Nonlinear Vibration of a Rotating System With an Electromagnetic Damper and a Cubic Restoring Force

Abstract

The nonlinear dynamics and stability of a rotating system with an electromagnetic noncontact damper are investigated. The rotating system model includes a cubic restoring force representing nonlinear behavior of shaft supports at the boundaries. Analysis of the rotor equilibrium state reveals that the system becomes unstable via a Hopf bifurcation when reaching a specific supercritical angular velocity. A closed-form solution for the radius of the limit cycle and the frequency of the self-excited oscillation are obtained. Forced vibration induced by the rotating system unbalance is investigated by a numerical simulation. System response includes periodic and quasi-periodic solutions. Analysis of the nonlinear rotating system enables a possible explanation of the aperiodic phenomena documented for rotors controlled by an electromagnetic eddy-current damper in high-speed operation.