The eccentric permanent-magnet (PM) pole technique is widely recognized as an effective technique for reducing cogging torque in surface-mounted PM motors (SMPMMs). This paper proposes a novel analytical approach based on bilinear mapping to determine the optimal PM reduction parameters. In this method, the outer surface of the PM and the stator inner bore are modeled as eccentric circles. Bilinear mapping is then used to transform a slotted stator bore into an equivalent slotless configuration with small slot-openings, allowing the optimal PM reduction to be identified. The key electromagnetic performance characteristics of SMPMMs—including torque, efficiency, mean air-gap flux density, and related parameters—are formulated as explicit mathematical functions of the PM reduction factor. The influence of the optimal PM reduction on both static and dynamic rotor eccentricity is also investigated. The results reveal that the bilinear mapping equations yield two distinct roots for the optimal PM reduction. Once the optimal values are known for a reference motor, those of other motors with different dimensions can be readily derived by scaling according to the ratio of the outer PM radii, without repeating the full calculation process. The proposed method is applicable to various SMPMM geometries, including radial, parallel, and bread-loaf configurations.
