Torque Equation of Induction Motor

     The torque T, of an induction motor is proportional to the product of stator flux per pole ( φ ), rotor current ( I ), and the power factor of the rotor. The torque of an induction motor is due to the interaction of the rotor and stator fields and is dependent on the strength of the fields and their phase relationship.

Thus,

T  α  I₂ Cos φ₂

Since rotor induced e.m.f/phase, E is proportional to the stator flux, φ.

i.e.,     E₂  α  φ

Therefore, 

T  α  E₂ I₂ Cos φ₂

But rotor current/phase, 

and

Rotor Power factor,

Therefore,

Where

        K  =  Constant of proportionality

             =     3*60 /  2π N_s

Another Method :

Let

       T  =  Torque developed by an induction motor

We know that

Rotor input,

P₂  =  2π N_s T / 60

Therefore Torque,

Now rotor input,

But rotor current / phase,

Therefore, rotor input,

Substituting the expression of 'P₂' in equation (1), we get

Torque,

Where 

       K  =  Constant

            =     3*60 /  2π N_s

     The above equation is the torque equation for an induction motor under running condition. So torque developed at any load condition can be obtained, by knowing the slip of the induction motor at that load condition.

Starting Torque :

The torque produced by the motor at start is called as starting torque, T_st.

At start, N = 0 and hence slip, s = 1

Therefore, starting torque can be obtained by substituting s = 1 in the equation (2)

i.e., torque equation under running condition.

Comparison of Torques :

     The performance of the motor is sometimes expressed in terms of comparison of various torques such as full-load torque, starting torque and maximum torque.

i. Relation Between Full-load and Maximum Torque :

   Let       s_f = F.L. slip 

The expressions for F.L torque, T_FL and maximum torque, T_max are,

The ratio of F.L torque to maximum torque is

Dividing Nr. & Dr. by X₂², we get 

ii. Relation Between Starting Torque and Maximum Torque :

The expression for starting torque, T_st and maximum torque, T_max are,

Dividing Nr. & Dr. by  X₂², we get