Amplitudes of magnetomotive force harmonics for fractional slot windings — I

Fractional slot windings have certain well-known attributes which cause them to be quite generally used in synchronous-machine design. However, it is recognized that occasionally a winding will be produced which will develop harmonics in the air gap magnetomotive force that will lead to excessive losses, vibration, and noise. The published methods for computing the amplitudes of these harmonics are laborious to use and make a special case of every winding. It is the purpose of this paper to develop general formulas for computing the distribution factor and pitch factor of any magnetomotive force harmonic set-up by three-phase fractional slot windings of normal design. It is believed that these should permit in many cases a choice of winding arrangement such as either to eliminate or at least to minimize any undesirable harmonic so that its ill effects would be negligible. It is believed that the formulas are sufficiently simple to permit a complete tabulation of distribution and pitch factors over the normal range of slots per phase per pole now used in fractional slot windings.