Nonlinear behavior of a rotor-AMB system under multi-parametric excitations
- 150 Downloads
A rotor-active magnetic bearing (AMB) system subjected to a periodically time-varying stiffness with quadratic and cubic nonlinearities under multi-parametric excitations is studied and solved. The method of multiple scales is applied to analyze the response of two modes of a rotor-AMB system with multi-parametric excitations and time-varying stiffness near the simultaneous primary and internal resonance. The stability of the steady state solution for that resonance is determined and studied using Runge-Kutta method of fourth order. It is shown that the system exhibits many typical non-linear behaviors including multiple-valued solutions, jump phenomenon, hardening and softening non-linearities and chaos in the second mode of the system. The effects of the different parameters on the steady state solutions are investigated and discussed also. A comparison to published work is reported.
KeywordsRotor-active magnetic bearing Time-varying stiffness Multi-parametric excitations Stability Multiple-valued solutions Jump phenomenon
Unable to display preview. Download preview PDF.
- 1.Zhang W, Zu JW (2003) 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 and exposition, Washington (DC), November 16–21, 2003. ASME, New York, pp 631–640 Google Scholar
- 14.Francesco S (2009) Rotor whirl damping by dry friction suspension systems. Meccanica 43:577–589 Google Scholar
- 18.Eissa M, Amer YA, Hegazy UH, Sabbah AS (2006) Dynamic behavior of an AMB/supported rotor subject to parametric excitation. ASME J Vib Acoust 182:646–652 Google Scholar
- 19.Eissa M, Hegazy UH, Amer YA (2008) A time-varying stiffness rotor-active magnetic bearings under combined resonance. J Appl Mech 75:1–12 Google Scholar
- 21.Amer YA, Hegazy UH (2008) A time-varying stiffness rotor-active magnetic bearings under parametric excitation. J Mech Eng Sci Part C 223:447–458 Google Scholar
- 22.Nayfeh AH (1991) Introduction to perturbation techniques. Wiley-Interscience, New York Google Scholar
- 24.Yakowitz S, Szidaouszky F (1992) An introduction to numerical computation. Macmillan, New York Google Scholar
- 25.Isaacson E, Keller H (1994) Analysis of numerical methods. Dover, New York Google Scholar