The calculation of harmonics, due to slotting, in the flux-density waveform of a dynamo-electric machine

Abstract

Equations derived from conformal-transformation theory are used to calculate the shape, and hence the harmonic content, of the tooth-ripple flux-density waveform at the pole-face in the air-gap of a dynamo-electric machine with smooth poles. Curves are included to enable the equation of the waveform to be obtained for any value of s/g and for 0 < s/λ < 0.8.The formulae for the calculation of the necessary elliptic functions and integrals are taken from ‘Numerical Evaluation of Elliptic Functions and Elliptic Integrals’ by L.V. King. These formulae do not appear to be well known, but they converge more rapidly than the q-series formulae.The numerical calculations were performed on an electronic digital computer.