Improved 3-D Hybrid Models for Open-Circuit Field Prediction in SPM Machines With Overhang Structures

This article proposes two improved 3-D hybrid models (HMs) combining subdomain (SD) and equivalent magnetic network (EMN) methods for open-circuit field prediction in two surface-mounted permanent magnet (SPM) machines with distinct overhang structures, simultaneously accounting for saturation effects and leakage flux influences. The 3-D HMs iteratively update the equivalent saturation surface current, which is used as part of the 2-D SD boundary conditions to characterize the saturation effect. The key lies in modifying the 2-D SD model to derive flux sources specific to overhang structures within the 3-D EMN model. Firstly, depending on the types of leakage flux, the machines are divided into several regions along the axial direction. Each subregion includes several slices. Then, for the PM overhang machine (POM), the flux source correction factor for each slice considering end and air-gap leakage fluxes is derived using the magnetic equivalent circuit (MEC) model. Additionally, the linkage fluxes supplied by the overhang PMs are calculated and injected into the EMN units corresponding to end slices. Meanwhile, in the stator overhang machine (SOM), the axial distribution of air-gap flux density is solved using the magnetic charge model, with both leakage flux types incorporated for flux source modification. Two prototypes are fabricated, and the high accuracy and efficiency of both proposed 3-D HMs are verified by 3-D finite element analysis (FEA) and experimental results.