The shape of pole-shoe required to produce a sinusoidal distribution of air-gap flux density

Considerable interest has recently been shown in the complete elimination of all harmonics from the induced E.M.F. wave-form of an alternator. The methods usually employed in practice for the purification of the wave-shape fall into two classes: (a) in which certain harmonics are removed by proper choice of the characteristics of the armature winding, and (b) in which an endeavour is made to attain the desired end by producing a sinusoidally distributed flux round the air-gap. The object of the present paper is to give the theory of a commonly used method of the second class, in which the reluctance of the gap from point to point is adjusted to the value proper to the sinusoidal flux by shaping the pole-face to give a gap of varying length, longer at the tip than at the centre of the pole. The problem is solved for the case of a smooth-core armature, or for one in which the slots have been closed by means of magnetic wedges, such as would be used in a wave-form standard. Flat and circular armatures with any number of poles are dealt with, the shape of the pole-shoes and the permeance of the gap being determined in each case. The paper concludes with a numerical example illustrating the theory given in the text.