In this paper, we present a mathematical model for determining the optimal radius of the iron pole shape in spoke type permanent magnet (STPM) machines in order to minimize the pulsating torque components. The proposed method is based on the resolution of the Laplace’s and Poisson’s equations in a Cartesian pseudo-coordinate system with respect to the relative permeability effect of iron core in a subdomain model. The effect of PM width on the optimal radius of the iron pole has been investigated. In addition, for initial and optimal machines, the effect of the iron core relative permeability on the STPM machine performances was studied at no-load and on-load conditions considering three certain PM widths. Moreover, the effect of iron pole shape on pulsating torque components with respect to certain values of iron core relative permeability was studied by comparing cogging torque, electromagnetic torque ripple and reluctance torque ripple waveforms. In order to validate the results of the proposed analytical model, three motors with different magnet widths were considered as case studies and their performance results were compared analytically and numerically. It can be seen that the analytical modeling results are consistent with the results of numerical analysis.
