# Magnetic saturartion in 2-D

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1. Sep 14, 2015

### Hassan2

Dear all,
I have a question about magnetic saturation and I can't find any sources addressing my questions.

I am relatively familiar with magnetic saturation and that the relative permeability of highly saturated iron becomes rather small. There are numerous sources with figures showing measured or typical magnetization curves discussing the phenomenon in one dimension. But how about the behavior in 2 or 3 dimensions? Let's have a highly saturated iron bar along x-direction and then apply a magnetic field of small or moderate strength in y-direction. How much would be the magnetic permeability in y-direction ( i.e. the response of the medium to the y-component of the applied field) ? I expect it to be smaller than the non-saturated iron but maybe much larger than the case when it is saturated in y-direction. Does anyone know of any measured data for such cases?

Your help would be appreciated.

Hassan

2. Sep 14, 2015

### gsal

Too many views and no replies...I only have a basic grasp of magnetics but I figure I'd throw a couple of thoughts into the mix, anyway.

Unlike classical analysis of external forces onto a body where one can think of the forces having components and then apply superposition, that is not the case for magnetic fields; the way I see it, there is no such thing as x and y, for a couple of reasons.

From the material's point of view, it has a finite amount of molecules, dipoles, whatever...and if it is magnetically isotropic, if it is saturated, it is saturated and it is saturated, it does not matter in which direction the magnetic field is...if anything, the influence of a second magnetic field may reduce the effect of the first one.

The thing is that I can't even think of magnetic fields as having components, in the first place. A magnetic field is typically thought of using magnetic lines; magnetic lines are continuous, unbroken and unbrakeable (they are very maleable, though), and, so, you cannot have magnetic lines in the x direction and others in the y direction...a magnetic line is a 3D object in the sense that even it is "goes" in the x direction, you cannot have another coming perpendicular and break through it...

...instead, when you have 2 or more sources of magnetic fields, they both add their strengths and then you get a single resultant at every spot in space. Magnetic fields either join or push each other out the way.

So, if I have a point P in space that sees magnetic lines from source 1 with a certain density and THEN I bring a second magnetic field, it could very well be that point P continues to only see magnetic lines from source 1 and non from source 2, but it certainly felt the influence of the second source in that the local density of the magnetic lines from source 1 probably increased and their direction changed.

bla, bla, bla...I don't know what I am talking about...;-)

ok, so, final thought: the way I see it, you really just need to calculate the resultant at every point in space before you can do anything.

3. Sep 14, 2015

### Hassan2

Thanks qsal for replying. Indeed your explanation is intuitive and helpful. But here, by magnetic field, I mean the so-called H-field. And to know what I mean by response in other direction, consider an inductance made up of a coil and a closed magnetic path with a very narrow air gap to determine the inductance.This is a typical and normal inductance and for example for an alternating (AC) current, the induced voltage across the inductance is the time-derivative of the flux linkage. The flux linkage depends on the magnetic flux density B or equivalently on the magnetic induction. Now if we apply a strong DC magnetic field perpendicular to the magnetic path, most magnetic dipole moments will be aligned with the DC field and little response will be expected to the AC field. Isn't this a variable inductance, controllable by some DC coil current? In other words, the magnetic permeability of the core along the AC magnetic path ( the part under the perpendicular DC field) is controlled by applying a DC field.

4. Sep 14, 2015

### gsal

I kind of see what you mean and I am trying to imagine your device...is this like a square core with 2 verticals and 2 horizontals with the AC coil in one of the verticals and possibly, precisely that vertical having a small gap to one of the horizontals? In this case, I guess the core just about short circuits the magnetic loop and the reluctance is govern by the gap.

Then, I presume, you are asking what happens if you "pre-load" the core with a DC field perperndicular to your device...well, of course is going to have some kind of influence, right? Don't know exactly what, but something.

If the core is laminated to favor the function of the AC inductor, well, actually, it will have little response to the perpendicular DC field, ha! You would probably need extra DC due to the laminations. What about "pre-loading" the device with a DC field coplanar with it? That way you benefit from the laminations, too, and probably have more influence against the AC fiel itself.

As you can see, I first imagined the entire devide being submerge in the DC field; but...

How about simply placing the DC coil in one of the other three sides of the core? This seems simpler and beneficial; then again, then again, it would probably also be too much a victim of the AC field.

In any case, I think I have to fall back to what I said before, I don't think you can declare the core "pre-saturated" with the DC field and expect the inductor to behave in a certain way given that it can no longer use the core as easily as before...the inductor itself is going to affect the influence of the external DC field...so, you really need to work out the resultant of the field for every instance in the cycle and at every spot in the core...and that's why magnetics is left to the FEM and computers.

5. Sep 14, 2015

### Hassan2

Yes exactly how you described it.
I have attached a figure illustrating the device. In the figure, cores 1 and 2 are the AC and DC ones respectively and they are coplanar. For comparison , another device could be made of one core only with the DC coil around another leg of the square core. The problem with this case is that the behavior of the core is not the same for both half-cycles of the AC field. In half-cycle the fields become additive increasing the saturation and in another half, the core may get out of saturation. This is not a nice inductor but the one with vertical DC field is expected to behave the same way in both half-cycles.

Others comments:

1. I don't think the analysis of such a simple model needs FEM. We can even simplify it to a 1-D a problem.
2. The main challenge is to keep the filed in DC core constant while AC field is varying. I think if the part of the DC which crosses the AC magnetic path is thin enough, we can keep the flux density constant by adjusting the current at any instant.
3. It is easy to make a FEM analysis of the problem but conventional material modeling, e.g. BH curves, are obtained from unidirectional measurement and I doubt they are valid for the problem even though the material is isotropic.

Thanks again,

Hassan

#### Attached Files:

• ###### twoCores.jpg
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6. Sep 15, 2015

### gsal

Aha! This is much clearer, now, thanks for the picture.
I like the arrangement and how the DC field is perpendicular to the AC field and coplanar to the laminations of that core, too.
Indeed, this is starting to look like something you can do with pencil and paper.
As you say, if the shared section of core is a relatively small part of the DC magnetic circuit, you could start by assuming that the DC flux does not change or changes very little.
On the flip side, the shared section of core could be a significant part of the AC magnetic circuit which is pre-crowded with magnetic lines from the DC circuit, and already operating at a higher flux density.
It all looks pretty doable except for the part as to how the BH curve of the shared piece of core looks like, then again, I don't think coming up with BH curves is rocket science... It is just a lab test.
There is a retired engineer who knows electromagnetics and is one of the smartest people I know... I will throw this exercise at him for his amusement and see what he has to say about it.

7. Sep 15, 2015

### gsal

The reply from my friend may a "while" though, I think he may check email only once a day or every other day... We shall see.

8. Sep 15, 2015

### Hassan2

Thanks for your effort to understand the problem, for your help, your corrections and clarifications.
There is no rush and I only need to find out if applying a very strong but practical DC current in the DC coil causes a significant reduction in the inductance of AC coil . For the middle values we may need an electronic circuit to control the inductance by adjusting the current.

9. Sep 18, 2015

### gsal

O.k., Hassan, I have some feedback from the retired engineer.

First, he says that the portion of the AC magnetic circuit that is modulated looks rather small; this will yield a not very efficient device.

Second, the BH curve will definitely be a problem. The operating B and H of the material not only will change in magnitude but also in direction, with the AC field going from positive to zero to negative, the resultant field will be a changing, of course, and wiggling about the axis of the DC component. As traditional BH curves for a given material are obtained with a field in just one direction, you would need A LOT of the traditional BH curves for different directions and for the one single material.

Lastly, and possibly more importantly, my friend tells me that these kind of modulators were invented so long ago, that they are no longer in used given the advent of high power semiconductor devices. To learn more about it, do a google search on "magnetic amplifiers".

I would be curios to hear your feedback after your research (if you don't already know about magnetic amplifiers) to see if it answered any of your questions.

gsal

10. Sep 18, 2015

### Hassan2

Thank you qsal and your friend.

I knew a little about the magnetic amplifiers but this time I read more on them. Some sort of saturable core devices are still in use and there are leading companies in China producing medium and high voltage motor soft starters based on the idea. At such voltages, e.g. 6.6kv and 11kv, using semiconductor devices is challenging.

There is a difference between my idea and that in the magnetic amplifier. In the magnetic amplifier, the control and power magnetic fields have the same direction while in my figure, their mean directions are perpendicular. I thought this would have advantages, one being that the response to AC source would be the same in both half-cycles. But now I know of some challenges, some pointed out by your friend. For example, if I increase the AC magnetic path of the shared part, this increases the inductance of the control coil, limiting the modulation frequency to a few Hz. I have been spending several months the idea but it may be time to give up.

Thanks again.

Hassan

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