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Various coil shapes, FEMM data

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Pinkamena

Sun Mar 04 2012, 06:53PM

Registered Member #4237 Joined: Tue Nov 29 2011, 02:49PM
Location:
Posts: 117

Hi.

Been playing around with FEMM (love it!), and I have compiled a bunch of data on the force on the projectile. I'm sure it'll be useful for someone else, so I thought that I'd make a thread here about it.

Anyways, I started by making a coil that has an inner radius of 1.1cm, outer radius of 3.1cm. The projectile has a radius of 1cm, that leaves an air gap of 1mm. The projectile is 10cm long, and the coil is 10 cm long too.

First, I changed the current density in the coil while keeping the projectile in a fixed position. One can see that up to a current density of about 100 A/mm^2, the force is proportional to the square of the current. After the current density crosses 100 A/mm^2, the force increases linearly, which is what one should expect due to saturation of the projectile.

I then wanted to see how the force on the projectile changed based on displacement from the center of the coil. I kept the current density at a constant 50 A/mm^2, and changed the position of the projectile from 13cm to 0 cm from the center in increments of 2 cm.
I changed the shape of the coil in order to see if there were any coil shapes that gave stronger force. Every time I changed the coil shape, I always kept the coil cross-area at 30cm^2.
The first thing I tested, was what would happen if I encased the coil in an iron sleeve. As one should expect, the force on the projectile got stronger, and it stayed stronger for much longer than the coil without a metal sleeve. Here are the force curves of the different coil and iron sleeve shapes.
Images of the coil shapes can be found here.
Graphs2

I also found another interesting thing. It appears that a trapezoidal coil shape will increase the force by a fair amount. Notice that I kept the cross-area of the coil at a constant 30 cm^2, so the extra force is not due to added cross-area.
But it's not all good, as the force curve of the trapezoidal and triangular force curve is below the force curve of the regular coil from displacement = -8cm to displacement = -10cm.
As we all know, the areal under the force curve is proportional to the work done on the projectile, which is proportional to the velocity.
By eyeballing the areal between the force curves of the regular coil and the trapezoidal curve, I'm pretty sure the net areal is positive. That means that the work done on the projectile by using a trapezoidal coil will be greater than the work done by a square regular coil. This is of course just an simulation. One would have to actually do some experiments in real life to see if it's true.

I then kept the projectile displacement at a constant 5cm (half way into the coil), and changed how trapezoidal the coil was. "Trapezoidalness" on the graphs x-axis means how far from the inner edges the outer edges are. In other words, if "trapezoidalness" is 4, then the outer length is 10cm-2*4cm=2cm. I found that the force increases approximately linear as a function of how trapezoidal the coil is.

Keep in mind that the force curves are not as the would be IRL. I'm keeping things like induced current, varying inductance, varying voltage, eddy currents etc out of the calculations.
Are there some other things I should test with FEMM? Come with some ideas and I'll happily do it. on the graphs x-axis means how far from the inner edges the outer edges are. In other words, if is 4, then the outer length is 10cm-2*4cm=2cm. I found that the force increases approximately linear as a function of how trapezoidal the coil is.

[link][img:width=200

Turkey9

Mon Mar 05 2012, 08:14AM

Registered Member #1451 Joined: Wed Apr 23 2008, 03:48AM
Location: Boulder, Co
Posts: 661

I would like to see a 3D plot with the trapesoidalness on one axis, for on the other, and distance into the coil on the last one. Perhaps the only thing changing is the place within the coil where the force is the greatest as the coil approaches a triangle.

Pinkamena

Mon Mar 05 2012, 02:52PM

Registered Member #4237 Joined: Tue Nov 29 2011, 02:49PM
Location:
Posts: 117

I did that for three different trapezoidal shapes, you can see the force curves in the curve diagram next to the FEMM screenshots.
"Trapezoidal" is 1 (trapezoidalness), "very trapezoidal" is 2.5, and "triangular" is of course 5.
You can kind of imagine how the other force curves will look.

Pinkamena

Mon Mar 05 2012, 03:48PM

Registered Member #4237 Joined: Tue Nov 29 2011, 02:49PM
Location:
Posts: 117

And here we have the dreaded variance of induction. This is for a coil with AWG12 (2mm diameter), and 750 turns. The coil is still 10x3 cm.
You can see that the incution changes more steadily when you have an outer shell, with specific starts (-11cm) and ends (0cm) of when the induction changes. Without an outer shell, the curve is more relaxed. The increase is still the same though, no matter if you have an outer shell or not.

The y-axis is in Henries.

Saz43

Mon Mar 05 2012, 08:50PM

Registered Member #1525 Joined: Mon Jun 09 2008, 12:16AM
Location: America
Posts: 294

I've seen it posted that a greater change in coil inductance as the projectile goes from outside of the coil to the coil's center means better magnetic coupeling- and thus is a good thing. I have to do some more reading though to understand the physics behind that.

Forty

Tue Mar 06 2012, 03:42AM

Registered Member #3888 Joined: Sun May 15 2011, 09:50PM
Location: Erie, PA
Posts: 649

I would of expected the inductance to go up a lot more than that with the addition of a core (the projectile)
A triangular coil? that's a new one.
I'd like to see how a coil made from a long strip of conductor would work (ie 1 turn per layer, many layers, but still as long as the projectile)
and one made from a flat stacked spiral of paralleled thin wires (ie 1 layer with many turns, but still lots of conducting material going radially outward from the center, like this @15:20

except done with paralleled wire)

Pinkamena

Tue Mar 06 2012, 11:15AM

Registered Member #4237 Joined: Tue Nov 29 2011, 02:49PM
Location:
Posts: 117

Forty wrote ...

I would of expected the inductance to go up a lot more than that with the addition of a core (the projectile)
A triangular coil? that's a new one.
I'd like to see how a coil made from a long strip of conductor would work (ie 1 turn per layer, many layers, but still as long as the projectile)
and one made from a flat stacked spiral of paralleled thin wires (ie 1 layer with many turns, but still lots of conducting material going radially outward from the center, like this @15:20

except done with paralleled wire)

Well, if the coil had been smaller, the relative increase of inductance would probably have been bigger. I'll test it with a smaller coil to see what happens.

I think that a coil mad from a long strip of conductor rolled up, and a coil made from a flat stacked spiral would work exactly the same if the current density was the same. They'll both pretty much be a solid "block", i.e. no air gaps.
I can test the difference of the force from a solid block-like conductor coil and a regular round wire coil though. I expect the force to increase with about 21 percent since a wire-based coil has 21 percent air in it.

Forty

Tue Mar 06 2012, 06:14PM

Registered Member #3888 Joined: Sun May 15 2011, 09:50PM
Location: Erie, PA
Posts: 649

well 21% sounds nice. If I made it with thin paralleled wires there'd still be some air gap though.
What if the air was replaced with something ferromagnetic and non conductive? would that help or hurt the field at the center of the coil?

Ah so the inductance didn't increase because of how massive your coil is. That makes a little more sense I guess. So the outer shell increases the inductance as well? That's something I'll have to take into account for estimating pulse lengths (my coils have external iron on two sides and the faces, they're rewound solenoids)

If you want your coilgun to be a portable one then you might want to look into coils that require less than 750 turns of 12awg lol (I know you're just simulating to learn and not actually designing your coil yet.) That's a lot of copper.

I think another good simulation to run (if possible) is a look at eddy currents and their effect on the net force. You could look at a conductive barrel with various resistances and possibly slot placement, and you could look at projectiles for the same two things as well as cross sectional layout (conducting shell + nonconducting interior and vice versa)

Does the skin effect apply to the eddy currents because of the short pulse time or not because the field isn't alternating?

Also, for the simulation you're currently doing, is it possible to change the core material and look at the effects of permeability and saturation?

(Sorry for obviously not having any idea what your FEMM program can and can't do)

Pinkamena

Tue Mar 06 2012, 09:03PM

Registered Member #4237 Joined: Tue Nov 29 2011, 02:49PM
Location:
Posts: 117

Changing the material between the wires is a good idea! I'll get on that.
And Eddy Currents aren't very easy to simulate with femm, it can't simulate eddy currents from movement, only from AC current.
I'll also take a look at what happens with different projectile materials.

Pinkamena

Tue Mar 06 2012, 11:41PM

Registered Member #4237 Joined: Tue Nov 29 2011, 02:49PM
Location:
Posts: 117

Ok, it's taking freaking FOREVER to manually change the geometry of the coil every time I want new data. So I'm gonna learn LUA scripting to automate the process.
Here's what I have so far though.

I started by measuring the change in induction for a 250-turn coil with an outer shell when the projectile moved into the coil, and then I did the same for an equal coil with no outer shell. I then compared that to what I had done previously, except that was for a 750 turn coil.

Inductancevariouscoils

That is what I had expected to see. The relative change of induction on a small coil was larger than the relative change on a big coil. I put the relative change (in percent) into a block diagram. I expected to see the same relative inductance increase. what I got, was this:

Inducincrease

When using the small coil with no outer shell, the relative increase of induction from air-cored to fully inserted projectile was SMALLER than when I used a coil with an outer shell! You can see how it's the exact opposite when using a large coil. I find this rather interesting, and it's definitively worth remembering when you're going to design the coil. For large coils, an outer shell will give you a smaller relative change of induction. When using small coils, it's the opposite.

I measured how the induction of a coil changed whether it had an air core or a projectile inside, and plottet the two curves in the same graph.
Notice how inductance based on turns increases much faster when it doesn't have an outer shell.
Inducbasedonturns

When I learn how to program in LUA, I will do a lot of measurements with different coil shapes with and without an outer shell and plot them against each other. Then we'll better be able to see how the coil shapes affects the relative change.
Meanwhile, I have this curve (getting the data for this single curve took me over an hour, so there's the reason I want to automate it with LUA :P). It shows the relative change between the two curves above (a 10-cm coil with an outer shell.) It seems to be proportional to the negative natural logarithm.
Percentendringavinduc

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