228 GENERAL DIAGRAMS FOR SYNCHRONOUS MOTORS 



In the case of a fractional pitch or short-chord winding, there is a 

 phase difference between the E.M.F.'s in the two sides of each coil, 

 or in the ordinary two layer winding, this same phase difference 

 exists between the E.M.F.'s of the two belts or groups of coil sides, 

 w r hich together make up one circuit between taps. This introduces 

 another reduction of the resultant E.M.F. If Xc is the coil pitch in 

 terms of full pitch, the pitch differential factor between the two belts 



is, for the fundamental (see Fig. 29), OB -^-(0 A -{-OB) = sin -Xc, 



2 



and for the wth harmonic is sin Xc. The ratio of the latter to the 



2 



former will be designated the pitch reduction factor for the wth har- 

 monic; it is 



kpm = 



X. 



sin m 

 2 



sn 

 2 



_ per cent, of with harmonic in fractional pitch winding 

 per cent, of tth harmonic in full pitch winding 



(7) 



This is plotted in Fig. 30 for various pitches and harmonics 

 (signs disregarded). 



If the phase belt begins and ends in the middle or within a coil 

 or slot bundle, there is a still farther reduction of the resultant 

 E.M.F. The corresponding fractional slot reduction factor is 



cos -^ (for half-slot connection). 



- 



cos 



2Ntp ' 6Nsp 



-- HCOS 



2Ntp 4Ns P 



(f r a one-third or a two- 

 thirds slot connection). 



mx (for a one-fourth or a three- 



- ,. . . 



fourths slot connection). 



(8) 



