Ubiquitous uncertainty from design, fabrication, and assembly often leads to erratic or infeasible cogging torque solutions, which observably enlarges the difficulty of the robustness-oriented design optimization (RDO) of PMSM. Robustness-oriented design optimization approaches based on FEA (finite element analysis) are still inefficient. Despite adequate surrogate and analysis models, RDO's efficiency and accuracy, considering multi-source uncertainty and repetitive elements, still need to be improved to meet practical needs. Therefore, a physically based surrogate model-assisted RDO approach is proposed in this study and comprises two main contributions. First, we develop an accurate and efficient physical-based surrogate model and the data-based layer model, including an improved vector superposition approach that characterizes both the relationship between rotor permanent magnet uncertainties and the additional harmonics, and the relationship between the rotor permanent magnet design parameters and the inherent harmonics of the cogging torque. The organic combination of these two models realizes the high-efficiency and high-precision calculation of the PMSM cogging torque. Second, we propose an overall RDO strategy for the various uncertainties and high dimensionality. This study presents and discusses the RDO results of the PMSM used in high-precision robots and machine tools. Experimental and simulation results are presented to validate the effectiveness of the proposed surrogate model, strategy, and approach.

A permanent magnet synchronous motor (PMSM) is a crucial device for power conversion in an energy system. The cogging torque of the PMSM is a crucial output characteristic, the robustness of which affects the operational reliability of the energy system. Therefore, the robust design optimization (RDO) of cogging torque has aroused widespread concern. There are several challenges in designing a robust cogging torque PMSM. In particular, some design parameters contain repetitive units, and the finite element analysis (FEA) method is time-consuming. State-of-the-art RDO methods usually treat these uncertainties from repetitive units as the same parameter, which neglects the fluctuation of the manufacturing process and cannot obtain a robust solution for the cogging torque of the motor efficiently and accurately. In order to solve this issue, an approximate modeling method based on manufacturing uncertainties analysis for RDO is proposed in this paper. First, the peak-to-peak value of cogging torque (T_cpp) is used to characterize the cogging torque, which is decoupled to an ideal component and fluctuation component produced by the center values and manufacturing tolerances of design parameters. The design of experiments (DoE) and simulation of the two components are carried out. Then, these two components are approximated separately, and the approximate model of T_cpp is obtained by adding the two components. Finally, the proposed approximate model is embedded into the RDO algorithm, and the PMSM design scheme for good T_cpp robustness is obtained. The effectiveness of the proposed method is verified through a case study of the PMSM.