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### lab electromagnet from scratch

Posted: Sat Jun 08, 2013 7:07 am
We've had occasional chatter here about using "large" NIB magnets to generate axial magnetic fields in disk-shaped spaces, as used in cyclotrons.
Among other contributors, George S. has posted some pictures, Chris B. has posted simulations and inside-out variants, and Richard H. has talked about how to safely position a pair of magnets onto a flux yoke. viewtopic.php?f=15&t=7236&p=51755

Now I'm about to get my hands dirty doing it the old-fashioned way, using many thousands of ampere-turns driven by wallplug power.Good chance to explore and demonstrate practical scrounging and DIY construction ideas for people with cyclotron dreams and tight budgets.
(The cyclotron lab at Houghton College uses a 6-inch commercial magnet from GMW, which weighs over 1,000 pounds and lists for about \$30,000.)
Another end result is a touchable demonstration of how many watts of electricity it takes for a resistive magnet to match a high-energy rare earth magnet of a given size. (The dimensional scaling of electromagnets, as with motors and transformers, makes I^2R losses become relatively smaller as the size goes up.)

My current plan is to start with a pilot scale unit. Three-inch coil assembly ID and pole diameter. Will aim for a 1 tesla field in a 1 inch gap, with a sensible trade-off between electric power requirement and the mass of copper or aluminum conductor (whose product is invariant if average turn diameter and material are held constant). Likewise, the voltage-current point will be determined by economics of power supply electronics and the cross-sectional areas of scroungeable conductors. H(air) x length(air) is about 20 kA; the only electrical benefit of small pole diameter is reduction of average turn length, voltage, and power. But steel mass can come down almost as the 3rd power of pole diameter, and 2 local dealers want a whole 60 cents/lb for used steel.

I'm pretty comfortable with the application of Ampere's Law to electromagnetic circuits.
So today my questions are about the permanent magnet options.
1. Can anyone give us the dimensions and measured field strength of an actual PM solution?
2. How does the field strength vary with gap length and magnet length, as shown on 2 axes in attached drawing? (There must be tutorials for industrial designers out there! )
3. Has anyone here bought N45, N50, etc. magnets and verified the purported energy product by magnetic measurements? It seems so easy for vendors on ebay etc. to overrate their product a bit, as with the optical power of lasers marketed to kids who want to burn stuff.

### Re: lab electromagnet from scratch

Posted: Sat Jun 08, 2013 11:09 am
Rich,

You'll find that I've answered and/or already given leads on how to determine those questions, but I'll go over them again here, and see if I can describe how I look at this problem, step by step.

However, just a mention on your electromagnet design first - depending on what you want the field to do, you can also use focussing poles. So if the windings wrap around a pole piece where it has a diameter D, but the piece then necks down conically to a diameter D/2, then you will increase the field level by x4.

But focussing a field to increase the strength with conical poles is not used for cyclotrons (excepting to shape the fields at the edge) because if you crunch the maths, you'll find that it makes no difference to the energy of particles you can accelerate - for a higher field strength it is only in proportion to an increase in the required centripetal force for a given particle velocity/energy. So instead using a focussed field only makes the applied frequencies higher and the engineering for the cyclotron itself smaller, which may be advantages or disadvantages depending on your objectives.

I am not convinced that there is an optimised way of balancing total conductor mass versus power like you said. Whenever I have done the calculation, whatever you do to increase the conductor thickness you reduce turns in direct proportion. All that does is give you control on the voltage/current combination, but not the power.

1. If you want actual measured values on my inverted yoke, then do the search and I'm sure you'll find them. The results tallied with the predictions that Maxwell SV gave me, close enough (which is a freeware student version of Maxwell which I recommend to you to do your analyses).

2. I will talk in 'practical' expressions here fit for an amateur builder, rather than explicitly scientific: A PM magnet has a certain amount of 'magnetic energy' locked into it. Magnetic fields can do no work, so that energy is never 'taken out' of the magnet. All that happens is that the magnetic energy in the magnet is re-distributed around it, according to the relative permeabilities of material in that space.

A given magnetic field in a given space [including the space of the magnet] *is* a given energy. The energy density is defined as B^2/2u (where B is the magnetic flux density [Teslas], u is the permeability). Now imagine you build a yoke like the ones you show here, with a gap of two inches and around one inch wide. Say you attach a magnet of one inch thickness and width to one of the poles so that there is a one inch gap left. What is the field strength?

OK, so imagine how the magnetic flux circuit flows around the yoke. There will be the same flux all around, it's like current the same all around. But now imagine the different parts are like resistors, and the air gap is the bigger resistor where the 'current' does the 'work'. So the magnet has this fixed energy that it will 'share out' to wherever its flux flows. In the metal yoke, the u, permeability, is very high, maybe 10,000's [relative permeability], so for a given B (which we are aiming to work out what it is) the magnetic energy in the yoke is very low. Whereas in the air gap, the u is 1, so the energy of the field in the gap is very high. Remember the B is the same all around the circuit. It's a magnetic flux density. It's like a superconducting current flux (it does no work). Let's say the flux path in the yoke is 10 inches and the u is 10,000. So that means the air gap energy is 99.9% of the total magnetic energy in the loop. We'll ignore the yoke from now on (of course, you can only do this if the yoke is made from high u material).

3. So now we examine the magnet's performance. Answering Q3, you can be sure that neodymium magnets you buy are rated for around the 1.1 to 1.3T range, and that they are like that, because it is simply down to the way that they are made and the nature of the materials. Let's say it is 1.1T, so it's energy density is “1.1T per magnet volume”. Now, IF that 1 inch gap was completely filled with the magnetic flux from the magnet as it flowed around that magnetic circuit, and there was no stray fields bulging outwards, then that'd mean the field level would be approx 0.55T, because that is simply the same volume as the magnet in the same space, and most of the energy of the circuit is focussed in the air gap and the magnet.

It's 0.55T because the permeability of the magnet itself is around 1, pretty much the same as the air gap. It's a bit like a current source with a big internal resistance. It has its own 'u'. The 1.1T 'current' that you see in magnet specs is equivalent to the 'short circuit/maximum current', so to speak. So whatever you do to make the magnetic flux flow around as smoothly and as unobstructed as you can, the magnet itself will limit how much energy density can flow into any air gap because it has only so much energy to 'give out', some of which it 'needs' to support the fields within it, itself.

So if you made the gap 2 inches for a one inch high magnet, the field would be ~0.36 T (ignoring field fringing effects). But if you put two one inch magnets on top of each other and a one inch gap, then there would be '2 units' worth of 1.1T/per inch of flux path now 'flowing' through 3 inches (viz. the two magnets and the one inch air gap). So now the flux would be ~0.7T.

This is saying that the flux through the magnet itself changes, according to the materials around it. A '1.1T magnet' only actually has 1.1T flux in it when it is clamped into a high permeability yoke with no air gaps. If you take a direct measurement of its surface, you might measure the fields as they 'short circuit' directly back into the magnet, and they don't do this evenly, depending on the magnet geometry. So if you had a 'perfect' magnetometer which did not interfere with the field itself, you'd find 'dead spots' on the surface of the magnet where the flux line is heading straight out of the magnet on some wild, long distance path through free space.

Let's go back to the one magnet scenario with one inch air gap. The bulging fields might double the volume if the magnet is one inch wide across a one inch gap. This would result in a, possibly disappointing, ~0.28T for those expecting to 'see a 1.1T field'. If you close that gap up, the relative percentage of 'bulge' to actual air space filled with a field would come down progressively until it can be almost neglected. Say you have a ¼ inch air gap. So now the 'one inch's worth of magnetic energy is being spread around 1.25 inch of permeability = 1 (we are still ignoring the energy in the rest of the yoke, because it will be relatively so low providing it is a high permeability). So now we'll get 1.1T x 4/5 = ~0.9T.

To hang some real numbers off this, sintered neo magnets are around the 300kJ/m^3 range (~N38). If we want to estimate the flux in a yoked air gap of 10 cm^3 total volume, and the total magnetic material in the yoke is 20 cm^3 of 300kJ/m type, then the total magnetic energy in the circuit = 300kJ x 0.00002 = 6J.

We use the formula E = 6J = B^2/2u, where u = 4x10^-7 pi. So B = sqrt{(6 x 2 x 4x10^-7 pi)] /0.00003} = ~0.7T.

Note on units: The energy content of magnetic materials is often quoted as Mega Gauss Oersted MGO. I believe the conversion is 1 MGOe = ~7.95 kJ/m^3. 'N38' means 38 MGO, so by definition, for example, N45 would be 357 kJ/m^3. If the energy content of a neo is 357 kJ/m^3, that means it is N45, and if it isn't then it isn't an N45!

(Just for completeness, here are the temperature ratings too: H = 120C, SH = 150C, UH = 180C & EH = 200C. Now you know what 'N45 SH' actually means!)

I've not seen discussions on magnets in such simple terms like this. I hope it helps serve to 'demystify' the workings of permanent magnets!

### Re: lab electromagnet from scratch

Posted: Sat Jun 08, 2013 6:22 pm
Thanks for the fast and detailed response, Chris.
Looks like we share a delight in teaching. In presenting apparently complicated subjects as simply as possible (but, as Einstein said, no simpler than that).

0. Regarding the tradeoff between electromagnet conductor mass and power: If you double the coil cross-sectional area without increasing the average turn length, then you have halved the electrical resistance. So same current with half the voltage, if the doubling were of the wire area. Or use twice as many turns of the original wire gauge, so 2x the resistance and half the current at same voltage. A point to take home: for given coil diameter and ampere-turn requirement, voltage depends on wire gauge and not on the number of turns.

As we reduce the amount of copper or aluminum to save money, the cost of power and power supply stuff goes up. Power density and cooling technology requirement go up as the square. Inspired by the interest of young Noah H., I recently held forth on this subject in another forum. http://4hv.org/e107_plugins/forum/forum ... ost_153043

By the way... It's well known that aluminum has a specific electrical conductivity twice that of copper, and enjoys an even greater edge in conductivity per unit of cost (I'll say dollar). In electromagnets that makes the coils more bulky & forces yoke to be longer & heavier. I found some studies, ranging from the 1910's to 1990's, exploring metallic sodium as an electrical conductor. It stands far ahead of the pack in conductivity per dollar of metal. The more recent study had it filling polyethylene tubes, and investigated things like fire hazard when breached. The older one had Na filling long steel pipes, and studied things like how to make and break joints in the field.

1. I will go back and read your inverted yoke thread more thoroughly. Browsing the archives is more troublesome on the new platform, because of broken links and new names. George Schemermund now appears to be delta9. As an alternative to learning Maxwell, do you know if FEMM comes with realistic permanent magnet material models?

2. Your tutorial about permanent magnet energies was great. Shows why rare earth magnets are necessarily made in various lengths. Since it's time to get up to speed on permanent magnet materials in "circuits", I will try to make a picture with a BH curve and a gap-dependent load line. They'll intersect at some operating point in the second quadrant. Might be used to illustrate why Alnico magnets can be partly demagnetized by disassembly of the yoke system.

3. I confirmed your conversion factor of 7.95 kJ/m^3 per MGO -- the exact value in SI units is 25000/pi, the reciprocal of 4e-5 * pi . An example point would be 1e4 gauss (= 1 T) times 100 Oe (= 7958 A/m).
Let me rephrase my original question 3. We know that N45 material means the BH curve reaches 45 MGO (around the knee in demagnetization quadrant). Can probably find that BH curve on some OEM website. Suppose we bought such a magnet from ebay vendor X, and suspected that he was selling lower grade stock as N45 -- what confirming measurements have been made by forum readers?
You talked about magnets sold with specifications of surface field strenth (or lifting power), and showed how those can be derived from BH curves and geometry.

Time to quit blabbing while the sun shines.
Regards,
Rich

### Re: lab electromagnet from scratch

Posted: Mon Jun 10, 2013 7:34 pm
I couldn't imagine a more interesting an concise discussion related to Rich's questions than that supplied by Chris. I actually sold a video tape back in my Tesla days that I did called "minimal magnetics", following much of Chris' explanations with demos.

Permanent magnetic technology, the making and the doing, is a rather black art and the fabulous, tell all, book, suitable for a real permanent magnetics engineer, is Moskowitz's book "Permanent Magnet Design and Application Handbook". (Expensive \$211.00 Amazon) and might be out of print, though Lindsey books once carried it.) My copy cost me \$75.00 back in 1992. There is a huge gap and different world view between permanent magnets and electromagnets. Yes, the actual "magnetic circuitry" is the same, but they are different worlds when it comes to the making and the doing.

I would be stunned if you could put a full, continuous tesla in a 1" air gap, electromagnetically, with a 3" electromagnet. Pulsed, yes, you could do that and perhaps even water cooled intermittently. A tesla is no mean feat in the world of electromagnets of any significant gap.... and 1 inch is a significant gap! 1 inch gap in a magnetic circuit is like a 10 megohm resistor in an electric circuit. Their are analogies between them but you can overdo such analogies.

Richard Hull

### Re: lab electromagnet from scratch

Posted: Mon Jun 10, 2013 8:55 pm
I appreciate the credit, Richard, thanks, as it took a while to write because I was aiming for it to be as useful to others as I could make it.

### Re: lab electromagnet from scratch

Posted: Tue Jun 11, 2013 5:05 pm
I had a period of magnetic enthrallment. Spent \$1000.00 in 1997 for a first quality Bell gauss meter with both axial and transverse probes. I recently found, at a hamfest, a Bell calibrated test standard block for a transverse probe of 1.0003 k gauss. Wow! It cost me \$2.00.

You just have to learn to "see at sight" at these events.... A term I coined, meaning that you need a wide net of stored visual experience so that you just don't glance over a table of offerings, but key to specific mental images of goodies you have seen in the past.

Magnetism, especially permanent, is certainly incredibly fascinating and a form of potential energy that is not extant in and of itself in nature and, like all electromagnetism, light, radio waves, etc., has its origins with true innate potential energy of primary particulate charge....charge that has been placed in motion. Charge in motion can create all the energy we see and use, but no magnetic/electromagnetic scenario can create nascent charge. Dyanmic-kinematic magnetism can cause already extant charge to move about, however. Interesting stuff for sure.

I keeping with my past posts, lIght and all EM radiation is a secondary force and not a primary nascent energy/force in the universe.

Richard Hull

### Re: lab electromagnet from scratch

Posted: Sat Jun 15, 2013 1:49 am
Sorry to have invited a permanent magnet discussion, in OP of a thread whose title is about ELECTRO magnets.
(Thanks to Chris's non-scary introduction, I now have a fair understanding of permanent magnet circuits. It was easy to follow up by reading websites of respectable PM vendors. For example, there are well-commented BH curves with load lines here, http://www.kjmagnetics.com/blog.asp?p=t ... um-magnets in discussion of why max operating temperature depends on magnet shape! )

Now back to the project announced in OP, for which I have not yet bought any material.
Here is a 75 mm classroom electromagnet, just under the nominal size (3 inch) that I'm aiming for.
http://www.svslabs.com/Products/Product ... tegoryID=1
The EMU-75 spec claims 11 kG in a 10 mm air-gap between flat pole pieces, using 270 watts of electricity. The designers kept the power down by using a ton of copper, figuratively speaking, in two great big air-cooled coils. A longish coil aspect ratio contributes to efficiency, so the pole pieces and connecting yoke are correspondingly long and heavy. I haven't tried to reverse-engineer the circuit and coils.

The same power should develop 10 kG (one tesla) in an 11mm air gap. To increase the 1-tesla gap to a full inch, current would have to increase by the length factor, 2.3. The power would go up by the square of that factor, to 1440 watts. Inertial cooling ought to allow at least a minute of operation at that power. Wire temperature could be monitored by the increasing voltage needed to keep the current constant.

- - -
My design was inspired by a couple of rectangular plates of cold rolled steel, found on a remnants shelf. They're 3/4 by 5-3/4 inches, and almost 19 inches long. Just thick enough to serve as the ends of an H-frame, spreading the flux from 3-inch round pole pieces without bottlenecking. Here's a scale drawing, with some annotation of current and flux paths for discussion next time. Grid and dimensions are in inches (as is most metal stock the USA).

### Re: lab electromagnet from scratch

Posted: Mon Jun 17, 2013 3:37 pm
You now see the issues in getting a Tesla in a large gap. Doable with a lot of iron and copper, a KW or two and maybe a bit of cooling or short duration operational periods. It's all about ampere-turns, circuit permeability and cross section.... Good luck on your efforts.

Richard Hull

### Re: lab electromagnet from scratch

Posted: Mon Jun 17, 2013 8:11 pm
Richard Hull wrote:You now see the issues in getting a Tesla in a large gap. Doable with a lot of iron and copper, a KW or two and maybe a bit of cooling or short duration operational periods. It's all about ampere-turns, circuit permeability and cross section.... Good luck on your efforts. Richard Hull
Thanks.
I knew the job was dangerous when I took it. (wink to Super Chicken, for those of a certain age).
http://www.digital-sledgehammer.com/sup ... gerous.wav
http://www.televisiontunes.com/Super_Chicken.html

Don't want to cut metal for pole pieces, until the deal for 55 lbs of 0.012 x 4 inch aluminum coil is sealed.

This is about exploring ways to minimize cost and fabrication effort.

George Schemermund expressed the same spirit in discussion about another yoke:
viewtopic.php?f=15&t=7236&start=20#p51771

So how can we adjust the pole gap? There's no provision for that in previous drawing.
It would not be easy for me to make a close-fitting hole in an end plate, in which a pole piece could slide.
[*]Plan 1 was to depend on interchangeable pole caps, a method which also allows different tip areas (as Chris alluded to).
[*]Plan 2 uses interchangeable spacers in series with the flux bars parallel to coil axis. Spacers can be made from bar or plate stock, which comes with two surfaces flat and parallel enough. The flux bars can still be bundles of scrounged bedframe angle iron, or rebar.
[*]Plan 3 is infinitely adjustable, but flux bar parts need 2 flat & smooth surfaces at right angles.
[*]Plan 4 is also infinitely adjustable. Flux bars need one flat smooth surface, but interfere with access to the gap.
By the way, the last two need adjuster screws that can resist the magnetic attraction between the pole pieces.
At 1 tesla it's tolerably close to 60 psi or 400 kPa. That value, and its dimensional unit of pressure,
are identical to the air gap energy per unit volume --
J/m^3. The formula is BH/2, or as Chris said, B^2/2u.

Any better ideas, or important caveats from the experts?
Someday I'd like to try using rectangular plates that are stacked in weight machines at the gym. "Cast iron" apparently saturates at only around 1 tesla, but that can be compensated by using more of it.

### Re: lab electromagnet from scratch

Posted: Tue Jun 18, 2013 6:21 pm
For Continous, Non-alternating current, many highly permeable carbon and silicon steels are available. Cast iron is OK, but as you are shooting for max flux, it is a weaker choice.

The pros almost always set up variable gap sections in max flux situations with interchangable pole pieces or pole inserts. Even though the gap appears to be zero with additions, there is still fringing and added reluctance losses unless mirror like near quater-wavelength flat finishes are maintained at joints. This is the cheapest high flux gap adjustment solution.

Sliding and continuously adjusting gaps, to be effective, demand special custom castings and milled components, more power and continuous cooling to maintain high flux in the gap.

Richard Hull