Unified Analytical Model from Radial to Axial Permanent Magnet Machine: Conical Flux Machine

The modeling of radial flux machines is well-known and developed, as well as the modeling of axial flux machines. However, these two models are radically different, and comparing them for a common set of parameters is often difficult. Therefore, this paper presents a common formulation in order to easily compare radial and axial flux machines for given specifications. This paper deals with a continuous unified model between radial and axial flux machines by defining a conical air-gap machine. It is formulated and solved on the basis of the magnetic scalar potential decomposed into Fourier series. The modeling developed in this paper thus includes the flux linkages in the air-gap. Validation by the finite element method is performed and analyzed to determine the validity range on a wide range of machine designs. The unified model is then used to calculate the electromagnetic torque in integral form. The volumetric performances of conical machines are compared with those of conventional machines. The advantages of conical machines are highlighted according to the angle of orientation of the air gap.