224 PRINCIPLES OF ELECTRICAL DESIGN 



clearances at the ends, including an allowance for " staggering" 

 the brushes, will probably require a minimum axial length of 

 commutator surface of 7^ in- 



Item (101): Flux Cut by End Connections. Refer Art. 48. 

 Assuming for the constant in formula (72) on page 159, the 

 value k = 2.4, we have: 



1> e = 0.4 V2 X 2.4 X 3 X 83.4 X ~ X 2.75 [ (log e ^ 



- l] = 31,300 maxwells. 



Item (102): Slot Flux. Refer Art. 49. The equivalent slot 

 flux, by formula (80), page 164, is 



., 1.6 X TT X 1 X 3 X 83.4 X 11 X 2.54 



& ** = Q x Q5 - = 11,730 maxwells. 



Items (103) and (104) : Average Flux Density in Commutating 

 Zone. Refer Art. 49 and 85. Also Art. 51, p. 171, if interpoles 

 are to be provided. By formula (81) page 164: 



$ c = (2 X 11,730) + 31,300 = 54,760 maxwells. The 

 average density is, therefore, by formula (83) : 



54,760 

 B < = 1.083 X 11 X 6.45 = 712 gaUSSeS ' 



Items (105) and (106) : Flux Densities at Beginning and End of 

 Commutation. The value of item (104) is the density of the 

 magnetic field at the middle of the zone of commutation. After 

 the current in the short-circuited coil has passed through zero 

 value (a condition attained only when the coil as a whole is 

 moving in a neutral field), the field should increase in strength 

 until, at the end of commutation, it is of such a value as to 

 develop I C R volts in the short-circuited coil. The resistance, R, 

 of the coil of one turn is 0.00132 ohm (item (42)), and the e.m.f. 

 to be developed in the coil at the beginning and end of commu- 

 tation is therefore 0.00132 X 83.4 = 0.11 volt, or 0.055 volt in 

 each coil-side. The flux to be cut by each coil-side to develop 

 this voltage is: 



Maxwells per centimeter _ _. volts X 10 8 



of armature periphery ~ rate of cutting, in centimeters per 



second 



60 



K 3,070 X 12 X 2.54 

 = 3,530 



