Rotating magnetic field

How rotating magnetic field is produced in Induction Motor ?

Consider 3-phase currents, displaced in time by 120⁰ as shown.

When 3-phase windings displaced in space by 120⁰ are fed by these 3-phase currents, individual phases produce magnetic fluxes and the assumed positive directions of these fluxes are shown below.

Lets analyse each of these fluxes and their resultant Φ, at every instant of time 60⁰ apart.

(1) when  ϴ=0⁰

As fluxes will be proportional to these currents, Let their values be

    

    Where,  Φ_m = maximum value of magnetic flux due to any phase.

Vectorically the fluxes are shown along with their resultant flux (in red )  Φ. The negative sign have been taken into account in vector diagram.  

The resultant flux  Φ  is given by 

 Φ = Φ_B cos 30⁰ + Φ_Y cos 30⁰      

        

         = 1.5 Φ_m 

So, resultant flux has magnitude equal to  1.5 Φ_m  and is vertically directed.

 (2) when ϴ=60⁰

The individual fluxes will be

   

    Represented in phasors as shown.

   

The resultant flux is given by

Φ = Φ_R cos 30⁰ + Φ_Y cos 30⁰    

        

So, resultant flux has magnitude 1.5 times maximum flux due to any phase and has rotated 60⁰ clockwise.

(3) when ϴ=120⁰

      

     

The individual fluxes along with the resultant are represented in  phasors as shown.

 The resultant flux is given by

 Φ = Φ_R cos 30⁰ + Φ_B cos 30⁰ 

        

So, resultant flux has magnitude 1.5Φ_m and has rotated 60⁰ clockwise from last position.

(4) when ϴ=180⁰

     

      

      

    The individual fluxes along with the resultant are represented in                 phasors as shown.

    

The resultant flux is given by

Φ = Φ_Y cos 30⁰ + Φ_B cos 30⁰    

        

Again, resultant flux has magnitude 1.5Φ_m and has rotated 60⁰ clockwise from last position.

Similar analysis can be continued for next  ϴs  upto full cycle i.e  ϴ=360⁰ .

From above, we observed that

(1) The resultant flux is of constant value = 1.5 Φ_m    i.e  1.5 times the    maximum value of flux due to any phase.

(2) The resultant flux rotates around the stator at a speed called synchronous speed.

Thus, it is true to assume that a rotating magnetic field is produced in space as if actual magnetic poles of permanent magnet were being rotated mechanically.