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The homoclinic tangency for a rotor-active magnetic bearings (AMB) system with the time-varying stiffness are considered in this paper. The zeros of Melnikov equation are paid more attentions and a 3-order zero was gained and some numerical results under the parameter perturbations were shown.

In this paper, the global bifurcation for a rotor-active magnetic bearings (AMB) system with the timevarying stiffness is investigated through discussing the zeros of the Melnikov function. Some critical conditions of chaos occurring are given. According to the results, the case that the order of Melnikov function is more than or equal to 2 is more general than other case (no zero or simple zero). In other word, homoclinic tangency may occur in several resonance relations.Keywords -Chaos, homoclinic bifurcation, rotor-active magnetic bearing 978-1-4244-4870-8/09/$26.00 ©2009 IEEE

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A cracked rotor-active magnetic bearings (AMB) system with the time-varying stiffness is modeled by a piecewise smooth system due to the breath of crack in a rotating shaft. The governing nonlinear equations of motion for the nonsmooth system are established and solved with the numerical method. The simulation results show that a grazing bifurcation, period-double bifurcation and chaotic motions exist in the response. These nonsmooth bifurcations can give rise to jumps between periodic motions, quasi-periodic motions and chaos.