LOSSES IN ARMATURES 103 



in the teeth will be again referred to when discussing the m.m.f. 

 necessary to provide the required flux; and formulas will be 

 developed for use in calculating the actual flux density in the 

 iron of the teeth. For the purpose of estimating the tempera- 

 ture rise, we shall assume that the whole of the flux from each 

 pole enters the armature through the teeth under the pole (the 

 effect of fringing at pole tips being neglected) ; and if the teeth 

 are not of uniform section throughout their length, the average 

 section will be used for calculating the "apparent" flux density. 

 Thus, let 



$ = the total flux per pole, 



T = pole pitch, 

 A = tooth pitch, 



t = width of tooth at center, 

 l n = net length of iron in armature, 

 pole arc 



r = ratio 



pole pitch 



then the number of teeth under each pole is r r- and the flux per 



<i>X 



tooth is The flux density in the tooth, on the assumptions 



previously *made, would, therefore, be ~r gausses if the dimen- 



TTtln 



sions are expressed in centimeters. 1 By referring to the curve 

 Fig. 34, the watts lost in the teeth per pound of iron can be found. 

 The length l n is simply the gross length of the armature core less 

 the space taken up by ventilating ducts and insulation between 

 armature stampings. The question of vent ducts will be taken 

 up immediately; but, even when a suitable allowance has been 

 made for the spaces between the assembled sections of the 

 armature core, a further correction must be made to allow for 

 the thin paper or other insulation between the stampings. The 

 space taken up by this insulation will vary between 7 and 10 per 

 cent, of the total space. Thus, if l a is the gross length of the 

 armature core, and l v the total width of all vent ducts, the net 

 length of the armature core would be 



l n = 0.92(Z a - l v ) 



if the space occupied by the insulation between laminations is 

 8 per cent. 



1 The tooth density depends upon the maximum value of the air-gap 



<f> 

 density which is here supposed to be given by the expression j- where l a 



is the gross length of the armature core. 



