Calculation of Shrapnel Velocities

[tae10]

Im trying to build a shield for a small scale brake dynamometer we have in our Department, and the shield will be protecting users from some very high speed, low torque projects they are testing. The shield is supposed to protect against catastrophic failures, when shrapnel is flung around.

I have gotten a few hints, from my Professors, that I will need to calculate what velocity I would expect shrapnel to be flung out, what energy it would carry, and whether a metal mesh with a plexi-glass sheet (which was my original concept) could actually stop it. How would I go about these calculations? I have the general dimensions of one of the projects, and the speed that it runs at. Is there a way to calculate the velocities at which shrapnel is flung out?

Any help is appreciated. Thanks

Tamir

 

[Solveer]

you kind of answered your own question (at least the way I understand it). The "flung out" part hints that the particles will at most have the tangential velocity of your rotating part that they are attached to. So the maximum velocity can be v=w*r or rotational speed (radians/sec) * radius of turning part (meters). Radians per Sec is just revolutions*2Pi per second.

 

[minger]

Yes, as mentioned your velocity will be straightfoward. However, determining the impact is tricky. When looking at things like containment, I've used for reference a ballistics paper that I have...let me find it...

"Missile Firing Tests at Stationary Targets in Support of Blade Containment Design", J.I. Goatham, and R.M. Stewart, Journal of Engineering for Power, April 1976 (no vol, sorry) pp 159-164

There are probably a few different papers and such talking about containment; they're your best bet. Make sure to use a hefty safety factor.

 

[FredGarvin]

There are a lot of different ideas around containment. It gets complicated with varying material energy absorbing capacities and rigidity of the structure itself and its footings. Most places I have been have developed their own internal procedures for doing them. My recommendation would be to make it as stout as you possibly can. It won't hurt anything if it is too thick. You just have to put some thought into putting it on tracks or something to make it easy to move out of the way so it isn't cumbersome to work around.

 

[tae10]

Thanks a lot for the responses. I've done some calculations for the Linear velocity and Kinetic Energy that one of the systems will be putting out (in terms of shrapnel) in the case of catastrophic failure, and the Kinetic Energy comes out to be about 3.62 E13 Joules. How will I be able to determine if a sheet of plexiglass can deflect that kinetic energy? Is there some formula I can apply? What if I used a wire mesh with a sheet of plexiglass?

Thanks.

 

[minger]

What have you tried so far? I provided a paper describing a decent approach for blade containment and Fred mentioned that companies will typically have in-house ways of determining this.

 

[tae10]

I haven't been able to test anything yet, because the entire dynamometer hasnt been built, and we're still in the design stage. I did look for that paper, but I have yet to read through it.

Considering we'll be dealing with stainless steel, and later on titanium devices that will be spinning at around 60k RPMs without load, and around 20k RPMs with a load, I should think that we'll be needing a decent shield, but cinder blocks used in high speed motor tests is definitely overkill. I was thinking of 0.25" impact-resistant plexiglass and a sheet of some wiremesh bolted to the frame, but as I said, Id like to run some calculations to make sure that the shield can absorb the impact of the shrapnel. Is there a yield strength of the material that I can use to compare that Kinetic energy number to?

Thanks.

 

[FredGarvin]

Think again. Even small masses turning at those speeds have a very high energy that needs to be dealt with. Remember, kinetic energy goes up with the square of the speed!

You need to be thinking of something along the lines of 1" thick steel. Don't screw around with plexiglass. It will shatter. I have seen small turbines that fit in the palm of my hand take huge chunks out of cinder blocks during an escape. If you don't want to go with steel, I would suggest making a dog house out of 4x4 or 6x6 square posts and then wrapping that with a 1/8" layer of steel. The wood acts as a great shield and is inexpensive to buy and build.

Seriously, this is not a design problem to optimize. You make it as stout as you can get away with. There is no such thing as overkill. Especially because you have no idea what is going to be tested in the future.

 

[minger]

Oh god no. As Fred mentioned, you'll need a pretty stout containment. 60k rpm is nothing to mess with. Recall that your energy is a function of speed squared, so you quickly get up there.

 

[tae10]

Wow, I had no idea. Thanks a lot for the advice, I'll try to come up with a better system. How can I know if a 1" thick steel plate will absorb the kinetic force? Is there a book that describes how to do the calculation?

Thanks again.

 

[FredGarvin]

Minger gave you a paper reference to look at.

 

[tae10]

Yes, as mentioned your velocity will be straightfoward. However, determining the impact is tricky. When looking at things like containment, I've used for reference a ballistics paper that I have...let me find it...

"Missile Firing Tests at Stationary Targets in Support of Blade Containment Design", J.I. Goatham, and R.M. Stewart, Journal of Engineering for Power, April 1976 (no vol, sorry) pp 159-164

There are probably a few different papers and such talking about containment; they're your best bet. Make sure to use a hefty safety factor.

Unfortunately after a lot of looking around, I couldn't find it. I tried searching their names, and even the ASME archives, and nothing. @Minger: do you happen to remember where you got yours from?

 

[FredGarvin]

That journal is now known as the Journal of Engineering for Propulsion and Power. You need to contact ASME since articles that old usually have to be scanned in or faxed to you.

 

[tae10]

Ok thanks.

 

[minger]

If you can't get a hold of those, here are a couple of papers I found going a quick search.

Jet engine fan blade containment using an alternate geometry
International Journal of Impact Engineering, Vol. 36, Issue: 5, May, 2009. pp. 720-728
Carney, K.S.; Pereira, J.M.; Revilock, D.M.; Matheny, P.

Aeroengine turbine blade containment tests using high-speed rotor spin testing facility
Aerospace Science and Technology, Vol. 10, Issue: 6, September, 2006. pp. 501-508
Xuan, Hai-jun; Wu, Rong-ren

 

[tae10]

Awesome, thanks, I'll see if I can track those down.