Topology optimization of magnetic composite microstructures for electropermanent magnet

Abstract

This paper presents topology optimization for the design of magnetic composite applicable to electropermanent magnet. Here, the magnetic composite is built from a periodic microstructure consisting of air, iron and permanent magnet (PM) materials. The combination of non-magnetic, soft and hard magnetic materials in a microscopic scale enables to produce its own persistent magnetic field like PM material, and also enables the control of the magnetic field by an external current like iron material. This work aims to find the optimal microstructure unit cell layout of the electropermanent magnet, and estimate its cross-property bounds. Here, the cross-property bounds connect the effective magnetic permeability and residual flux density, which are calculated using the asymptotic homogenization method. The design objectives (i.e. desired effective properties) are theoretically studied with consideration of application to electromechanical devices. Then, an multi-objective optimization problem to achieve desired effective properties is formulated and solved with a multi-material gradient-based topology optimization formulation. As a result, the optimal composite unit cell layouts that constitute the Pareto fronts are successfully obtained. From the Pareto fronts, cross-property bounds of the electropermanent magnet are numerically constructed and discussed.