In this paper, we present a mathematical model for determining the optimal radius of the iron pole shape in spoke-type permanent-magnet (PM) machines (STPMM) in order to minimize the pulsating torque components. The proposed method is based on the formal 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 STPMM 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, ripple and reluctance torque waveforms. In order to validate the results of the proposed analytical model, three motors with different PM widths were considered as case studies and their performance results were compared analytically and numerically. Two prototype spoke-type machines were fabricated and the experimental results was compered to analytical results. It can be seen that the analytical modeling results are consistent with the numerical analysis and experimental results.
