COMMUTATION 



153 



actual flux is not objectionable, and the active conductors A A' 

 in Fig. 59 may be considered as moving in a field of which the 

 density is represented by the length MN t since the portion of 

 the field flux represented by the distance between the point 

 N and the datum line is neutralized by the armature flux at 

 this point. Let ABC represent the position of the end connec- 

 tions of the coil undergoing commutation, then the portion AB is 

 cutting end flux due to the armature currents in all the end con- 

 nections, and the direction of this flux will be the same as that 

 represented by the curve Z, all as indicated by the direction of the 

 shading lines. The portion BC of the short-circuited coil will 

 be cutting flux of the same nature as the armature flux cut by the 

 slot conductors CC", and the e.m.f. due to the cutting of the end 

 fluxes will be of the same sign as that due to the cutting of the 

 armature flux Z', that is to say, it will tend to oppose the reversal 

 of current and must therefore be compensated for by a greater 

 brush lead or a stronger commutating pole. Similar arguments 

 apply to the end connections A'B'C' at the other end of the 

 armature. A means of calculating the probable value of the 

 effective end flux will be considered later; but for the present 

 it may be assumed that the average value of the density B e 

 of the field cut by the end connections is known. It may, there- 

 fore, be used for correcting the ordinate of the curve Z at the 

 point 0. Thus, the flux cut by the portion ABC of the end 

 connections (see Fig. 59) in the time t c is 



or 



>e = B e X x X length of ABC 

 e = B e W a sin a X length of ABC 



where a is the angle between the lay of the end connections and 

 the direction of travel, and W a is the arc covered by the brush, 

 expressed in centimeters of armature periphery. The equivalent 

 flux density B a which has to be cut by the slot conductors A A' 

 to develop the same average voltage is obtained from the relation 

 B a W a X length AA' = B e W a sin a X length ABC 

 which gives 



length ABC 



B a = B, sin a X 



or, if preferred, 



length A A' 



(69) 



2(BH) 

 e (AA') 



