Abstract
Two-dimensional (2-D) analytical modeling of Interior Permanent Magnet (IPM) machines is a challenging problem due to the saturated bridges and non-cylindrical boundary conditions between the rotor core and the permanent magnets (PMs). The use of prism-shape rotor frame with polygon bases could mitigate the cogging torque and the torque ripple in such machines but it further complicates the analytical solution procedure. This paper presents a general 2-D open-circuit analytical representation of IPM machines with arbitrary rotor frame (e.g., polygon prism, cylindrical). First, the interior PMs are mapped to the rotor surface and the IPM machine is represented by an equivalent Surface Mounted Permanent Magnet (SPM) machine. This forms a rotor geometry with cylindrical symmetry, and facilitates solving Maxwell equations with 2-D boundary conditions. Next, Maxwell equations are solved on the selected subdomains to calculate no-load characteristics of the machine (i.e., PM flux distribution, back-EMF, and cogging torque). Meanwhile, the effect of the stator slots on flux distribution is captured by injecting proper amount of surface current on the slot opening. The accuracy of the analytical results is validated through Finite Element (FE)-based simulations and experimental tests.
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