164 PRINCIPLES OF ELECTRICAL DESIGN 



being one and one-half times the equivalent slot flux given by 

 formula (77). The equivalent flux when the total slot flux enters 

 the tooth top instead of passing through root of tooth is no longer 

 expressed by formula (77); it may be calculated thus: 



The magnetic lines represented by the expression d$ = 



x dx x 



0.47T (27 7 / c ) -5 no longer link with 2T -3 conductors, but with 



2T- -j - conductors (see Fig. 62). The equivalent flux, when 



no part of this flux passes into the armature core below the teeth, 

 is therefore 



x i 



d-x 



- 21 C 



a jo 



X 



I 



d 



d 



x(d x)dx 

 / 



J-frrt* TJ , /o m 



-^-11 da 



or just half the equivalent slot flux as given by formula (77). 

 The question now arises : What is the necessary total flux enter- 

 ing the tops of the teeth comprised in the commutating zone to 

 develop the proper voltage component in the short-circuited 

 coil? 



A total slot flux as given by formula (79) has the "equivalent" 

 value as given by formula (80) ; that is to say, it is on the basis 

 of the assumptions previously made three times as great as 

 the equivalent flux. The total flux entering the teeth comprised 

 in the commutating zone should therefore be 



$ c = 3<p' e8 -f- flux passing directly into armature core through 

 the teeth. 



but &ea + $d = $ e , where 3> e is, in this particular instance, the 

 equivalent value of the total flux to be cut by the "active" 

 portion of the short-circuited conductors. 

 Thus 



ft. --29V+*, (81) 



or, if preferred, 



, , /Qf)\ 



Cp cp f- Q5 I o^ ) 



where $ e . is the equivalent slot flux as originally calculated and 

 expressed by formula (77). 



