118 PRINCIPLES OF ELECTRICAL DESIGN 



of the iron in the tooth becomes equal to unity that is to say, 

 equal to the permeability of the air paths that this parallelism 

 of the flux lines would occur, and the equivalent air gap would 

 be b e d, to which would have to be added another air gap of 

 length d (Fig. 37) to represent the reluctance of the teeth and 

 slots. This is an extreme, and indeed an impossible, condition; 

 but, since the actual distribution of the lines of flux in tooth and 

 slot cannot be predetermined, the calculations for very high 

 densities are usually made by assuming the flux lines to be 

 parallel, as indicated in Fig. 37. It is when this assumption is 

 made for low values of the density that appreciable errors are 

 likely to be introduced. The following method of calculating 

 the joint reluctance of tooth and slot should not be used for tooth 

 densities below 20,000 gausses. 



Considering 1 cm. only of axial net length of armature core 

 (i.e., 1 cm. total thickness of iron), the reluctance of the air 

 gap and tooth, taken over the width of one tooth only, is, 



*.* (d + d) 



**1 7 I 4 ~ 4 



t id pt 



The reluctance of the slot portion of the total tooth pitch is, 



The air gap of the equivalent smooth-core armature being the 

 reluctance per square centimeter or the reciprocal of the perme- 

 ance per square centimeter is, therefore, 



Se = T^T 



Rl RZ 



which can be put in the form, 



_ . 



d + s 



This equivalent air gap includes the reluctance of the tooth itself 

 when the flux density is high, but does not take account of the 

 flux in the vent ducts and spaces between stampings. It is 

 seen to depend upon the permeability of the iron, and, therefore, 

 upon the actual flux density in the tooth. In order to make use 

 of formula (59) , a value for the flux density in the tooth must be 

 assumed. A method of working which involves a change in the 



