Full load torque formula for induction motor is as follows:
full load torque formula for induction motor
 

Starting Torque Formula for Induction Motor

 
The starting torque of a motor is that torque which is produce by it at start. It is denoted by Tst and corresponds to s = 1. So by substituting s = 1 in above expression, we get the expression for starting torque. Therefore starting torque formula for induction motor is as follows:
 
starting torque formula for induction motor
 

Maximum Torque at Start

 
The condition for maximum torque is
 
s = R2/X2  or R2 = sX2
 
 R2 = X2 (since at start s = 1)
 
Thus to obtain maximum torque at the start, the value of rotor resistance must be equal to the rotor reactance at standstill.
 
However, the normal rotor resistance is quite small as compared to the reactance, otherwise, the rotor losses will be high and the efficiency of the motor will be low.
 
Hence to obtain maximum (higher) at the start some external resistance is added in the rotor circuit which is only possible in the case of slip ring induction motors. Once motor picks up speed this external resistance is reduced to zero and slip rings are short-circuited.
 
To obtain higher starting torque in case of squirrel cage induction motor another cage is applied on the rotor and the motor is called a double cage motor.
 

Maximum Torque Formula for Induction Motor

 
The maximum torque is denoted by Tm and occurs at s = R2/X2. The value of slip which corresponds to maximum torque is denoted by sm. So by substituting s = R2/X2 in full load torque expression, we get the maximum torque expression. Therefore maximum torque formula for induction motor is as follows:
 
maximum torque formula for induction motor
 
The above expression indicates that the maximum torque Tm does not depend upon the value of rotor resistance R2.
 
Although Tm is independent of R2, the value of slip sm at which Tm occurs is directly proportional to the rotor resistance R2.
 
Moreover, the maximum torque Tm inversely proportional to the rotor reactance at standstill X2. Therefore to achieve a higher value of maximum torque, the leakage reactance of the rotor should be kept the minimum.
 
This is achieved by placing the rotor conductors very near to the outer periphery of the rotor and reducing the air gap between stator and rotor up to the smallest possible value.
 
The maximum torque Tm obtained at sm is also called pull out torque or break down torque. If the load torque increases beyond the pull-out torque then the induction motor will be pushed into the unstable region and will finally come to a standstill.
 

Effect of Change in Supply Voltage on Torque

 
In the full load torque expression expression, as written above, E2 the rotor induced EMF is proportional E1 i.e. the stator supply voltage.
 
Therefore, T α  sE12
 
Thus torque at any speed is proportional to the square of the stator supply voltage. Therefore, when the supply voltage is changed, it changes load torque T under running condition also.
 
If supply voltage decreases, torque decreases abruptly and in order to maintain the same torque, slip increases or speed decreases.  Hence the motor draws extra current from the supply mains.
 
Thanks for reading about induction motor torque formula.
 

Induction Motors — 3 | Objective Type Question Answers

 

#1 The torque developed by a 3-phase induction motor least depends on

shaft diameter

#2 In an induction motor if air-gap is increased

the power factor will be low

#3 When R2 is the rotor resistance. X2, the rotor reactance at supply frequency and s is the slip, then the condition for maximum torque under running conditions will be

R2 = sX2

#4 In case of a double cage induction motor, the inner cage

has high inductance and low resistance

#5 In case of a double cage induction motor, the inner cage

has high inductance and low resistance

#6 The low power factor of induction motor is due to

all of the above

#7 Insertion of reactance in the rotor circuit

reduces starting torque as well as maximum torque

#8 Insertion of resistance in the rotor of an induction motor to develop a given torque

rotor current remains same

#9 For driving high inertia loads best type of induction motor suggested is

slip-ring type

#10 Temperature of the stator winding of a three-phase induction motor is obtained by

all above methods

#11 In a squirrel cage motor the induced E.M.F., is

slip times the stand still  E.M.F. induced in the rotor

#12 Less maintenance troubles are experienced in case of

squirrel cage induction motor

#13 A squirrel cage induction motor is not selected when

higher starting torque is the main consideration

#14 Reduced voltage starter can be used with

squirrel cage as well as slip-ring induction motor

#15 In a star-delta starter of an induction motor

#16 The torque of an induction motor is

directly proportional to slip

#17 The rotor of an induction motor runs at

below synchronous speed

#18 The starting torque of a three phase induction motor can be increased by

either by increasing slip or by increasing current

#19 Insertion of resistance in the stator of an induction motor

decreases the starting torque

#20 An induction motor is identical to

asynchronous motor

#21 An induction motor is identical to

asynchronous motor

#22 An induction motor is identical to

asynchronous motor

#23 The starting torque of a 3-phase squirrel cage induction motor is

1.5 times the full load torque

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