Analysis of the Hysteresis Machine - Part I

A theoretical model has been developed for the hysteresis motor by solving Laplace\´s equation for the field in the air gap and the rotor ring subject to appropriate boundary conditions. The hysteresis phenomenon is accounted for through the use of an elliptical approximation for the hysteresis loop. The relation between the magnitude of the fundamental components of the B and H waves is assumed to be linear and the phase shift between them, due to hysteresis, is assumed to be constant. However, an iteration procedure is described to account for the nonlinearity in the actual machine. A similar approximation is used to represent the minor loops described by the harmonic components of the field, and the effect of MMF and slot harmonics on machine performance is thus estimated. Rigorous analysis predicts and evaluates the "gap leakage field," which constitutes a part of the main field without penetrating the rotor material. The inclusion of this field in the model is shown to eliminate the nonrealistic assumption that the B and H waves in the rotor material are in phase. The model is used to evaluate the output torque and the EMF and power factor of the stator windings. A simple equivalent circuit is developed, in which the three fields present inside the machine, two in the air gap and one in the rotor, are represented by individual elements. The nonlinearity of the rotor material is represented in the equivalent circuit by a nonlinear impedance whose characteristics are directly predictable from the shape of the B-H curve. A comprehensive model has been obtained which is flexible enough to handle the different nonlinearities. It has been rigorously derived from the field equations, and therefore is expected to be very useful in further investigations of the hysteresis machine.