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Pulse rating of wire

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Ben Solon

Wed Apr 11 2012, 11:08PM

Registered Member #3900 Joined: Thu May 19 2011, 08:28PM
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Posts: 600

To determine what the maximum pulse current in a wire is, is there any formula or rule of thumb? My best guess would be to take into account the pulse duration, magnitude, and resistance of wire to say whether or not the wire has heated up beyond its melting point(or whatever maximum temperature you desire

). Any help?

Patrick

Thu Apr 12 2012, 12:21AM

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

this is really complicated math, that ME's and Physics majors study. But you also need to consider the time between pulses, not just pulse duration. The heat has tobuild up, then decay, presumably a state function i think. any way an actual experiment or overbuilding may be easier.

Ben Solon

Thu Apr 12 2012, 12:55AM

Registered Member #3900 Joined: Thu May 19 2011, 08:28PM
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Posts: 600

It's just theoretical coilgun stuff, so in this aplication, it's just a single pulse.

Screwing around with my sstc today, I used it as just a pulse power generator by replacing the primary with coils and filiments. I drove the feedback with a constant high signal, and used the interupt to control burst length and frequency. The filament heated yellow(26 awg wire), and the coil got so hot the solder melted(16? 18?) Keep in mind this was a class e coil run with a 50v bridge.

this gave me a good idea of pulse ratings at these power levels, but what about 300-500v straight through the coil? I care about heat, I want to be able to fire about once a minute when demoing, but I don't want to use some heavy 12awg for a low power like 500J.

And as this is taking more of a coilgun direction as I intended, if an admin would be as kind as to move this thread, it would be apreciated.

Mattski

Thu Apr 12 2012, 12:55AM

Registered Member #1792 Joined: Fri Oct 31 2008, 08:12PM
Location: University of California
Posts: 527

To a first approximation which can be accurate for very short pulses and full cooling between pulses you can say that no heat is conducted, convected, or radiated away, so the temperature will be the energy dissipated in the wire times the heat capacity of the wire. And this overestimates the heat rise because as pulse lengths are longer more energy is removed, so it can still be used to help set an upper limit for pulse current.

Pinky's Brain

Thu Apr 12 2012, 01:22AM

Registered Member #2901 Joined: Thu Jun 03 2010, 01:25PM
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Posts: 837

So basically you just do I^2*R*t to determine the energy, divide it by the specific heat times mass of the metal and determine at what point it reaches the melting temperature of the insulation or solder.

This doesn't set an upper limit though, it gives a (very) conservative estimate.

Ben Solon

Thu Apr 12 2012, 02:15AM

Registered Member #3900 Joined: Thu May 19 2011, 08:28PM
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Posts: 600

Ok, sounds good, thanks for the help!

klugesmith

Thu Apr 12 2012, 03:35AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Good question, Ben. It's asked frequently here, and perhaps we ought to have a place for FAQ answers.

"Adiabatic heating" is a good word for the model that Mattski and PB described.
Here's one standard, practical way to express the result:
give the maximum I^2.t value for a given metal, wire gauge, and insulation system. The number will be proportional to the fourth power of wire diameter, and to the allowable temperature rise.

It's even simpler at the scale of a coilgun: just determine the number of kilograms of copper to absorb 100% of the stored energy with acceptable temp. rise per shot.

To check your math, there are some numbers given in the bottom half of this recent post

and the industrial document it refers to.

That doc has charts for an important standard case: Sudden temperature increase in Cu wire of 75 degrees C (from 75 degree steady state to 150 after short-circuit protection works).
Bottom line (of my unreviewed reduction of tabulated values):
Allowable I^2.t is around 10900 A^2.s per square mm squared.
That's 1000 A/mm^2 for 10.9 ms, or 100 A/mm^2 for 1.09 seconds.
Or 10 kA/mm^2 for 109 us, considering only thermal effects.

Ben Solon

Thu Apr 12 2012, 02:34PM

Registered Member #3900 Joined: Thu May 19 2011, 08:28PM
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Posts: 600

Alright, this is the good info! I think I may go a little deeper into this using this info as a starting point. It may help coilguners significantly if I can put together a web calculator for using the appropriate gauge. I know I for one don't like when a coil simply falls apart due to thermal expansion and/or the form melting.

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