Analytical Model for Eccentric IPMSM via a New Equivalent Transformation Method and Its Rotor Vibration Calculation Considering the Coupling Effect

Due to the inherent assembly errors, rotor eccentricity in motors is an inevitable phenomenon. In the case of the interior permanent magnet synchronous motor (IPMSM), its relatively short air-gap length makes it more susceptible to the effects of eccentricity. Therefore, this study proposes a new analytical model and a rotor vibration calculation model for IPMSM in eccentric scenarios. First, the theoretical feasibility of equivalent transformation for eccentricity is analyzed. A novel equivalent transformation method for rotor eccentricity is presented. The nonuniform air gap resulting from eccentricity can be represented as the superposition of a uniform air gap and a virtual surface permanent magnet (VSPM). By maintaining constant air-gap flux density before and after equivalence, the remanence distribution of the VSPM is determined, thereby achieving the unity of the stator and rotor geometric centers. Second, to consider the complex magnetization patterns and structures of interior permanent magnet (IPM), this article presents an improved subdomain model that combines equivalent current and subdivision while also incorporating the core’s nonlinear saturation. Third, based on the magnetomotive force (MMF)-permeability method, a new analytical equation of the unbalanced electromagnetic force (UEF) considering rotor vibration is derived. Furthermore, an analytical model of rotor vibration is established, which appropriately considers the mutual coupling effect between the UEF and the rotor vibration displacement. Finally, all the proposed methods are verified and analyzed.