146 



PRINCIPLES OF ELECTRICAL DESIGN 



Returning to a consideration of the case represented by Fig. 

 54, it must not be overlooked that the armature coil there shown 

 is not of a practical shape, the end connections are shown parallel 

 to the direction of travel of the coil, and the cutting of fluxes by 

 these end portions of the coil has not been considered. When 

 we consider the end fluxes, or the effect of commutating inter- 

 poles, especially when these are not equal in number to the main 

 poles or do not extend the full length of the armature core, then 

 the flux cut by the short-circuited conductors at any given part 

 of their total length such as the center of the "active" portion, 

 whether on a smooth core or in slots may have an appreci- 

 able value; but if we consider the total flux cut by all parts of 

 the wire forming the commutated coil, when the current i in this 

 coil is passing through zero value, it is most emphatically true 

 that the coil as a whole is moving in a "neutral field/' i.e., a 

 resultant field which is either of zero value (when the sum of all 

 its components is correctly taken) or of which the direction is 

 parallel to the direction of travel of the conductors. 



-4 



wvww 



<- - "-> 



FIG. 56. Diagram of coil and commutator during commutation. 



At the beginning and end of the commutation period the 

 field in which the coil moves should be such as to produce an 

 e.m.f. in the short-circuited coil of the value e = I C R, where I 

 is the value of the current per path of the armature circuit and 

 R is the resistance of the short-circuited coil. On the assumption 

 of a uniform current density over the surface of the brush, the 

 brush contact resistance need not be taken into account, as 

 will be clear from the following considerations. Fig. 56 shows a 

 brush of width W covering several segments of the commutator. 

 The total current entering the brush is 21 c , and since the density 



