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This article proposes a rapid and optimum design method that considers axial flux leakage for a coaxial magnetic gear (CMG). Conventional CMG optimum design methods perform two-dimensional (2D) finite element analysis (FEA) to evade the long computational time of three-dimensional (3D) FEA. However, conventional design methods do not consider axial flux leakage and are therefore less accurate than computationally exhaustive optimum design through 3D FEA. Therefore, as an alternative to reduce computational time, this article proposes a method that considers axial flux leakage for predicting the CMG performance combining correlation coefficients and 2D FEA instead of 3D FEA. The correlation coefficient is determined as the ratio of the square of the radial direction air gap flux in the equivalent magnetic circuit (EMC) that considers axial flux leakage to the square of the radial direction air gap flux in the EMC that does not consider axial flux leakage. The electromagnetic performance of the CMG predicted by the proposed method is used to develop a surrogate model for reducing computational time during the optimum design process. Based on the surrogate model, the optimum CMG design is analyzed to fabricate a prototype, and the proposed design process is validated through experiments.

In this study, the radial vibration of fractional-slot concentrated winding (FSCW) permanent magnet synchronous motor (PMSM) was analyzed according to pole/slot combination considering phase relationship of modulated radial, tangential forces, and moment. First, to calculate the modulated forces and moment according to pole/slot combination, the amplitude and phase of modulated radial, tangential force and moment converted by radial air-gap electromagnetic force density (AEFD) are analytically derived. Since the lever arm effect by tangential force varies according to the tooth length, tangential force was translated on the yoke and an equivalent modulated moment was derived. Subsequently, to analyze the radial vibration caused by modulated forces and moment, the radial displacement response owing to a unit radial AEFD is calculated using 3D structural finite element analysis by applying unit modulated forces and moment. It was found out that the tooth modulation effect hardly varied with pole/slot combination and shape of the PMSM such as tooth length. Rather, it was confirmed that the tooth modulation effect was significantly influenced by the slot opening width. Especially, it was analyzed that the radial vibration of PMSM is not simply reduced by optimizing the slot opening width with reduced modulated radial force, but the amplitude and phase of the modulated tangential force and moment should also be considered. Finally, four prototypes of the PMSM with different slot opening widths of two 12-slot 10-pole and two 12-slot 14-pole are fabricated, and the test and simulation results are compared and verified.