Dynamics of a Rotating System With a Nonlinear Eddy-Current Damper

Abstract

We investigate the nonlinear dynamics and stability of a rotating system with an electromagnetic noncontact eddy-current damper. The damper is modeled by a thin nonmagnetic disk that is translating and rotating with a shaft in an air gap of a direct current electromagnet. The damper dissipates energy of the rotating system lateral vibration through induced eddy-currents. The dynamical system also includes a cubic restoring force representing nonlinear behavior of rubber o-rings supporting the shaft. The equilibrium state of the balanced rotating system with an eddy-current damper becomes unstable via a Hopf bifurcation and exact solutions for the limit cycle radius and frequency of the self-excited oscillation are obtained analytically. Forced vibration induced by the rotating system mass imbalance is also investigated analytically and numerically. System response includes periodic and quasiperiodic solutions. Stability of the periodic solutions obtained from the balanced self-excited motion and the imbalance forced response is analyzed by use of Floquet theory. This analysis enables an explanation of the nonlinear dynamics and stability phenomena documented for rotating systems controlled by electromagnetic eddy-current dampers.