This problem investigates the advantages of short-pitching the stator coils of an ac machine. Figure shows a single full-pitch coil in a two-pole machine. Figure b shows a fractional-pitch coil for which the coil sides are ? radians apart, rather than ? radians (180?) as is the case for the full-pitch coil. For an air-gap radial flux distribution of the form where n = 1 corresponds to the fundamental space harmonic, n = 3 to the third space harmonic, and so on, the flux linkage of each coil is the integral of Br over the surface spanned by that coil. Thus for the nth space harmonic, the ratio of the maximum fractional-pitch coil flux linkage to that of the full-pitch coil is It is common, for example, to fractional-pitch the coils of an ac machine by 30 electrical degrees ?= 5?/6 ? 150?). For n ? 1, 3, 5 calculate the fractional reduction in flux linkage due to short pitching.

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B, cos ne B, = %3D n odd 8/2 B, cos ne de B, cos no do cos ne de -B/2 I-B/2 12 = Isin (nB/2)| S, S, cos no de Bn cos no de -/2 N-turn coil Rotor Rotor Stator Stator (a) (b)