Abstract
The asymptotic perturbation method is used to analyze the nonlinear vibrations and chaotic dynamics of a rotor-active magnetic bearing (AMB) system with 16-pole legs and the time-varying stiffness. Based on the expressions of the electromagnetic force resultants, the influences of some parameters, such as the cross-sectional area Aα of one electromagnet and the number N of windings in each electromagnet coil, on the electromagnetic force resultants are considered for the rotor-AMB system with 16-pole legs. Based on the Newton law, the governing equation of motion for the rotor-AMB system with 16-pole legs is obtained and expressed as a two-degree-of-freedom system with the parametric excitation and the quadratic and cubic nonlinearities. According to the asymptotic perturbation method, the four-dimensional averaged equation of the rotor-AMB system is derived under the case of 1 : 1 internal resonance and 1 : 2 subharmonic resonances. Then, the frequency-response curves are employed to study the steady-state solutions of the modal amplitudes. From the analysis of the frequency responses, both the hardening-type nonlinearity and the softening-type nonlinearity are observed in the rotor-AMB system. Based on the numerical solutions of the averaged equation, the changed procedure of the nonlinear dynamic behaviors of the rotor-AMB system with the control parameter is described by the bifurcation diagram. From the numerical simulations, the periodic, quasiperiodic, and chaotic motions are observed in the rotor-active magnetic bearing (AMB) system with 16-pole legs, the time-varying stiffness, and the quadratic and cubic nonlinearities.
Highlights
As a kind of new support device, active magnetic bearings (AMBs) can realize the active control and have many advantages, including little friction, absent lubrication, high rotatory speed, extreme working conditions, and better dynamic characteristics
It can be observed that the rotorAMB system is modeled as a two-degree-of-freedom nonlinear dynamic system. e four-dimensional averaged equation of the two-degree-of-freedom system is obtained though the asymptotic perturbation method under the case of 1 : 1 internal resonance and 1 : 2 subharmonic resonances. e stability of the steady-state solutions of the modal amplitudes for the rotor-AMB system with 16-pole legs is investigated under different parameters by using the frequency-response curves. e influences of the external excitation on nonlinear dynamic behaviors of the rotorAMB system with 16-pole legs are numerically studied
It is found that the occurrence of the periodic, quasiperiodic, and chaotic motions depends on the magnitude of the external excitation in the rotor-AMB system with 16-pole legs and the time-varying stiffness under certain parameter conditions
Summary
As a kind of new support device, active magnetic bearings (AMBs) can realize the active control and have many advantages, including little friction, absent lubrication, high rotatory speed, extreme working conditions, and better dynamic characteristics. Zhang et al [26, 27] investigated the transient and steady nonlinear dynamic responses and the global bifurcations and chaos of a rotor-active magnetic bearing system with the time-varying stiffness. There are many investigations focusing on the nonlinear dynamics of the rotor-AMB systems with 8-pole legs, but few researchers make contribution to a rotor-AMB system with 16-pole legs, the time-varying stiffness, and the quadratic and cubic nonlinearities. Is paper investigates the nonlinear and chaotic dynamics of a rotor-AMB system with 16-pole legs, the time-varying stiffness, and the quadratic and cubic nonlinearities by using the asymptotic perturbation method [6,7,8,9]. It can be concluded that the parameter b14 related to the eccentricity of the rotor in the AMB system has significant influences on the vibration states of the rotor-AMB system with 16-pole legs, and the influences should be considered in the structural design and optimization
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
