Non-linear oscillations of a rotor-magnetic bearing system under superharmonic resonance conditions

Abstract

The effect of non-linear magnetic forces on the non-linear response of the shaft is examined for the case of superharmonic resonance in this paper. It is shown that the steady-state superharmonic periodic solutions lose their stability by either saddle-node or Hopf bifurcations. The system exhibits many typical characteristics of the behavior of non-linear dynamical systems such as multiple coexisting solutions, jump phenomenon, and sensitive dependence on initial conditions. The effects of the feedback gains and imbalance eccentricity on the non-linear response of the system are studied. Finally, numerical simulations are performed to verify the analytical predictions.