A Forward Approach for Topology Optimization and Magnetization Direction Optimization of Permanent Magnets

The paper proposes a forward method to determine the optimal direction of the magnetization of permanent magnets as well as its optimal shape in order to maximize the magnetic flux in a coil. The method can be advantageously used, for example during the design stage of an electrical machine in order to maximize the flux in the stator windings generated by the permanent magnets located on the rotor. The method is first developed in the continuous domain. It appears that the optimal permanent magnet configuration can be determined from the magnetic flux density distribution generated by the coil when it is supplied by a current of 1A. No need to solve any inverse problem to find the optimal configuration since the procedure is explicit. It is shown that this method remains still valid in the discrete domain when the finite element method is applied and can take advantage of this method for topology optimization. Two configurations of permanent magnet magnetization are considered having either a continuously variable direction or made with blocks on which the direction is constant as in an Halbach array. In the same way, for topology optimization, two cases are considered when the magnetization is fixed or considered as a variable to be optimized. A 3D example is treated in order to illustrate the effectiveness of the method.