In order to optimize the electromagnetic performance of a permanent magnet synchronous motor (PMSM) during operation, this paper takes the size of the stator slot structure of the motor as the optimization variable and the peak cogging torque and no-load back electromotive force (EMF) amplitude of the motor as the optimization objectives. A multi-objective optimization method based on the particle swarm optimization (PSO) algorithm is adopted to obtain a structural parameter combination that minimizes the peak cogging torque and no-load back EMF amplitude while meeting the reasonable range requirements of magnetic flux density amplitude. The optimized motor structure design prototype is experimentally verified. The results show that through multi-objective optimization based on the PSO algorithm, the electromagnetic performance of the motor has been improved, with a reduction of 36.33% in peak cogging torque and 2.65% in peak no-load back EMF, indicating a reasonable magnetic flux density amplitude. The experimental results of the optimized prototype show that the difference between the theoretical simulation values and the experimental values is within a reasonable range, which verifies the effectiveness of the multi-objective optimization method.

In this paper, the multi-objective optimization of the 12-pole radial active magnetic bearing (RAMB) is investigated. In the optimization of the RAMB, the decision-maker is more interested in the Pareto-optimal solutions in a certain region. This paper proposes a decomposition-based and preference-based multi-objective evolutionary algorithm (MOEA/D-Pref). The proposed MOEA/D-Pref not only allows the number of Pareto-optimal solutions to be more concentrated in the region of interest but also preserves solutions in other regions. These preserved solutions enable decision-makers to observe a more complete Pareto front, thus gaining more comprehensive insights. In this paper, a mathematical model of the 12-pole RAMB is established, and, with the help of this model and the proposed algorithm, the optimal design of the 12-pole RAMB is completed. The difference between the current stiffness coefficients of the optimized RAMB, calculated by the proposed algorithm and by the finite element method, is 2.3%. The difference between the displacement stiffness coefficient of the optimized RAMB as calculated by the proposed algorithm and by the finite element method is 3.9%. These differences, being less than 4%, are relatively low and verify the reliability of the mathematical model established.