Cogging Torque Computation in an Asymmetrical Interior Permanent Magnet Machine for Electric Vehicles

This article computes the cogging torque in an asymmetrical 36-slot 4-pole interior permanent magnet (IPM) machine designed for high torque density and transportation applications. Cogging torque causes acoustic noise and vibration. Therefore, it is important to know the value of cogging torque in the asymmetrical IPM machine. The cogging torque of the asymmetrical permanent magnet machine is computed based on a Fourier series expansion of air gap flux density in an equivalent slot-less IPM machine and relative air gap permeance function. The flux distribution of the asymmetrical IPM machine is computed using an equivalent lumped magnetic circuit based on flux distribution obtained using the finite-element analysis (FEA) method. The computed flux distribution follows the FEA results and thus the lumped magnetic circuit is validated. Then, the cogging torque of the asymmetrical IPM machine is derived. The Fourier coefficients of the flux distribution and relative air gap permeance in the asymmetrical IPM machine are analyzed and used to compute the cogging torque and compared to the FEA results. The computed cogging torque follows the FEA results and thus the newly derived cogging torque is justified by FEA and measurement. The FFT of the cogging torque is analyzed. Skewing technique is used to minimize cogging torque.