I Don't Understand Transformers/How to Apply Them

[Charles Link]

I gave the electrical transformer some additional thought, and there are a couple of things, besides just the formulas, that make it so remarkable. The primary coil with electrical current running through it creates a magnetic field that is greatly enhanced by the iron core. With an alternating current, this creates an alternating magnetic field, and amazingly enough, the secondary coil is able to pick up on this alternating magnetic field, and have a voltage (by Faraday's law) and current generated in the secondary coil, with nearly one hundred per cent power transfer. Having a toroidal geometry with primary and secondary coils around the torus makes for almost complete magnetic flux coupling. The one problem that occurs, with eddy currents in the iron from the Faraday EMF in the iron, is readily solved by having laminations in the iron. The transformer is truly a remarkable invention. It is also truly amazing that nature allows it to be so simple in design.

 

[alan123hk]

The one problem that occurs, with eddy currents in the iron from the Faraday EMF in the iron, is readily solved by having laminations in the iron

This is another outstanding invention related to iron core transformers. Of course, the experiment can prove that the lamination in the iron core can reduce the eddy current loss, but I think the reasoning method described in the link below is also very convincing.

https://www.physicsforums.com/threa...-commercial-transformer.1002491/#post-6489247

 

[Baluncore]

Notice in that link, how between adjacent laminae, the eddy currents counter flow, so cancel internally. But locally they are needed to get the field into the conductive magnetic material. The result after cancellation of internal sheet currents is the peripheral current that flowed without laminations.

Skin effect dictates the thickness of laminations. If you did not have sufficient gaps in the core material the magnetic field could not get in and out again before the field reversed.

It is the orientation of the laminations that reduces eddy current losses.

 

[davenn]

looks like we long since lost the OP

 

[Charles Link]

I think I see the eddy current problem slightly different than that of the link of post 32. Iron is a conductor and the Faraday EMF in the iron will cause significant current flow of the same symmetry (concentric with the core) as the Faraday EMF's that are generated by the coil windings (compare to a solenoid with an iron core). Laminations block this current flow in a capacitive manner=it only takes a little bit of charge to accumulate on the lamination to create a voltage opposing the Faraday EMF. The diagram of the link seems to mix the eddy current concept with the bound surface currents that are not blocked by the laminations. Basically the magnetic surface current per unit length $K_m=M \times \hat{n}/\mu_o$, with or without laminations. Perhaps I am missing something here, but that is my interpretation. (Note: Unlike the eddy currents, the magnetic surface current does not involve any charge transport).

and note, the paths the eddy currents take will be circular, (concentric with the center of the core), and laminations in a horizontal direction will be effective in blocking these circular paths. The neat thing is that the laminations don't block the magnetic surface currents, and the magnetic material (iron) behaves like it needs to=with laminations it is simply minus the eddy currents.

 

[alan123hk]

I think I may not express it clearly, if so I am sorry, please allow me to describe my thoughts in detail again.

For ferromagnetic materials, assuming that the uniformly distributed magnetic flux density does not change, the effective surface magnetization current caused by the magnetic moment induced by the external magnetic field will not change due to the partition cutting of the magnetic core, as shown in the figure below.

​

But what we are interested in now is the eddy current caused by the induced EMF inside the iron core based on Faraday's law, and this eddy current will produce energy loss based on Ohm's law, as shown in the figure below.

Now we must try to use an approximate method to evaluate this eddy current loss.
Simplify the expression form of the eddy current caused by Faraday's law in the iron core, and calculate the eddy current loss, as shown in the figure below.

Note that the effective resistance does not change with $L$, but for fixed $D$ and $B$, the eddy current loss is proportional to $L^4$.

The above reasoning method is enough to convince me that the laminations in the iron core can indeed reduce the eddy current loss greatly. Of course, it is usually cut into long thin pieces instead of square pieces, but they work on the same principle.

 

[Charles Link]

Thank you @alan123hk , but I still think I see the scenario a little differently. Consider a long solenoid with an iron core, to simplify the scenario. The $B$ field is uniform over the cross sectional area, but you can not look at a small cross section of this iron core with uniform $\dot{B}$ and compute the $E_{induced}$. Instead, the $E_{induced}$ computation needs to use the symmetry of the core, and then you have $E_{induced}=E_{induced}(r)$.
(It might appear that a small cross section of the core contains complete symmetry in solving for $E_{induced}$, but that is not the case).

$\mathcal{E}= E_{induced}(r) 2 \pi r=\dot{B} \pi r^2$.

Laminations will not affect the $E_{induced}$ from the changing $B$ field from the changing current in the coil.

That's where I envision the eddy currents to follow along the lines of $\vec{E}_{induced}$ in concentric circles . Horizontal barriers that create a voltage from the capacitance (charge will accumulate at the lamination barrier) when current starts to flow will greatly reduce the flow of current.

 

[alan123hk]

Consider a long solenoid with an iron core, to simplify the scenario. The B field is uniform over the cross sectional area, but you can not look at a small cross section of this iron core with uniform B˙ and compute the Einduced. Instead, the Einduced computation needs to use the symmetry of the core, and then you have Einduced=Einduced(r).

Thank you for your reply. I believe I probably understand what you mean.
Please refer to the figure below.

The four blocks here have the same magnetic flux density and uniform distribution, and there are insulating gaps between them.

Now we consider the eddy current of block 1, because it is a square, so I don't know the exact eddy current distribution, but the eddy current distribution caused by its own magnetic flux should have a certain symmetry. Of course, the magnetic field from the other three blocks will also generate induced current through block 1 through the capacitance of the insulation gaps, but these induced currents are not an eddy current confined to block 1, because the capacitance of the insulation gap is small, and the operating frequency of transformer using iron core is not high, I believe that in this case, these induced currents generated by the other three blocks can be ignored in block 1.

And I emphasize again that I just do an approximate calculation.

 

[Charles Link]

I don't agree with the drawing of the eddy current loops in the sense that it seems to be assuming a solution of computing $E_{induced}$ simply by looking at it as the case of a uniform $\cdot{B}$ over the entire plane, and assuming a symmetry about the center of the chosen section. If you do that with the solenoid problem, you get a contradiction, and the correct solution is $E_{induced}=E_{induced}(r)$, where $r$ needs to be chosen as the center of the cylinder.
(Consider the problem of a uniform $\dot{B}$ into the paper over the entire plane. The computation of $\vec{E}_{induced}$ will give different answers for different choices of the origin, and it leads to a dilemma that is resolved by seeing in a real live scenario, the coil creating the uniform field has a single origin. Only about this origin does the assumed symmetry actually exist).

Meanwhile, I think the mechanism for blocking the eddy currents is the current flow getting stopped at the insulating barrier, with the result being a charge build-up, with a voltage that opposes the Faraday EMF.

 

[Baluncore]

Now we consider the eddy current of block 1, because it is a square, so I don't know the exact eddy current distribution, ...

The eddy currents will only flow in the surface of the block.

One thing being ignored here is that due to skin effect the deeper volume of the core is not
accessible to the field, so there will be no eddy current there. Deep magnetic core is a waste of material. It also wastes energy because magnetic field that enters thick core will be over-run by the next reverse half cycle, cancelling the earlier magnetisation investment. The presence of inaccessible core also requires longer and thicker windings to surround more material.

Laminations make the full volume of the core material accessible to the changing magnetic field. The orientation of the laminations reduces eddy currents.

 

[Charles Link]

The eddy currents will only flow in the surface of the block.

@Baluncore
With laminations, the magnetic field will be nearly the ideal value even deeper into the core. Eddy currents will also be present in the core. The calculations I'm doing above are just considering the $E_{induced}$ from the coil in the absence of eddy currents. With the eddy currents at the surface creating an opposing magnetic field in the case of no laminations, the transformer simply would not work properly.

 

[Baluncore]

Then I think you had better explain why.

 

[Charles Link]

Then I think you had better explain why.

@Baluncore I removed the comment where I think you might have a couple of concepts incorrect, because I now see the logic to what you presented.

Once the eddy currents are "under control" with laminations, you can then assume a magnetic field $B$ in the core that is approximately that from the current in the coil alone, (edit=along with the magnetic surface currents that basically enhance the $H$ from the coil by a factor of $\mu_r$). From there, you can then compute $E_{induced}$ and see that there will be eddy currents, but their effect is greatly reduced by the laminations that will be a barrier where charge accumulates as soon as the current starts to flow and offsets the $E_{induced}$.

Edit: Without the laminations, the eddy currents would not be under control, and then yes, there would be tremendous eddy currents at the surface,(as you mentioned above), and it would be pointless to assume the $B$ that I did in the paragraph above.

 

[artis]

The field is uniform over the cross sectional area, but you can not look at a small cross section of this iron core with uniform and compute the . Instead, the computation needs to use the symmetry of the core, and then you have .
(It might appear that a small cross section of the core contains complete symmetry in solving for , but that is not the case).

I think the answer could be in that for a solid core , it almost acts like a real secondary winding because the induced eddy currents can be simply considered induced secondary currents so a solid core acts somewhat like a short circuited coil where the most current runs at the periphery and that is why you cannot consider just a small portion of it, meanwhile for laminated core each lamination is the same as each next one as since they are electrically isolated (at least when new and haven't rusted through yet) then each lamination "gets" the same field strength while producing minimal induced currents and so allowing the field to pass along.
I might be mistaken but I think the reason why a solid core is not good is because the induced secondary current in the core itself is a type of "back EMF" which opposes the primary field and current and so very little field can pass further.
I think a similar scenario is when one has a large and thick short circuited single turn secondary on a transformer. If there are any other "normal" secondaries on the same core , they will get very little induction as a result.

 

[Charles Link]

I think the answer could be in that for a solid core , it almost acts like a real secondary winding

Yes. See the Edit of post 43 above. It is clear that the laminations are necessary.

 

[artis]

While on the topic of lamination I do wonder why they don't make them even thinner yet, or could it be that after some threshold thickness making them any thinner doesn't increase the efficiency considerably so they don't go the extra step.

 

[Baluncore]

It is clear that the laminations are necessary.

No. The surface area (aligned with the B field) to one skin depth is necessary to prevent saturation.
Laminations are one way to increase the efficiency by reducing the length of the wire needed to wrap the core.

 

[Baluncore]

While on the topic of lamination I do wonder why they don't make them even thinner yet, or could it be that after some threshold thickness making them any thinner doesn't increase the efficiency considerably so they don't go the extra step.

Audio transformers have thinner laminations than do power transformers. The thickness is determined by the skin effect in the material. Once all the material can be reached and reversed in one cycle, there is no advantage in thinner laminations.

The surface of the laminations is chemically treated to become an insulator. With thinner laminations, the proportion of insulation in the core becomes greater, so a transformer should use the thickest laminations that will work at the greatest frequency of interest.

 

[Charles Link]

No. The surface area (aligned with the B field) to one skin depth is necessary to prevent saturation.
Laminations are one way to increase the efficiency by reducing the length of the wire needed to wrap the core.

We do seem to have a disagreement here on the fundamentals of what is going on in the transformer with laminations. Perhaps with some further discussion we can resolve the differences.

 

[Baluncore]

We do seem to have a disagreement here on the fundamentals of what is going on in the transformer with laminations. Perhaps with some further discussion we can resolve the differences.

I thought that was just what we were doing.

I tire of everyone chanting "the laminations are there to stop the eddy currents". They are not. They are there to shorten the length of wire needed for the windings.

 

[Charles Link]

I am tired of everyone chanting "the laminations are there to stop the eddy currents". They are not. They are there to shorten the length of wire needed in the windings.

I can't guarantee that my approach is correct, but it is consistent with everything else I know about E&M. The transformer with laminations to me is very much like the ideal textbook problem, in that once the eddy currents are under control, the magnetic field of the core can be computed as it is for a coil and a core in the DC case, without any Faraday effect to complicate matters. The "skin depth", etc., is also no longer a problem.

I believe my approach to be correct, because the textbook type calculations work out so well. The transformer with laminations has all of the properties that you would want it to have, and that's exactly why it has seen such widespread use, and why it has been so successful.

 

[artis]

I tire of everyone chanting "the laminations are there to stop the eddy currents". They are not. They are there to shorten the length of wire needed for the windings.

But isn't that the same, eventually? Having a solid core would result in large circular induced currents which mostly would concentrate at the outer layers of the core if looked upon from it's cross section. So the core would "steal" much of the current that would otherwise be able to reach secondary coil. So to overcome this one would need as you say thicker wire, more current , more power for the same amount of secondary load, since now the core would also be a major "load".I think I get your point in that this solid core example the parasitic eddy currents would not exist throughout the core instead being at the point of the primary coil and their existence there would hinder the B field from effectively penetrating the core downwards and only able to "flow" along the very outside of it, which is why I believe you said that such a core would waste most of it's material.

 

[Charles Link]

The eddy currents, besides heating the core, also generate an opposing magnetic field, and without laminations, there would be so much eddy current, that the magnetic flux would be greatly reduced. The transformer would be nearly useless without laminations. More windings would not solve the problem.

The laminations get the eddy current completely under control, and the mechanism is a simple one. The currents are blocked and the result is a static charge build-up at the barrier.

 

[Baluncore]

... in that once the eddy currents are under control ...

The thickness of the laminations is decided by skin depth, not the size of the eddy currents, nor the degree of eddy current "control" required.

But isn't that the same, eventually?

No. With a solid core of the same mass, there is insufficient inductance to limit the magnetising current. With a laminated core, a wire bundle, or a particulate core such as iron powder or a ferrite, the inductance would be much higher for the same mass of core material.

 

[Charles Link]

The thickness of the laminations is decided by skin depth, not the size of the eddy currents, nor the degree of eddy current "control".

My objection here is that this seems to be a qualitative theory that you are presenting to explain what occurs, rather than looking at the calculations that work so well to successfully explain what is observed.

The laminations work so well to reduce the eddy currents that in a number of textbook problems with transformers, they treat the iron core as if it were ideal,(without eddy currents), and work the problem as an ideal transformer. In many cases, they totally omit the description of the iron core as having laminations=a detail that could almost fall by the wayside, and it needs to be brought into the discussion for completeness every so often.

 

[Baluncore]

The laminations work so well to reduce the eddy current that in a number of textbook problems with transformers, they treat the iron core as if it were ideal, and work the problem as an ideal transformer. In many cases, they totally omit the description of the iron core as having laminations=a detail that could almost fall by the wayside, and needs to be brought into the discussion for completeness every so often.

Ignorance is bliss.
Who then calculates the thickness of the laminations to be used?
What equation do they use for that computation?

 

[Charles Link]

Who then calculates the thickness of the laminations to be used?

at 60 Hz, it doesn't seem to be real fussy.(The laminations are readily visible when looking at a transformer on its side). Higher frequencies would take a little more work, but some of it is probably determined experimentally. For the calculations I was referring to above, it is the basic calculation of the magnetic flux in the core. The eddy currents, to a very good approximation, can be totally ignored, if there is sufficient laminations.

The Faraday $E_{induced}$ becomes larger at higher frequencies, (it is proportional to $f$). Further calculations are necessary to determine how this might affect things.

 

[Baluncore]

For the calculations I was referring to above, it is the basic calculation of the magnetic flux in the core.

I was referring to the calculation of the required lamination thickness, not the flux.

The eddy currents, to a very good approximation, can be totally ignored, if there is sufficient laminations.

Your statement is a truism and totally ignores the computational approach used by lamination stamping factories to decide the thickness of the material.

 

[Charles Link]

Your statement is a truism and totally ignores the computational approach used by lamination stamping factories to decide the thickness of the material.

I've presented how I see the lamination concept as well as I can. I can't guarantee that it is correct, but it is consistent with the calculations on transformers that I have done which basically ignore the eddy currents. It would be interesting to get a couple other opinions.

The calculation of the eddy currents could be done by calculating $E_{induced}$ for the ideal case of no eddy currents, and using the conductivity of iron, along with a very simple capacitor geometry for the lamination. I have yet to do that, but I wouldn't be surprised if that's how they would compute it.

There also seems to be a couple different things that could be computed=e.g. what is a good thickness for the insulating layer? a google gives a company that specializes in this kind of thing: https://www.thomas-skinner.com/transformer-laminations/

 

[Baluncore]

There also seems to be a couple different things that could be computed=e.g. what is a good thickness for the insulating layer?

The rule of thumb there is to expect about 5% insulation 95% magnetic. It seems the B field passes rapidly through the insulation at about 0.7 c, (due to dielectric constant of the insulation), then diffuses into the magnetic material at closer to 100 m/sec.