Periodic and Chaotic Motions of a Rotor-Active Magnetic Bearing with Quadratic and Cubic Terms and Time-Varying Stiffness

Abstract

In this paper, we use the asymptotic perturbation method to investigate nonlinear oscillations and chaotic dynamics in a rotor-active magnetic bearings (AMB) system with 8-pole legs and the time-varying stiffness. The stiffness in the AMB is considered as the time varying in a periodic form. Because of considering the weight of the rotor, the formulation on the electromagnetic force resultants includes the quadratic and cubic nonlinearities. The resulting dimensionless equations of motion for the rotor-AMB system with the time-varying stiffness in the horizontal and vertical directions are a two-degree-of-freedom nonlinear system with quadratic and cubic nonlinearities and parametric excitation. The asymptotic perturbation method is used to obtain the averaged equations in the case of primary parametric resonance and 1/2 subharmonic resonance. 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 the time-varying stiffness. It is seen from the 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. 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.

Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom

“…Ji et al [10] utilized the normal form method to investigate the nonlinear vibrations in the horizontal and vertical directions of a rotor suspended by active magnetic bearings. Zhang and Zhan [11] studied the periodic and chaotic motions of a rotor-AMB system with 8-pole legs and the time-varying stiffness. Kumar et al [12] investigated the effect of the vibration attenuation for a 12-pole radial AMB in the case of the rotor unbalance.…”

Global bifurcations for a rotor-active magnetic bearings system

“…In fact, the system in [10] can model the general electromagnetic suspension system. So, the results in the paper are suitable for more general systems.…”

“…The nonlinear vibrations for the rotor-AMB can described by the following system with time-varying stiffness (more details in [10] …”

“…In this paper, we investigate the homoclinic bifurcation of a rotor-AMB system with time-varying stiffness, The governing nonlinear equation of motion is established for the rotor-AMB system with single-degreeof-freedom and the quadratic and cubic nonlinear terms, which can be found in [10].…”

Nonlinear study of a rotor–AMB system under simultaneous primary-internal resonance

“…An AMB provides an adjustable stiffness and damping, which makes accurate rotor positioning possible. Zhang et al [1][2][3][4][5] established a parametrically excited rotor-AMB system with 8-pole legs and time-varying stiffness. A multi-pulse chaotic dynamics and a new jumping phenomenon are discovered for this rotor-AMB system.…”