An analytical solution for the field of a hysteresis motor based on complex permeability

A closed-form solution for the electromagnetic field distribution inside a hysteresis motor is presented. The solution is based upon Maxwell´s field equations, considering the case of a circumferential-flux-type machine at synchronous speed. A hysteresis loop in the shape of an inclined ellipse is adopted. The application of the complex permeability concept to space rotating vectors is explained. A new form for the general solution of Laplace´s equation is used. This new form makes it possible to obtain a proper matching between the field components at the rotor outer surface when the scalar potential function is used and the hysteresis is considered. The torque equation is developed in order to allow comparison with test results. The proposed solution is simple, accurate, and rigorous. Comparison with test results shows the accuracy of the method