Saturation-based active controller for vibration suppression of a four-degree-of-freedom rotor–AMB system

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

doi:10.1007/s11071-013-1166-3

Cited by 25 publications

(30 citation statements)

References 22 publications

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“…The nonlinear dynamical behaviors of the cracked Jeffcott-rotor system are analyzed numerically utilizing the bifurcation diagram for the primary, superharmonic, and subharmonic resonance cases. The numerical integrations for the system Equations (13) and (14) are performed utilizing the standard Matlab solver ODE45. The bifurcation diagrams are obtained via the temporal simulation of the system response up to t = 6000, discarding the interval 0 ≤ t ≤ 400, to get the steady-state motion [53][54][55][56].…”

Section: Numerical Analysis Results and Discussionmentioning

confidence: 99%

“…Equations (13) and (14) are analyzed utilizing the multiple scales perturbation method as in Appendix A. It is found that the system resonance conditions are: Introducing the dimensionless parameters…”

Section: Crack-breathing Mathematical Modelmentioning

confidence: 99%

“…Equations (13) and (14) are analyzed utilizing the multiple scales perturbation method as in Appendix A. It is found that the system resonance conditions are: (1) primary resonances (Ω ω 1 and Ω ω 2 ), (2) superharmonic resonances (Ω 2 3 ω 1 and Ω 2 3 ω 2 ), and (3) subharmonic resonances (Ω 2ω 1 and Ω 2ω 2 ).…”

Section: Crack-breathing Mathematical Modelmentioning

confidence: 99%

“…Utilizing perturbation methods [58,59], one can obtain an approximate solutions to Equations (13) and (14) up to the second-order in the form:…”

Section: Appendix Amentioning

confidence: 99%

“…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%

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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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