CHAP. XII] INDUCTANCE OF WINDINGS 223 



action of the consecutive phases, the length of this flux is approx- 

 imately T/m, where r is the pole pitch and m is the number 

 of the stator phases. Part of the flux is linked with the primary 

 current belt, and part with the secondary belt. The conditions 

 are essentially the same as between the transformer windings 

 P! and S 1 in Fig. 50. Knowing the equivalent permeances 

 of the individual paths the inductance can be calculated from 

 eq. (150). 



In an induction machine with a squirrel-cage rotor the total 

 leakage in the embedded part may be resolved into three com- 

 ponents shown in Fig. 54, namely: 



(1) The primary slot leakage, Q tl \ 



(2) The secondary slot leakage, 0, 2 I 



(3) The tooth-tip or zigzag leakage, 4> g . 



The fluxes <D 8l and 0, 2 are alternating fluxes of the frequency 

 of the corresponding currents. The zigzag flux 2 varies according 

 to a much more complicated law, because the permeance of its 

 path changes from instant to instant in accordance with the 

 relative position of the stator and rotor teeth; compare posi- 

 tions (1) and (2) in Fig. 23. Moreover, Fig. 54 shows only the 

 simplest case, which never occurs in practice, namely; when 

 the stator tooth pitch is equal to that in the rotor. In reality, 

 the two pitches are always selected so as to be different, in order 

 to avoid the motor sticking at sub-synchronous speeds (due to the 

 higher harmonics in the fluxes and in the currents). Therefore, 

 the paths of the zigzag leakage flux are much more complicated 

 than is shown in Fig. 5-1, and in calculations the average per- 

 meance of the zigzag path i- u> <1. 



In a machine with a phase-wound rotor the main flux is 

 further distorted, due to the fart that the primary and secondary 

 phase-belts are not exactly in space opposition at all moments. 

 While the total m.in.fs. of the primary and secondary are 

 balanced, then- is a local unl>alanrm<: which changes from 

 in-taut to instant. This distortion is the same as if it were due 

 to an additional 1 ak;i- . which was named ly Professor C. \ 

 Adams the belt 1 This part of the leakage usually 



constitutes but a small part of the total leakage, and will not 

 be considered here separately. Those interested are ivtVrred to 



1 C. A. Adams, The Leakage Reactance of Induction Motors, Trans. 

 Intern. EUctr. Congrtw, St. Louis, 1904, Vol. 1 . ,. 71 1 . 



