Calculation of inductance in permanent-magnet DC motors

The classical literature on DC motor design tends to focus on commutating inductance rather than total armature inductance, and does not provide a complete procedure for all the inductance calculations that are needed in permanent-magnet motors. The armature inductance is important, partly because of its effect on the electrical time constant, and partly because of its effect on the current waveform and torque when the motor is supplied from a phasecontrolled converter or chopper. The inductance formulas needed in PM motors differ appreciably from those used with wound-field machines. The paper presents a comprehensive but concise account of the theory and computation of both the armature inductance and the commutating inductance in a form suitable for rapid computer calculation. In the armature inductance, new formulas for the airgap component are introduced and its importance is underlined by the fact that it accounts for about half the total inductance in several of the motors tested. This is an unexpected result, since the airgap component appears to have been overlooked in previous literature. Results are verified by experiment and finite-element analysis, and the paper describes the theoretical basis for the necessary connections to achieve the correct inductance by measurement.