Active magnetic bearing-based tuned controller to suppress lateral vibrations of a nonlinear Jeffcott rotor system

Saeed, Nasser A.; Kamel, M.

doi:10.1007/s11071-017-3675-y

Cited by 43 publications

(25 citation statements)

References 26 publications

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“…Hutterer et al [42] presented a new method for the magnetic bearing system to maintain better dynamic behaviors by using a self-sensing structure. Saeed and Kamel [43] gave an active magnetic bearing-based tuned controller to suppress lateral vibrations of a nonlinear Jeffcott rotor system. Wojna et al [44] gave the numerical and experimental study of a double physical pendulum with the magnetic interaction.…”

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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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 influences of the several controller parameters on the system FRC has been taken in to account. In this respect, Saeed and Kamel [10] were studying the whirling activity of a nonlinear Jeffcott rotor model. They were using a tuned PPF absorber to decrease the oscillation of this system.…”

Section: Introductionmentioning

confidence: 99%

The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

Amer¹,

EL-Sayed²,

Abdelwahab³

et al. 2019

J. vibroeng.

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In this paper, we applied three different control methods; Positive Position Feedback (PPF), Integral Resonance Control (IRC) and Nonlinear Integrated Positive Position Feedback (NIPPF) added to a Duffing oscillator system subjected to harmonic force. An analytic solution is introduced using the multiple scales perturbation technique (MSPT) to solve the nonlinear differential equations, which simulate the system with NIPPF controller. Before and after control at the primary and superharmonic resonances, the nonlinear systems' steady-state amplitude and stability are studied and examined. The influences of various parameters of the system after being connected to NIPPF are illustrated. Optimum working conditions for the NIPPF controller are obtained at internal resonance ratio 1:1. A Comparison is also made to validate the closeness between the numerical solution and the analytical perturbative one at time-history and frequency response curves (FRC). Finally, a comparison with the available results in the literature is presented. From this comparison, we find that the best control to the system is via the NIPPF controller.

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“…The authors have obtained the period-1, period-2, period-3, period-8, quasiperiodic, and chaotic responses of the system analytically utilizing the shaft spinning speed as a bifurcation control parameter. Because of the dangerous vibrations on these machines, many research papers investigated the possibility of controlling the oscillations of such systems [13][14][15][16][17][18][19]. In addition, more advanced control techniques that can be applied in future work can be found in references [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Periodic, Quasi-Periodic, and Chaotic Motions to Diagnose a Crack on a Horizontally Supported Nonlinear Rotor System

2020

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This work aims to diagnose the crack size of a nonlinear rotating shaft system based on the qualitative change of the system oscillatory characteristics. The considered system is modeled as a two-degree-of-freedom horizontally supported nonlinear Jeffcott rotor system. The influence of the crack size on the system whirling motion for the primary, superharmonic, and subharmonic resonance cases are investigated utilizing the bifurcation diagram, Poincaré map, frequency spectrum, and whirling orbit. The obtained numerical results revealed that the cracked system whirling motion is subjected to a continuous qualitative change as the crack size increases for the superharmonic resonance case, where the system can exhibit period-1, period-2, quasi-periodic, period-3, period-doubling, chaotic, and period-2 motions, sequentially. In addition, an asymmetry is observed in the system whirling orbit due to both the shaft weight and shaft crack. Moreover, it is found that the disk eccentricity does not affect the nature of these motions. Accordingly, we illustrated a simple method to diagnose the existence of such a crack and to quantify its size via monitoring the system lateral vibrations at the superharmonic resonance. Finally, all the obtained numerical results are concluded and a comparison with already published work is included.

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Active magnetic bearing-based tuned controller to suppress lateral vibrations of a nonlinear Jeffcott rotor system

Cited by 43 publications

References 26 publications

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

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

The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

Periodic, Quasi-Periodic, and Chaotic Motions to Diagnose a Crack on a Horizontally Supported Nonlinear Rotor System

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