This paper describes an analytical subdomain model to predict the magnetic field distributions in the semi-closed surface-mounted permanent magnet synchronous machines (PMSMs) due to magnet segmentations with radial magnetization (RM). The magnet segments per pole can be virtually represented by finite number of permanent magnet (PM) blocks and Fourier decompositions. The model can also determine the optimum magnet pole-arcs for each segment and the optimum airgap spacing between the segments. The analytical model is then applied to evaluate the performance of a three-phase, 12-slot/8-pole, surface-mounted PMSM having two segmented magnets per pole with RM. With design objective for minimum cogging torque and minimum total harmonic distortion in phase back-emf waveforms, we obtain that the optimum settings are 147.6° elect. for magnet segment pole-arc and 11.2° elect. for airgap spacing between the magnet segments. These analytical results are further compared and validated by 2-D finite element analysis (FEA). Additionally, we also compare the results with those from the optimum magnet pole-arc of one magnet segment per pole machine. It is observed that the cogging torque and total harmonic distortion THDv of the phase back-EMF are significantly reduced by 89% and 25%, respectively, with constraint and assumption that both machines utilize similar total magnet volume.
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