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# Designing a fairly simple electromagnet and need help2

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## Designing a fairly simple electromagnet and need help

(OP)
Hello,

My first post here - great forum!

I am building an electromagnet for a magneto-optical study, I am hoping someone can point me in the right direction

My specs are fairly straightforward:
C shape electromagnet with a 5cm or so gap
varaiable 0 - 150 Gauss max field

I know the core should be 1010 or soft FE, can someone point me toward how to calculate the # of terms and the expected flux?  I can't seem to find any good resources on this topic (except in this forum).  Any good books on the topic?

Thank you in advance,
Mike

### RE: Designing a fairly simple electromagnet and need help

Gap is really important. Small changes will change the answer a lot.

What is the cross section of the core?

Is it continuous or intermittent duty?

Is the coil on one side of gap or both?

What DC power supply do you have available? Voltage/KW

### RE: Designing a fairly simple electromagnet and need help

(OP)
MJR2,

Thanks for the reply!

(150 Gauss field)
-I'll say 2.5cm for the gap.  That's the smallest it can be.
-Cross section of the core could be .75" square.  This can change.
-I am envisioning the coil opposite of the gap in the C shape. Is this an incorrect configuration?
-Somewhat continuous, a max continuous up time of 3 hours to be safe.  Never on overnight or anything like that.
-Power supply: I have plenty available, say 10V, 5A to start.  I can find others to fit my needs if need be.

The purpose of the unit is to excite magnetic samples for magneto-optical Kerr effect studies.  The magnet will be mounted on the stage area of a (modified) microscope.

As I said before, I pretty much need a guide how to go about building the unit.  I have a machine shop at my disposal, as well as any other facility I would need to fabricate the electromagnet.

Thanks again!
Mike

### RE: Designing a fairly simple electromagnet and need help

Mike, I think you will have difficulty finding a suitable formula because the airgap is relatively large compared with the pole face area.  This results is a significant amount of flux fringing (flux lines between the pole faces progressively spreading out to form curved paths) and flux leakage (flux lines not reaching the opposite pole), reducing the airgap flux density and making it very non-linear.  If you move a Hall probe across the middle of the gap, parallel to one of the pole faces, you will see a large bell-shaped variation in flux density.

Analytically this is a difficult problem and highly dependent on specific geometry, so although there may be a few empirical results around (e.g. Herbert Roters book) mostly people resort to basic finite element analysis for accurate prediction.

In your case, you are not asking for a high value of flux density (150G being about 10%-ish of the saturation flux density of steel).  So with a reasonable amount of confidence you might just go ahead and build a prototype, the materials are cheap and construction is straight-forward, and take trial measurements with a Hall probe.

### RE: Designing a fairly simple electromagnet and need help

In my post above I am assuming that you mean a C-core where the poles are brought around to face each other and are parallel, not like in a horse-shoe magnet where they are side-by-side.  The latter will give poorer results (lower flux density and more non-linearity).

Incidentally, Arnold Magnetics have some good info:
http://www.arnoldmagnetics.com/mtc/index.htm
(the picture at the top of the web-page shows the type of parallel gap I was talking about, with fringing flux lines visible.  It's a finite element plot).

### RE: Designing a fairly simple electromagnet and need help

(OP)
Thanks for the reply UKpete!

You are correct - this is going to be a C shape magnet with the faces pointing.  Thank you for the fringe field caution - I will make the faces as big as I can.

I would like to go right ahead and build a prototype, but I have some very basic questions since I have not built a device like this before:

-where do I get the materials?  core material, what kind of wire for the winding etc...
-how do i assemble the C core?  should I machine it out of a solid piece of 1010 steel? or should I bolt togther pieces of square stock to form the C?
- is there any special way to wind the coil?

Thanks again,
Mike

### RE: Designing a fairly simple electromagnet and need help

Mike, regarding the construction, you can use solid steel (you only need to laminate for an ac coil) and it doesn't really matter if you use a single piece or bolted together pieces, whichever is easier.  Any airgaps between bolted pieces will be insignificant compared to the main airgap.

I think low-carbon steel is recommended for dc cores, 1010 will do (I see Matweb describes it as "Suitable for magnet core applications").

For the coil, you need to apply some insulation first to the steel, particularly the edges, in sheet or tape form.  PVC tape isn't very good as it has low temperature capability, a suitable glass-fibre or laminate card will do.  The winding should use enamelled copper wire, base the diameter on a current density of around 5A/mm² otherwise it will get too hot.

You can have a quick stab at the required ampere-turns, using the basic formulae (all in SI as I'm from a metric part of the world):

reluctance S = g/(μ0*A)

where g is the airgap length (m), A is the airgap cross-sectional area (m²),
μ0 is permeability of free space 4*pi*10-7

flux Φ = NI/S  where N = no. of turns, I = current (A)

flux density B = Φ/A  - in Tesla (1T = 10000G), A is airgap csa as above.

So first find the reluctance S for a proposed airgap goemetry, then flux for the proposed ampere-turns, then flux density.  Note that this will give you an optimistic answer, because it assumes that the steel has zero reluctance (in practice it may have something like 10-20% of the airgap value, depending on the geometry), and particularly it ignores the effect of fringing and leakage, which may reduce the gap flux density by at least half say.

### RE: Designing a fairly simple electromagnet and need help

(OP)
Thanks UKpete! - Ill do some back of the envelope calculations a little later tonight.

-Mike

### RE: Designing a fairly simple electromagnet and need help

I put some numbers thru the program I have here. Unfortunately it doesn't take less than 1000 gauss, never needed it that low before. The results are nearly linear in ampturn requirements however. If the coil is really to much for you than cut the ampturns by 85 percent. So for 1000 gauss, 0.98 inch air gap, 0.75 inch square pole face. I put a taper of 45 degrees on the pole face for a distance of 1 inch. Then an additional 2 inches of 2.75 x 2.75 inches cross section before turning the leg on the 'C'. Carry the cross section around the entire circuit. The taper will make a big difference in uniformity of field across the pole face.

The coil is 574 turns of #14 copper wire with a film type insulation. ID is 4 inches. Insulate the ID well with glass tape or nomex insulation. OD will be about 6-5/8 inches if carefully wound. Weight will be 9.85 pounds. Total ampturns 2872. And as I said it is more than you need so it could be turned down. But the benefit is you could have much higher fields than planned for very little extra cost. It will run at 50 watts continuous but expect it to stabilize hot at about 3.5 amps. It will be hot to the touch. Perhaps 180F. But at only 15 percent input power it will probably only get warm.

If your yoke length is excessively long we will use some of the ampturns in losses thru the steel.

Oh. Put a plate behind the coil (away from gap) of about 3/8 inch thick. For the fields you are talking about here most any steel is going to work. But I assumed C1020.

Ought to work just fine.

### RE: Designing a fairly simple electromagnet and need help

(OP)
Thanks MJR2!

This looks great.  Before I was looking into using a smaller gauge wire with more turns, but I like the possibility of a bigger coil running cooler than a small one running hot.

My main question now is what kind of wire to use - I found some specific 14AWG Belden Magnet wire in Mouser (http://bwccat.belden.com/ecat/pdf/8073.pdf) but it only comes in 80' spools. I called Belden and they didn't have a good method for linking it together since I will need a lot more than 80'.  Is there a specific type you'd reccomend?

Thanks - Mike

### RE: Designing a fairly simple electromagnet and need help

This is listed as lead wire. While it may be fine as you say 80' spools is not the best when you need about 800' Well you would solder it and wrap with kapton or other suitable insulation.

Do a google search for magnet wire. You will find many sources. Try for a 180C class insulation system. Probably a bit of overkill but not much. Well if you only run it at 150 gauss all of the time it will be.

You can buy spools of this.

If you were in the Dominican Republic you could go to the local hardware store and get whatever you need. They make their own transformers for their homes. When I first saw the wire that was my guess but I could not believe it. But it wasn't until later that I found out it was true.

### RE: Designing a fairly simple electromagnet and need help

Mike, I've just realized from reading MJR's post that I mis-read your required value of flux density.  150G is nearer 1% of the saturation flux density of steel, not 10% as I said above.  That makes it even easier, you could probably use standard pvc-covered hookup wire rather than enamelled wire.

MJR2, is the value of 2872At for the 1000G field?  If you assume the field is linear with ampere-turns (certainly reasonable as there won't be any saturation anywhere), presumably only about 430Amp-turns will be needed.  On this basis it would probably be better to go for a smaller gauge wire and a significantly reduced number of turns.

The coil equations are as follows (again all in SI):

coil voltage V = I*R  (that's Ohm's Law!)
where I = current
R = coil resistance = ρ*L/ACu
and L = total length of copper, ACu = copper csa
ρ = resistivity of copper (about 1.9x10-8Ωm, bearing in mind it will warm up a bit)

If you substitute in the ampere-turns F you end up with:

coil voltage V = F * ρ * LMT / ACu
where LMT is the length of mean turn for the coil

To find your wire size, rearrange this equation to give ACu.

So knowing the approximate diameter of your coil hence the LMT, the Ampere-turns F (say about 430 as given above although you may want to allow some extra just in case) and the voltage (convenient value to suit your power supply), you can calculate the copper area and find your wire size.  Then  assume a fairly gentle current density of say 2A/mm² max, get your current value, then from the assumed AT calculate the number of turns and that's it.  You may want to go back and check your initial mean coil diameter at this stage and iterate if necessary.

I hope I've got all that right.  Incidentally, the simple reluctance formula gives fair agreement with MJR's program bearing in mind the amount of fringing.

### RE: Designing a fairly simple electromagnet and need help

Actually it is what you need for 1000 gauss. I know the program I have is good for that range. And it should be very linear to 150 gauss. But for a 20 minute design that's what he gets.

However 2872 represents 10% SF and 25% reduction in current for heating.

Another coil with 50 watts and 150/1000 * 2872 = 431 NI would be .153 lbs of #23 2" long with 4" ID 93 turns OD of less than 4.1" for 467 total NI. The previous coil was 2" long if I didn't mention that.

The heat this coil will make might damage the insulation of standard PVC unless maybe you can get 105C. And Looking at the DC amps I'm not to sure you want to run 5 amps in #23 wire. I don't think I would.

Your space factor with PVC insulation will make for a lot of waste. Enameled wire is not that hard to get.

Within the limits I have used my programed equations fringing has not been a problem. However that is why the pole is tapered.

### RE: Designing a fairly simple electromagnet and need help

MJE2, I'm with you on all of that.
Regards - Pete

### RE: Designing a fairly simple electromagnet and need help

(OP)
Thanks again for the help guys -

I have locacted a source for the magnet wire.  Now I just need to find a source for the steel - hopefully my local machine shop has some already.

Ill keep you updated on my progress and Im sure Ill have more questions...

Mike

### RE: Designing a fairly simple electromagnet and need help

Hello KerrMike,

I can offer our CMI-C Ultra-low Carbon core iron for this application.  In the annealed condition, it has the lowest coercive value in Ultra-low carbon family.

lloyd@cmispecialty.com

ie. Magnetic Iron Guy

### RE: Designing a fairly simple electromagnet and need help

I'm designing an electromagnet also and found this thread very helpful, especially UKpete's formula tutorial. I've been playing around with those formulas, but I would like to try to refine the calculations and try to get the calculations as accurate as possible. I want to figure in the reluctance of the yoke and pole pieces and also hopefully calculate losses due to fringing and leakage which was not part of the calculations shown below. Can anyone describe how to do that using the same type of formulas provided by UKpete below. I would prefer to avoid calculus as I only had one year and that knowledge is rapidly rusting away (no line integrals please)

*********************************************************
reluctance S = g/(?0*A)

where g is the airgap length (m), A is the airgap cross-sectional area (m²),
?0 is permeability of free space 4*pi*10-7

flux ? = NI/S  where N = no. of turns, I = current (A)

flux density B = ?/A  - in Tesla (1T = 10000G), A is airgap csa as above.
******************************************************
I combined and rearranged these so that I can estimate my amp turns needed; NI = Bg/?0

My electromagnet will differ in that it will have two coils in what I believe is called an "H" configuration instead of a "C" configuration and will be larger and more powerful than the one previously discussed. It will be about 6" or 15.24 cm dia. at the pole faces and generate a field of about 1.5 T across a 1.5 cm gap and I plan to try to design it so that it can be air cooled, I'm not sure what type of steel or iron the yoke and pole pieces will be made of yet.

Thanks for any help
-Todd619

### RE: Designing a fairly simple electromagnet and need help

Could you please restart this in a new thread.

A bit more information on just what you mean by and H circuit would be useful. Do you mean two airgaps?

A 1.5T field will require significant ampturns and power.

I'll check in when I get back from my elk hunt in two weeks.

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