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

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Proud Mary

Tue Aug 26 2014, 08:19AM

Registered Member #543 Joined: Tue Feb 20 2007, 04:26PM
Location: UK
Posts: 4992

Uzzors2k wrote ...

I have the impression most people just wing it and use something that "feels right" in terms of turns/wire thickness and inductance.

This is science.

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

Dr. Slack

Tue Aug 26 2014, 08:22AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

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.

uzzors2k

Tue Aug 26 2014, 09:37AM

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

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!

Steve Conner

Tue Aug 26 2014, 09:53AM

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

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?

Patrick

Tue Aug 26 2014, 04:07PM

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

Proud Mary wrote ...

Uzzors2k wrote ...

I have the impression most people just wing it and use something that "feels right" in terms of turns/wire thickness and inductance.

This is science.

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

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.

Uspring

Thu Aug 28 2014, 09:39AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
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@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.

BigBad

Thu Aug 28 2014, 08:18PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
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Posts: 600

Steve Conner wrote ...

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?

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:

uzzors2k

Sat Aug 30 2014, 04:22PM

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

Uspring wrote ...

@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.

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.

Uspring wrote ...

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

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.

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?

Uspring

Sat Aug 30 2014, 06:15PM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
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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.

BigBad

Sun Aug 31 2014, 01:48PM

Registered Member #2529 Joined: Thu Dec 10 2009, 02:43AM
Location:
Posts: 600

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.

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