# Torque Equation of Three-phase Induction Motor Let us define some parameters to find the torque produce by the induction motor. = Developed torque = Synchronous speed = Rotor speed = Power transfer from stator to rotor = air gap power = Total mechanical power developed by rotor

(1) (2) #### Developed Torque ( )

The torque generated by the conversion of electrical to mechanical power is known as the developed torque. This torque is also known as the electromagnetic torque. The developed torque define as ratio of the mechanical power developed by rotor to the mechanical angular velocity of the rotor. (3) So, developed torque

(4) This torque is differs from the torque actually available at the terminals by the friction and windage torque in the induction motor. As shown in equation (4), the developed torque depends on the air gap power and synchronous speed . The synchronous speed is independent of loading condition and it is constant. Hence, we get torque if air gap power is known.

#### Torque equation

Electrical power generate in rotor

(5) The power generates in rotor is same as rotor copper loss.

Hence,

Rotor copper loss = Electrical power generate in rotor

Input power to rotor = slip rotor input = rotor copper loss

(6) #### Starting Torque

At starting condition, rotor speed is zero. Therefore, slip is equal to 1. So, by putting, s=1 in above equation, we can obtain starting torque.

(7) #### Torque at synchronous speed

At synchronous speed, slip is equal to zero. So, from equation (6) .

#### Condition for maximum torque

From equation (6), torque in running condition is given as,

(8) For the given supply voltage , remains constant, if the impedance of stator winding assume as negligible.

Hence, (9) (10) For maximum value of developed torque develop when the right hand side of equation (10) is a maximum which is possible when

(11) (12) (13) So, The maximum torque is

(14) (15) So, from equation (15), we can conclude two things,

1. is independent of the rotor resistance.
2. is inversely proportional to the standstill reactance of rotor.