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.