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This paper presents a robust optimal design method using a hybrid response surface method (H-RSM) which directly finds an optimal point satisfying a target Z-value or a probability of failure. Through three steps, this paper achieves the goal that is to increase the open-circuit airgap flux (OCAF) in a surface-mounted permanent magnet motor and decrease its variation caused by variations of the airgap lengths including an additional one between permanent magnets and rotor back yoke. First, the OCAF equation is derived from the magnetic equivalent circuit (MEC) considering the additional airgap. Then, the equation is validated by comparing its results with those of the finite element method (FEM) modeled by the slotless stator. Next, the tolerance sensitivity analysis, using the partial derivative of the OCAF equation with respect to the airgap length, is performed to investigate the effects of design variables on the OCAF. It is shown that increasing the magnet thickness is effective for both increasing mean of the OCAF and reducing its variation. Finally, robust optimal design is performed using the H-RSM, in which all data are obtained from the FEM modeled by the slotted stator. The results of the robust optimal design are verified using the FEM.


This article originally appeared in Energies, available at

This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.



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