. Electric traction and transmission engineering . s AD. The average value of the electromotive force due to therotation of the armature in a bipolar field is V Erotav = ^/Na — lO ^00 where V is the armature speed in rev. per min. and $/ isthe field flux; and the effective value of this is Ero. = ^^3 • ^ (S) and is in time phase with the field flux, but appears as acounter at the brushes AD. When an alternating current is passed through the fieldcoils, the alternating field flux is set up, and this flux pro-duces a reactive in the field winding lagging 90°behind the flux i
. Electric traction and transmission engineering . s AD. The average value of the electromotive force due to therotation of the armature in a bipolar field is V Erotav = ^/Na — lO ^00 where V is the armature speed in rev. per min. and $/ isthe field flux; and the effective value of this is Ero. = ^^3 • ^ (S) and is in time phase with the field flux, but appears as acounter at the brushes AD. When an alternating current is passed through the fieldcoils, the alternating field flux is set up, and this flux pro-duces a reactive in the field winding lagging 90°behind the flux in phase, exactly as in a choke coil. Themagnitude of this is TYPES AND PERFORMANCE CURVES OF MOTORS. 33 Ef = 2 irf^tJJf (6) where */„ is the maximum value of the field flux, and Njis the number of field turns. The electromotive force, E, which is impressed upon themotor terminals, is equal and opposite to the vectorialsum of Ea, E„t, Ej, and the IR drop of the armature andfield windings, as shown in Fig. 14, where / is the current. Fig. 14. flowing through the field and armature, and # representsthe phase of the flux. In this diagram, eddy current andhysteresi% losses are ignored. The impressed electromotiveforce is therefore E = V(£„, + /^)2 + (£„ + £/^ (7) In the series motor, the same current passes throughfield and armature windings, and, if uniform reluctancearound the air gap be assumed, then the armature and fieldfluxes will be proportional to the equivalent armature turnsand field turns respectively. Representing by t the ratio 34 TRACTION AND TRANSMISSION. of field turns to effective armature turns ^am _ N Nj2T _ I $/m ~ Nf~ Nf ~ T (8) whence $/m = r^am. Substituting this value in (5), together with the equivalentof Ealf to be derived from (4), there results _ r F I V and Erot = ~r-^fZZ- fr •60 Neglecting the armature and field resistance drop, theimpressed shown in (7) reduces to ^=^V(^/+(^^+^)^ (9) which is the fundamental equat
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