Non-Linear Behavior of a Magnetically Supported Rotor

Non-linearity is an inherent and essential characteristic of active magnetic bearings. For simplicity, only the non-linearity between force, current and displacement of the electromagnets is considered while other nonlinearities are neglected. The nonlinear response of a rotor in active magnetic bearings is investigated for the case of a primary resonance. The method of multiple scales is used to obtain four first-order ordinary differential equations that describe the modulation of the amplitudes and phases of oscillations in the horizontal and vertical directions. The steady state response and its stability are obtained numerically from the reduced equations. In the regime of multiple coexisting solutions, two stable solutions are found. Finally, the analytical results are verified by integrating the governing equations.