182 PRINCIPLES OF ELECTRICAL DESIGN 



and it will be advisable to add about 25 per cent, to the values 

 of voltage drop as read off the curves of Fig. 69. 



The losses under item (2) are less easily calculated because 

 the coefficient of friction will depend not only upon the quality 

 of the carbon brush but also on the condition of the commutator 

 surface. 



Let P = the pressure of the brush on the commutator, in 

 pounds per square inch of contact surface (usually 

 from 1H to 2 Ib. increasing to 2^ Ib. with copper- 

 graphite brushes); 

 c = the coefficient of friction; 

 A = the total area of brush contact surface (square 



inches) ; 



v c the peripheral velocity of the commutator in feet 

 per minute; 



then the friction loss is cPAv c foot-pounds per minute. 



If D c is the diameter of the commutator in inches, and N is 

 the number of revolutions per minute, 



7TJDJV 



V < = -12~ 

 The friction loss, expressed in watts, is 



cPANDcir X 746 

 12 X 33,000 



The coefficient of friction with carbon brushes may be as low 

 as 0.17 and as high as 0.48. The value of c for a good quality of 

 carbon brush of medium hardness might lie between 0.2 and 0.3; 

 but this coefficient is not reliable as it depends upon many fac- 

 tors which cannot easily be accounted for. 



The watts that can be dissipated per square inch of commu- 

 tator surface will depend on many factors which cannot be 

 embodied in a formula. The peripheral velocity of the com- 

 mutator surface will undoubtedly have an effect upon the cool- 

 'ing coefficient; but the influence of high speeds on the cooling 

 of revolving cylindrical surfaces is not so great as might be 

 expected. The design, of the risers i.e., the copper connections 

 between the commutator bars and the armature windings 

 has much to do with the effective cooling of small commutators; 

 but this factor is of less importance when the axial length of the 

 commutator is considerable. 



