286 



ELEMENTS OF ELECTRICAL ENGINEERING. 



rotor windings, is equivalent in its effects to a certain amount of external inductance 

 P (or a certain reactance uP) connected in series with each of the stator windings, 

 exactly as in the transformer as described in Arts. 117 and 1 1 8. 



Figure 247 shows a stator slot S and a rotor slot R, the rotor being supposed 

 to have the same number of slots as the stator, and the dotted lines t and t' in Fig. 

 247 are the center lines of adjacent stator and rotor teeth. The magnetic reluctance 

 of the iron is entirely negligible in comparison with the reluctance of the long air 

 paths through which the leakage flux passes, and the only influence of the windings 

 in adjacent stator slots (or in adjacent rotor slots) on each other, in so far as magnetic 

 leakage is concerned, is the entirely negligible influence which may be stated as fol- 

 lows : If one pair of slots alone is con idered, 

 as shown in Fig. 247, then the leakage flux in 

 the very narrow gap space comes out of the 

 iron at t and flows into the iron again at t', 

 whereas, if a whole band of slots is considered 

 simultaneously the leakage flux at t and t f 

 continues straight along the air gap, as shown 

 in Fig. 247. Any flux crossing the gap space 

 at / and t' would encircle both slots S and 

 R and would not be leakage flux. Therefore 

 the discussion of magnetic leakage may be 

 based upon the consideration of a single pair 

 of slots S and R, as shown in Fig. 247. If 

 the number of rotor slots is greater (or less) 

 than the number of stator slots, then the easiest 

 method of procedure is to assume that the 

 rotor slots are the same in number as the stator 

 slots, and to consider each rotor slot as in- 

 creased (or decreased) in width both at top 

 and at bottom, in proportion to the assumed 

 decrease (or increase) in the number of rotor 

 slots. 



Let P 8 be the inductance equivalent of magnetic leakage across one pair of stator 

 ,and rotor slots. Then the inductance equivalent per phase is equal to nP s where 

 n is the number of stator slots per phase, all of the stator conductors of one phase 

 being connected in series ; and the reactance equivalent of magnetic leakage per 

 phase is unP s . 



The inductance equivalent of the magnetic leakage across one pair of stator and 

 rotor slots is given by the equation : 



in which N f is the number of wires in one stator slot, i* is any assigned value of 

 current in the stator winding, and 4 )/ , ^ and & ff are three equivalent parts of the 

 leakage flux corresponding to the current i' as explained below. 



The actual leakage flux consists of three parts, namely, the flux a, Fig. 247, which 

 crosses the stator slot through the winding of wire, the flux b which crosses the rotor 



