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Coin/Can crusher simulations, or how to determine the work coil parameters?

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uzzors2k

Sun Aug 24 2014, 04:03PM

Registered Member #95 Joined: Thu Feb 09 2006, 04:57PM
Location: Norway
Posts: 1308

Hi all, long time no see! I've been working on my can crusher lately, and was wondering how the size of the work coil is determined? I haven't seen this mentioned anywhere, and I have the impression most people just wing it and use something that "feels right" in terms of turns/wire thickness and inductance. And to be honest, I'm not even sure what is desirable for a work coil.

The naive idea would be that many turns = stronger magnetic field = more crushing force. But is this the case? I found though some simple SPICE simulations of my particular capacitor bank and work coils of various inductances, that a low inductance will give a large single spike in current which dies down in a single cycle. Alternatively, using a higher inductance coil lowers the peak current, but in return allows the current to slosh around for a few cycles before ebbing out. Perhaps some inertia effect in the work piece must be considered, and a longer pulse with some current reversal is better suited?

I tried to model a coil and coin in FEMM 4.2, but the results aren't what I was expecting, and I'm not sure I was even doing it right. Has anyone tried to model a coin/can crusher? Or have any math/theories on how to design an optimal work coil?

klugesmith

Sun Aug 24 2014, 06:55PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

Hi Uzzors. Good to see you here. I never got as far as you did with radiography.

Can crushers is what originally brought me to 4hv.org, but I never got around to posting models, measurements, FEMM simulations, etc.
Maybe time to start that now! I wonder how often tesladownunder checks in here these days?

[written last] How would you like to compare physical models and simulations against measured RLC parameters? I would like to share a simple circuit that fires a RLC discharge repeatedly at, say, 10 volts. From the voltage and/or current waveform we can calculate R, L, and C. Can use real work coils, and real pulse discharge capacitor or a more portable low-voltage capacitor. With or without a can in the coil. RLC parameters and waveshape should be invariant as we scale up the energy, until we reach the level where the aluminum moves (and gets hot) during the discharge. Low-energy discharges can be repeated fast enough to view and measure with analog oscilloscopes. [\written last]

My hope was to have a discussion about efficiency. For a given capacitor, how to optimize the work coil to make the largest indentation with the smallest stored energy. Part of the exercise is how to measure the amount of crushing. A problem waiting for standardization. Volume reduction is easy (weigh the can filled with water), but severely crushed cans leak. Circumference reduction is easy -- time to document my simple fixture of cardboard and string, that directly reads "reduction in circumference" in cm. There's a lower bound: energy enough to make a detectable ripple in the can. (about 25 J in my case). One upper bound is energy to cut a can in two. (less than 1000 J in my case). That's with "12 FL OZ (355 ml)" soda cans that weigh around 13 grams IIRC.

It's been about 5 years since I charged my capacitor, but it should be easy to dig it out and reproduce old experiments.

I experimentally charted the amount of crushing vs. stored energy with different coils. Found the optimum for my 52 uF capacitor was 4 turns -- about a 2 uH work coil. Would expect that number to change with different capacitors, to keep the time constant about the same (say 15 kHz ringing of unloaded LC circuit). That also means constant volts per turn, for a given stored energy; 1000 volts per turn can make a nice hourglass shape out of a can. That's why I bet can crushing with electrolytic capacitor banks is relatively inefficient.

Coil length is a factor also. For coils of the same N, or same inductance, the longer coil couples to a wider, lower-resistance single turn of can material. That 1000 volts per turn will induce more current, for more radial force, but accordingly more metal to move. By the way, have you measured the sheet resistance of can metal? I found it to be higher than resistance of same thickness or weight of pure aluminum, by factor between 1.5 and 2 IIRC. Attributed that to the higher resistivity of the can alloy, which is easy to look up.

Got to run. Sorry, no old pictures at hand on this computer. Oh, but here's the camera and ... here's the old stuff.
-Rich

IamSmooth

Sun Aug 24 2014, 07:24PM

Registered Member #190 Joined: Fri Feb 17 2006, 12:00AM
Location:
Posts: 1567

Have you seen this site?

klugesmith

Sun Aug 24 2014, 09:00PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

Oh yes, Barry's coilgun site is a classic. When I was doing my can crushing, there were thoughts of learning enough Web design to make a can crushing version.

In the 4HV forum organization, can crushing logically belongs with Electromagnetic Projectile Accelerators. Much more like a disk launcher (induction repulsion) than a coilgun (reluctance motor). Unlike coilguns, can crushing doesn't scale down to energies and voltages safe for thousands of schoolchildren.

Here we've seen accounts of disk launchers with huge capacitor banks, falling far short of performance expectations. I usually attribute that to poor tuning, that is a coil and capacitor combination poorly matched to the projectile system. If there's enormous force which ends before the projectile has time to move, no mechanical work is done. At the other extreme, the projectile could fly away and become uncoupled while most of the original energy is still in the capacitor and/or the magnetic field.

Back to Uzzors's question about number of turns. We can borrow a page from coilgun design. Suppose you have an assortment of coils with identical length, ID, and OD. Each coil has a different wire gauge, hence a different number of turns and a different inductance.
If we try them all with the same capacitor and same initial voltage, and we neglect the wire resistance, then peak magnetic field strength will be the same for all coils. After 1/4 cycle of undamped oscillation, all of the CV^2/2 energy from capacitor will have transferred to LI^2/2 energy in the coil. The coil with 2x as many turns and 4x the inductance will have 0.5x the peak current and 1.0x the peak ampere-turns. Its oscillation will be 2x slower, which might be more or less well matched to an accelerating projectile.

uzzors2k

Mon Aug 25 2014, 10:23AM

Registered Member #95 Joined: Thu Feb 09 2006, 04:57PM
Location: Norway
Posts: 1308

I've been using LTspice to simulate the capacitor/work coil circuit. The capacitor parameters are based on measurements taken on my microwave oven capacitor bank.

After giving this some more thought, I have a hypothesis that achieving the highest possible peak current, and also shortest possible pulse duration is the real goal here. My reasoning is that a substantial force is needed to overcome the yield strength of the work piece and crush it. In the case of a slow, drawn out, oscillating discharge, as is the case with large inductance/capacitance the force on the work may very well stay below the yield strength the entire time, and cause no deformation. No matter how long the force is applied! Contrary with a very rapid pulse of high current, the crushing force should easily overcome the yield strength. In addition, a more sudden magnetic field change will induce more current in the work piece than a slowly changing magnetic field.

I've played with FEMM some more, and integrated the results for total current density in a copper coin. The total current density should provide a measure of the crushing force exerted on the coin, as the current circulating in the coin gives rise to a magnetic field opposed to that of the work coil. These two fields create the force which crushes the coin. In the simulations the current in the work coil is either 1, 10 or 100kHz. The other parameters are kept the same. While jumping from 1kHz to 10kHz increases the current by a factor of 10 (which seems intuitive, given Faraday's law), jumping from 10 to 100kHz gives a much larger increase in coin current. I didn't simulate for 1MHz, as it doesn't seem very realistic to achieve a real world capacitor/work coil combination with such a high resonant frequency. The results for an aluminium can were similar, showing a large increase in the real part of the current at 100kHz compared to 10kHz.

1408961351 95 FT165559 Femm Sim Freq Compare

Having some way to test this is the next problem. My current capacitor bank has too much leakage inductance for a 100kHz test!

Patrick

Mon Aug 25 2014, 06:46PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

which FEMM did you use for the plots? they look good. FEMM is a real plus in these cases. It was super important in my HV probe building and verifications...

uzzors2k

Mon Aug 25 2014, 06:57PM

Registered Member #95 Joined: Thu Feb 09 2006, 04:57PM
Location: Norway
Posts: 1308

I used FEMM 4.2. I had some previous experience with it when working with a magnetic levitator project, and am quite satisfied with it so far.

EDIT: I've played with the Lua scripting ability of FEMM 4.2 and run simulations for frequencies ranging from 100Hz up to 10MHz. From the resulting plot (made in scilab) there appears to be a point of diminishing returns up at 500kHz, and a point of "increasing returns" beyond 20kHz. I'll try some different coin/can and work coil geometries tomorrow and see if they impact the results much.

1409000727 95 FT165559 Coin Current Results Plot

2Spoons

Mon Aug 25 2014, 11:49PM

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM
Location:
Posts: 615

If i may hazard a guess here: The optimum frequency probably matches the skin effect to the metal thickness. Reasoning: for skin depth >> metal thickness there is lots of field penetration that is essentially wasted. For skin depth << metal thickness, only surface current flows and the effective resistance of the can increases, reducing the induced current, reducing effectiveness.

Does this seem reasonable?

Steve Conner

Tue Aug 26 2014, 06:57AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

This reminds me of induction motor theory. The point of maximum torque in an induction motor is when the slip frequency equals the rotor time constant.

So maybe for maximum crushing force, you want to choose your frequency so that the inductive reactance of the workpiece is equal to its resistance.

This is just a wild-assed guess with no supporting theory except that the crushing setup looks a bit like a single-use induction motor.

Patrick

Tue Aug 26 2014, 07:18AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Having considered your problem further, I'm thinking its mostly or entirely a current issue, with a possible contributing problem of skin effect resistance. (also causing insufficient current, yet high heat.)

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