Non-linear oscillations of a rotor in active magnetic bearings

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 diff erential equations that describe the modulation of the amplitudes and phase s of vibrations in the horizontal and vertical directions. The steady state response and the stability of the solutions are determined numerically fro m the reduced system. It is shown that the steady state solutions lose thei r stability by either saddle-node bifurcation or Hopf bifurcation. In the r egime of multiple coexisting solutions, two stable solutions are found. The effect of imbalance eccentricity, as well as the effect of the proportiona l 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. (C) 2001 Academic Press.