A Nonlinear 3-D Hybrid Model for Surface-Mounted Permanent Magnet Machines Considering End Effect

In this article, a new subdomain (SD) and magnetic circuit (MC) 3-D hybrid model (HM) is proposed for field prediction in surface-mounted permanent magnet machines considering end effect and magnetic saturation in both stator and rotor iron. The machine is divided into several slices along the axial direction. Then, the 3-D HM is implemented by a 3-D MC and multiple 2-D SDs iterating through the equivalent surface currents in slots and line currents on the rotor iron surface. Meanwhile, to quantify and consider the PM end fringing effect, a PM flux leakage factor is defined and only plays a role in end sections of a machine during the 3-D HM iteration. Finally, by the nonlinear 3-D finite-element analysis and experimental results, the effectiveness and speed superiority of the 3-D HM are validated. It can accurately predict the magnetic field and machine performances considering the end effect and heavy magnetic saturation under load conditions with low time consumption.