Dynamics of an AMB-rotor with time varying stiffness and mixed excitations

A rotor- active magnetic bearing (AMB) system with a periodically time-varying stiffness subjected to multi- external, -parametric and -tuned excitations is studied and solved. The method of multiple scales is applied to analyze the response of the two modes of the system near the simultaneous sub-harmonic, super-harmonic and combined resonance case. The stability of the steady state solution near this resonance case is determined and studied applying Lyapunov’s first method. Also, the system exhibits many typical nonlinear behaviors including multi-valued solutions, jump phenomenon, softening nonlinearities. The effects of the different parameters on the steady state solutions are investigated and discussed. Simulation results are achieved using MATLAB 7.0 program.

[1]  Colin H. Hansen,et al.  Approximate solutions and chaotic motions of a piecewise nonlinear–linear oscillator , 2004 .

[2]  A. Nayfeh.  Introduction To Perturbation Techniques , 1981 .

[3]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[4]  Lie Yu,et al.  Effect of Thrust Magnetic Bearing on Stability and Bifurcation of a Flexible Rotor Active Magnetic Bearing System , 2003 .

[5]  David A. Robb,et al.  The dynamics of a cracked rotor with an active magnetic bearing , 2003 .

[6]  M. Eissa,et al.  Nonlinear Behavior of Tuned Rotor-Amb System with Time Varying Stiffness , 2011, Int. J. Bifurc. Chaos.

[7]  J. Zu,et al.  Global bifurcations and chaos for a rotor-active magnetic bearing system with time-varying stiffness , 2008 .

[8]  Y. A. Amer,et al.  A time-varying stiffness rotor-active magnetic bearings system under parametric excitation , 2008 .

[9]  H. Keller,et al.  Analysis of Numerical Methods , 1969 .

[10]  Andrew Y. T. Leung,et al.  Non-linear oscillations of a rotor-magnetic bearing system under superharmonic resonance conditions , 2003 .

[11]  H. S. Bauomy,et al.  Nonlinear behavior of a rotor-AMB system under multi-parametric excitations , 2010 .

[12]  Y. A. Amer,et al.  Dynamic Behavior of an AMB/Supported Rotor Subject to Parametric Excitation , 2006 .

[13]  J. I. Inayat-Hussain.  Geometric coupling effects on the bifurcations of a flexible rotor response in active magnetic bearings , 2009 .

[14]  Y. A. Amer,et al.  Dynamic behavior of an AMB supported rotor subject to harmonic excitation , 2008 .

[15]  Wei Zhang,et al.  Transient and steady nonlinear responses for a rotor-active magnetic bearings system with time-varying stiffness , 2008 .

[16]  Colin H. Hansen,et al.  Non-linear oscillations of a rotor in active magnetic bearings , 2001 .

[17]  J. Cole,et al.  Multiple Scale and Singular Perturbation Methods , 1996 .

[18]  Jiangeng Li,et al.  Investigation of relation between singular points and number of limit cycles for a rotor–AMBs system , 2009 .

[19]  Wei Zhang,et al.  Analysis of Nonlinear Dynamics for a Rotor-Active Magnetic Bearing System With Time-Varying Stiffness: Part I — Formulation and Local Bifurcations , 2003 .

[20]  J. I. Inayat-Hussain.  Nonlinear dynamics of a statically misaligned flexible rotor in active magnetic bearings , 2010 .

[21]  Y. A. Amer,et al.  Resonance behavior of a rotor-active magnetic bearing with time-varying stiffness , 2007 .

[22]  H. S. Bauomy,et al.  Nonlinear Oscillation of a Rotor-AMB System With Time Varying Stiffness and Multi-External Excitations , 2009 .

[23]  Wei Zhang,et al.  Periodic and Chaotic Motions of a Rotor-Active Magnetic Bearing with Quadratic and Cubic Terms and Time-Varying Stiffness , 2005 .

[24]  Wei Zhang,et al.  Multi-pulse chaotic motions of a rotor-active magnetic bearing system with time-varying stiffness , 2006 .

[25]  Y. A. Amer,et al.  A Time-Varying Stiffness Rotor Active Magnetic Bearings Under Combined Resonance , 2008 .