Chaos in the imbalance response of a rigid rotor in active magnetic bearings

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Active magnetic bearings exhibit highly nonlinear characteristics that can be detrimental to the performance of the rotating machinery supported by them. There are several sources of nonlinearity in an active magnetic bearing system, of which the most prominent is the relationship between the forces generated in the electromagnetic actuator and the coil current and the air gap between the rotor and the stator. Cross-coupling between the electromagnetic forces acting in two orthogonal directions that arise due to the geometry of the actuators is also a source of nonlinearity in a magnetic bearing system. 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 level for rotating machinery, may possibly occur with eroded rotors or in the event of a partial or entire blade failure.

Original languageEnglish
Title of host publication12th International Congress on Sound and Vibration 2005, ICSV 2005
Pages3686-3693
Number of pages8
Volume4
Publication statusPublished - 2005
Event12th International Congress on Sound and Vibration 2005, ICSV 2005 - Lisbon, Portugal
Duration: 11 Jul 200514 Jul 2005

Other

Other12th International Congress on Sound and Vibration 2005, ICSV 2005
CountryPortugal
CityLisbon
Period11/07/0514/07/05

Fingerprint

magnetic bearings
rigid rotors
rotors
chaos
vibration
nonlinearity
cross coupling
machinery
electromagnetism
fractals
coils
air currents
actuators
stators
blades
mathematical models
breakdown
routes

All Science Journal Classification (ASJC) codes

  • Acoustics and Ultrasonics

Cite this

Inayat Hussain, J. I. (2005). Chaos in the imbalance response of a rigid rotor in active magnetic bearings. In 12th International Congress on Sound and Vibration 2005, ICSV 2005 (Vol. 4, pp. 3686-3693)
Inayat Hussain, Jawaid Iqbal. / Chaos in the imbalance response of a rigid rotor in active magnetic bearings. 12th International Congress on Sound and Vibration 2005, ICSV 2005. Vol. 4 2005. pp. 3686-3693
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abstract = "Active magnetic bearings exhibit highly nonlinear characteristics that can be detrimental to the performance of the rotating machinery supported by them. There are several sources of nonlinearity in an active magnetic bearing system, of which the most prominent is the relationship between the forces generated in the electromagnetic actuator and the coil current and the air gap between the rotor and the stator. Cross-coupling between the electromagnetic forces acting in two orthogonal directions that arise due to the geometry of the actuators is also a source of nonlinearity in a magnetic bearing system. 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 level for rotating machinery, may possibly occur with eroded rotors or in the event of a partial or entire blade failure.",
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Inayat Hussain, JI 2005, Chaos in the imbalance response of a rigid rotor in active magnetic bearings. in 12th International Congress on Sound and Vibration 2005, ICSV 2005. vol. 4, pp. 3686-3693, 12th International Congress on Sound and Vibration 2005, ICSV 2005, Lisbon, Portugal, 11/07/05.

Chaos in the imbalance response of a rigid rotor in active magnetic bearings. / Inayat Hussain, Jawaid Iqbal.

12th International Congress on Sound and Vibration 2005, ICSV 2005. Vol. 4 2005. p. 3686-3693.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Inayat Hussain JI. Chaos in the imbalance response of a rigid rotor in active magnetic bearings. In 12th International Congress on Sound and Vibration 2005, ICSV 2005. Vol. 4. 2005. p. 3686-3693