Periodic and Chaotic Motions of a Rotor-Active Magnetic Bearing with Quadratic and Cubic Terms and Time-Varying Stiffness
- 414 Downloads
In this paper, we use the asymptotic perturbation method to investigate nonlinear oscillations and chaotic dynamics in a rotor-active magnetic bearings (AMB) system with 8-pole legs and the time-varying stiffness. The stiffness in the AMB is considered as the time varying in a periodic form. Because of considering the weight of the rotor, the formulation on the electromagnetic force resultants includes the quadratic and cubic nonlinearities. The resulting dimensionless equations of motion for the rotor-AMB system with the time-varying stiffness in the horizontal and vertical directions are a two-degree-of-freedom nonlinear system with quadratic and cubic nonlinearities and parametric excitation. The asymptotic perturbation method is used to obtain the averaged equations in the case of primary parametric resonance and 1/2 subharmonic resonance. It is found that there exist period-3, period-4, period-6, period-7, period-8, quasiperiodic and chaotic modulated amplitude oscillations in the rotor-AMB system with the time-varying stiffness. It is seen from the numerical results that there are the phenomena of the multiple solutions and the soft-spring type and the hardening-spring type in nonlinear frequency-response curves for the rotor-AMB system. The parametric excitation, or the time-varying stiffness produced by the PD controller is considered to be a controlling force which can control the chaotic response in the rotor-AMB system to a period n motion.
Key wordsPD controller periodic and chaotic motions rotor-active magnetic bearings the asymptotic perturbation method time-varying stiffness
Unable to display preview. Download preview PDF.
- 1.Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, Wiley-Interscience, New York, 1979.Google Scholar
- 5.Zhang, W., ‘Further studies for nonlinear dynamics of one dimensional crystalline beam’, Acta Physica Sinica (Overseas Edition) 5, 1996, 409–422.Google Scholar
- 6.Wang, K. W. and Lai, J. S., ‘Parametric control of structural vibrations via adaptable stiffness dynamic absorbers’, ASME Journal of Vibration and Acoustics 118, 1996, 41–47.Google Scholar
- 7.Zhang, W. and Zu, J. W., ‘Nonlinear dynamic analysis for a rotor-active magnetic bearing system with time-varying stiffness, Part I. Formulation and local bifurcation’, in Proceedings of 2003 ASME International Mechanical Engineering Congress & Exposition, Washington DC, November 16–21, 2003, ASME, New York, 2003, pp. 631–640.Google Scholar
- 9.Virgin, L. N., Walsh, T. F., and Knight, J. D., ‘Nonlinear behavior of a magnetic bearing system’, ASME Journal of Engineering for Gas Turbines and Power 117, 1995, 582–588.Google Scholar
- 11.Wang, X. and Noah, S., ‘Nonlinear dynamics of a magnetically supported rotor on safety auxiliary bearings’, ASME Journal of Vibration and Acoustics 120, 1998, 596–606.Google Scholar
- 19.Ye, M., Sun, Y. H., Zhang, W., Zhan, X. P., and Ding, Q., ‘Nonlinear oscillations and chaotic dynamics of an antisymmetric cross-ply laminated composite rectangular thin plate under parametric excitation’, International Journal of Bifurcations and Chaos, in press.Google Scholar
- 20.Wen, B. C., Gu, J. L., Xia, S. B., and Wang, Z., Advanced Dynamics of Rotor, China Machine Industry Press, Beijing, 2000.Google Scholar
- 21.Siegwart, R., Design and Application of Active Magnetic Bearing (AMB) for Vibration Control, von Karman Institute Fluid Dynamics Lecture Series 1992-06, Vibration and Rotor Dynamics, 1992.Google Scholar
- 22.Nusse, H. E. and Yorke, J. A., Dynamics: Numerical Explorations, Springer-Verlag, New York, Berlin, 1997.Google Scholar