Asymmetrical Magnet Shape Optimization Based on S-C Mapping for Torque Profile Mitigation in Unidirectional Application of SPMS Machine

Surface-mounted permanent magnet synchronous (SPMS) machines are widely used in applications that require low-torque ripple, reduced vibration, and acoustic noise. For those applications of SPMS machine (SPMSM) in which only unidirectional operation is needed, asymmetric design optimization shows to acquire significant advantages over symmetric designs. In this paper, an analytical method based on Schwarz–Christoffel mapping is presented for asymmetrical magnet shape optimization in SPMS machine. In this method, the permanent magnet is divided into finite cells so that each cell can be assigned with either air (off) or magnet (on). The optimization problem is solved using genetic algorithms (GAs). In order to remove nonmanufacturable shapes, the cluster of materials and cleaning method is used and applied to magnet and air cells, respectively. The minimum number of cells in a cluster ( $N_{\text {min}}$ ) is defined as an integer design parameter. The analytical method can significantly reduce the computational time used by the optimization process as compared with methods based on finite-element analysis (FEA). This method is applied to a 12-pole SPMS machine. Validation of the S-C mapping method and final results are carried out using 2-D and 3-D FEAs. The results obtained demonstrate that asymmetrical magnet shape improves the cogging torque and torque ripple performance of SPMS machine by a significant margin.