Magnetic systems could be of two types they are singly exited and multiply exited magnetic systems.

In singly exited magnetic systems usually one electrical source is employed.It is generally used to attract or repel hence to make devices like relays,electromagnets etc.

Single Excited Electromagnetic System

Let us look how an energy build up happens in a single exited electromagnetic system.

Suppose in a relay if we are giving electrical energy the static part gets magnetized and attracts the movable armature to it hence a part of that magnetic energy is converted into mechanical energy.so

Electrical energy input = mechanical energy output + increase in field energy

The above equation is based on the assumption that there is magnetic core loss in the conductor and no leakage flux.The above equation could be represented as

idψ = F fld.dx +dW fld (where ‘fld’ stands for field)

It means a change in electric field due to change in flux(dψ)is equal the force developed when it moves a distance ‘dx’ and the increase in magnetic field energy(dW fld) .

Ψ-flux linkage = NØ(N- number of turns in conductors ,Ø-flux across each conductor)

So the above equation could be written after substituting and rearranging

F fld.dx = idψ- dW fld

(dW fld is the energy stored in the medium and is a function of inductance ‘L ‘and distance ‘x’ therefore dW fld = ½ dL(x)i2 )

So a increase in flux linkage dψ = i × dL(x) (got by differentiating)

Therefore the equation colud be written as

F fld.dx = i2 dL(x) – ½ i2dL(x) = ½ i2dL(x)

This equation indicates that out of the total energy given half of it is converted into mechanical energy and the other half is stored in the magnetic field itself.

Let L(x) = N2/S(x) where s –reluctance of magnetic circuit

Then equation becomes

F fld = ½ i2d/dx[N2/S(x)]

=-1/2 (Ni)2/S(x) × dS(x)/dx =1/2Ø2 dS(x)/dx (where Ø = Ni/S)

For linear machines, force Ffld = d Wfld(i,x)/d(x) For rotating machines,torque Tfld = d Wfld(i,θ)/d(θ)

It indicates that force acts in a direction to increase the coil inductance and reduce the reluctance of magnetic circuit.

Multiple Excited Magnetization systems

This type of system is much similar to that of an single excited system.In short it could be assumed as a combination of more than one single excited system.Machines like alternators,synchronous motor etc requires two excitation or electrical source for its working and hence it produces two field and due to the interaction of these field it works.

Mathematically it could be represented as

dWfld(ψ1,ψ2,θ) = i1.dψ1+i2dψ2 -Tflddθ

i1= ∂dWfld(ψ1,ψ2,θ)/∂ ψ1] ψ2,θ

i2= ∂dWfld(ψ1,ψ2,θ)/∂ ψ1] ψ1,θ

Tfld= ∂dWfld(ψ1,ψ2,θ)/∂ θ] ψ1, ψ2

Torque production in rotating machines

When an excitation is given to rotor and stator of a rotating machine both of it will produce individual fields and these fields try to align themselves and these will produce South poles and North poles on the surface of rotor as well as stator and the interaction of these poles would produce a rotating torque.

If you enjoyed this post, make sure you subscribe to my RSS feed!