Analytical Modeling of On-Load Magnetic Fields in High-Speed SPM Machines Considering PM Overhang and Stator Saturation

This paper proposes an improved 3-D hybrid model (HM) for high-speed surface-mounted permanent magnet (SPM) machines featuring a PM overhang structure. The HM integrates a 2-D subdomain (SD) model for air-gap magnetic field prediction, a 3-D equivalent magnetic network (EMN) model for stator magnetic saturation characterization, and a magnetic circuit (MC) model for end linkage flux quantification and leakage effect evaluation. First, an axial segmentation method is proposed to discretize the stator of the PM overhang machine (POM) into slices. The 3-D EMN is then established by modeling each slice as a 2-D EMN unit. Next, diffusion equations are established to account for eddy current reactions in the alloy sleeve and PM regions. Then, leakage correction factors derived from the MC model are applied to refine the air-gap flux predicted by the SD model, accounting for both air-gap and end leakage effects. Finally, the MC model calculates the end linkage fluxes injected by overhang PMs into axial-end EMN units to quantify the overhang effect. Finite element (FE) simulations and prototype testing validate that the proposed 3-D HM achieves computational accuracy comparable to that of a 3-D FE model while reducing computation time by 95%.