Purpose This paper aims to present a novel analytical approach based on the bipolar coordinates mapping method to determine the optimal magnet reduction (eccentricity) in surface-mounted permanent-magnet (SPM) and surface-mounted permanent-magnet motors for minimizing cogging torque. Furthermore, it formulates key motor performance parameters as functions of the magnet reduction factor and investigates the impact of optimal magnet shaping on motors with rotor eccentricity. Design/methodology/approach The core idea is to model the outer magnet surface and the slotted stator bore as eccentric circles. The bipolar mapping is then used to transform the slotted stator geometry into an equivalent slotless one, a condition known to minimize cogging torque. Solving the resulting mapping equations yields the optimal geometric parameters for magnet eccentricity. Findings The proposed method produces three distinct, physically valid roots (solutions) for the optimal magnet reduction. A key finding is the scalability of these solutions: the optimal values for a new motor can be obtained by scaling a reference motor’s solutions by the ratio of their rotor radii, thereby eliminating repetitive calculations. The method is universally applicable to radial, parallel and bread-loaf type SPM motors. Originality/value The primary originality of this work lies in the application of the bipolar coordinates mapping method to the magnet shape optimization problem. This provides a robust analytical framework for predicting optimal eccentric pole designs that effectively reduce cogging torque, even in the presence of static or dynamic rotor eccentricity. The derived performance formulations offer quick insights into the trade-offs involved.
Jabbari et al. (Mon,) studied this question.