Analytical Magnetic Circuit Modeling and Parameter Estimation of a PMSM for Spatial Harmonics and Radial Forces Characterization

Electromagnetic excitations originating from air-gap flux distortions and radial forces are a dominant source of noise and vibration in Permanent Magnet Synchronous Motor (PMSM) operating at low-to-medium speeds. While finite-element analysis provides detailed insights into these effects, it is computationally intensive and often requires precise geometrical data. Conversely, conventional dq0-based models fail to represent slotting effects and nonsinusoidal fluxes, limiting their accuracy in harmonic prediction. This paper proposes an analytical model of a three-phase PMSM based on a Magnetic Equivalent Circuit (MEC) to accurately identify spatial harmonics and compute current-induced radial forces. An offline parameter estimation procedure is employed to characterize the magnetic circuit, making the model adaptable to various motor topologies and pole configurations without relying on detailed geometry. The proposed approach enables the derivation of the machine’s electrical and mechanical equations to predict current harmonics, torque, and radial forces. Comparative studies with finite-element simulations validate the model’s ability to reproduce force components and the results establish the framework as a reliable and computationally efficient tool for vibro-acoustic assessments of PMSMs.