Analytical Model of Air-Gap Magnetic Field in Doubly Slotted Electrical Machines with Distributed Windings

The quantities of interest in an electrical machine (e.m.f. and torque) can be evaluated once known the air-gap flux density. The paper shows how to analytically model this flux density distribution, as a function of time and of the rotor position, considering the actual disposition of slots and conductors and the geometrical characteristics of the air-gap periphery. The winding m.m.f. is evaluated by summing suited step functions; as regards the slots, specific field notch functions are obtained, by analytical field solutions and applying suited superposition techniques. The method is applied to constant air-gap machines, neglecting magnetic saturation.