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Global bifurcations and chaos for a rotor-active magnetic bearing system with time-varying stiffness

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  • Zhang, W.
  • Zu, J.W.
  • Wang, F.X.

Abstract

In this paper, we investigate the global bifurcations and chaotic dynamics in the rotor-active magnetic bearings (AMB) system with 8-pole legs and time-varying stiffness. From the averaged equation obtained in another paper, the theory of normal form is applied in this paper to find the explicit formulas of normal forms associated with a double zero and a pair of pure imaginary eigenvalues. Since the normal form obtained here is not the simplest one, the methods of choosing other complementary space and utilizing the inner product are presented to further reduce the normal form and obtain a simpler normal form. Based on simpler the normal form obtained above, a global perturbation method is utilized for the analysis of global bifurcations and chaotic dynamics of the rotor-AMB system. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Silnikov type single-pulse homoclinic orbit in the averaged equation of the rotor-AMB system with the time-varying stiffness. These results indicate that the chaotic motions can occur in the rotor-AMB system with time-varying stiffness. Numerical simulations verify the analytical predictions. The jumping and catastrophic phenomena of the amplitude for the chaotic oscillations in the system are also found by using numerical simulations.

Suggested Citation

  • Zhang, W. & Zu, J.W. & Wang, F.X., 2008. "Global bifurcations and chaos for a rotor-active magnetic bearing system with time-varying stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 586-608.
    • Handle: RePEc:eee:chsofr:v:35:y:2008:i:3:p:586-608
    DOI: 10.1016/j.chaos.2006.05.095
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    Cited by:

    1. Wang, Xia & Chen, Fangqi, 2012. "Global dynamics of two coupled parametrically excited van der Pol oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1551-1571.
    2. Zhang, Wei & Zu, Jean W., 2008. "Transient and steady nonlinear responses for a rotor-active magnetic bearings system with time-varying stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1152-1167.
    3. Inayat-Hussain, Jawaid I., 2009. "Geometric coupling effects on the bifurcations of a flexible rotor response in active magnetic bearings," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2664-2671.
    4. Cao, D.X. & Zhang, W., 2008. "Global bifurcations and chaotic dynamics for a string-beam coupled system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 858-875.

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