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 level for rotating machinery, may possibly occur due to a gradual degradation of the rotor balance quality during operation.
| Original language | English |
|---|---|
| Pages (from-to) | 912-927 |
| Number of pages | 16 |
| Journal | Chaos, Solitons and Fractals |
| Volume | 31 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 01 Feb 2007 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematics(all)
- Physics and Astronomy(all)
- Applied Mathematics
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Chaos via torus breakdown in the vibration response of a rigid rotor supported by active magnetic bearings. / Inayat-Hussain, Jawaid I.
In: Chaos, Solitons and Fractals, Vol. 31, No. 4, 01.02.2007, p. 912-927.Research output: Contribution to journal › Article
TY - JOUR
T1 - Chaos via torus breakdown in the vibration response of a rigid rotor supported by active magnetic bearings
AU - Inayat-Hussain, Jawaid I.
PY - 2007/2/1
Y1 - 2007/2/1
N2 - 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 due to a gradual degradation of the rotor balance quality during operation.
AB - 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 due to a gradual degradation of the rotor balance quality during operation.
UR - http://www.scopus.com/inward/record.url?scp=33747467199&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33747467199&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2005.10.039
DO - 10.1016/j.chaos.2005.10.039
M3 - Article
AN - SCOPUS:33747467199
VL - 31
SP - 912
EP - 927
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
SN - 0960-0779
IS - 4
ER -