Nonlinear oscillations of rotor active magnetic bearings system

Saeed, Nasser A.; Eissa, M.; El-Ganini, W. A.

doi:10.1007/s11071-013-0967-8

Cited by 42 publications

(34 citation statements)

References 16 publications

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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Rotor active magnetic bearings system is the most efficient supporting technique of high-speed rotating machinery. This work aims to explore the dynamical behaviors of the 6-pole rotor active magnetic bearings system for the first time. Two different control strategies are introduced to mitigate the considered system lateral vibrations and the corresponding whirling motions. The first control technique (Radial control) is suggested such that the attractive magnetic force in each pole is proportional to both the radial displacement and radial velocity of the rotating disk toward that pole. The second control strategy (Cartesian control) is proposed such that the controlled magnetic force in each pole is designed to be proportional to both the cartesian displacement and cartesian velocity of the rotating disk in two perpendicular directions. Based on the proposed control strategies, two nonlinear dynamical models are derived and then analyzed by applying perturbation methods. Different response-curves and bifurcation diagrams are plotted utilizing the disk spinning-speed and the disk eccentricity as bifurcation control parameters. The main obtained analytical and numerical results illustrated that the considered system can perform a circular forward whirling motion only under the first control technique, while four whirling modes (that are forward whirling , backward whirling, both forward and backward whirling, and oscillation along a straight line) are noticed in the second control method depending on the disk spinning speed. Moreover, it is found that the radial control method is robust against the system instability than the cartesian control one, especially at large disk eccentricity. However, the cartesian control method could exhibit a vibration suppression efficiency higher than the radial control one at small disk eccentricity.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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“…Awrejcewicz and Dzyubak [32] investigated the chaos and saturation phenomena of the vibrations for a rotor supported by the magnetohydrodynamic bearings. Saeed et al [33] applied the method of multiple scales to construct an analytical approximate solution of a rotor-AMB system subjected to the primary resonance and 1 : 1 internal resonance. Inayat-Hussain [34] discussed the geometric coupling effect on the bifurcations of a rotor response in the active magnetic bearings using numerical methods.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

2020

Shock and Vibration

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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.

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“…Ji and Hansen [6] considered the cubic nonlinear term into the magnetic bearing system. In addition, owing to the magnetic bearings having the sophisticated nonlinear characteristics, there are many interesting nonlinear phenomena in systems as given in [7], such as jumping, bifurcation, multisolution, sensitivity to initial conditions, and even chaos. References [8,9] utilized numerical simulation methods to analyze the bifurcation phenomena in active magnetic bearing systems.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter

Wang

Hao³

et al. 2019

Complexity

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In this paper, the Hopf bifurcation and control of the magnetic bearing system under an uncertain parameter are investigated. Firstly, the two-degree-of-freedom magnetic bearing system model with uncertain parameter is established. The method of orthogonal polynomial approximation is used to obtain the equivalent magnetic bearing model which is deterministic. Secondly, combining mathematical analysis tools and numerical simulations, the Hopf bifurcation of the equivalent model is analyzed. Finally, a hybrid feedback control method (linear feedback control method combined with nonlinear stochastic feedback control method) is introduced to control the Hopf bifurcation behavior of the magnetic bearing system.

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Nonlinear oscillations of rotor active magnetic bearings system

Cited by 42 publications

References 16 publications

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

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

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

Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter

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