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# Measuring BlackMagic3D's ferromagnetic filament

Measuring hysteresis curve to determine how useful is that stuff for building motors and magnetic circuits

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In my other project, I wanted to build a linear stepper motor. So, I found there is a ferromagnetic filament around, and I ordered some.

The filament is PLA with iron powder in it. Sounds like great thing for making motors and inductor cores - 3d printed, no eddy currents to worry about.. brilliant! or not...

Unfortunately, the manufacturer (blackmagic3d) does not provide any quantitative characteristics of the filament. All they say is "strongly attracted to magnetic fields". That doesn't tell me if it's good for making motors. So I am measuring its H-B hysteresis curve to determine permeability, saturation flux and losses.

## <Spoiler>

Permeability is about 2. This is hopeless for making motors and the like. Permeability of electric steel (found in transformers) is about 4000, for comparison. Permeability of inductor gap-less core material is typically about 50.

## Printing the core

This part is reasonably straightforward. I chose a relatively thin and small toroidal core. Small to not need to spend too much wire for the test coil, thin to not get uneven field distribution through its section, and toroidal because it is very easy geometry to calculate.

I think it's important to choose solid concentric infill. This is because gaps across B-field influence results seriously, and need to be minimized to measure the material properties, not properties of a gapped core. Concentric infill results in a serious gap that slices the core in two rings, but gap is along B-field (not across), so it can easily be corrected for by lowering the cross-section area in calculations.

model parameters:

middle-circle radius R = 8 mm = 8e-3 m

core cross-section area S = 23.38 mm^2 = 23.38e-6 m^2

## Making a test inductor

Simply wound a testing coil. It is quite important to distribute the turns evenly, to avoid magnetic field leak to outside and skew the results. Other than that, the more copper - the better chances of achieving saturation.

Here's my winding, I think I did a good job in terms of even-ness.

The coil has N = 124 turns. It measures 0.527 Ohms of DC resistance, and has an inductance of 21 uH.

## Measuring the inductor

To measure B-H curve, I drive the coil with square wave generator. I can obtain B field by integrating voltage across ideal part of inductor, and H field by measuring current through coil.

On this circuit:

* to the left is high-current square-wave generator

* DUT is the inductor. I approximate it as an ideal winding around the core (made of superconductor) plus DC resistance of the coil. I assume that skin effect and proximity effect are negligible, since I'm driving it at quite low frequencies (around 20KHz).

* 0.1 ohm resistor is a current sense resistor

* scope probes are connected to points labeled Ch.1 and Ch.2. Scope's ground is connected to the point where the blue ground symbol is (so, the generator MUST NOT be grounded!)

So, on Channel1, I get total voltage waveform across the inductor, and on Channel2, I get an inverted value of current.

* capacitor isolates DC component of square wave from biasing the inductor. The capacitor is a large electrolytic cap. The more - the better.

This is how the circuit looks when it's built:

And this is what I get on the scope:

Note that current waveform (cyan) is inverted due to the way probes are connected.

## H-field

H-field can be directly calculated from coil current by using Ampere's circuital law:

i.e. integral of H-field along a contour equals total current passing through that contour.

Choosing the contour to be the center-circle of the core, we get:

H * 2*pi*R = N * i

where R is radius of core's center circle, N is the number of turns in the coil, and i is the current through the coil. So, H field waveform is:

H(t) = N*i(t) / (2*pi*R)

## B-field

Deriving B-field is quite a bit more involved, and that's what I capture voltage waveform for.

Voltage across the ideal part of the coil is tied to the rate of change of magnetic flux by law of electromagnetic induction:

dФ/dt = U(t) / N

where Ф is B-field flux through the section of the coil toroid, which equals B*S assuming B is constant throughout core section area S, and the coil is tight.

U(t) is the voltage across the ideal part of the coil, which can be calculated by subtracting resistance dropout R_DC*i(t) from the total voltage across the real coil:

U(t) = U_real(t) - i(t)*R_DC

So,

B(t) = integral over time( (U_real(t) - i(t)*R_DC) / N ) / S + offset

'offset' is a constant, that should be chosen so that time-averaged B-field is zero.

## Results

On this plot, B and H field wavefoms are shown. H was multiplied by permeability of vacuum mu0, to bring it into a comparable scale...

### scope waveforms.csv

Ch1 in Volts, Ch2 in Amps. Time intervals in seconds.

ms-excel - 37.78 kB - 04/17/2016 at 21:52

### test core 1 model and g-code.zip

x-zip-compressed - 122.34 kB - 04/17/2016 at 21:50

• ### Is it possible to make better ferromagnetic filament?

So, did BlackMagic3D fail to make a useful thing because they haven't worked/researched hard enough, or the idea of 3d-printable ferromagnetic material is doomed from the beginning?

I don't have the answer, but I have a guess. To make something go smoothly through extruder, one needs to put quite a lot of plastic into it. A wild guess will be 60% by volume has to be plastic.

Ferromagnetic particles can have permeability that is very high. But it probably doesn't matter how high it actually is, because as it is mixed with non-magnetic material, the gaps between particles will probably become the dominant reluctance of the system, and will totally determine the permeability. So, it will probably make little difference to mix in particles with a permeability of 100 or of 100000. It will look more like a gapped inductor with a huge gap of 60% or so of length of magnetic circuit. That is, like made of material having permeability of about 1/60%, i.e. about 2.

So, to me it looks like the idea of making 3d-printable ferromagnetic material by adding metal powder to plastic is fundamentally doomed. But I would love to be proven wrong on this opinion.

PS. Do you think a material with permeability of 2 is useful for something? Post a comment! So far, I haven't invented any application.

• ### Other properties of the filament

Here are some other impressions from 3d printing with this filament.

The filament diameter measures 1.75 mm spot on, thumbs up BlackMagic3D.

It prints very well with a nozzle diameter of 0.5 mm. I like the quality, and the lack of stringing.

Surface texture is rough, with shiny black surface (it somewhat resembles that of ferrites, or of an iron rod heavily oxidized by heating in air, or packages of integrated circuits). It's a pleasure to touch.

The printout is not particularly heavy. It is heavier than normal PLA, but not much.

I had some problems with sticking to glass. First time it went perfectly, but second time it peeled off like hell. I don't know what happened, but wiping glass with acetone helped.

My printouts were small to say anything about warping, but those small prints did not suffer any delamination due to warping.

As for attraction to magnets. It is attracted. But ferrites beat it by a large margin. And bulk iron gets even much stronger attraction than ferrites. So... yes, it, attracts, but I struggle to find any real use for the filament.

• ### Quick crude result

EDIT: WRONG CURVE! Found an error!

I've just measured and did calculations. Arrived to a result.

I will publish the methodology and calculation formulas later, verifying them in the process. This is just a kind of teaser.

From this B-H curve, I obtained a permeability of the material of about 2. That is, two times more than that of vacuum. That's absolutely and totally hopeless, I have to say. To consider the material any kind of useful, I need the value of at least 10.

For comparison, typical permeability of transformer core steel is about 4000, according to Wikipedia.

And look at that huge area! This means that losses are huge!

So, the conclusion so far is that the material is useless. Hopefully, I will find a mistake in my crude calculations. But from how it attracts to magnets, I can pretty much tell that permeability=2 is plausible.

I could not achieve saturation with my test coil. This is very much expected considering the very low permeability.

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## Discussions

Andrew Smart wrote 08/09/2017 at 22:59 point

See this study from 1996 funded by the Office of Naval Research "Relative Magnetic Permeability of Polymeric Composites with Hybrid Particulate Fillers":  http://www.hfmi.stevens.edu/publications/110.PDF (unfortunately the last page of figures is missing from this scan)

Increasing ferromagnetic material added to the polymer increases magnetic permeability quadratically, not linearly. Though it is essentially linear up to around 15%-20% ferromagnetic filler (look at figures 1-2).

Note especially figure 4, where they have experimental evidence backing their hypothesis that a hybrid of ferromagnetic fillers increases the magnetic permeability substantially higher than their individual sum. Magnetic permeability of >120 is reached with a LDPE polymer, 60% NiZn 60 µm diameter powder, and 20% Metglas 2705M flakes (% by volume).

From what I understand in rheology the addition of up to a few percent talc or potassium carbonate will reduce wear on the machinery from the polymer fillers with high hardness.

This will make a nice core for the solenoids of an electric motor. I've seen another work where the solenoid core was wrapped with a sheet of a ferromatic alloy in order to increase the rated magnetic saturation of the core volume.

Are you sure? yes | no

matt venn wrote 05/14/2016 at 18:43 point

thanks for doing such a detailed study of this - was considering trying it out to improve a motor I've built - but now I won't bother!

Are you sure? yes | no

Brian wrote 04/17/2016 at 22:51 point

Proto-Pasta has a composite PLA that may work better for your application.

https://www.proto-pasta.com/products/magnetic-iron-pla

Are you sure? yes | no

DeepSOIC wrote 04/18/2016 at 10:28 point

Cool! I've seen them already, but I didn't notice they specify permeability!

They specify "5 to 8 at frequencies up to 1MHz". That seems to be much better than blackmagic3d, but still very low. Saturation B-field of 0.13 T doesn't impress much either.

Are you sure? yes | no

Brian wrote 04/18/2016 at 22:35 point

I wonder if you could make your own with better properties? I guess you would need to build a filament extruder first, but then you could experiment with different fillers for the highest relative permeability.

You might also think about a resin based approach. You could easily test different fillers with simple epoxy first, and then move to a light curable resin (assuming the fillers don't inhibit the cure).

Are you sure? yes | no

Andrew Smart wrote 08/08/2017 at 17:42 point

@DeepSOIC  Christoph Laimer printed a stator using Proto-Pasta's iron PLA, and they claim over 80% efficiency for their motor: http://hackaday.com/2017/05/08/powerful-professional-brushless-motor-from-3d-printed-parts/

And an inferior solenoid core (3D printable ferromagnetic PLA) could be made up for by using more current and stronger magnets... i.e. a larger motor (I guess?): http://hackaday.com/2014/07/30/a-3d-printed-brushless-motor/#comment-1675396

I think a magnetic saturation of .13 T is actually pretty good when looking at the competition: https://en.wikipedia.org/wiki/Saturation_(magnetic)  But I am still learning. Hopefully more research is made to improve this.

Thank you for this project DeepSOIC, very helpful!

@Brian Here is a melt flow analysis of a 10% iron ABS composite: http://ieeexplore.ieee.org/document/6075763/ It would be awesome to have a filament extruder for this. I suspect talc could possibly help decrease the wear on the extruder (IIRC I read a document regarding wear on large extruders, it said that adding talc to the plastic with other more abrasive stuff reduces wear, but I could be remembering things wrong).

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