The effect of load on the air-gap field and forces in induction machines

An accurate method is given for the determination, under load conditions, of the tooth-ripple flux and force pulsations produced by the relative motion of the slotted stator and rotor surfaces in induction machines. These pulsations are obtained using a conformal transformation field solution and the Maxwell stress fiction. When using conformal transformation to solve the field in the air-gap region, or in any region having a complicated polygonal boundary, it is necessary to evaluate integrals containing singularities numerically. A number of quadrature methods for performing this process are reviewed and two methods are described for the evaluation of Cauchy Principal Values which arise with boundaries having parallel sides. The tooth-ripple flux and force pulsations are computed, for a given stator slot number, and a range of rotor slot numbers and rotor positions. The results are presented graphically. In order to assess the influence of slot combination on these pulsations, the peak to peak values of the largest flux, normal and tangential force pulsations are used as defining quantities. A number of simple equations are derived relating these quantities to the slot pitch difference, and these equations are used to determine the conditions under which the flux and force pulsations into a stator or rotor tooth are minimal. Furthermore, conclusions are drawn about the choice of slot combination. In addition, the fundamental tooth-ripple components of torque are computed for the same slot combinations as the flux and force pulsations. The influence of slot combination on this torque component is examined. Conclusions of practical value are drawn from the results obtained.