122 



PRINCIPLES OF ELECTRICAL DESIGN 



should, in the first place, be the width of the narrowest part of 

 the tooth, as it is important that the density at this point be 

 known; it rarely exceeds 25,000 gausses in continuous-current 

 machines, and is less in alternators. When the field system 

 revolves, as in most modern alternators, the armature teeth 

 will usually be wider at the root than at the top, and but little 

 error will be introduced by taking for t the average width, for 

 the purpose of calculating the average density B t and the ampere- 

 turns required for the teeth. 



The case of a tooth with considerable taper, in which the 

 density at root is in excess of 10,000 gausses, may be dealt with 

 by the application of SIMPSON'S rule. Having determined the 

 density B t at the root of the tooth, by applying formula (62) or 

 (63) as the case may demand, the assumption is then made that 

 the total flux in the tooth remains unaltered through other 

 parallel sections. 1 



FIG. 38. Taper tooth. 



The value of the magnetizing force H (or the ampere-turns 

 required per unit length) can then be determined for any section 

 of the tooth by referring to the B-H curves for the iron used in 

 the armature. It is sufficient to determine H for three sections 

 only. 

 Let these values be: 



H n at narrowest section 

 H w at widest section 



(MJ *j 



i.e., where the value of B m is - " o ' / 



1 This is not a correct assumption when the root density is very high, be- 

 cause in that case flux will leak out from the sides of the tooth to the bottom 

 of the slot; and at some distance from the bottom of slot (the taper being 

 as indicated in Fig. 38) the total flux in the tooth will be greater than at the 

 root cross-section. 



