I Don't Understand Transformers/How to Apply Them

[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.

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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.

 

[Charles Link]

an additional input or two: On a somewhat specialized topic like these laminations in a transformer, it is possible there will be some relatively new ideas presented that provide for a better understanding and better way of looking at it. On a somewhat related topic, Feynman mentions the presentation of the $H$ field in some of the textbooks https://www.feynmanlectures.caltech.edu/II_36.htmln as something that has caused confusion (see just before 36.33). Even J.D. Jackson treats $H$ as a second type of magnetic field, and I believe Feynman has it correct when he calls the $H$ a "derived idea".

On the eddy current/lamination subject, it seems it may also be necessary to find the source that treats it most accurately. I see the lamination as one that simply blocks the eddy current, but perhaps further research is in order. My calculations on the topic are very much of the quasi-static kind. It could be a rather complex problem to treat what is going on in the magnetic domains in real time.

 

[alan123hk]

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 Einduced simply by looking at it as the case of a uniform ⋅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 Einduced=Einduced(r), where r needs to be chosen as the center of the cylinder.

You seem to completely disagree with this calculation method, which really disappoints me a bit.

However, since the induced EMF and current will vary with the distance from the origin, I also admit that the validity of this approximate calculation method has not been rigorously proven by mathematics. Although I intuitively accept this calculation method, but maybe you are right, it does have some flaws and inaccuracies.

In any case, I think I should mention that there may be inaccuracies in my interpretation, but this method of calculation and explanation is not invented by myself, please refer to the following link (Figure 13.4 illustrates a square, before and after it has been cut in four..)

https://www.sciencedirect.com/topics/engineering/eddy-current-loss

 

[Charles Link]

You seem to completely disagree with this calculation method, which really disappoints me a bit.

One post of mine that you might find of interest is post 43. That kind of sums up my starting point, where the eddy currents are assumed to be under control by the laminations, and the Faraday EMF in the core can then be modeled in a simple manner. I do see the merit in what you presented, and perhaps that is one of the easier ways to model the eddy currents with laminations, particularly if a manufacturing process is available that can make the square units.

My assessment of it as saying the laminations simply block the eddy currents and get them under control is rather qualitative, and perhaps the best thing we have at present for a simple ballpark estimate of the eddy currents is the scenario that you presented. :)

On another note, computing the eddy currents without the laminations is no simple task, because there will be limited flux in the core with surface eddy currents canceling coil currents and surface magnetization currents. With my starting point, the eddy currents are already assumed to be under control by the laminations, so that the flux from coil currents and surface magnetization currents will be present throughout the core.

 

[alan123hk]

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.

I totally agree with this statement.
I found that the skin depth of the iron core used in the transformer is much smaller than I thought. Fortunately, laminations can greatly reduce eddy currents while reducing the skin effect. I think we should consider these two important factors at the same time when determining the optimal laminate thickness. I believe there should be special software to help solve this complicated problem.

It also wastes energy because magnetic field that enters thick core will be over-run by the next reverse half cycle, cancelling the earlier magnetization investment.

Sorry, I don’t understand this, please explain further or provide some reference links

The presence of inaccessible core also requires longer and thicker windings to surround more material.

This is a very undesirable situation. Of course, the most appropriate and effective method is to try to avoid the magnetic saturation of the laminations caused by the skin effect.

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.

When the changing magnetic field passes through the conductor, an eddy current will be generated. When the frequency increases, this eddy current will accumulate on the surface of the conductor due to the skin effect. Of course, it is very intuitive that the use of laminated sheets can reduce the negative impact of skin effect. However, if according to the reasoning method I quoted, when the skin effect is negligible, the lamination can still further reduce the influence of the eddy current.
Therefore, the thickness of the laminate will affect the adverse effects caused by the skin effect and the adverse effects caused by eddy currents, which are intertwined with each other. When the frequency increases, the proximity effect makes the situation more complicated, so I think it may not be so easy to generalize which one is the key problem to be solved. In practice, it may vary depending on the specific situation.

 

[hutchphd]

I seem to have come upon a morass.
Does everyone understand that the eddy currents are real currents and the "surface currents" are a useful fiction often used to describe bulk magnetization? They have quite different properties. It seems the crux of the misunderstanding but I cannot ascertain. Please ignore me if I misunderstand.

 

[Charles Link]

It would be interesting to find out the present state of the art. e.g. What kind of magnetic materials are being used, and are laminations still in widespread use or have they solved the eddy current problem with alternate materials? I'm referring here to f=60 Hz. Electrical power is being efficiently delivered over large distances and also distributed very effectively.

On another note, the fundamentals of magnetostatics in regards to the $B$ and the $H$, and the magnetic surface currents and pole method were taught somewhat poorly when I was in school, (around 1975-1980). It seems they didn't have a complete handle on the subject at the time. (I have since been able to put a good part of that puzzle together). These laminations and eddy currents seem to be another topic where a good number of the textbooks are lacking in a complete description.

To add to the above, it comes as a surprise to me, (is this for real?), that the deeper part of the core is not being used in a transformer, or that eddy currents would still be so prevalent that larger currents are needed in the windings to get the desired flux, that the transformer would have the problem of magnetic saturation occurring. I think these problems have been largely solved over the past 50 years or more. @alan123hk Is this not the case? @hutchphd This goes along with your post 65.

 

[alan123hk]

@alan123hk Is this not the case?

Because almost all switching transformers of small electronic products use ferrite cores or powdered iron cores, I have no working experience with power transformers using bulky laminated silicon steel , but I believe they are still used in those large power transformers, motors and generators, etc.

I think that the relationship between eddy current, skin effect, magnetic saturation and lamination thickness is indeed a complex and specialized topic. It may be that only experts engaged in this area have a more comprehensive and in-depth understanding.

I just found an article by AK Steel. There is a section titled Lamination Thickness for 50 and 60 Hz Applications, which mentions relevant information. I think it is of great reference value. I extracted part of the text as follows.

The thickness of electrical steel influences the core loss under A-C and pulsating conditions due to its marked effect upon the eddy current component of core loss. Under most conditions, the eddy current loss will vary approximately as the square of the thickness of flat-rolled magnetic materials. This limits the maximum thickness that can be used to advantage for laminations carrying magnetic flux alternating at 50 to 60 hertz or higher...

“Skin effect,” caused by eddy currents within each lamination, results in crowding magnetic flux out of the midthickness section of the laminations. This occurs because eddy currents set up a counter magnetomotive force. If the lamination is too thick for the frequency of alternation of the magnetic flux, or if permeability of the material is quite high, only a portion of the lamination cross section will be effective in carrying the flux. Consequently, effective thickness of the lamination is less than actual thickness. Therefore, the A-C permeability considering the entire cross section will apparently be less than that normal for D-C flux or A-C flux of low frequency.

If the average flux density of the entire cross section of a lamination is high enough, the skin effect at comparatively high frequency may be sufficient to cause saturation of the surface layers. The exciting current then may be quite high. However, under such conditions, excessive core loss usually results from these high eddy currents before the saturation of the surface layers of the lamination becomes a limiting factor. This is especially true when both the flux density and frequency are high.

The production and fabrication costs per unit weight of electrical steels increase rapidly as thickness is
decreased. While the thinnest materials may be warranted for certain applications, use of thinner laminations than absolutely necessary is wasteful.

https://www.brown.edu/Departments/Engineering/Courses/ENGN1931F/mag_cores_dataAKSteel-very good.pdf

 

[Charles Link]

I think that the relationship between eddy current, skin effect, magnetic saturation and lamination thickness is indeed a complex and specialized topic. It may be that only experts engaged in this area have a more comprehensive and in-depth understanding.

Yes @alan123hk What we can hope for is that in describing the basics in posts such as these on Physics Forums, that we give the student who is trying to learn the subject a reasonably accurate description of what is going on. In any case, a very good reference that you found. Thank you very much. :)

 

[Baluncore]

What we can hope for is that in describing the basics in posts such as these on Physics Forums, that we give the student who is trying to learn the subject a reasonably accurate description of what is going on.

The problem with the mantra “the laminations are there to stop the eddy currents” began during WW2 when the syllabus for training technicians did not include an understanding of skin effect. Some of those tech's, after the war, became physics teachers who have since perpetuated the ignorant brush-off. You continue to perpetuate it today.

In this thread it has been clearly stated and accepted that any core inaccessible due to skin effect, represents a real liability. That is why the lamination thickness is always calculated from skin depth in the core material, and never ever calculated from the acceptable power loss due to eddy currents in the core. It only takes a few laminations to reduce eddy current power loss to an acceptable figure.

A transformer with insufficient accessible core material will have a lower inductance, and so will have a higher flux, and saturate earlier. The lamination thinness simply gives the field access to all of the core. The orientation of the laminations is important, and always aligned so field lines can enter the volume of the core, through the insulation between laminae.

The cheapest and easiest core to fabricate is a low scrap EI stamped core. A powdered iron core is more expensive and so is restricted to use at higher frequencies when metal shim becomes too thin to handle, or the proportion of insulation begins to dominate the core volume. Insulation thickness is as bad as inaccessible core, since the windings must encompass both. If the volume of core insulation exceeds 5%, you should start to look for a different core material or insulation.

 

[Charles Link]

that any core inaccessible due to skin effect, represents a real liability. That is why the lamination thickness is always calculated from skin depth in the core material

Here is where I no doubt am lacking very much for an intuitive feel for what the skin effect is all about. There is a lot, (almost too much), going on with magnetic fields getting created by the currents in the transformer windings, and getting enhanced by the magnetic material. Somehow the magnetic flux then doesn't get to the complete core, but I also don't understand how the saturation then occurs. Perhaps I am a little slow in picking up the concepts, or maybe it isn't a very easy one to learn in detail. Thank you for your patience. :)