CHAP. VII] M.M.F. OF DISTRIBUTED WINDINGS 



123 



p' 



Q' 



flux would be gained by placing a narrow coil near the center of 

 the pole, at a considerable expense in copper, and in power loss for 

 excitation. The total flux, which is proportional to the area of the 

 curve in Fig. 336, must be of the magnitude required by eq. (31) 

 for the induced e.m.f. If greater accuracy is desired, the curve in 

 Fig. 336 is resolved into its fundamental sine wave and higher 

 harmonics; the area of the fundamental curve must then give 

 the flux which enters into eq. (31). 



Single-phase Distributed Winding. Let us consider now the 

 stator winding of an induction motor, and in particular the m.m.f. 

 created by the current in one phase. We begin with the simplest 

 case of a winding placed in one slot per pole per phase (Fig. 34). 

 The reluctances of the 

 stator core and of the 

 rotor core are small as 

 compared with that of 

 the air-gap and the 

 teeth, and are taken 

 into account by in- 

 creasing the reluctance 

 of the active layer of 

 the machine (air-gap 

 and teeth). If P. and 

 Q are the centers of 

 the slots in which the 

 opposite sides of a coil 

 are placed, the m.m.f. 

 distribution along the air-gap is that shown by the broken line 

 RPP'Q'QS. In other words, the m.m.f. across the active layer, 

 at any instant, is constant over a pole pitch, and is alternately 

 positive and negative under consecutive poles. 



Let n be the number of turns per polo, and i the instanta- 

 neous current ; then the height PP* of the rectangle is equal to ni. 

 It is understood of course that such an m.m.f. acting alone does 

 not produce the sinusoidal distribution of the flux density assumed 

 in the previous chapters: In a single-phase motor the sinusoidal 

 distribution is due to the simultaneous action of the stator and 

 rotor currents, and also to the fact that the windings are distrib- 

 uted in several slots per pole. In a polyphase machine the simul- 

 taneous action of the two or three phases also helps to secure a 



FIG. 34. The m.m.f. of a single-phase unislot 

 winding resolved into its harmonics. 



