Particle Swarm Optimization on Size of Halbach Array Permanent Magnets

This paper addresses the size optimization of Halbach array permanent magnets in a maglev planar motor and proposes a design method based on Particle Swarm Optimization (PSO) algorithm. By establishing an analytical model of the electromagnetic force between the Halbach array and a two-phase Lorentz coil, the spatial magnetic field distribution characteristics are analyzed, revealing significant issues in traditional designs, such as low magnetic field utilization and instantaneous force fluctuations. To address this, the equivalent average force (F<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ave</inf>) is introduced as a performance evaluation index, ensuring that the average force within half a cycle can support the platform in achieving magnetic levitation and moving with a specified acceleration. The goal of this study is to use PSO as a method to reduce the cost of the magnets in the Halbach array and to design their sizes in a way that reduces manufacturing costs and design cycle time. This paper details the dimensions and optimization process of the Halbach array machine, with the objective function aiming to minimize the magnet volume to reduce costs. An exterior penalty function is used to convert the objective function into an unconstrained problem, and the optimal solution is searched within the two-dimensional parameter space using PSO. Finally, the results of the electromagnetic force analytical model are compared with those from finite element simulations, validating the effectiveness of the proposed method.