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When the end leakage flux or end leakage inductance cannot be ignored in a permanent magnet (PM) machine (e.g., a PM machine with a short axial length), the analysis of the machine is a time-consuming three-dimensional (3-D) issue. Existing research has made the end leakage inductance no longer to hinder that the performance calculation of fractional slot concentrated-winding surface permanent magnet (FSCWSPM) machines is simplified into a time-saving 2-D issue. However, no such mature research exists for end leakage flux. This paper proposes a novel end leakage flux function that can be used to accurately quantify the end leakage flux of FSCWSPM machines. Then, based on sensitivity research and regression analysis, a parametric model is established to quickly construct the end leakage flux function. Thus, even for FSCWSPM machines with nonnegligible end leakage flux, the results comparable to those from the 3-D finite element method (FEM) can be easily obtained using the proposed end leakage flux function and parametric model to revise the results from 2-D FEM. Moreover, the application of the above function and model is briefly described. Finally, FEM and experimental results are used to verify the calculation precision, adaptability, and timeliness of the proposed methodology.

Investigation of the End Leakage Flux in Fractional Slot Concentrated-Winding Surface Permanent Magnet Machines