DYNAMICS OF A ROTATING SYSTEM WITH A NONLINEAR EDDY-CURRENT DAMPER

W investigate the nonlinear dynamics and stability of a rotating syste m with an electromagnetic noncontact eddy-current damper. The damper i s modeled by a thin nonmagnetic disk that is translating and rotating with a shaft in an air gap of a direct current electromagnet. The damp er dissipates energy of the rotating system lateral vibration through induced eddy-currents. The dynamical system also includes a cubic rest oring force representing nonlinear behavior of rubber o-rings supporti ng the shaft The equilibrium state of the balanced rotating system wit h and eddy-current damper becomes unstable via a Hopf bifurcation and exact solutions for the limit cycle radius and frequency of the self-e xcited oscillation are obtained analytically. Forced vibration induced by the rotating system mass imbalance is also investigated analytical ly and numerically. System response includes periodic and quasiperiodi c solutions. Stability of the periodic solutions obtained from the bal anced self-excited motion and the imbalance forced response is analyze d by rue of Floquet theory. This analysis enables an explanation of th e nonlinear dynamics and stability phenomena documented for rotating s ystems controlled by electromagnetic eddy-current dampers.