DIRECT-CURRENT MACHINERY 181 



Substituting these values in equation gives 



or 



e = L \ 2 ~ r ( 1 ~ 2 )\ > ...... (208) 



which gives at the beginning of commutation t = 0, 



.......... (209) 



and at the end of commutation t = T, 



. . ....... (210) 



This e.m.f. is proportional to the current I c but is independent 

 of the brush resistance r c . 



If the e.m.f. generated in the coil is less than that required to 

 reverse the current completely in time T, commutation is imperfect 

 and there is a tendency to spark, and if the e.m.f. is so large that 

 the current is more than reversed there is a tendency to spark due 

 to overcommutation. 



The contact resistance helps to prevent sparking when the 

 e.m.f. generated in the coil by rotation is either too great or too 

 small to produce perfect commutation. 



When commutation is produced by the high-resistance brush 

 contact without the aid of any e.m.f. generated in the coil, it is 

 called " natural " or " resistance" commutation; when it is as- 

 sisted by an e.m.f. generated in the coil, it is called " forced " or 

 "voltage " commutation. 



Resistance commutation can never be perfect unless the self- 

 inductance of the coil is negligible, but at light loads it will reverse 

 the current without injurious sparking. Assume that the brushes 

 of a generator delivering half load are set on the corresponding 

 neutral line and that commutation is satisfactory. If the load 

 is increased the increased m.m.f . of the armature causes the neutral 

 line to move ahead so that the coil short circuited is cutting a 

 field of such a direction as to tend to maintain the current or even 

 to increase it. The reversal of the current is therefore retarded 



