COMMUTATION 



wherein k is the ratio of the permissible density at brush tip to 

 the average density over brush-contact surface. 



For values of A above 30 amp. to the square inch, the voltage 

 drop # C A, with carbon brushes, is usually about 1 volt. It fol- 

 lows that, if the value of k may be as high as 2.5, the actual e.m.f . 

 in the short-circuited coil may differ from the ideal e.m.f. by 

 about 1.5 volts. This is, however, a case for experimental 

 determination ; but once a safe value for k or for A w has been 

 determined, the allowable variation in the commutating flux 

 $ c as given by formulas 82, page 164, and 85, page 167 may 

 readily be calculated. If the assumed value of 1.5 volts varia- 

 tion is permissible, it follows that the amount by which the flux 

 entering the teeth in the commutating zone may differ from the 

 ideal value is 



10 



2T C 



3t c X 10 8 

 4 



T e 



maxwells 



(88) 



wherein t c is the time of commutation in seconds, and T c is the 

 number of turns in the short-circuited coil. 



Apart from all considerations of a mechanical nature, commu- 

 tation can be improved by increasing the thickness of insulation 

 between commutator bars. This might in many cases be made 

 considerably thicker than the usual J-^2 m - with advantage in 

 the matter of sparking; but it is not always easy to obtain large 

 spacing between bars, and thick mica insulation is otherwise 

 objectionable. 



When calculating the equivalent slot flux, the assumption 

 made virtually supposes the slot to contain a large number of 

 small wires all connected in series. With solid conductors of 

 large cross-section, the local currents in the copper would alter 

 the distribution of the slot flux and call for a reversing field 

 differing slightly from the field calculated by the aid of the 

 formulas given in this chapter. Again, the field due to the 

 armature m.m.f. is usually assumed to be stationary in space. 

 This is practically true when the number of teeth is large and 

 the brush arc is a multiple of the bar pitch. With few teeth 

 and a brush covering a fractional number of bars, the oscilla- 

 tions of the armature field (of small magnitude but high fre- 

 quency) may have some slight effect on commutation; but with 

 12 



