EXAMPLE OF ALTERNATOR DESIGN 



on a power factor of 0.8, it is necessary to know the maximum 

 armature m.m.f. and also the position on the armature surface 

 (considered relatively to the field poles) at which this maximum 

 occurs. It was shown in Art. 94, Chap. XIII, that the armature 

 m.m.f. can be represented by a sine curve of which the maximum 

 value (by formula (100)) is 



48 X 3 X 700 X \/2 

 (SI) a = - , - = 11,340 ampere-turns per pole. 



The displacement of this m.m.f. curve relatively to the center of 

 the pole is obtained approximately by calculating the angle /3 as 

 explained in Art. 98. The vectors representing the component 

 m.m.fs. have been drawn in Fig. 137, the angle ty' being calculated 

 from the previously ascertained values of the voltage vectors 

 (see calculations under item (40)). Thus 



cos \j/' 



0.763 



(0.8 X 3,810) + 8.4 

 4,000 



whence V = 40 40'. 



Since 27,000 ampere-turns per pole are required to develop 

 3,810 volts per phase, and since the saturation curve does not 

 depart appreciably from a straight line, the m.m.f. vector OM 

 to develop OE' (i.e., 4,000 volts) must represent approximately 

 27,OC 4,OC ^ 00 ampere . turns> and the required angle is, 



CM. 



ft = tan 



3,810 



where 



and 



OC 



CM = CM + MM = OM sin 

 = 29,740 



OC = OM cos $' 

 = 21,650 



+ 11,340 



The angle ft is thus found to be 53 57' or (say) "54 degrees. 



The sine curve M a representing armature m.m.f. can now be 

 drawn in Fig. 142, with its maximum value displaced (54 -f 90) 

 degrees beyond the center of the pole. The required field 

 ampere-turns are given approximately by the length of the vector 

 OM (Fig. 137), except that the increased tooth saturation has 



not been taken into account. The length OM is ^ <j = 



