Iron core barely boosting field strength

[canuck123]

Hello, I am a chemistry intern currently running a project that involves both chemistry and electromagnetism. Bottom line, I'm a little out of my depth and have much to learn, and I'm having a bit of trouble with the coils I constructed.

My setup will consist of four coils positioned horizontally around a microscope objective, and one underneath, such that the coils opposite each other will create a homogeneous field in the center, with a downwards gradient from the lower magnet. distance between opposite coils will be approximately 3 inches, so that's why I believed an iron core would be needed to achieve 15mT at the center.

I machined aluminum bobbins to act as a heat sink for the coil, as I'm fairly certain the aluminum shouldn't affect the field at all, although I do have delrin that I could use instead. For the cores, I bought some VIM VAR core iron (99.85-99.9% Fe, less than 0.01% C), machined them to press fit in the bobbins, and had the magnetically annealed in wet hydrogen to homogenize and maximize the relative permeability.

The relative permeability is supposed to reach as high as 15000 with the heat treating, imagine my surprise when the flux density was only 2.5x stronger with the core inserted. A current of 1.4A yields a flux density of 40 gauss at the mouth of the bobbin with air core, and 100 gauss with the iron core inserted.

My own calculations, as well as an online calculator I used from the company I bought the current amplifiers from, told me I should be easily able to achieve my desired field strengths, so this leads me to believe I either built something wrong, or was sold the wrong material.

Is this something that you guys would be able to help with, or is there a better forum for this?

EDIT: Here are images of my current coil that I'm troubleshooting:

It is currently 175 turns of 20AWG enameled magnet wire, but I have different wire gauges and stock to make bobbins from, so I can make more or less turns if needed.

Here is a screenshot of the calculator I've been using to help me. It's called a helmholtz calculator, but it works for any distance to radius ratio as you can input the distance yourself. The link to calculator is https://www.accelinstruments.com/Helmholtz-Coil/Helmholtz-coil-calculator.html


Here are some screenshots from a study I am trying to replicate. They detail the field shape and field strengths, frequencies, as well as the setup they used.


The experiment involves an elliptical rotating field out of plane generated by the Z and Y coils, with an additional AC field at a different frequency applied in the X axis.

 

[berkeman]

Welcome to PF.

Can you upload some pictures of the setup? Use the "Attach files" link below the Edit window to do the uploads.

Also, can you upload a sketch of the desired field shape? I'm a little confused when you say "uniform field" but you also have a pole below the microslope slide. What direction(s) do you want the field to point?

Without the bottom pole, I would have assumed that you wanted to be able to switch on either a field in the x-direction or a field in the y-direction, but with another pole below the slide I'm not so sure.

 

[hutchphd]

My own calculations, as well as an online calculator I used from the company I bought the current amplifiers from

Can you show these calculations/results (including all the geometry if possible). These are DC? Something is amiss. Need complete specs including # turns and direction thereof. What are you measuring? I have done very similar work I think.

 

[Drakkith]

My setup will consist of four coils positioned horizontally around a microscope objective, and one underneath, such that the coils opposite eachother will create a homogenous field in the center, with a downwards gradient from the lower magnet. distance between opposite coils will be approximately 3 inches, so that's why I believed an iron core would be needed to achieve 15mT at the center.

Are you certain this arrangement of magnets will provide a uniform magnetic field? Could you inert some or all of your setup inside a solenoid instead? A quadrupole arrangement typically produces very little field at the very center but rapidly increasing field strength as you move away:

Adding a 5th coil underneath probably won't give you the uniform field you want.

 

[canuck123]

These are AC, I am actually trying to replicate a study I read for the first part of my experiment. I've included an image taken from that study, which shows the field shape, frequencies, and field strengths they used. I have also attached some images of my first coil and core, which I've been troubleshooting.

Specs of coil are as follows:

25mm bobbin ID
27mm coil ID
25mm core OD
175 turns
20ga enameled magnet wire
0.7ohm coil resistance
frequency 10-20Hz
desired z axis field strength 15mT
desired x axis field strength 2.5mT
desired y axis field strength 5mT
distance between opposite coils 75mm

As well, I have attached a screenshot from the calculator I have been using from https://www.accelinstruments.com/Helmholtz-Coil/Helmholtz-coil-calculator.html

The screenshot should show the expected results with even a permeability of 100, much less what I should be actually getting.

 

[canuck123]

Are you certain this arrangement of magnets will provide a uniform magnetic field? Could you inert some or all of your setup inside a solenoid instead? A quadrupole arrangement typically produces very little field at the very center but rapidly increasing field strength as you move away:

View attachment 341273

Adding a 5th coil underneath probably won't give you the uniform field you want.

I shouldn't have said uniform. Not each pair of coils will be producing the same field. There will be an eliptical AC rotating field produced by the Z and y axis coils (90 degrees out of phase at function generator), and a weaker AC field applied through the x pair of coils. I've attached an image from the study I'm trying to replicate for the first part of my experiment.

 

[Baluncore]

The aluminium bobbin transforms into a shorted secondary turn when it is used as an AC coil former.
You need to cut a slot in the bobbin, to break the circular electric conductive path, or switch to a non-conductive bobbin.

 

[canuck123]

Welcome to PF.

Can you upload some pictures of the setup? Use the "Attach files" link below the Edit window to do the uploads.

Also, can you upload a sketch of the desired field shape? I'm a little confused when you say "uniform field" but you also have a pole below the microslope slide. What direction(s) do you want the field to point?

Without the bottom pole, I would have assumed that you wanted to be able to switch on either a field in the x-direction or a field in the y-direction, but with another pole below the slide I'm not so sure.

Sorry I shouldn't have said uniform, the field shape is not uniform, I simply meant that in each axis, the field would be uniform radially from the center. Each axis of coils are producing different field strengths and frequencies, so the sum field shape is not uniform. The idea is that this specific field shape should help to disaggregate magnetic particles. Check out the picture I posted in another reply for a visualization of the field.

 

[canuck123]

The aluminium bobbin transforms into a shorted secondary turn when it is used as an AC coil former.
You need to cut a slot in the bobbin, to break the circular electric conductive path, or switch to a non-conductive bobbin.

I'm not sure I understand. Why would it short the coil if the wire is enameled? an induced field? Sorry if this is stupid, I guess I just need to learn more. I was able to generate the exact expected field strength with an air core, is this expected even if the bobbin is a problem?

 

[berkeman]

I simply meant that in each axis, the field would be uniform radially from the center. Each axis of coils are producing different field strengths and frequencies, so the sum field shape is not uniform. The idea is that this specific field shape should help to disaggregate magnetic particles. Check out the picture I posted in another reply for a visualization of the field.

Thanks for the additional details and the diagram; they help some.

The comment by @Baluncore about being careful introducing shorted turns is very important for AC magnetic fields. Please ask for more details if that is not clear. Also, what frequencies are we talking about for the AC component of the excitation?

It's important to start thinking early-on about completing the magnetic path to help to increase the strength of the B-field in the gap volume. If you just have isolated ferrous cores for the coils, that is not a good way to design such a setup. You want the only gap volume to be in the test volume, and all other parts of the magnetic paths are through ferrous metal. The longer the magnetic path length through air, the higher the "Reluctance" along that magnetic path, and the lower the B-field strength that you can create with your drive current.

Finally, you mention a 3" gap length in the microscope slide region, but given your diagram and typical microscopes that I work with, I'd estimate the max gap dimension at closer to 1.5"-2". You want to minimize that distance as well, in order to give you the strongest field from your drive current.

 

[Baluncore]

You have unknowingly wound a transformer. The Al bobbin has become the secondary winding.

The solid magnetic core you are inserting into the bobbin will also act as a shorted turn to the primary coil. The core should be laminated, or have an insulated matrix containing iron powder or ferrite.

So you have two shorted turns, both of which must be replaced with bulk non-conductive material.

 

[canuck123]

Thanks for the additional details and the diagram; they help some.

The comment by @Baluncore about being careful introducing shorted turns is very important for AC magnetic fields. Please ask for more details if that is not clear. Also, what frequencies are we talking about for the AC component of the excitation?

It's important to start thinking early on about completing the magnetic path to help to increase the strength of the B-field in the gap volume. If you just have isolated ferrous cores for the coils, that is not a good way to design such a setup. You want the only gap volume to be in the test volume, and all other parts of the magnetic paths are through ferrous metal. The longer the magnetic path length through air, the higher the "Reluctance" along that magnetic path, and the lower the B-field strength that you can create with your drive current.

Sorry, I guess I don't really understand the problem with the aluminum. I could make it instead with delrin (plastic). Frequencies are 10-20Hz, so pretty low.

Are you saying I shouldn't have a bobbin, and just wind directly around the core? Is the 1mm wall thickness of bobbin creating a big problem?

 

[Baluncore]

Is the 1mm wall thickness of bobbin creating a big problem?

Yes. There is an AC current, induced by transformer action, running in the aluminium.

I could make it instead with delrin (plastic).

That would be a good move.

 

[canuck123]

You have unknowingly wound a transformer. The Al bobbin has become the secondary winding.

The solid magnetic core you are inserting into the bobbin will also act as a shorted turn to the primary coil. The core should be laminated, or have an insulated matrix containing iron powder or ferrite.

So you have two shorted turns, both of which must be replaced with bulk non-conductive material.

Oh. So even if I wound directly around the iron core, it would be bad? I thought winding directly around a core was pretty common, I have seen it done in many places, including the study I am trying to recreate. Why would an insulated matrix of powder be better than a solid iron core? Sorry, this is just very counter-intuitive to me based on the limited stuff I researched.

 

[canuck123]

You have unknowingly wound a transformer. The Al bobbin has become the secondary winding.

The solid magnetic core you are inserting into the bobbin will also act as a shorted turn to the primary coil. The core should be laminated, or have an insulated matrix containing iron powder or ferrite.

So you have two shorted turns, both of which must be replaced with bulk non-conductive material.

When you say the core should be laminated, are you saying the kind of thin laminates that you find in a transformer to reduce eddy currents? Or that the core should be encased in something non-conductive? Becasue in that case the delrin bobbin would solve both problems

 

[berkeman]

Oh. So even if I wound directly around the iron core, it would be bad? I thought winding directly around a core was pretty common, I have seen it done in many places, including the study I am trying to recreate. Why would an insulated matrix of powder be better than a solid iron core? Sorry, this is just very counter-intuitive to me based on the limited stuff I researched.

You need to avoid eddy currents and creating a shorted turn for the frequencies that you are trying to drive through your magnetic circuit. Think of a 60Hz transformer -- have you noticed the laminations that the core is made up of?

If you were working just with DC fields, that would not be an issue; with AC field generation, it is definitely something that you need to consider.

 

[Baluncore]

Solid cores are used for DC electromagnets, or DC relays that must be delayed in turning off.

When you say the core should be laminated, are you saying the kind of thin laminates that you find in a transformer?

Laminated, or non-conductive, so circular currents cannot flow around the core.

 

[canuck123]

Solid cores are used for DC electromagnets, or DC relays that must be delayed in turning off.

Laminated, or non-conductive, so circular currents cannot flow around the coil.

Oh I see. Here's a picture of the setup from the study I am trying to recreate. Do you know why this setup of winding directly around a solid iron bar would have worked for them?

 

[Baluncore]

The magnetic cores in that picture are non-conductive ferrite or iron powder.
The magnetic parts come from some form of stock or kit transformer elements.
They complete a magnetic circuit around the outside of the area.

 

[berkeman]

Here's a picture of the setup from the study I am trying to recreate.

Can you give us a link to their published paper? That will be a lot more effective than us asking 20 questions about that picture. Thanks.

 

[canuck123]

Can you give us a link to their published paper? That will be a lot more effective than us asking 20 questions about that picture. Thanks.

Here is the link to the supplementary information from the paper, this has all the important stuff about the setup: https://www.rsc.org/suppdata/c5/lc/c5lc00294j/c5lc00294j1.pdf

 

[canuck123]

The magnetic cores in that picture are non-conductive ferrite or iron powder.
The magnetic parts come from some form of stock or kit transformer elements.
They complete a magnetic circuit around the outside of the area.

I see, I had not considered that the border around them was the same stuff. They simply stated that the cores were pure ARMCO iron.

 

[Baluncore]

They simply stated that the cores were pure ARMCO iron.

That may be acceptable, for a low frequency setup.
Do we know the properties of the iron bars, so we can calculate the skin depth?

It is hard to identify materials when it has all been painted an even colour, the same colour as iron powder cores. It looks like there are screws holding the iron bars together.
I wonder what the flat baseplate is made from, plywood?

Solid iron cores will get hot due to eddy currents inside and close to the coils. Cutting a cross of two thin slits in a solid core at the coils, will significantly reduce the eddy currents and so, cool the coils.

 

[Vanadium 50]

First, I would test the field with DC before going to AC. I'd also check every part separately, and I would double check the polarity so the fields of the two coils were in the right relative direction.

Second, these dimensions are weird - they aren't exactly Helmholtz coils, but the desired field region is far from the coils. I'm not sure what fields you want, but I'd be surprised if this were the best way to do this.

Finally, it looks as if the core extends far past the coil. Is this right? If so, I don't believe the magnetic field lines will want to go through the pole, and then take a high reluctance path through the air to get back to the opposite end. They will instead exit the iron as soon as they can and head back.

If that is correct, the field will be driven by the reluctance in air, and the core - pretty much no matter what its permeability is - will only roughly double the field. And that's what you see, right?

 

[Vanadium 50]

<crickets>
Was it something I said?

 

[canuck123]

First, I would test the field with DC before going to AC. I'd also check every part separately, and I would double check the polarity so the fields of the two coils were in the right relative direction.

Second, these dimensions are weird - they aren't exactly Helmholtz coils, but the desired field region is far from the coils. I'm not sure what fields you want, but I'd be surprised if this were the best way to do this.

Finally, it looks as if the core extends far past the coil. Is this right? If so, I don't believe the magnetic field lines will want to go through the pole, and then take a high reluctance path through the air to get back to the opposite end. They will instead exit the iron as soon as they can and head back.

If that is correct, the field will be driven by the reluctance in air, and the core - pretty much no matter what its permeability is - will only roughly double the field. And that's what you see, right?

I tested with DC and the air core value was again as expected, but the iron core strength was much lower than expected. Yes the dimensions are weird, I was trying to make it fit with my microscope objective and available fluid cells, since it is a pretty big objective and the fluid cell is machined precisely to fit some special components. I clearly was not aware that the flux would decrease so drastically once out of the core. Can you tell I'm dumb? So the solution here would be to have a core that goes right up close to the sample right? And link the cores around the perimeter with more iron? I was only able to get the 1" round iron before, but I may be able to find some longer thinner stuff. DO you think a mild steel would work well enough for this application if the cores were very close to the sample? Becasue it most likely will be incredibly hard to source more pure iron.

 

[berkeman]

So the solution here would be to have a core that goes right up close to the sample right? And link the cores around the perimeter with more iron?

That will help to shorten the magnetic path lengths in air, yes. And it looks like the original assembly from the paper also linked to the back surface of the bottom core with ferrous material as well.

 

[Vanadium 50]

You want the coil as close to the sample as you can get.

In general, you want to think about where the magnetic field lines go - called the magnetic circuit. The reluctance is determined by the amount of air the field lines need to traverse. Getting a super-high permeability is not necessary and not helpful.

If you think about the equivalent electric circuit, if I have two 1000 Ω resistors in series and I replace one with a much smaller one, it won't make much difference if that smaller one is 1 or 2 ohms. Same here - the reluctance in air dominates.

 

[canuck123]

You want the coil as close to the sample as you can get.

In general, you want to think about where the magnetic field lines go - called the magnetic circuit. The reluctance is determined by the amount of air the field lines need to traverse. Getting a super-high permeability is not necessary and not helpful.

If you think about the equivalent electric circuit, if I have two 1000 Ω resistors in series and I replace one with a much smaller one, it won't make much difference if that smaller one is 1 or 2 ohms. Same here - the reluctance in air dominates.

Thank you. By saying super high permeability doesn't matter, does that mean mild steel would be good enough? Does the coil have to be super close to the sample, or does the core just have to extend super close?

 

[berkeman]

Does the coil have to be super close to the sample, or does the core just have to extend super close?

To get as much of the magnetic field from the coils into the ferrous core as possible, you want the windings as close the core as possible. That minimizes the "leakage inductance" of the coil (where some B-field leaks out of or bypasses the core before performing whatever task). So if you have a choice of bunching up the coils in one spot with 10 layers thick, or spreading them out with 2 layers thick, choose the lower profile coil configuration.

 

[Vanadium 50]

A random piece of iron ot steel has μ=150 or so. So 3mm of steel has the same effect as less than half a millimeter of air. So the steel doesn't matter. Just the air. So you need to get as much of the air gaps out of your system as possible.

The alternative is to crank up the current. The problem is you are already near the 20 AWG limit. OK, so instead increase the number of turns - but that increases the resistance and now you need more voltage. So I think you are stuck with fixing the geometry.

 

[hutchphd]

I have mentioned this before, but I was tasked with a similar problem (also involving magnetic particles) and thought "no sweat" how hard can this be?. My best decision was to get a program (called Vizimag as I recall) and start playing with it. One should not skip this step...I learned so much about this stuff in a few days of just farting around. Unfortunately I think the software does not exist anymore, but surely equivalent ones do. I too tried for super large permeability (not useful) and confirmed the nasty idea that size (volume) and voltage matters because more turns always means less current otherwise. I ended up producing a good solution despite my initial ignorance.

 

[canuck123]

I have mentioned this before, but I was tasked with a similar problem (also involving magnetic particles) and thought "no sweat" how hard can this be?. My best decision was to get a program (called Vizimag as I recall) and start playing with it. One should not skip this step...I learned so much about this stuff in a few days of just farting around. Unfortunately I think the software does not exist anymore, but surely equivalent ones do. I too tried for super large permeability (not useful) and confirmed the nasty idea that size (volume) and voltage matters because more turns always means less current otherwise. I ended up producing a good solution despite my initial ignorance.

I am certainly feeling the stupidity now. I know programs like COMSOL would be good but those licenses are like 4000$ or something. I initially wanted to make the exact same setup as pictured in the research paper, but my microscope objective is so frickin wide that I can't get a coil close to the sample. What did you end up doing?

 

[Vanadium 50]

There exist free versions of software to calculate magnetic fields. OpenEMS is one.

Unfortunately, it doesn't make on an expert in designing magnetic systems, any more than Excel makes someone an accountant. It also sounds like it won't solve you problem - if you need a high field far from the coils, you are going to need ampere-turns. Plain and simple.

 

[berkeman]

Yes the dimensions are weird, I was trying to make it fit with my microscope objective and available fluid cells, since it is a pretty big objective and the fluid cell is machined precisely to fit some special components.

but my microscope objective is so frickin wide that I can't get a coil close to the sample.

Do you have any options to machine some different fixturing for your microscope? Or maybe use a different microscope? Maybe those would be better options comparing to going 10x on your coil drive power...