Three-dimensional analytic model for permanent magnet electric machines with finite core length

An analytically extended PM model with fictitious PM arrays is presented in the paper for solving the field problem of PM electric machines in three dimensions. To consider the effect of finite core length, each PM array is assumed to face a fictitious core array together with the actual armature core. By using the analytic approach and the PM model presented, the three-dimensional field problem for PM machines with different magnet aspect ratios and different axial magnet extensions may be accurately and efficiently solved. Two computed examples using the analytic approach have been verified by test results. Design curves given in the paper would be useful in PM machine design practice.