TORQUE OF MOTOR 185 



107. Torque of Induction Motor 



If T = torque exerted by motor,* in Ib.-feet, and 1* = number of 

 pairs of poles in motor, then corresponding to a slip s the speed of the 



rotor i< ~ J revs, per sec., and the total mechanical power is 



2ir(l - -s)i T . 2ir(l - *)ni T 



p - ~TT horse-power, or - x 746 watts 



But if X = number of phases in rotor winding, wo must have 



whence 



T = 0-737 n . NVI 2 



(1 - s)p 



or, using (1) 



where p = 2ir X primary frequency. 



T = 0-737' 2 . ^ 2 . (3) 



108. Study of Transformer Equivalent of Induc- 

 tion Motor. Vector Diagram 



We may now study the behaviour of the motor by substituting 

 for it the equivalent transformer shown in Fig. 126, which replaces 

 each phase of the winding ; Xi and X 2 denoting those portions of the 

 primary and secondary self-inductances which do not contribute 

 anything towards the mutual inductance.! The non-inductive resist- 

 ance h, shown as a shunt across T'T", is intended to represent a load 

 equivalent to the hysteresis and eddy-current loss in the stator core. 

 This loss will not be quite constant, for with increasing load the p.d. 

 across T'T" will decrease, and with it also the hysteresis and eddy- 

 current loss. As an approximation, however, we may suppose this 

 loss to remain constant at all loads, which is equivalent to supposing 

 h connected across Tl". 



Provisionally, however, we shall neglect the hysteresis loss entirely, 



* T stands for the total torque developed by the rotor, and not merely for the useful 

 torque available at the pulley. 



t A, and A, may be termed the lenlunje telf-inductances of the windings; by many 

 writers they are, incorrectly, called the self-inductances of the windings simply. 



