Multiple attractors in the response of a flexible rotor in active magnetic bearings with geometric coupling

Abstract

Numerical results on the response of a flexible rotor supported by nonlinear active magnetic bearings are presented. Nonlinearity arising from the magnetic actuator forces that are nonlinear functions of the coil current and the air gap between the rotor and the stator, and from the geometric coupling of the magnetic actuators is incorporated into the mathematical model of the flexible rotor - active magnetic bearing system. For relatively large values of the geometric coupling parameter, the response of the rotor with the variation of the speed parameter within the range 0.05 Ω 5.0 displayed a rich variety of nonlinear dynamical phenomena including sub-synchronous vibrations of periods -2, -3, -6, -9, and -17, quasi-periodicity and chaos. Numerical results also reveal the occurrence of bi-stable operation within certain ranges of the speed parameter where multiple attractors may co-exist at the same speed parameter value depending on the operating speed of the rotor. © 2008 IOP Publishing Ltd.