Topology optimization of IPM motors with V-shaped permanent magnets using a grayscale free phase-field-based level set method

Purpose This study aims to optimize the internal structure of an interior permanent magnet synchronous motor (IPMSM) with V-shaped magnets to maximize torque. Specifically, it addresses the issue of grayscale (intermediate density) regions that appear near material interfaces in conventional phase-field-based level set methods. The primary objective is to eliminate these intermediate regions to prevent inaccuracies in finite element analysis and to resolve ambiguities in practical manufacturing. Design/methodology/approach The proposed method employs a phase-field-based level set framework combined with a dynamic remeshing technique. Unlike conventional approaches that rely on fixed meshes, the computational mesh is regenerated after each update of the level set function so that the mesh explicitly conforms to material boundaries. The optimization problem is formulated to maximize instantaneous torque, and sensitivity analysis is conducted using the adjoint variable method. In addition, the sensitivity of the optimization algorithm to different initial shapes and interface parameters is systematically investigated. Findings The proposed remeshing strategy successfully suppresses the formation of grayscale regions, resulting in optimal structures that are completely free of intermediate density regions and exhibit improved structural clarity and manufacturability. The method also demonstrates low sensitivity to variations in the initial shape, yielding stable optimization results. However, the final geometry and torque performance depend strongly on the appropriate selection of the interface propagation speed and diffusion coefficient. Ultimately, the optimized design achieves a 146.2% increase in torque compared with the initial configuration. Originality/value This research provides significant value by addressing the persistent issue of grayscale regions near material interfaces in phase-field-based topology optimization for electric machines. While prior studies typically relied on fixed meshes, this work integrates a dynamic remeshing strategy tailored for IPMSM design to achieve strictly grayscale-free optimal structures. Furthermore, the study contributes original insights by systematically investigating the sensitivity of the optimization algorithm to initial conditions, an aspect that has received limited attention in electromagnetic topology optimization literature.