Research on Matching Interpolation Functions and Field Calculation Methods in Multi-Material Topology Optimization of Electric Machine

The Solid Isotropic Material with Penalization (SIMP) method is highly regarded in the field of topology optimization due to its ease of implementation and conceptual clarity. However, in the realm of multi-material topology optimization for electric motors, the non-linear characteristics of soft magnetic materials make the choice of interpolation function crucial, as it significantly impacts the computational results. Through analysis, it is revealed that the matching relationship between interpolation methods and magnetic field calculation methods is crucial, specifically, interpolation functions should not be placed in the denominator of the dependent variable for field calculations, as it leads to computational instability. To validate this hypothesis, it was confirmed that the permeability interpolation based on magnetic scalar potential electromagnetic field calculation is also stable.