COMMUTATION 



163 



>rush. This is generally true, although it must be remembered 

 that the formula (78), in common with other formulas pre- 

 viously derived, is not of general application. Within the limits 

 of this chapter, it is not possible to consider all special cases; 

 and commutation formulas of general applicability cannot be 

 developed. When there is more than one coil per slot, and when 

 there are "dead coils," inequalities occur which complicate the 

 problem and make it impossible to obtain ideal commutation 

 with every coil on the armature. In such cases the slot flux must 

 be calculated for the coils that are differently situated in regard 

 to the brush position and an average value selected for use in the 

 calculations. 



Knowing the slot flux & e , and the previously calculated end flux 

 3> e cut by the conductors of the short-circuited coil while travel- 

 ling over the distance W a , the correct brush position is found when 

 the reversing flux entering the teeth comprised in the commu- 

 tating zone of width W a , is approximately & ea + $ e maxwells. 

 The flux actually cut by the one coil-side is, however, only $; 

 the component $ e of the total flux entering the commutating 

 zone merely supplies the leakage from tooth to tooth across the 

 slot. The presence of the slot flux undoubtedly tends to com- 

 plicate the problem of commutation. It should be noted that 

 the slot flux $es, if calculated by formula (77), is what has been 

 referred to as the equivalent slot flux; that is to say, a flux of 

 this value, if cut by an imaginary concentrated winding of T 

 turns, would develop the same voltage in the coil as the actual 

 slot flux develops in the actual winding. The condition of 

 importance to be fulfilled is simply that the "equivalent" flux 

 cut by the coil-side in the reversing field shall have the value $ c . 

 The flux cut by the coil-side may be separated into two parts: (1) 

 the flux passing through the teeth into the armature, which links 

 with all the conductors in the slot, and (2) the equivalent slot 

 flux. It is important to note that although the total or actual 

 .slot flux is the same whether it enters the top or the root of the 

 tooth, the flux linkage and therefore the developed voltage have 

 not the same value in the two cases. The total slot flux, on the 

 basis of the assumptions previously made, is 

 2X0.47T 



ds 



C 



xdx 



(79) 



