264 ELEMENTS OF ELECTRICAL ENGINEERING. 



126. Relation between speed and efficiency of an induction motor. 



Of the total power delivered to an induction motor, part is lost 

 in heating the stator windings and in heating the stator iron on 

 account of eddy currents and hysteresis, and the remainder is 

 delivered to the rotor ; this power which is delivered to the rotor 

 is partly lost in heating the rotor windings, and the remainder * 

 appears as mechanical power in driving the rotor ; and this me- 

 chanical power which drives the rotor is partly lost in mechanical 

 friction in the motor bearings and in air friction, and the remainder 

 is delivered by the motor as its mechanical output. Let us for 

 the present ignore all of the losses of power except the power lost in 

 heating the rotor windings. 



Under this assumption all of the power delivered to the stator 

 windings is to be thought of as being used to produce the rotating 

 stator magnetism, exactly as if this delivered power were me- 

 chanical power used to revolve an ordinary field magnet as indi- 

 cated in Fig. 226. Let T be the torque which this revolving 

 field magnet exerts on the rotor, then of course the rotor reacts 

 and opposes the rotation of the field magnet with the same torque 

 T. The power required to drive the field magnet at speed n 

 against this opposing torque T is equal to 2.irnT^\ and the 

 power developed by the torque T in driving the rotor at speed 

 n 1 is equal to 2irn'T. That is, the power input is 27rnT and the 

 power output is 2irn' T y so that (ignoring the various losses above 

 specified, losses which are, however, by no means really negligible) 

 the efficiency of the motor, output divided by input, is n' In. 



Efficiency and rotor resistance. According to Art. 125 an 

 induction motor with a given load runs the more nearly at syn- 

 chronous speed the less the resistance of the short-circuited rotor 

 windings. Therefore the efficiency of the motor, which is ap- 

 proximately equal to n' /n, is the greater the less the resistance 

 of the short-circuited rotor windings ; and therefore, when pro- 



fEddy current and hysteresis losses in the rotor iron are generally quite small and 

 these losses are here ignored. 



* If T is expressed in pound-feet and n in revolutions per second, then 2/rw T 

 expresses the power in foot-pounds per second. 



