Y. Kligerman et O. Gottlieb, DYNAMICS OF A ROTATING SYSTEM WITH A NONLINEAR EDDY-CURRENT DAMPER, Journal of vibration and acoustics, 120(4), 1998, pp. 848-853
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.