A Hybrid Analysis Method for SPMLSMs With Non-Uniform Air-Gap Length

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Optimizing permanent magnet and slot shapes improves surface-mounted permanent magnet motor thrust performance. However, this optimization complicates air-gap boundary conditions, creating electromagnetic analysis challenges. To address this, this paper proposes a hybrid analytical method integrating equivalent magnetic network and subdomain approaches. Two key innovations enable its application in motors with non-uniform airgap length: First, arc-shaped permanent magnets are converted into rectangular equivalents. This geometric transformation achieves planar interfaces between PMs and air-gap regions, thereby reducing the computational complexity of magnetic vector potential solutions. Secondly, extending the equivalent magnetic network into the air-gap region decouples the core from the boundary. This eliminates repeated EMN discretization during slot shape optimization. The hybrid analytical model is employed to predict back electromotive force, detent force, and load thrust, which are validated by the finite element analysis. During motor optimization, the hybrid analytical model achieves an 89% computation time reduction compared to finite element method. Experimental results align with both the finite element method and hybrid model predictions, confirming the method’s applicability for rapid surface-mounted permanent magnet motor design.