Three-dimensional finite element solution of permanent magnet machines

The development of new types of permanent magnet material, particularly the rare earth-cobalt class, has created new interest in the design of electrical machines, torque couples, lifting magnets, and other electromechanical devices. In all of these cases, the magnetic field is the medium for energy conversion. The accurate computation of these magnetic fields is essential for realistic performance predictions at the design stage. Techniques for field computation have generally been restricted to the two-dimensional closed form [1] and numerical analysis[2,3]. However, permanent magnet electrical machine topologies are essentially three-dimensional [4], and, therefore, two-dimensional solutions may not yield the desired accuracy for certain applications. A three-dimensional field distribution which uses a magnetic scalar potential function may be obtained by using finite element analysis[5,6]. This paper presents a model for a permanent magnet material that leads to a simplified energy functional. Although the method is generally applicable to nonlinear anisotropic magnets, such as alnicos, this paper has verified that this approach is appropriate for an axial-field electrical machine that has SmCo5magnets which have linear characteristics.