Structural optimization of ferromagnetic materials based on the magnetic reluctivity for magnetic field problems

Topology optimization of ferromagnetic materials in magnetic fields using the homogenization method and the density method has been attempted from an angle of the interpolation scheme based on the magnetic permeability. However, optimization results based on such methods may have poor convergence history in comparison with the structural topology optimization of an elastic problem. This study intends to verify that the interpolation scheme using the magnetic permeability may cause problems in the sensitivity analysis for the structural optimization in magnetic fields and suggests a novel interpolation scheme based on the magnetic reluctivity. Numerical examples are focused on magnetic actuators to maximize the magnetic force attracting an armature. This study is focused to maximize force itself using the Maxwell stress method and the sensitivity analysis by the adjoint variable method whereas previous work to maximize force are based on the magnetic energy computation mostly without considering the actuating direction. It is confirmed that optimal models by the proposed method have improved performance and better robust iteration history compared with the previous method.