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This paper establishes the force-harmonic coupling model considering phase angle characteristic for the analysis and reduction of the slot frequency force harmonic of PMSMs. Compared with the traditional analytical model, the significant influence of the force phase angle on the coupling relationship among force components is considered in the model. Firstly, the force-harmonic coupling model considering phase angle characteristic is deduced based on the Maxwell stress tensor, and considering the influence of the force phase angle on the coupling relationship among force components contributing to the slot frequency force harmonic, these force components are divided in to a series of combinations of positive and negative components. Combined the finite element model, the coupling model is verified. Based on the coupling relationship, the principle of the rotor-step skewing is further explained as the mutual compensation effect of the positive and negative force components, and the slot frequency vibration is effectively offset through choosing the appropriate segment number and skewed angle. Finally, the optimized prototype is tested, and the measured results are in good agreement with the FEM results.

Analysis and Reduction of Slot Frequency Vibration of PMSMs With the Force-Harmonic Coupling Model Considering Phase Angle Characteristic