CHAPTER XII 



103. Assumptions underlying approximate theory of induction motors 104. Leakage 

 coefficients 105. Behaviour of motor independent of number of turns in rotor 

 winding. Rotor slip 106. Induction motor replaced by equivalent transformer 

 107. Torque of induction motor 108. Study of transformer equivalent of 

 induction motor. Vector diagram 109. Transformation of vector diagram. 

 Deduction of circle diagram 110. Construction for slip and torque 111. Case 

 of negligible primary resistance. Heyland's circle diagram 112. Effect of 

 resistance in (1) stator and (2) rotor 113. Use of starting resistances 114. 

 Effect of stator core loss. Efficiency of motor. 



103. Assumptions underlying Approximate 

 Theory of Induction Motors 



IN dealing with the theory of induction motors, it is convenient 

 to make certain assumptions which, though not corresponding exactly 

 to the actually existing conditions, lead to results sufficiently near 

 the truth for all practical purposes. We shall assume the stator and 

 rotor windings to be identical in every respect, each consisting of the 

 same number of conductors arranged in the same number of similar 

 slots.* We shall, further, assume that the reluctance of the iron path 

 is negligible in comparison with that of the air-gap ; this assumption 

 is equivalent to supposing the flux to be proportional to the current. 

 As in 20, we shall assume the rotating waves of magnetic flux 

 produced by the stator and rotor currents to be distributed in space 

 according to the simple sine law, and we may also conveniently 

 assume all the p.d.'s, e.m.f.'s, and currents to follow the same law with 

 respect to time. 



Since (apart from the question of phase difference) the phases of 

 an induction motor may be regarded as practically identical, we shall 

 confine our attention to one phase, and study the changes taking 

 place in the current, power factor, etc., of that phase as the load 

 changes. A precisely similar series of changes will take place in the 

 remaining phases. 



When an induction motor is running, we may regard the systems 

 of polyphase currents in the stator and rotor windings as each giving 



* In practice, the number of slots in the stator and that in the rotor are chosen so as 

 to have the least possible common factor ; otherwise the torque corresponding to different 

 relative positions of stator and rotor will fluctuate very considerably. See 65. 



