Force calculation of electric machines with a flat air-gap using hybrid finite element mesh

The macro air-gap element and its torque formulation were proposed earlier by Abdel-Razek et al. for modeling electrical machines with an annular air-gap. This paper extends the existing formulation for force calculation in the finite element model incorporating a two-dimensional Cartesian macro air-gap element. The new formulation can be useful for force or torque calculation of some special electric machines with a flat air-gap such as linear and axial flux machines. For validation purpose, the new formulation is implemented to model a single-sided axial flux permanent magnet machine with non-overlap concentrated windings. The solution generated using the new formulation is validated by comparing it with that of the virtual work method and measurements. It shows that the new formulation is computationally efficient and accurate.