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Dr. Shark

Thu Apr 03 2008, 01:32PM

Registered Member #75 Joined: Thu Feb 09 2006, 09:30AM
Location: Montana, USA
Posts: 711

Hello everybody,
it's been about 9 month since I last posted here, but now the HV bug has bitten again. I left off with a half-finished induction coilgun

and and half-baked theory of operation

, and that where I am picking it up again now. I have some new ideas, and I also got my experimental system up and running again, so lets see where it's heading this time

My "pet theory" of pulsed linear motors goes by analogy with a barrel rolling down a slope. You start of with some potential energy that is gradually exchanged for kinetic energy. Except here, the potential energy is the magnetic energy stored in a coil of wire, and the steepness of the slope is the inductance gradient caused by the movement of the armature.
Starting with the simple relations for the energy

E=.5 L i^2

and the flux

Phi=L i

some simple manipulations and the assumption that flux is conserved gets us the power going into the armature

P=.5 v i^2 L'

where v is velocity and L' the inductance gradient.
Notice how similar this looks to the power going into resistive losses,

P=i^2 R

I think this is rather cool, since it gives you a (admittedly very rough) way of estimating efficiency. The take-home message would probably be: If you can't get the resistance of the circuit to be low enough to be on the order of the inductance gradient, you will never see double digit efficiencies. It also shows that big guns (no pun intended) always have an edge over small amateur ones. Firstly since the will have less R and more L' just by scaling up any given design. Secondly, the higher the velocity, the more power is transfered to the armature.
Finally, and this is _very_speculative, this shows how the total output energy is related to the action of the system. Action is defined as

S=Integral i^2 dt = E/R

and energy also happens to be the time integral of the power. Maximizing the action seems to be a good thing then, and we can do that by maximizing the ratio of stored energy to total resistance. Take home message: Always wire capacitors in parallel, as this maximizes the action.

I have a rather more sound theory in the works which involves numerically solving differential equations, but I am not very good at that so I don't expect results all that soon. I also have some measurements of inductance gradients from a small railgun and a small coilgun, I'll put them into a separate post, together with some pictures.
So come on, reply!

TheMerovingian

Thu Apr 03 2008, 08:38PM

Registered Member #14 Joined: Thu Feb 02 2006, 01:04PM
Location: Prato/italy
Posts: 383

this isn't different from the Rp = dL/dt (or dL/dx * v), where R is projectile load on the circuit

basically you would want Rp >> Rresistive , to achieve good efficiency. Instead most coilguns have Rresistive > Rp, hence the efficiencies in the 3-5% range

Dr. Shark

Thu Apr 03 2008, 09:40PM

Registered Member #75 Joined: Thu Feb 09 2006, 09:30AM
Location: Montana, USA
Posts: 711

Where does that formula you posted come from? I have not seen it before, but heck, it is so simple to derive that people seriously interested in coilguns probably just take it for granted. Anyway I promised some picture, so here they are:

I don't know whether I should be proud or ashamed of that hacked SCR (yes, I ground down that stud and drilled and tapped it), but the inductance is sure quite low this way. I bought some of these

SCRs bricks on eBay today, so things will be easier in the future.
The capacitor is 4mF 400V, but I am limiting myself to 200V right now.
The coil changes its inductance from .2uH to .9uH as the copper pipe projectile moves out, so I have an L' of 50uH/m, which is about 100 times better than a railgun would get, but probably (I'm guessing here) by the same factor worse than a reluctance coilgun.

Anyway, I took some scope shots:

both are 100us / div horizontal and 50V /div vertical. First one is voltage across the coil, second one shows voltage across the switch (top) and across capacitor (bottom). The SCR opens fully in about 10us (could be faster but my scope would not show), and the full pulse takes about 100us. Probably not too bad for a single electrolytic capacitor, but apparently way to slow for an induction gun: The projectile barely makes it out of the coil.

I also made a small mock up of a railgun to take some measurements

It has a two turn series augmentation, which takes the inductance gradient from 0.5uH/m to 1.8uH/m, as I mentioned this is terrible compared to the coilgun.

To make matters worse, not only is the L' smaller, but there is the added resistance from the sliding switch. I used acrylic with copper brushes here, which is supposed to give a very good contact compared to solid projectiles, but I could not get the resistance to measure below 20mOhm. This is devastating, so I probably don't even have to mention that the projectile does not move at all.

This disk launcher is the only thing that actually works, even though I have no idea why.

This one goes from 1uH loaded to 3uH empty. That's roughly 100uH/m, so it isn't actually that much better than the coilgun above. It's a single layer coil of 1.5mm magnet wire potted in fiber reinforced epoxy.

(EDIT 4.4.08)
I wonder how the decaying magnetic field in the armature comes into the equation. Many people have noticed that the thickness of the disk in a disk launcher plays an important role, so I guess it could be argued that the LR time constant _inside_ the armature determines how much acceleration it gets.

WaveRider

Fri Apr 04 2008, 05:53PM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

Hi,
Maybe I shouldn't engage in too much shameless self-promotion,

but if you want lots of mathematical description of coilguns, why not look here? The motional resistance formula that Mero described is derived there too...

There are also some numerical schemes available for download for you to use or improve on...

Cheers!!!!

Dr. Shark

Fri Apr 04 2008, 07:07PM

Registered Member #75 Joined: Thu Feb 09 2006, 09:30AM
Location: Montana, USA
Posts: 711

Oh my god! It's you who wrote these IEEE papers!!! I am bowing down in respect to you, that is some REALLY good stuff you did there. Just a shame that you limited your studies to reluctance coilguns, but hey, that leaves a bit of work for me.
As I pointed out in the edit to the above post, I think the decaying magnetic field in the armature might have something to do with the horrible performance of inductance guns. At least that is my pet theory right now, since the inductance gradient cannot be the whole story. I compared some preliminary measurements, and they surely don't explain the difference in performance.
I'll keep thinking about this, but I also welcome more input...

WaveRider

Sat Apr 05 2008, 08:28AM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

The theory is just as valid for induction coilguns too... I used my FEM code to model a Thomson gun. See the movie in the 4HV archives. Scroll down a bit....it's near the end of the thread.

Induction guns were not included in the IEEE papers because I had no way to generate reliable experimental data for them...

Have fun!

Dr. Shark

Sat Apr 05 2008, 11:48AM

Registered Member #75 Joined: Thu Feb 09 2006, 09:30AM
Location: Montana, USA
Posts: 711

Bill, the thread you linked to is actually the one I have in my archive picks in the archive discussion section. Told you I respect your work

I guess I should just play around with your code a bit, it seems it's much better than I could ever do. With the FEM treatment of the eddy currents, you can probably get a detailed look at how the field in the armature changes, and thereby confirm or disprove my speculations above.

Anyway I made some progress on the experimental front and build a Rogowski coil for current measurements. I have a few pictures here:

I followed the proven design of stripping a piece of coax cable of it's outer conductor, wrapping it in 0.1mm magnet wire and headshrinking it. I also constructed some kind of connector to hold the loop together

The scope trace shows voltage (bottom trace) and the derivative of the current current (top trace). I have not constructed an integrator for the Rogowski probe yet. The waveform looks rather as expected though, for a critically-ish damped RLC circuit. I suppose the peak towards the end of the trace is when the SCR stops conducting and the diode takes over.

WaveRider

Sat Apr 05 2008, 12:43PM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

Thanks for the compliments! You are correct that the simple inductance argument is not the whole story. Penetration of the magnetic field into the conductive armature over time must be considered too.. I think the US DOE built a model of induction guns using inductive coupling arguments.... Google <<slingshot coilgun simulator>> to find links to their work...

Nice Rogowski coil you have there.. I notice your O-scope looks digital.. Can you recover the numerical samples from your scope? If so, you can do the integration numerically using a short piece of code...

Dr. Shark

Sat Apr 05 2008, 01:49PM

Registered Member #75 Joined: Thu Feb 09 2006, 09:30AM
Location: Montana, USA
Posts: 711

Thanks for your thumbs-up on the Rogowski Coil, I have added an integrator to it now. While my scope is in fact digital, it does not talk to my computer, so I had to do in in hardware (which I prefer anyway).

My waveforms are rather slow (up to a ms), so I decided to choose the time constant of the RC integrator to be 10ms with R=100k and C=100nF. This means the gain is rather low, and in fact I had to use the 5mv/div setting on my oscilloscope to capture the following waveform.

I am still quite happy with the result though!

The current trace is the bottom one, 100us/div, and it is really neat how the sinusoidal oscillation changes into an exponential decay exactly at the center line. This is where the SCR stops conduction and the freewheel diode takes over.
Now I'll just have to play with my RLC simulation code for a bit to figure out what the peak current is, but I believe it to be around 5kA.

WaveRider

Sat Apr 05 2008, 02:54PM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

You can estimate the current, if you know the capacitor capacitance, from I=-C * dV/dt. The slope of your capacitor voltage curve will allow you to estimate coil current.

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