Inductances of a Practical Slip-Ring Primitive I - An Analytical Study

Complete inductance expressions for the windings of practical slip-ring machines are derived in terms of air-gap magnetomotive force and air-gap specific permeance. These expressions are presented in a form which facilitates verification by experiment. Deviations between the inductances of the practical and the idealized slip-ring primitive machines are-noted for a variety of winding configurations. It is shown that the existence of a nonzero third harmonic of magnetomotive force plays a significant role in the form of the cylindrical-salient and cylindrical-cylindrical inductance expressions, especially with regard to similarities between the two. Moreover, it is demonstrated that, for conditions which result in zero third-harmonic magnetomotive force in the air gap, the inductance quantities just mentioned revert to a form which, for practical machines, is consistent with that of an ideal generalized machine.