Torque - Slip Characteristic of the Induction Motor

The torque in the three phase induction motor is given by

• T = KFSE₂R₂ / [ R₂² + ( SX₂ )² ]

Torque at standstill condition ( S = 1 )

• The starting torque does not become zero at starting condition or at standstill condition ( S = 1 ) and it is known as starting torque.

Starting condition

• The slip of the three phase induction motor is very high particular at starting condition. 
• If the supply voltage is kept constant, the stator flux F  and rotor induced emf E₂ also becomes constant. 
• As the value of ( SX₂ )² is very high as compared to R₂², the rotor resistance is neglected therefore the starting torque is directly proportional to

        T_s a S / ( SX₂ )² 

        T_s a 1 / S    ( As rotor reactance X₂ is constant )

• Therefore the starting torque is inversely proportional during starting condition. 
• The shape of the torque – slip curve is rectangular hyperbola. As the slip decreases the torque increases and vice versa. 
• The torque increases up to its maximum limit or say maximum torque. The maximum torque occurs at a slip of S = R₂ / X₂ .

Running condition

• The value of slip becomes very low during running condition of induction motor therefore the SX₂ is neglected as compared to rotor resistance R₂. 
• The torque in the induction motor during this condition is directly proportional to

                 T a S  ( As F, E₂ and R₂ are constant )

• Therefore the torque slip graph is straight line during running condition. 
• As the slip increases, the torque increases and vice versa.

Effect of rotor resistance

• As the rotor resistance increases, the starting torque also increases. 
• The rotor resistance does not affect the maximum torque. 
• The speed or slip at which maximum torque occurs is depends upon rotor resistance. 
• The maximum torque remains same for difference value of rotor resistance but it occurs at different slip or speed as shown in the Figure A.

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