Magnetic Field Analysis of Notched SPMSM Using Conformal Mapping

We present an analytical method for applying conformal mapping to the notched geometry of a surface permanent magnet synchronous motor to calculate the cogging torque. First, the complex relative air-gap permeance (CRAP) of the notched air-gap is calculated by multiplying the CRAP of a slotted air-gap with the notch sensitivity coefficient, which is defined by the relation of slot and notch shapes. Secondly, the no-load air-gap flux density (AFD) is derived from the CRAPs of the notched and slotted air-gaps. Finally, the cogging torque of the notched motor is calculated by the no-load AFD and is verified using the 2D finite element analysis (FEA) result. A 4-pole and 12-slot surface permanent magnet synchronous motor with the notch is used herein.