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

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.

Radial Versus Cartesian Control Strategies to Stabilize the Nonlinear Whirling Motion of the Six-Pole Rotor-AMBs

“…(2), we get According to the schematic diagram of the 6-pole Rotor-AMBs given in Fig. 1a, the net electromagnetic forces in and directions after expanding denominators of Eqs (6) using Mclaurin series up to the third-order approximation, can be expressed as follows [1][2][3][4][5][6][7][8][9][10][11][12][13][14]: This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.…”

“…Therefore, AMBs is an inherently nonlinear system, where every design for AMBs has its own dynamical behaviors. Therefore, many research articles have been dedicated to explore the nonlinear dynamics for different configurations of Rotor-AMBs [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Ji et al [1] explored the nonlinear dynamical behaviors of the four-pole Rotor-AMBs.…”

“…On the other hand, many papers have been dedicated for lateral vibration analysis and control of the 16-pole Rotor-AMBs. Zhang et al [10][11][12][13] explored the nonlinear dynamics of the 16-pole rotor AMBs with time varying stiffness. They applied the multiple time scales to obtain the amplitudephase modulation equations at primary and subharmonic resonance cases.…”

Control Performance, Stability Conditions, and Bifurcation Analysis of the Twelve-Pole Active Magnetic Bearings System

“…The dynamical characteristics and motion bifurcation of the sixteen-pole AMBS system were explored under different control algorithms [17][18][19][20][21][22][23]. Saeed et al [17,18] introduced a detailed investigation for the sixteen-pole system with constant stiffness coefficients.…”

“…The authors reported that the rotor system has quartic stable periodic motions in the case of Cartesian control, while the system behaves like a Duffing oscillator with a hardening spring characteristic at the radial control case. Zhang and his team introduced a detailed investigation for the sixteen-pole AMBS' having time-varying stiffness coefficients [19][20][21][22][23]. The capability of the active magnetic bearings system on generating a controllable magnetic attractive force without physical contact with the rotor has attracted scientists and engineers to employ the AMBS with some control algorithms to serve as an adaptive actuator that can be Appl.…”