Nonlinear vibration of permanent magnet synchronous motors in electric vehicles influenced by static angle eccentricity

Abstract

An additional transverse electromagnetic moment caused by the inclination of the rotor of the permanent magnet synchronous motors in electric vehicles is modeled based on Maxwell stress tensor method. The model of this moment is suitable for the case of pole-pair number larger than 3 and is independent of time; its nonlinearity results in multiple equilibrium points of the conservative generalized force: an isolated equilibrium point and a continuum of equilibrium points. The continuum is symmetric with respect to the isolated equilibrium point; a pitchfork bifurcation occurs as the system stiffness of the rotor in the non-inclined state passes through zero. When static angle eccentricity is introduced, the symmetry is lost and the continuum degrades into two unstable equilibrium points. This parameter leads to a generic bifurcation with defect. However, considering it as a bifurcation parameter, a pair of saddle-node bifurcations appears. Eigenvalue-based stability analysis and center manifold theorem are employed to determine the stabilities of the multiple equilibrium points. The frequency characteristics of the forced response caused by the static angle eccentricity are developed by harmonic balance method, and the stability of the steady-state solution is studied with Routh–Hurwitz criterion in a rotating system. The frequency response curve generally passes through all the equilibrium points. For a disk-shaped rotor, the frequency characteristics exhibit hardening and the solution has the same stability as the equilibrium point in the same branch. For a cylindrical rotor, the characteristics show softening and only the solution running near the equilibrium point has the same stability as the equilibrium point in the same branch. Furthermore, there is a frequency band in which the forced response is globally unstable. However, for comparatively large damping, large inertia ratio, small stiffness ratio and small static angle eccentricity, the frequency characteristics of a cylindrical rotor are similar to those of a disk-shaped rotor. The globally unstable frequency band diminishes and then vanishes. All of the solutions have the same stability in a branch.