Semi-Analytical Calculation of the Unsaturated Magnetic Field Distribution of a Slotted Spoke-Type Interior Permanent Magnet Machine With Conformal Mapping Method

The performances of an electric machine are closely related to magnetic field, and the magnetic field calculation is the basic work of machine design and optimization. In slotted spoke-type interior permanent magnet (IPM) machines, the analytical calculation of magnetic field is complicated because the boundary of machine is difficult to model. Therefore, this article introduces a conformal mapping (CM) method to calculate the magnetic field semi-analytically. First, the interior magnet is transformed into the surface-mounted magnet to reduce the complexity of boundary conditions. The air-gap magnetic field of the slotless spoke-type IPM machine is calculated by using the boundary conditions of the transformed surface-mounted permanent magnet machine. Then, based on the magnetic field of the slotless air gap, the magnetic fields of the slotted air gap and teeth are also calculated by the CM method. All the semi-analytically calculated magnetic fields are directly verified by the FEM simulation and indirectly verified by the comparison of torque and back EMF. In addition, the comparison of computation time between the semi-analytical method and the FEM shows that the semi-analytical method is time-saving.