A Mathematical Model of a Reactive Two-Pole Electric Machine with Anisotropic Permeance of the Rotor

A mathematical model of a reactive electrical machine with anisotropic permeance of the rotor is discussed. Calculations of the power performance characteristics for this electrical machine, a description of the magnetic field of a two-pole machine with anisotropic permeance of the rotor, and a mathematical description of its permeances are presented. Analytical relations for determining the magnetic field direct and quadrature components are obtained based on the machine magnetic circuit equivalent circuit diagram. The introduced magnetic asymmetry coefficient is an indicator from which the influence of fastening recesses, as well as the rotor inter-pole air gap on the machine characteristics is estimated. The graphic dependence of the magnetic asymmetry coefficient on the rotor pole overlap coefficient with the anisotropy equal to unity demonstrates the effect these parameters have on the quality and power performance characteristics of a reactive electrical machine with anisotropic permeance of the rotor. A conclusion has been drawn from the data presented that an increase in the magnetic asymmetry coefficient results in that the sinusoidal distribution of magnetic induction becomes distorted, and that higher harmonic components appear in the pulsations of the stator phase winding inductances, and as a consequence, pulsations appear in the machine electromagnetic torque.