A Multimaterial Topology Optimization Considering the PM Nonlinearity

Density-based topology optimization (TO) methodologies in magnetostatics interpolate either the magnetic permeability $\mu $ or the magnetic reluctivity $\nu $ to define intermediate materials and compute the problem sensitivities. These choices may lack physical interpretation and are not suited to model realistic permanent magnets. This work proposes the interpolation of the vector magnetic polarization $\boldsymbol {m}$ as a more general alternative, which can model any magnetic material. It is then applied to the multimaterial TO of the rotor of a permanent magnet synchronous machine. The case of an ideal permanent magnet with a constant magnetic polarization is compared to that of AlNiCo. The results show that considering the nonlinearity of the permanent magnet can significantly impact the optimized geometry.