Three-dimensional field computation for permanent magnet electric machines with finite axial magnet length

Using the method of separate variables, the three-dimensional magnet field solution expressed in Fourier's expansion for permanent magnet (PM) machines with finite axial magnet length is presented in this paper. From the analytic results obtained, much useful and interesting design information for PM machines in three dimensions may be quantitatively deduced. Design curves of the leakage factor and the air gap field characteristic coefficients for PM machines in three dimensions are given and compared with those in two dimensions. All the design curves given in the paper would be useful in preliminary performance calculations for both a.c. and d.c. PM machines.