Nonlinear PD-controller to suppress the nonlinear oscillations of horizontally supported Jeffcott-rotor system

Abstract This paper investigates the vibration control of a horizontally suspended Jeffcott-rotor system. A nonlinear restoring force and the rotor weight are considered in the system model. The system frequency (angular speed) -response curve is plotted at different values of the rotor eccentricity. The analysis illustrated that the system has a high oscillation amplitude and exhibits some nonlinear behaviors before control. A Proportional-Derivative (PD)-controller is integrated into the system via two pairs of electromagnetic magnetic poles. The nonlinearity due to the electromagnetic coupling is considered in the system model. A second-order approximate solution is obtained by utilizing multiple scales perturbation method. The bifurcation analyses of the controlled system are conducted. The results showed the high efficiency of the controller to mitigate the nonlinear vibrations of the considered system. Numerical simulations are carried out to validate the accuracy of the analytical results. The numerical results confirmed the excellent agreement with the analytical solutions. Then, the optimal working conditions of the system are concluded. Finally, a comparative study with previously published work is reported.

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

[2]  G. Schweitzer,et al.  Magnetic bearings : theory, design, and application to rotating machinery , 2009 .

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

[4]  H. S. Bauomy,et al.  Dynamics of an AMB-rotor with time varying stiffness and mixed excitations , 2012 .

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

[6]  Daniel Lazard,et al.  Quantifier Elimination: Optimal Solution for Two Classical Examples , 1988, J. Symb. Comput..

[7]  E. L. Rees,et al.  Graphical Discussion of the Roots of a Quartic Equation , 1922 .

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

[9]  Vimal Singh,et al.  Perturbation methods , 1991 .

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

[11]  H. S. Bauomy,et al.  Stability analysis of a rotor-AMB system with time varying stiffness , 2012, J. Frankl. Inst..

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

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

[14]  Tsuyoshi Inoue,et al.  Nonlinear normal modes and primary resonance of horizontally supported Jeffcott rotor , 2011 .

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

[16]  M. Eissa,et al.  Nonlinear oscillations of rotor active magnetic bearings system , 2013 .

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

[18]  Balakumar Balachandran,et al.  Torsional oscillations of a rotor with continuous stator contact , 2014 .

[19]  H. S. Bauomy,et al.  Nonlinear study of a rotor–AMB system under simultaneous primary-internal resonance , 2010 .

[20]  M. Eissa,et al.  Saturation-based active controller for vibration suppression of a four-degree-of-freedom rotor–AMB system , 2014 .

[21]  Ali H. Nayfeh,et al.  Resolving Controversies in the Application of the Method of Multiple Scales and the Generalized Method of Averaging , 2005 .

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

[23]  Andrew Y. T. Leung,et al.  BIFURCATION BEHAVIOR OF A ROTOR SUPPORTED BY ACTIVE MAGNETIC BEARINGS , 2000 .

[24]  Tsuyoshi Inoue,et al.  Vibration Suppression of Nonlinear Rotor Systems Using a Dynamic Damper , 2007 .

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