Analytically determined graph based solution for minimum cogging in spm motors with integer slots per pole

This paper presents an analytically determined graph based technique to estimate the optimum pole embrace of magnets for minimum cogging torque. Existing closed form solutions for optimum embrace were derived considering only normal fields. In the proposed approach, analytical expressions for Fourier coefficients of cogging torque are presented in a form that helps in obtaining optimum pole embrace value, without neglecting the tangential field component. The method presented here is applicable only for Surface Mounted Permanent Magnet (SPM) motors with integer number of slots per pole. With the help of case studies, it is shown that the embrace value given by this technique will be within a small tolerance window with respect to a more accurate value obtained using FEA or numerical optimization approaches.