Chaos via torus breakdown in the vibration response of a rigid rotor supported by active magnetic bearings
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Chaos, Solitons & Fractals
Volume 31, Issue 4, February 2007, Pages 912-927
Chaos via torus breakdown in the vibration response of a rigid rotor supported by active magnetic bearings
Author links open overlay panelJawaid I.Inayat-Hussain
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https://doi.org/10.1016/j.chaos.2005.10.039
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Abstract
This work reports on a numerical study undertaken to investigate the response of an imbalanced rigid rotor supported by active magnetic bearings. The mathematical model of the rotor-bearing system used in this study incorporates nonlinearity arising from the electromagnetic force—coil current—air gap relationship, and the effects of geometrical cross-coupling. The response of the rotor is observed to exhibit a rich variety of dynamical behavior including synchronous, sub-synchronous, quasi-periodic and chaotic vibrations. The transition from synchronous rotor response to chaos is via the torus breakdown route. As the rotor imbalance magnitude is increased, the synchronous rotor response undergoes a secondary Hopf bifurcation resulting in quasi-periodic vibration, which is characterized by a torus attractor. With further increase in the rotor imbalance magnitude, this attractor is seen to develop wrinkles and becomes unstable resulting in a fractal torus attractor. The fractal torus is eventually destroyed as the rotor imbalance magnitude is further increased. Quasi-periodic and frequency-locked sub-synchronous vibrations are seen to appear and disappear alternately before the emergence of chaos in the response of the rotor. The magnitude of rotor imbalance where sub-synchronous, quasi-periodic and chaotic vibrations are observed in this study, albeit being higher than the specified imbalance lvel for rotating machinery, may possibly occur due to a gradual degradation of the rotor balance quality during operation