A Novel 3-D Analytical Modeling Method of Trapezoidal Shape Permanent Magnet Halbach Array for Multi-objective Optimization

In this paper, a novel three-dimension magnetic flux density analytical model of linear permanent magnet (PM) Halbach arrays with trapezoidal shape PMs, is established based on the theory of magnetic charge. The proposed analytical model is numerically efficient and can be utilized to evaluate the effects on motor performance caused by varying their configurations. Furthermore, the configurations of PMs for both single and double-sided structures are optimized exploiting a surrogate model assisted by a multi-objective optimization algorithm, where the surrogated model is constructed by the kriging method with expected improvement utility function. The validity and accuracy of this proposed analytical model is verified via finite element modeling, the optimization results with different schemes of weight distribution show the further improvement of magnetic flux density distribution.