Asymmetric effect of static radial eccentricity on the vibration characteristics of the rotor system of permanent magnet synchronous motors in electric vehicles

Considering static radial eccentricity, a Jeffcott rotor model is established for the rotor system of the permanent magnet synchronous motors in electric vehicles. The system conservative force, including unbalanced magnetic pull, which results in nonlinearity is analyzed, and center manifold theorem and Lyapunov method are used to determine the stabilities of multiple equilibrium points. This analysis shows that static eccentricity spoils the symmetry of the equilibrium points, although they are distributed in the line along the direction of the static eccentricity. This asymmetry leads to the pitchfork bifurcation of equilibrium points to a generic bifurcation with a defect. This analysis provides two stability conditions for the rotor system. Furthermore, the effect of the asymmetry on the dynamic characteristics that can induce backward whirling motion coupled with forward whirling motion is quite different from the case without static eccentricity. These characteristics are investigated by multi-scale method. As a result, the analytical solution of the system at steady state is obtained. The frequency characteristics of the main resonance are analyzed, and the stability of the solution is determined using Routh–Hurwitz criterion and the geometric constraint of the rotor whirling motion. The characteristics reveal that a globally unstable frequency band appears due to the geometric constraint. However, this frequency band narrows and even vanishes with increases in damping and electromagnetic stiffness and decreases in mass imbalance, mechanical stiffness and static eccentricity. The analysis by multi-scale method is based on the assumption of the time invariance of the forward and backward whirling amplitudes, which is validated by the numerical method. The results of the two methods agree well, which indicates that this assumption and the analysis are reasonable.