I Don't Understand Transformers/How to Apply Them

[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.