148 



PRINCIPLES OF ELECTRICAL DESIGN 



At the beginning and end of commutation, when w is equal to 

 W or to zero, the maximum value of the required voltage is 

 e = I C R. 



In this study of the voltage to be developed in the coil under- 

 going commutation in order to produce a uniform current 

 distribution over the brush surface, the resistance of the brush 

 itself has been considered negligible; but with the assumption 

 of a uniform current distribution over the cross-section of the 

 brush the actual resistance of the brush material, even if it 

 is relatively high, will not appear as a modifying factor in the 

 general formula (68). 



Referring again to Fig. 55, if the flux curve BB' may be con- 

 sidered a straight line, the current (i = ) will also obey a 

 straight-line law. It will fall from the value +/ c to zero in 

 the time ^ and rise again to the value I c at the end of the 



period t c , according to the simple law expressed by the straight 

 line in Fig. 55. If the change of current actually occurs in this 

 manner, we have what is called "straight-line" or ideal com- 

 mutation. The commutation is then ideal or perfect, not only 

 because it relieves the designer of much intricate and discouraging 

 mathematical work, but because it is the only means by which 

 the current density can be maintained constant over the brush 

 surface of the usual rectangular form. It is generally the aim of 

 the designer to maintain this current density as nearly constant 

 as possible, because unequal current density leads to local varia- 

 tions of temperature and resistance in the carbon brush, and in 

 those parts where the density attains very high values the ex- 

 cessive heating leads to pitting of the commutator surface even 

 if visible sparking does not occur. Whatever method of study- 

 ing commutation phenomena is followed, it is usual to assume 

 some law connecting the variable current i with the time t 

 and then investigate the causes which will bring about this 

 condition. The straight-line law will therefore be assumed, but 

 the thing of immediate moment being in fact the whole problem 

 of commutation in its broader aspect is the location, or the 

 creation, of a neutral zone where the actual resultant flux cut by 

 the coil undergoing commutation will be zero. 



Although the assumption of a smooth-core armature very 

 greatly simplifies the problem, especially when an effort is made 



