Question

Q10. Based simply on the concept of rotor induction, explain what happens as the rotor approached synchronous speed and why the rotor, practically, will always be slower than synchronous speed. What causes the rotor mmf? How must the rotor move with respect to the stator magnetic field in order to have a rotor mmf? What happens to torque as the rotor mmf (rotor flux density) decreases?

Answer 1

The induction motor works on the principle of electromagnetic induction.

When three phase supply is given to the stator of induction motor, if the stator windings are physically displaced in space by an angle of 180degrees electrical and if the three phase currents flowing through the windngs of the stator are displaced in time by 180degrees electrical, a rotating magnetic field is created which is called as stator rotating magnetic field.

Now stators conductors are stationary and hence this rotating magnetic field cuts the stator conductors and an emf is induced in it at supply frequency.

E_{​​​​​​1} = 4.44*flux*f*N_{​​​​​​1}

At starting rotor conductors are also stationary and the emf induced in the rotor conductors at supply frequency.

E_{​​​​​​20} = 4.44*flux*(f)*N_{​​​​​​2}

Now, current starts flowing through the rotor conductors as they have a closed path and these current carrying conductors under the influence of magnetic field produce torque(by Lorentz force principle). Hence the rotor starts to rotate in the same direction as that of rotating magnetic field according to Lenz law.(cause here is emf induced and the effect is the torque production)

The rotor always tries to catch the stator magnetic field, but settles at a speed little less than synchronous speed called​ rotor speed(N_{​​​​​​r}).

If the rotor tries to attain the synchronous speed (N_{​​​​​​s}) there would be no relative speed between rotor conductors and the rotating magnetic field,because of which no flux cutting happens and hence no emf is induced in the rotor conductors ====> no currents pass through rotor conductors and no torque is produced( as no Lorentz force is happening).

The emf in rotor at running condition is E_{​​​​​​2}= 4.44*flux*(sf)*N_{​​​​​​2}

Hence rotor cannot attain synchronous speed, it always settles at speed little less than synchronous speed====> the rotor rotates with slip frequency (sf).

Now as there is rotor emf, the rotor conductors carrying current and hence they produce flux(or rotor mmf) according to right hand thumb rule.

Therefore for the production of torque the relative speed between rotor magnetic field and the stator magnetic field is zero.

Torque is directly proportional to strength of stator field, strength of rotor field and the sine of angle between them.

Therefore as the rotor mmf decreases, the torque produced also decreases.