GENERAL THEORY OF THE INDUCTION MOTOR. 287 



slot through the winding of wire, and the flux *"' which crosses between the stator 

 and rotor windings. The flux a is equivalent to a certain flux $' crossing between 

 the windings, and the flux b is equivalent to a certain flux <I> // crossing between the 

 windings exactly as described in Art. 119, and the values of $' and f are given 

 by the equations of Art. 119, namely, 



and 



in which N' is the number of conductors in one stator slot, "k is the length of stator 

 and rotor iron parallel to the motor shaft, and X, Y, s and s' are the dimensions 

 shown in Fig. 247, all being expressed in centimeters. 



The value of the flux $'" which actually crosses between the coils may be roughly 

 calculated from the length and section of each part of the air path through which 4> //x 

 passes, the magnetomotive force producing 4> /// being 47r/io X -N't'. 



It is evident that any accurate estimate of 4> x// is impossible. In fact the value 

 of <f> /// for a given value of z y varies considerably as the rotor slots sweep past the 

 stator slots, for, at certain instants the stator teeth bridge across the openings of the 

 rotor slots, and the broad ends of the rotor teeth bridge across the stator slots. This 

 variation of 4> //x for a given current means that the inductance equivalent of magnetic 

 leakage is a pulsating inductance, the frequency of the pulsations being equal to the 

 product of the rotor speed times the number of rotor slots. 



Calculation of equivalent resistance of the rotor per stator phase. If the 

 rotor were wire wound with the same number of phases and the same number of con- 

 ductors per phase as the stator winding, and if each one of these rotor phases were 

 short circuited on itself, then the short-circuit resistance R' f of one of these rotor 

 phases would be the value of R f/ to be used in the calculation of performance curves 

 from the circle diagram. In practice, however, the rotor frequently has a squirrel- 

 cage winding, and in this case the value of R ff may be defined as that resistance which 

 multiplied by the square of the load current P in one stator phase will give I / q of the 

 RI* losses in the rotor, where q is the number of stator phases. To determine R ff , 

 therefore, it is necessary to find the rotor RI Z losses for a given value of load current 

 in the stator. For this purpose the rotor may be supposed to be stationary, with the 

 given value of load current flowing in each stator phase. Under these conditions let 

 us consider the rods of the rotor winding in groups or bands corresponding to the 

 bands of the stator winding (see Figs. 227 and 228). In each of the rods of one of 

 these bands the current is I" = Z' f \Z' X S', where Z' is the total number of stator 

 conductors, and Z" is the number of rods in the squirrel-cage winding.* Therefore, 

 knowing the length and sectional area of each rod, we can find its resistance and then 

 calculate the total RI 2 loss in the rods. To determine the RI* loss in the short- 

 circuiting rings proceed as follows : 



For the case of a two-phase stator winding. Let n be the number of rods in one 

 of the above mentioned bands ( Z /x /2/), then nP f is the total current entering an 



*This assumes that the windings in each pair of slots, S and R, Fig. 247, 

 balance each other's magnetizing action. See Appendix B, Art. 17. 



