Topology optimization of Halbach magnet arrays using isoparametric projection

Topology optimization using isoparametric projection for the design of permanent magnet patterns in Halbach arrays is proposed. Based on isoparametric shape functions used in the finite element analysis, the permanent magnet strength and magnetization directions in a Halbach array are simultaneously optimized for a given design goal. To achieve fabrication feasibility of a designed Halbach magnet array, two design schemes are combined with the isoparametric projection method. First, a penalization scheme is proposed for designing the permanent magnets to have discrete magnetization direction angles. Second, an extrusion scheme is proposed for the shape regularization of the permanent magnet segments. As a result, the method systematically finds the optimal permanent magnet patterns of a Halbach array considering manufacturing feasibility. In two numerical examples, a circular shaped permanent magnet Halbach array is designed to minimize the magnitude of the magnetic flux density and to maximize the upward direction magnetic flux density inside the magnet array. Logical extension of the method to the design of permanent magnet arrays in linear actuators is provided, where the design goal is to maximize the actuator magnetic force.