FLUX DISTRIBUTION 



121 



whence 



d 



fw\ 



Considering, now, the total flux entering the armature over 

 one slot pitch, this is made of two parts: 



1. The flux in the iron of the teeth, of value J3tf. 



2. The flux in the slots and ducts, of value 



B s [&la +t(l a - In)] 



or 



B, (U - l n t) 



The total flux entering through one slot pitch can also be 

 expressed in terms of B g , being: 



$x = B \l a 

 Thus 



B g \l a = B t tl n + B 8 (\l a - tl n ) (61) 



Substituting in (61) the value for B 8 given by formula (60) in 

 terms of B t) and solving for B 0) we get: 



By assuming values of B t ranging between 20,000 and (say) 

 26,000 gausses, the corresponding values of B can be calculated 

 by formula (62), and a curve plotted from which values of B t can 

 be found when B g is known. 



The fact that this formula is based on assumptions justified 

 only if the value of B t is very high should not be lost sight of. 

 For very low values of B t it may be assumed that all the flux 

 entering through one slot pitch passes through the iron of the 

 tooth. This leads to the expression: 



H R a 



Bt - 



(63) 



Curves may be plotted from the formulas (62) and (63) and a 

 working curve, which shall be a compromise between these two 

 extreme conditions, can then readily be drawn. This will be done 

 when working out a practical design in a later chapter (p. 216). 

 38. Correction for Taper of Tooth. The assumption of parallel 

 sides to the tooth is justified only when the diameter of the 

 armature is large relatively to the slot pitch or when taper slots 

 are used in order to provide a uniform cross-section throughout 

 the whole length of the tooth. The dimension t in formula (62) 



