218 



THE MAGNETIC CIRCUIT 



[ART. 65 



of the armature windings. This inductance affects the per- 

 formance of the machine, because the leakage fluxes created 

 by the armature currents induce e.m.fs. in the machine. Such 

 leakage fluxes are shown in Figs. 23 and 36, in an induction 

 machine and a synchronous machine respectively. For purposes 

 of theory and computation these leakage fluxes are usually 

 subdivided into three parts, namely: 



(a) Leakage fluxes linked with the parts of the windings 

 embedded in the armature iron (Figs. 36 and 54). These paths 

 are closed partly through the slots, and partly through the tooth- 

 tips (slot leakage and tooth-tip leakage). 



(b) Leakage fluxes linked with the parts of the armature 

 windings in the air-ducts. 



" N 



"& 



l e 



FIG. 52. Undivided end-connections. FIG. 53. Divided end-connections. 



(c) Leakage fluxes linked with the end-connections of the 

 armature windings (Figs. 52 and 53). 



Usually the fluxes (a) and (6) are merely distortional com- 

 ponents of the main flux of the machine, and only the fluxes 

 (c) have a real existence. 



It will be readily seen that the paths of the tooth-tip leakage 

 and of that around the end-connections are too complicated 

 to allow the corresponding permeances to be calculated theo- 

 retically. For this reason, various empirical and semi-empirical 

 formulae are used in practice for estimating the leakage inductance 

 of armature windings, the coefficients in these formulae being 

 determined from tests on similar machines. 



The most rational procedure is to express the inductance 

 through the equivalent permeance of the paths, as defined by 

 eq. (106a) in Art. 58. Let there be C PP conductors per pole 



