Electrical Machines · Induction Motors

Rotating Magnetic Field Magic: 3-Phase Induction Motor Heartbeat

Dr. Mithun Mondal BITS Pilani, Hyderabad Campus Electrical Machines

Demonstrative Video

SECTION 01

Production of Rotating Field

  • Stationary coils wound and supplied for \(2-\phi\) or \(3-\phi\), respectively produce a uniformly rotating (or revolving) magnetic flux of constant value

    • Consider two windings P and Q placed at \(90^\circ\) w.r.t each other

    • Exciting with \(2-\phi\) supply the flux produce is purely sinusoidal (assume)

    • Direction of the flux is assumed positive whereas its opposite side indicates negative values

\[\begin{aligned} \Phi_{P} & =\Phi_{m}\sin\theta\\ \Phi_{Q} & =\Phi_{m}\sin\left(\theta-90^\circ\right) \end{aligned}\]
rmf2
Rmf2
The instantaneous value of flux:
Conclusion:
\[\begin{aligned} \Phi_{P} & =0; ~ \Phi_{Q} =-\Phi_{m}\\ \Phi & =\sqrt{P^{2}+Q^{2}-2PQ\cos{\theta}}\\ & =\sqrt{0+\left(-\Phi_{m}\right)^{2}-0}\\ & =\Phi_{m} \end{aligned}\]
\[\begin{aligned} \Phi_{P} & =\Phi_{m} ; ~ \Phi_{Q} = 0\\ \Phi & =\sqrt{P^{2}+Q^{2}-2PQ\cos{\theta}}\\ = & \sqrt{\left(\Phi_{m}\right)^{2}+0}\\ & =\Phi_{m} \end{aligned}\]

Conclusion:

  • The magnitude of the resultant flux is constant and is equal to \(\Phi_m\) – the maximum flux due to either phase

  • The resultant flux rotates at synchronous speed by \(N_s=120f/P\) rpm

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Rpm2
Key Concepts
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Rmf3
Point 1
point 1
Point 1
Point 2
point 2
Point 2
Conclusion:

Conclusion:

  • The magnitude of the resultant flux is constant and is equal to \(1.5\Phi_m\) – the maximum flux due to either phase

  • The resultant flux rotates at synchronous speed by \(N_s=120f/P\) rpm

Why does the Rotor rotates?

Why does the Rotor rotates?

  • The 3-phase supply given to the stator winding produce a magnetic flux of constant magnitude but rotating at synchronous speed

  • The flux passes through the air-gap, sweeps past the rotor surface and so cuts the rotor conductors which as yet are stationary

  • Due to the relative speed between the rotating flux and the stationary conductors, an emf is induced in the latter, according to Faraday’s laws of electro-magnetic induction

  • The frequency of the induced emf is the same as the supply frequency

  • Its magnitude is proportional to the relative velocity between the flux and the conductors and its direction is given by Fleming’s RHR

  • Since the rotor bars or conductors form a closed circuit, rotor current is produced whose direction is given by Lenz’s law, is such as to oppose the very cause producing it

  • In this case, the cause which produces the rotor current is the relative velocity between the rotating flux of the stator and stationary rotor conductors

  • Hence, to reduce the relative speed, the rotor starts running in the same direction as that of the flux and tries to catch up with the rotating flux

    • Assume stator field is rotating clockwise

    • The relative motion of the rotor w.r.t stator is anticlockwise

    • Thus by RHR, the induced emf in the rotor is outwards

    • Using LHR or combined effect, the rotor conductors experience a force tending to rotate them in clockwise

    • Thus, rotor is set into rotation in the same direction as that of the stator flux

torque IM
Torque Im