Non-linear oscillations of a rotor in active magnetic bearings

Abstract

The non-linear response of a rotor supported by active magnetic bearings is investigated, and both primary and internal resonances are considered. 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 vibrations in the horizontal and vertical directions. The steady state response and the stability of the solutions are determined numerically from the reduced system. It is shown that the steady state solutions lose their stability by either saddle-node bifurcation or Hopf bifurcation. In the regime of multiple coexisting solutions, two stable solutions are found. The effect of imbalance eccentricity, as well as the effect of the proportional and derivative gains of the controller on the non-linear response of the system, are studied. Finally, numerical simulations are performed to verify the analytical predictions.