AIR-GAP FLUX DISTRIBUTION 



285 



calculated by assuming the current in the slot conductors to be 

 acting independently of the field magnetomotive force. Thus, in 

 Fig. 113 the total slot flux is the sum of three component 

 fluxes: < t passing through the space occupied by the copper, a 

 portion of which will be cut by some of the conductors; $2 

 crossing the space above the windings, usually occupied by the 

 wedge; and < 3 which leaks from tooth top to tooth top. If the 

 conductors were concentrated as a thin layer at the bottom of 

 the slot, the loss of voltage due to reduction of core flux (see 

 Fig. 112) could be calculated by assuming that the useful flux is 

 reduced by an amount equal 



to the slot flux. The portion ,--''* '"""**< 



$1, however, in Fig. 113, be- /' ^'*"~$s **-**. \ 



ing cut by some of the con- 

 ductors, requires the calcu- 

 lations to be based on an 

 equivalent slot flux which, if 

 cut by all the conductors, 

 would develop an electromo- 



.-< -. 



.2? 



7 



4 



.1 



I 



FIG. 



113. Illustrating method of cal- 

 culating slot leakage flux. 



tive force equal to the actual 



loss of pressure. This flux 



may be calculated as follows: 



The amount of flux in the small strip dx deep (Fig. 113) of 1 cm. 



axial length, i.e., perpendicularly to the plane of the paper, is d^ 



= m.m.f. X dP, where dP is the permeance of the air path the 



reluctance of any iron in the path of the lines being neglected. 



Whence 



where T 8 is the number of conductors per slot; i, is the current 

 per conductor in amperes; and the dimensions d z and s (see Fig. 

 113) are in centimeters. Since, however, this flux element (see 

 Fig. 112, B) is cut by T 8 (d^ x^/d^ conductors, the loss of 

 pressure is due to the fact that it is not cut by T 8 x/d l conductors. 

 The "equivalent" flux to cause the same loss of pressure would, 

 if it did not link with any of the conductors, therefore be 



Thus 



(equivalent) "' 

 (equivalent) ~ 



' 4 ! r f 8 ^ ( 'x z dx 

 ass ; 



0.4 Trdt 



T.i. 



