Eddy current loss help please

[Physicist3]

Hi, I have been trying to understand eddy current loss in transformer cores but seem to have run into a bit of a misunderstanding with one of the books I have read, and I was wondering if someone could just clarify if I have got this all right.

starting with the beginning, if the magnetic flux varies sinusoidal, then the flux at one instant would be;

∅ = ∅_msin(ωt) (I have been told this should be done in degrees and not radians?)

value of induced emf in core at any time (t) =

$\frac{d∅}{dt}$ = ω∅_mcos(ωt)

Am I correct in saying that from this second equation, ωθ_m = E_m (Max induced EMF in core)?

If E_s = rms value of emf induced in core, this = $\frac{1}{\sqrt{2}}$ω∅_m = $\sqrt{2}$∏f∅_m = $\sqrt{2}$∏f(AB_m)

Eddy current Power Losses = [itex]\frac{E_s²}{R_s}[/itex]
= [itex]\frac{2*∏²*f²*A²*B_m²}{R_s}[/itex]

The next bit is the section of the notes that seems to confuse me,

Eddy current Power Loss = P_E = K_E*f²*B_M², where K_E = Constant = 2*∏²*A²/R_s.

The book then says 'hence eddy current losses = α (f²*B_M²)

Does this mean that K_E is the same as α and eddy current power loss is the same as eddy current loss, or are these two different things? As far as I can see they appear the same but I just wanted to make sure from someone who has a bit more experience or knowledge of this.

thanks

 

[NascentOxygen]

value of induced emf in core at any time (t) =

$\frac{d∅}{dt}$ = ω∅_mcos(ωt)

Am I correct in saying that from this second equation, ωθ_m = E_m (Max induced EMF in core)?

That would be emf induced per turn in the winding around the core, I think.

The book then says 'hence eddy current losses = α (f²*B_M²)

Lose the equals sign. I think that should be a simple proportionality:

eddy current losses α (f²*B_M²)

 

[hisham.i]

Eddy current Power Loss = PE = KE*f2*BM2, where KE = Constant = 2*∏2*A2/Rs.

The book then says 'hence eddy current losses = α (f2*BM2)

Both are the same, eddy current losses means the power loss due to eddy current.

 

[jim hardy]

Try a search on Steinmetz - he figured it out by experiment late 1800's
some old textbooks are showing up online nowadays with first-hand explanation.