64 



THE MAGNETIC CIRCUIT 



[ART. 26 



a? nearly as possible the pole shoes are shaped as shown 

 in the sketch, that is to say, so as to make a variable air-gap and 

 thus grade the llux density from the center of the pole to the edges. 

 In high-speed turbo-alternators the field structure often has a 

 smooth surface, without projecting poles (Fig. 33), in order to 

 reduce the noise and the windage loss. Such a structure is also 

 stronger mechanically than one with projecting poles. The grad- 

 ing of the flux is secured by distributing the field winding in slots, 

 so that the whole m.m.f. acts on only part of the pole pitch. 



Consider a conductor at a during the interval of time during 

 which the flux moves by one pole pitch T. The average e.m.f. 



FIG. 15. The cross-section of a synchronous machine. 



induced in the conductor is, according to eq. (26), equal to 

 where $ is the total flux per pole in webers, and T is the time of 

 one complete cycle, corresponding to 2r the space of two pole 

 pitches. But T=\/f, so that the average voltage induced in a 

 conductor is 



(29) 



The value of e ave thus does not depend upon the distribution of the 

 flux in the air-gap. 



If the pole-pieces are shaped so as to give an approximately 

 sinusoidal distribution of flux in the air-gap, the induced e.m.f. is 

 also approximately a sine wave, and the ratio between the effect- 



