### Abstract

Numerical investigation on the unbalance response of a rigid rotor supported by squeeze-film dampers without centering springs revealed some complex bifurcation features that have not been previously reported in the literature. With the variation of the unbalance parameter (U), the period-1 solution was found to undergo a sequence of period-doubling bifurcations that eventually resulted in chaotic motion. The existence of a period-3 solution, which formed a closed bifurcation curve consisting of a pair of saddle nodes, was for the first time observed in such a system. The chaotic attractor arising from the period-doubling cascade of the period-1 solution, which was observed to co-exist with the period-3 attractor in a narrow range of U values, was eventually annihilated in a collision with the unstable period-3 orbit in a boundary crisis. Similar to the bifurcations of the period-1 solution, the period-3 solution was also found to bifurcate into solutions of period-6 and period-12, which eventually led to chaotic motion. A chaotic attractor was also observed to co-exist with a period-4 orbit. The period-4 orbit was found to undergo a sequence of reverse period-doubling bifurcations resulting in a large amplitude period-1 orbit. The occurrence of non-synchronous and chaotic motion in rotating machinery is undesirable and should be avoided as they introduce cyclic stresses in the rotor, which in turn may rapidly induce fatigue failure. The magnitude of rotor unbalance where non-synchronous and chaotic motion were observed in this study, although higher than the permissible unbalance level for rigid rotating machinery, may nevertheless occur with in-service erosion of the rotor or in the event of a partial or an entire blade failure.

Original language | English |
---|---|

Pages (from-to) | 929-945 |

Number of pages | 17 |

Journal | Chaos, Solitons and Fractals |

Volume | 13 |

Issue number | 4 |

DOIs | |

Publication status | Published - Mar 2002 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematics(all)
- Physics and Astronomy(all)
- Applied Mathematics

### Cite this

*Chaos, Solitons and Fractals*,

*13*(4), 929-945. https://doi.org/10.1016/S0960-0779(01)00068-6

}

*Chaos, Solitons and Fractals*, vol. 13, no. 4, pp. 929-945. https://doi.org/10.1016/S0960-0779(01)00068-6

**Chaos in the unbalance response of a rigid rotor in cavitated squeeze-film dampers without centering springs.** / Inayat-Hussain, Jawaid Iqbal; Kanki, Hiroshi; Mureithi, Njuki W.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Chaos in the unbalance response of a rigid rotor in cavitated squeeze-film dampers without centering springs

AU - Inayat-Hussain, Jawaid Iqbal

AU - Kanki, Hiroshi

AU - Mureithi, Njuki W.

PY - 2002/3

Y1 - 2002/3

N2 - Numerical investigation on the unbalance response of a rigid rotor supported by squeeze-film dampers without centering springs revealed some complex bifurcation features that have not been previously reported in the literature. With the variation of the unbalance parameter (U), the period-1 solution was found to undergo a sequence of period-doubling bifurcations that eventually resulted in chaotic motion. The existence of a period-3 solution, which formed a closed bifurcation curve consisting of a pair of saddle nodes, was for the first time observed in such a system. The chaotic attractor arising from the period-doubling cascade of the period-1 solution, which was observed to co-exist with the period-3 attractor in a narrow range of U values, was eventually annihilated in a collision with the unstable period-3 orbit in a boundary crisis. Similar to the bifurcations of the period-1 solution, the period-3 solution was also found to bifurcate into solutions of period-6 and period-12, which eventually led to chaotic motion. A chaotic attractor was also observed to co-exist with a period-4 orbit. The period-4 orbit was found to undergo a sequence of reverse period-doubling bifurcations resulting in a large amplitude period-1 orbit. The occurrence of non-synchronous and chaotic motion in rotating machinery is undesirable and should be avoided as they introduce cyclic stresses in the rotor, which in turn may rapidly induce fatigue failure. The magnitude of rotor unbalance where non-synchronous and chaotic motion were observed in this study, although higher than the permissible unbalance level for rigid rotating machinery, may nevertheless occur with in-service erosion of the rotor or in the event of a partial or an entire blade failure.

AB - Numerical investigation on the unbalance response of a rigid rotor supported by squeeze-film dampers without centering springs revealed some complex bifurcation features that have not been previously reported in the literature. With the variation of the unbalance parameter (U), the period-1 solution was found to undergo a sequence of period-doubling bifurcations that eventually resulted in chaotic motion. The existence of a period-3 solution, which formed a closed bifurcation curve consisting of a pair of saddle nodes, was for the first time observed in such a system. The chaotic attractor arising from the period-doubling cascade of the period-1 solution, which was observed to co-exist with the period-3 attractor in a narrow range of U values, was eventually annihilated in a collision with the unstable period-3 orbit in a boundary crisis. Similar to the bifurcations of the period-1 solution, the period-3 solution was also found to bifurcate into solutions of period-6 and period-12, which eventually led to chaotic motion. A chaotic attractor was also observed to co-exist with a period-4 orbit. The period-4 orbit was found to undergo a sequence of reverse period-doubling bifurcations resulting in a large amplitude period-1 orbit. The occurrence of non-synchronous and chaotic motion in rotating machinery is undesirable and should be avoided as they introduce cyclic stresses in the rotor, which in turn may rapidly induce fatigue failure. The magnitude of rotor unbalance where non-synchronous and chaotic motion were observed in this study, although higher than the permissible unbalance level for rigid rotating machinery, may nevertheless occur with in-service erosion of the rotor or in the event of a partial or an entire blade failure.

UR - http://www.scopus.com/inward/record.url?scp=0036489533&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036489533&partnerID=8YFLogxK

U2 - 10.1016/S0960-0779(01)00068-6

DO - 10.1016/S0960-0779(01)00068-6

M3 - Article

AN - SCOPUS:0036489533

VL - 13

SP - 929

EP - 945

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

IS - 4

ER -