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The nonlinear dynamics of rotors suspending in the active magnetic bearings (AMBs) with eight pole pairs are investigated. The nonlinear governing equations of two degree-of-freedom (2DOF) are obtained considering the rotor with proportional–derivative (PD) controller. By studying the conservative free vibrations of the general 2DOF nonlinear systems, three types of motions are found, namely, in-unison modal motions, elliptic modal motions, and quasi-periodic motions. The method of multiple scales is used to obtain the amplitude-phase portrait to demonstrate the three types of motions by introducing the energy ratios and phase differences. It is found that in-unison modal motions do not exist due to the symmetry feature of the rotors in the AMBs. The effect of the PD controller and damping to the vibration suppression is discussed by the idea of the rolled-up amplitude-phase portrait.

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