Topology Optimization Based on Regularized Level-Set Function for Solving 3-D Nonlinear Magnetic Field System with Spatial Symmetric Condition

Topology optimization (TO) is an effective method for producing practical design of electrical machines. TO is conventionally implemented based on the material density; however, this approach can yield a large number of grayscale areas and unfeasible shapes. On the other hand, when the level-set function is applied to the TO of the magnetic field problem, the potential for obtaining a feasible solution improves. This paper implemented a TO method that uses the regularized level-set function to solve the 3-D nonlinear magnetic field problem. Furthermore, a spatial symmetry condition (SSC), which can introduce the mirror and periodic symmetry of the level-set function from the viewpoint of the electromagnetism, is proposed. To achieve symmetry in the electromagnetic field distribution, the validity of the SSC is investigated and confirmed in a 3-D magnetic shielding problem.