Open-Circuit Electromagnetic Analysis of Interior Permanent Magnet Machines With Arbitrary Rotor Frame Using a 2-D Analytical Model

Two-dimensional (2-D) analytical modeling of interior permanent magnet (IPM) machines is quite challenging due to the nonuniform permeability of the rotor core. The choice of a non-cylindrical rotor frame (e.g., rotor frame with cosine shape) further increases the complexity of the model. This article presents a methodology for the 2-D modeling of IPM machines with cylindrical and non-cylindrical rotor frames. In this model, interior magnets are first mapped to the surface of the rotor body using the equivalent magnetic circuit model. In other words, the IPM machine is transformed into an equivalent surface-mounted permanent magnet (SPM) machine. The rotor shape is modeled by the proper adjustment of the permanent magnet (PM) magnetization pattern of the equivalent SPM machine. Next, the radial and tangential flux components of the equivalent (SPM) machine are computed by solving Maxwell's relations and applying 2-D boundary conditions. The effect of the stator slotting on the distribution of magnetic flux is accounted using the theory of virtual current. The accuracy of the presented model is verified against the finite element (FE) and experimental measurements.