Time-delayed control to suppress the nonlinear vibrations of a horizontally suspended Jeffcott-rotor system

Saeed, Nasser A.; El-Ganaini, W. A.

doi:10.1016/j.apm.2017.02.019

Cited by 50 publications

(27 citation statements)

References 25 publications

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“…Inayat-Hussain [34] discussed the geometric coupling effect on the bifurcations of a rotor response in the active magnetic bearings using numerical methods. Saeed and El-Ganaini [35] investigated the time-delayed control to suppress the nonlinear vibrations of a horizontally suspended Jeffcott rotor system. Ghazavi and Sun [36] studied the bifurcation onset delay in the magnetic bearing systems by the timevarying stiffness.…”

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 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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“…The authors reported that timedelay can enhance the control performance at specific values of the loop-delay. Saeed et al [13][14][15] applied the time-delayed position-velocity feedback controller to suppress the primary resonance vibrations of nonlinear dynamical systems. The authors explained a simple technique to design the optimum values of the loop-delays to enhance the controller's efficiency.…”

Section: Introductionmentioning

confidence: 99%

Time-Delayed Nonlinear Feedback Controllers to Suppress the Principal Parameter Excitation

et al. 2020

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Time-delayed control to suppress the nonlinear vibrations of a horizontally suspended Jeffcott-rotor system

Cited by 50 publications

References 25 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

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

Time-Delayed Nonlinear Feedback Controllers to Suppress the Principal Parameter Excitation

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