68 THE MAGNETIC CIRCUIT [ART. 28 



(c) In a two-pole or four-pole machine it is necessary to use a 

 fractional-pitch winding in order to be able to place machine- 

 wound coils into the slots. 



A disadvantage of the fractional-pitch winding is that the 

 e.m.fs. induced on both sides of the same coils are not exactly in 

 phase with each other, so that for a given voltage a larger number 

 of turns or a larger flux is required than with a full-pitch winding. 

 Fractional-pitch windings are used to a considerable extent both 

 in direct- and in alternating-current machinery. 



Thus, the induced e.m.f . in an alternator or an induction motor 

 is reduced by the distribution of the winding in more than one 

 slot, and also by the use of a fractional-winding pitch. It is 

 therefore convenient to consider the breadth factor k b as being 

 equal to the product of two factors, one taking into account the 

 number of slots, and the other the influence of the winding pitch. 

 We thus put 



(32) 



where k 8 is called the slot factor and k w the winding-pitch factor. 



For a full-pitch winding k w =l, and kb = k s ', for a fractional- 

 pitch unislot winding k s =l, and k b =kw. The factors k 8 and kw 

 are independent of one another, and their values are calculated 

 in the next two articles. 



28. The Slot Factor k s . Let the stator of an alternator (or 

 induction motor) have two slots per pole per phase, and let the 

 centers of the adjacent slots be displaced by an angle a, in electri- 

 cal degrees, the pole pitch, T, corresponding to 180 electrical 

 degrees. If E (Fig. 17) is the vector of the effective voltage 

 induced in the conductors in one slot, the voltage E' due to the 

 conductors in both slots is represented graphically as the geometric 

 sum of two vectors E relatively displaced by the angle a. We see 

 from the figure that \E' = E cos i, or E' = 2E cos i. If both sets 

 of conductors were bunched in the same slot we would then have 

 E'= 2E. Hence, in this case the coefficient of reduction in 

 voltage, or the slot factor, k 8 = cos%a. 



Let now the armature stamping have S slots per pole per phase, 

 the angle between adjacent slots being again equal to a electrical 

 degrees. Let the vectors marked E in Fig. 18 be the voltages 

 induced in each slot; the resultant voltage E' is found as the geo- 



