs with the time-varying stiffness. The parametric excitation, or the time-varying stiffness produced by the PD controller is considered to be a controlling force which can control the chaotic response in the rotor-AMB system to a period n motion.