## 1 Introduction
To address the challenges associated with the complex structure, intricate design, and difficult processing and assembly of permanent magnet bearings, another paper [12] proposed a modular permanent magnet bearing. This work introduced the bearing's operating principle and examined its performance through computer simulations. The widespread use of composite materials also opens up new possibilities for the structural design of permanent magnet bearings. One study [13] proposed a new type of composite material used to construct a permanent magnet bearing applied in a level gear-coupled rotor system. This study involved the optimization of structural parameters, analysis of the magnetic field, and assessment of dynamic stiffness in the permanent magnet bearings, demonstrating the advantages of composite material applications. Additionally,optimized design remains a key strategy for improving bearing load-carrying performance. Another study [14] introduced a simplified numerical method to predict the performance of various permanent magnet bearings and subsequently optimized parameters such as the number of permanent magnet rings and the air gap. Permanent magnet motors represent another key application of permanent magnet drive systems. The design of permanent magnet bearings is influenced by several factors, including the arrangement of permanent magnets, the materials used, the method of embedding, the shape of the magnets, and the application of finite element analysis techniques. To investigate the impact of different magnet arrangements on the performance of permanent magnet motors, researchers [15] constructed three different types of permanent magnet motors, analyzed their performance using finite element analysis, and calibrated the output power range for each configuration. The choice of material also significantly impacts the performance of permanent magnet motors. Research referenced in [16] investigated the effect of using different permanent magnet materials, examining how variations in the number of materials influence motor characteristics through finite element simulations, thus revealing the complex relationship between the material properties and motor performance. Additionally, nanostructured permanent magnet materials are considered a promising option for the next generation of high-strength permanent magnets. However, the mass production of nano-sized permanent magnets remains challenging, as traditional sintering processes are unable to produce nano-sized permanent magnets directly. The authors of [17] reviewed the research progress in aspects such as grain size control, interface modification, and the generation of anisotropy of nano permanent magnets, providing certain guidance for the manufacturing and application of nano permanent magnets. Due to the high cost of permanent magnet materials, the expense of using a large number of permanent magnets in propulsion systems is often economically unfeasible. To address this, [18] introduced an innovative approach to reduce the number of permanent magnets required to create a permanent magnet drive train. This method, which minimizes or eliminates the use of rare-earth permanent magnet materials, led to significant cost savings while still meeting performance requirements. When analyzing permanent magnet rotational systems using the finite element method (FEM), the enormous computational volume often consumes considerable resources. To overcome this, [19] proposes a new optimization algorithm that constructs a high-precision agent model while reducing the need for extensive FEM analysis. The optimization results and the accuracy of the FEM analysis are subsequently verified through experiments, demonstrating the efficacy of this approach in improving computational efficiency.