Modeling of radial forces due to eccentricity in a permanent-magnet synchronous motor using perturbation theory

In this paper, we derive an analytical model describe the radial forces due to eccentricity in a non-salient permanent-magnet (PM) synchronous motor. The simplified geometry of the machine in which the rotor is displaced from the origin by ε is shown. The potential equation of eq . (1) governs the magnetic field in the air gap between the PM rotor and the stator. When there is no eccentricity, the potential function and the magnetic field can be expressed by eq . (2) and (3), respectively, where β₁ is defined in eq . (4).