COMMUTATION 



161 



the value <i> e as given by the formula (72), to compensate for the 

 end fluxes, plus the total slot flux 4> 8 , which is twice the leakage 

 from tooth to tooth in one slot when the conductors are carrying 

 the full armature current. 1 In practice, when we wish to cal- 

 culate the volts generated in the coil of T turns by this slot 

 leakage flux, it is the equivalent slot flux that must be considered, 

 because the total number of lines crossing between the sides of 

 adjacent teeth does not link with all the wires in the coil. 



It will be convenient to assume the same number of slots 

 as there are commutator bars, and the whole of the slot space 

 to be filled with 2T conductors, each carrying a current of I e 

 amp. (this follows from the assumption of a full-pitch winding). 

 Thus no account will be taken of the fact that a small space 

 occurs between upper and lower coils, where the slot flux will 

 not pass through the material of the conductors. The lines of 

 the slot flux will be supposed to take the shortest path from tooth 

 to tooth; the small amount of flux that may follow a curved 

 path from corner to corner of tooth at the top of the slot will be 

 neglected. Refinements of this nature may be introduced, if 

 desired, when solving the problem for a concrete case. 2 If the 

 usual assumption is made that the reluctance of the iron in the 

 path of the magnetic lines is negligible in comparison with the 

 slot reluctance, the small portion of slot flux in the space dx 

 (Fig. 62) considered 1 cm. long axially (i.e., in a direction per- 

 pendicular to the plane of the paper) is 



d$ = m.m.f. X dP 

 where dP is the permeance of the air path. Thus, 



/Y> fty 



d$ = 0.47T (277 C ) -j X - 

 a s 



1 In the case of short-pitch windings, or when there are more commutator 

 bars than there are slots on the armature, the amount of the slot flux must 

 be calculated for the instant when the coil enters or leaves the commutating 

 zone. This flux will depend not only upon the dimensions of the slot but 

 also upon the current carried by each conductor and the position of the 

 latter in the slot. 



2 With short-pitch windings, or when there are several coils per slot, all 

 the conductors in the slot may not be carrying the full armature current 

 when the coil enters or leaves the commutating zone. In such cases the 

 actual conditions must be studied, an average value for the slot flux being 

 readily arrived at. If necessary, the straight-line law of commutation 

 may be assumed in order to estimate the current values in the coils passing 

 through the intermediate stages of commutation. 



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