Spatial Discretization Methods for Air Gap Permeance Calculations in Double Salient Traction Motors

Weight limitations in electric/hybrid cars demand the highest possible power-to-weight ratio from the traction motor, as in double salient permanent magnet (PM) machines. Their high flux densities in the air gap result in nonlinear analytical models, which need to be time optimized. The incorporated reluctance networks are sensitive to the correctness of air gap permeances. Conventionally, in these networks, air gap permeances are calculated by approximating flux paths; however, it is time inefficient. For an improved simulation time, spatial discretization techniques are presented to calculate air gap permeances in double salient PM machines. The spatial techniques discussed here cover the tooth contour method and Schwarz-Christoffel (SC) mapping as semidiscrete methods, which are used to discretize only the air gap region. Their results are verified by the spatial discrete method and finite element method, which discretizes the whole machine geometry. For consistency in this paper, all methods are explained on a three-phase 12/10 flux-switching PM motor. Obtained air gap permeances show a very good agreement with only 0.8% difference. Further on, machine characteristics such as phase flux linkage and cogging torque are also compared to show the impact of the modeling techniques. The total machine simulation time is improved by 20% using the SC method. Although methods are explained particularly for double salient PM machines, formulas are generalizable for other machine types as well.