Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force

Vibration analysis is important to explain and control the various kinds of vibration problems in magnetically levitated mechanical systems. This study investigates the vibration phenomena of the one-degree-of-freedom magnetically levitated system considering the effect of the nonlinearity of the electromagnet. It is difficult to apply the conventional nonlinear analysis techniques for the magnetically levitated system, since the magnetic force has a strong nonlinear characteristic that varies in inverse proportion to the square of the gap. This paper performs theoretical analyses using the shooting method, clarifies the stability and bifurcation characteristics, and verifies them experimentally. We conclude that the shape of the resonance curve becomes soft-type, superharmonic resonances occur, and period-doubling bifurcations occur at the main resonance and at superharmonic resonances.