Prediction of Horseshoes Chaos in Active Magnetic Bearings With Time-Varying Stiffness

Abstract

The paper considers a model of an active magnetic bearing with time-varying stiffness and investigates the effects of the control gain parameters on the appearance of horseshoes chaos. The Melnikov method is used to derive the critical conditions for chaos and numerical simulations are performed to determine the basins of attraction. It is shown that the domain of chaotic motion strongly depends on the gain parameters and that this domain increases with the magnetic force and decrease with the static current. The controller frequency ω is found to be a key parameter and has a critical effect on the enlargement of the chaotic domain.