Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
klugesmith, Sun Aug 24 2014, 06:55PM

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

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
IamSmooth, Sun Aug 24 2014, 07:24PM

Have you seen this site?

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
klugesmith, Sun Aug 24 2014, 09:00PM

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.

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
uzzors2k, Mon Aug 25 2014, 10:23AM

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.




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

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
Patrick, Mon Aug 25 2014, 06:46PM

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...

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
uzzors2k, Mon Aug 25 2014, 06:57PM

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.

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
2Spoons, Mon Aug 25 2014, 11:49PM

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?

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
Steve Conner, Tue Aug 26 2014, 06:57AM

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.

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
Patrick, Tue Aug 26 2014, 07:18AM

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.)

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
Proud Mary, Tue Aug 26 2014, 08:19AM


This is science.

We accept great heaps of rubbish upon our shoulders without thinking about it.

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
Dr. Slack, Tue Aug 26 2014, 08:22AM

There are two things happening with a can or coin. The Lorentz force from the current is obviously one, but the Joule heating to get the metal soft enough to move with less force is also critical to the effect. As the yield stress versus temperature is decidedly non-linear, I'm not sure it will be possible, even in theory, to get an expression for the optimum configuration that scales. Just be aware that an 'inefficient' configuration that delivers more heat than peak force might produce a smaller waist to the can.

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
uzzors2k, Tue Aug 26 2014, 09:37AM

In the previous graphs the "coin" I simulated with was actually just 0.7mm in diameter. I have since changed the coin and coil size to more realistic values. This has actually brought the frequencies involved down to those commonly encountered in can and coin crushing work. The overall shape of the graph remains the same, as one would expect.

I found a chart over skin depths , and it seems the skin depth equals the radius at the point where the current begins to increase. This is the case with both the small diameter coin and the larger diameter one, and perhaps the opposite of what would be expected. Notice that for the 0.7mm radius coin used in the first simulations, the corresponding skin depth occurs at ca 9kHz. For the 9.25mm radius coin used in later simulations, the "skin depth = radius" point occurs at ca 60Hz. From each graph this is also where the current begins to pick up.



I've plotted the phase of the current this time along with the magnitude. Since the phase approaches zero as the current stops increasing, my guess is that the peak current point is where the inductive reactance becomes neglible compared to the resistive losses in the coin. This would also seem to explain the break upwards near the "skin effect = radius" frequency. Prior to this point the reactance of the coin would be largely inductive, and afterwards increasingly resistive, hence the phase of the current. Sooooo, if all of this is correct, it only means that the frequencies commonly used for coin and can crushing are already in the optimal range!

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
Steve Conner, Tue Aug 26 2014, 09:53AM

Thanks for the chart Uzzors. My hypothesis is that you will get the maximum crushing effect at the frequency where the phase is 45 degrees. Does anyone have any data that would confirm or deny this?

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
Patrick, Tue Aug 26 2014, 04:07PM

yes, ill agree. but coupling factor "K" in high frequency transformers and such can have a mysterious "fudge factor" where it kinda works, but above and below it doesnt. coupling may not be calculable due to the many stray factors that become influential in the math.

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
Uspring, Thu Aug 28 2014, 09:39AM

@Uzzors, I'm wondering, what phase that is, you've plotted. For a loose coupling, I wouldn't expect such a change of phase between work coil voltage and current. It looks more like phase between work coil and coin current.
The way the coin is positioned in the simulation, the forces on it won't be isotropic, leading to an oval shape. I believe, usually the coin is placed inside the coil, where the field is largest and forces are strictly radial.

I agree with klugesmith, that for a given cap and voltage, max field is more or less independent of coil inductance.

The current in the coin is low for low frequencies since the voltage induced in the coin will be low and its resistance will limit the current. At higher frequencies, the current in the coin will cause a field countering the external field, so the current will saturate at the level, where they cancel.

When you think of the coin of being a single loop of wire, the frequency, where this happens is when 2*pi*f*L = R. L being the inductance of the loop and R its resistance. A loop is not a bad approximation, since the skin effect will push out the current to the rim of the coin. Since loop inductance and resistance are both roughly proportional to diameter, I'd expect this frequency to be independent of diameter, but to decrease with thickness and conductivity of coin material.

The force on the coin is proportional to the product of field and coin current. As said, the field does not depend much on the frequency and the coin current maxes out somewhere. Increasing f beyond this won't increase force but will increase losses in the caps and the work coil due to the higher work coil currents.

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
BigBad, Thu Aug 28 2014, 08:18PM

If you hold the current constant then the crush should only go up with greater frequency, but you pretty soon hit the voltage limit of your cap for the same current due to the resistance and inductance.

It's basically a linear induction motor all round the coin:

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
uzzors2k, Sat Aug 30 2014, 04:22PM

You're entirely correct, that is a plot of the coin current phase, relative to the current in the work coil. I guess I should have explicitly mentioned that somewhere.

So if I've understood correctly this would imply that, when ignoring losses: as long as the resonant frequency of the system is above the frequency where the current flattens off, the exact geometry of the work coil will not influence the force on the coin?

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
Uspring, Sat Aug 30 2014, 06:15PM

I wasn't clear on that. I meant to say, that the field is independent of inductance if the shape of the coil, i.e. diameter and height stay the same. For e.g. a higher inductance, that implies more turns in the same space.

Wrt to the optimal frequency, you could try a measurement of the phase between coil voltage and current using a sine generator. You shouid see a change from the purely inductive 90 degrees to a lower value when frequency is increased. The bigger the change is, the better is your geometry and frequency. These experiments should also be made without coin or can in order to distinguish between coil loss resistance and dissipation in the shrinking object.

I believe a suitable (Spice) model would be a transformer with some coupling and a secondary winding loaded with a resistance.

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
BigBad, Sun Aug 31 2014, 01:48PM

At high frequency the force flattens out anyway. And power and force are proportional (they both go as i^2, although the constants are R and L respectively)

And as has been pointed out, the coil, the capacitor and the coin form a transformer with a resistive secondary.

The maximum power theorem says you want to match the effective resistance of the coin and the capacitor/coil resistance, so you can tune the frequency to give a skin depth in the coin to give the correct resistance.

So you can use thicker or thinner wire and fewer or more turns to tune the resonant frequency to get a good match.

Re: Coin/Can crusher simulations, or how to determine the work coil parameters?
Uspring, Mon Sept 01 2014, 09:51AM

I'd like to view the optimum frequency as a compromise between

a) The max f possible. This is sensible until the force flattens out. That is a property of the coin, i.e. its inductance and resistance. This max sensible f could be established by a low power measurement.

and

b) The losses in the caps, wiring, switch and the coil. Higher f implies larger currents and bigger losses. These losses are a property of the driving circuitry. Preferably these losses are still low at the "sensible f" from a).