Active　Magnetic　Bearings　(AMBs)　have　been　widely　used　in　industry,　aeronautics　and　astronautics　for　some　significant　advantages.　The　sensor　is　one　of　the　important　parts　of　the　electromagnetic　bearing　system,　the　features　of　the　sensor　can　affect　the　performance　of　the　whole　system.　The　nonlinear　electromagnetic　force　may　cause　the　considerable　oscillations　of　the　rotor　with　some　parametric　excitation.　Thus,　the　research　on　characters　of　the　nonlinear　dynamics　and　the　stability　for　the　rotor-ABMs　system　has　practical　implication.　The　works　in　this　current　study　focus　on　the　study　of　the　existence　of　the　periodic　solution,　the　numerical　simulation　of　the　solution　and　the　stability　of　the　periodic　solution.　Firstly,　we　present　the　motion　equations　of　the　rotor-　ABMs　system,　by　applying　the　multiple　method　of　scale　to　the　equations,　we　have　the　average　equations　and　we　get　the　sufficient　condition　of　the　existence　of　the　periodic　solution　through　using　transformations,　the　Poincare　mapping　and　the　Melnikov　function.　Then,　we　have　the　phase　diagrams　by　using　the　Matlab　calculation　software;　we　also　analyze　the　phase　diagrams　which　were　under　different　parameters.　The　simulation　results　demonstrate　the　theory　of　the　paper　is　correct.　©　2014　IFSA　Publishing,　S.　L.