120 PRINCIPLES OF ELECTRICAL DESIGN 



slots as consisting of two reluctances in series, (a) the reluctance 

 of the equivalent air gap (as calculated by formula (58) for the 

 center of the pole face), and (6) the reluctance of the tooth. 

 The calculation of this latter quantity depends upon a knowledge 

 of the actual flux density in the tooth. For low densities in the 

 iron up to about 20,000 gausses the actual tooth density will 

 be approximately equal to the apparent density; that is to say, 

 practically all the flux entering the armature over one tooth 

 pitch will pass into the core through the root of the tooth. For 

 densities exceeding 20,000 gausses, a closer estimate of the correct 

 value of the tooth density may be made by assuming the con- 

 dition of Fig. 37. 

 Let the meaning of the symbols be as follows: 



B g = the average air-gap flux density at armature surface; 

 i.e., the average density over one tooth pitch of width 

 t + s and length l a . 



B t the actual tooth density. 



B 8 = the density in the slot and air spaces. 



$x = the total flux entering armature core in the space 

 of one slot pitch. 



l n = the net length of the armature core (iron only). 

 The other dimensions as given on the sketch Fig. 37. 



If the assumption is made that the lines of flux lie in a plane 

 exactly perpendicular to the axis of rotation, it might be argued 

 that the flux in the ventilating ducts and in the insulating spaces 

 between the iron laminations does not enter the iron of the 

 armature core; and the reluctance of the paths followed by this 

 flux would therefore be very high. This argument is not justi- 

 fied since the flux lines in the ventilating ducts will actually 

 find their way into the core immediately below the bottom of 

 the slots, even if the iron in the teeth is practically saturated. 

 We shall therefore assume two equipotential surfaces, one being 

 the pole face and the other being the cylindrical surface passing 

 through the roots of the teeth. The flux density in the air ducts 

 and spaces not occupied by iron will therefore be the same as 

 the density, B 8 , in the slots, and the m.m.f required to overcome 

 the reluctance of air gap proper and slot will be the same as 

 the m.m.f. required to overcome the reluctance of air gap proper 

 and tooth; therefore 



B.(d -{- 5) = d + B t d 



