COMMUTATION 



155 



seems more natural, and is more helpful to the understanding of 

 commutation phenomena, than what might be termed the 

 academic method, in which more or less reasonable assumptions 

 are made in respect to self- and mutual inductances; but it is 

 not suggested that the one method is necessarily superior to the 

 other so far as practical results are concerned. 1 While moving 

 from the position at the commencement of the commutation 

 where the current is +/ c to the position at the end of commuta- 

 tion where the current is 7 C , the short-circuited coil has cut 

 through the flux of self- and mutual induction through the 

 whole of it, not merely through certain components of the total 

 flux in the particular region considered. This is well expressed 

 by MR. MENGES when he says 2 : "... Self-induction is in 

 no way distinguishable from other coexistent electromagnetic 

 induction. Therefore, when the real magnetic flux resulting 

 from all causes, and its changes relative to a given circuit, are 

 taken into account, the self-induction is already included, and 

 it would be erroneous to add an e.m.f. of self-induction." 



48. Calculation of End Flux. With a view to calculating 

 within a reasonable degree of accuracy the flux density in the 

 zone ABC of Fig. 59, it is necessary to make certain assumptions 

 and to use judgment in applying the calculated results, because 

 it is not possible to determine this value with scientific accuracy 

 even when the exact shape of the armature coils and the con- 

 figuration of the surrounding masses of iron are known. 



In the first place, the angle a of Fig. 59, will be taken as 45 

 degrees, which, although perhaps slightly greater than the 

 average on modern multipolar machines, has the advantage 

 that it permits us to treat the wires AB and BC as being at right 

 angles to each other. The further assumption will be made 

 that the armature is of large diameter, and the developed view 

 of the end connections, as shown in Fig. 60, can therefore be 

 considered as lying in the plane of the paper. The flux in the 

 zone occupied by the portion AB of the coil undergoing commu- 



1 As a matter of fact, a careful study of the problem will show that the 

 total armature flux cut by one commutating coil during the period of short- 

 circuit being the difference between the number of lines threading the coil 

 immediately before and immediately after commutation is almost 

 entirely due to the changes of current that have taken place in the coils 

 under the brushes during the period of commutation. 



2 C. L. R. E. MENGES in the London Electrician, Feb. 28, 1913. 



