Page 121 - Handbook of Electrical Engineering

INDUCTION MOTORS 103

Figure 5.3 Approximate deep-bar resistance reactance curves for four-pole motors rated from 10 kW to
10 MW.
The torque T e developed in the rotor shaft can be expressed as a function of the air-gap
voltage V m :-
2
sR 2 V m
T e = 2 Newton metres
R 2 + (sX 2 ) 2
Where R 2 and X 2 are both functions of the slip s as explained above. The air-gap voltage can be
found from the supply voltage V s by noting that a voltage divider circuit exists which consists of the
series components of the stator and the parallel combination of the magnetising branch and the rotor
circuit. Hence V m becomes:-
V s Z 2m
V m =
Z 1 + Z 2m
where
Z 1 = R 1 + jX 1
and
1
Z 2m =
1 1 1
+ +
R c jX m R 2 + R out + jX 2
but
R 2
R 2 + R out =
s
and
R 2 (1 − s)
R out =
s