Nonlinear normal modes and primary resonance for permanent magnet synchronous motors with a nonlinear restoring force and an unbalanced magnetic pull

The unbalanced magnetic pull (UMP) in permanent magnet synchronous motors (PMSMs) leads to the generation of vibrations and noise because of mechanical and magnetic coupling effects. This paper investigates the nonlinear oscillations of a PMSM based on a Jeffcott rotor-bearing system, and the effects of the UMP, nonlinear restoring forces due to the Hertz contact force and bearing clearance, rotor weight and rotor mass eccentricity are considered. A second-order approximate solution in the primary resonance case is obtained by applying the multiple-scale perturbation method. The Routh–Hurwitz criterion is utilized to investigate the stability of the obtained solution. The linear natural frequencies of the horizontal and vertical modes show little difference based on the constructed model. The localized oscillations and nonlocalized oscillations of the rotor-bearing system are analyzed through its frequency response curves by introducing different values of system parameters. The response curves exhibit hard spring characteristics with unstable regions and jump phenomena. Detailed numerical research including Poincare map and bifurcation diagram reveals the effect of excitation amplitude on the system. Additionally, this work provides some theoretical and practical guidance for the design of PMSMs with strong dynamic behaviors.