I Don't Understand Transformers/How to Apply Them

[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. :)

 

[artis]

@Baluncore I suppose we could say that laminations perform somewhat like a waveguide for the magnetic field because a field cannot travel within a solid metal as it would be constantly opposed by eddy currents even small ones, but it can travel at some considerable fraction of the speed of light through plastic insulation or air so it travels fast through the gaps between laminations and then "seeps" into the laminations themselves uniformly along the length of them?

I guess one could compare this to burning a book, if the book pages are tightly pushed together as we all know its very hard to burn a book that way , you need to have small openings between the pages in order for the flame to get through and when it does it then burns each page uniformly almost.
Another analogy could be that of flowing water down a sheet of paper, as the water flows down it first flows down to the bottom and then almost uniformly seeps into the page but again if I took a 500 page stack and pressed it together firmly I wouldn't be able to make the water penetrate the stack. This is like with the solid core where the field cannot penetrate the depth of the core because it receives very powerful opposition at the very uppermost layers of it.

@Charles Link I think @Baluncore meant that if the laminations are too thick for a given frequency the field as I said above does penetrate through the whole core because of the gaps but it then in the short time it has before cycle reversal doesn't have the "time" to penetrate each lamination to it's full cross section because if it's too thick the eddy currents due to skin effect will effectively block the inner part of the metal to be reached. So you have a certain cross section of the core that gets shielded. A small portion from each lamination.
So in a case like this for the same core cross section you get a much smaller effective cross section and the core performs as if it were a smaller core and it is easier to saturate a smaller core.

 

[Baluncore]

Somehow the magnetic flux then doesn't get to the complete core, but I also don't understand how the saturation then occurs.

The field travels through the insulation at close to the speed of light, determined by the dielectric constant of the insulation. The field then diffuses into the lamination from both sides at a much lower speed, determined by the material conductivity and permeability. If the two do not meet at the centre of the lamination before the field reverses, that central sheet of material plays no part in creating the inductance of the primary. The primary inductance limits the reactive magnetising current that creates the flux in the core.

 

[Charles Link]

The field travels through the insulation at close to the speed of light, determined by the dielectric constant of the insulation. The field then diffuses into the lamination from both sides at a much lower speed, determined by the material conductivity and permeability. If the two do not meet at the centre of the lamination before the field reverses, that central sheet of material plays no part in creating the inductance of the primary. The primary inductance limits the reactive magnetising current that creates the flux in the core.

Thank you @Baluncore This is not what I would have guessed, but it is very interesting. Very glad for your expertise. :)

 

[alan123hk]

I am glad that this thread has made more and more in-depth discussions on transformers, and there are some important messages that I have not considered in detail before.

I personally think that there are two situations that cause lamination magnetic saturation to be considered.

When a fixed AC excitation voltage and frequency are applied to an inductor or transformer, according to Faraday's law, the relative magnetic flux must be fixed.

If only a portion of the lamination cross section can effective in carrying the flux, the magnetic flux density must be increased proportionally. When this magnetic flux density exceeds the rated saturation value of the magnetic core material, the permeability will drop to very low, so the excitation current of the power source will increase greatly.

However, there are two situations that will cause the lamination effective cross section area to decrease. The first is the skin effect caused by the counter magnetomotive force of the eddy current, and secondly, the high magnetic permeability and relatively high electrical conductivity of the laminations, which causes the propagation speed of the internal magnetic field to be much slower. If the magnetic field has not reached the center of the lamination when the direction is reversed, it will also reduce the effective cross-sectional area of the lamination.

I am not sure whether these two situations describe essentially the same physical process or different physical processes.

By the way, I think I understand that the field through the insulating gap is a very important part of establishing the flux of the lamination, but I think that if the relative permeability of the lamination is very high, then the width of the insulating gap can be very narrow.

 

[The Electrician]

It only takes a few laminations to reduce eddy current power loss to an acceptable figure.

What thickness of lamination would reduce eddy current power loss to an acceptable figure?

 

[Baluncore]

What thickness of lamination would reduce eddy current power loss to an acceptable figure?

It depends on what eddy current power loss you would find acceptable.
It is certainly thicker than is demanded by skin effect.

Your question is moot as the computation of eddy current loss is unnecessary, so the appropriate equations are not in common use.

Looking at the internal core topology, the shape of the components must be made of insulated elements, having a minimum cross sectional area (to reduce voltage), with a maximum peripheral boundary (to increase resistance). That will minimise the eddy current to I = V/R.
At the same time the magnetic elements must be small enough that the maximum distance of any magnetic material from the surface of a core element is one skin effect.

The solution is to use a flat sheet of magnetic material, oriented edge on to the field. Laminations come remarkably close to that ideal, while at the same time being easy to roll from steel, stamp with low scrap, insulate chemically, and stack together into a functional transformer core.

 

[alan123hk]

What thickness of lamination would reduce eddy current power loss to an acceptable figure?

For the practical application level, you can refer to the manufacturer's specifications, they will provide the core loss of different lamination thicknesses under the specified frequency and magnetic flux density, and then choose according to your own acceptance.

The general simple eddy current loss formula is only a simplification of the actual conditions. It is very useful for learning basic principles, but if it is applied to actual engineering design, it may not be accurate and reliable. For example, the simple eddy current formula does not consider the skin effect, and hysteresis loss is another factor that will affect the overall loss, so it should also be considered.

I believe the information provided by the manufacturer will be more accurate because they should evaluate the actual data through laboratory tests.

 

[The Electrician]

It depends on what eddy current power loss you would find acceptable.
It is certainly thicker than is demanded by skin effect.

What thickness is demanded by skin effect in modern grain oriented silicon steel? Give me a typical value.

 

[Baluncore]

What thickness is demanded by skin effect in modern grain oriented silicon steel? Give me a typical value.

See the graph at; https://en.wikipedia.org/wiki/Skin_effect#Examples
Read the blue line for FeSi at 60 Hz, to get about 0.26 mm.
Doubling that, since the field enters from both sides, gives a thickness of 0.52 mm.

Typical laminations are 26 gauge = 0.0185” = 0.47 mm.
Given the variation in the physical properties and processing of Si steel, I would call that close enough.

 

[Charles Link]

I am glad that this thread has made more and more in-depth discussions on transformers, and there are some important messages that I have not considered in detail before.

Yes, I found the discussions very enlightening as well. The explanation offered by @Baluncore of the magnetic field propagating through the insulation, (basically completely), and then diffusing rather slowly into the iron from both sides of the iron layer came as a surprise, but I think it is a good one, and I am very glad he provided us with this detail. The actual diffusion process with eddy currents and bound magnetic surface currents in a highly conductive medium is no doubt rather complex, but we now have a much better picture of it than previously.

 

[alan123hk]

@Charles Link Yes, I agree with you very much.

The following two parameters obtained by Maxwell's equation for the solution of the plane wave are very useful.

The skin depth is calculated by $\frac 1 \alpha$, and the speed is calculated by $\frac {2\pi f} {\beta}$.

For electric steel, suppose its relative permeability is $4000$ and the resistivity is $4.72×{10}^{−7}Ω·m$, so the calculated skin depth is 0.7mm and speed is 0.243mm/ms.
https://en.wikipedia.org/wiki/Electrical_steel

That is to say, at this speed, the travel distance of a 50Hz half cycle is only 2.34mm, and this speed refers to the transmission of electromagnetic wave in any direction in the electrical steel.

These values did surprise me a bit, and I also thought about whether the insulating layer between the laminates can help increase the actual energy transfer speed from the primary coil to the secondary coil, but even so, quantitative analysis of this can be a very complex task.

Back to the topic, I think the lamination thickness will be affected by different factors. Although the reduction in lamination thickness may further reduce the eddy current loss, it also increases sheet manufacturing costs and assembly costs. In addition, eddy current loss is a part of the overall core loss, there are other losses, such as hysteresis loss. If the eddy current loss already accounts for a small part of the total loss, further reducing the thickness will not achieve the cost performance.

 

[Charles Link]

whether the insulating layer between the laminates can help increase the actual energy transfer speed from the primary coil to the secondary coil

For this part, I believe the calculation might involve an effective $\mu$, where what is often taken as a real constant for simple calculations would then become a complex number with a phase. It's likely to be a complicated calculation in any case.