152 



THE MAGNETIC CIRCUIT 



[ART. 48 



by fictitious poles of the same shape as the main poles, because 

 harmonics of appreciable magnitude are thereby neglected. How- 

 ever, actual experience shows that the performance of a machine, 

 calculated in this way, can be made to check very well with the 

 observed performance, by properly selecting the coefficients of the 

 direct and the transverse reaction. In a generator, the flux is 

 crowded against the direction of rotation of the poles (Fig. 36) ; 

 consequently, the fictitious poles lag behind the real poles, as 

 shown in Fig. 39. In a synchronous motor they lead the real 

 poles by 90 electrical degrees. 



If the ratio of the pole arc to pole-pitch were equal to unity, 

 as with non-salient poles, the whole wave of the demagnetizing 



Actual distribution 

 !" trans verse flux 



Flux distribution 

 due to fictitious pole 



Rotation 



FIG. 39. The direct and transverse armature reactions in a synchronous 

 machine, represented by fictitious poles and field windings. 



m.m.f. of the armature would be acting upon the pole, and the 

 equivalent concentrated m.m.f. M d on the pole would have to be 

 equal to the average value of the actual distributed armature 

 m.m.f. We would have then 



(78) 



where the maximum armature m.m.f. is determined by eq. (64), 

 Art. 43, and 2/K = 0.637 is the ratio of the average to the maximum 

 ordinate of a sine wave. In reality, only a part of the armature 

 m.m.f., the one near its amplitude, acts upon the poles, the action 

 of lower parts of the wave being practically zero because of the 

 gaps between the poles. Therefore, the ratio between the maxi- 

 mum m.m.f. M sin $ and the average equivalent m.m.f. Md is 



