FEA for HPA - it's not out of reach for us

[WobblyHand]

The recent thread on a ruptured pressure vessel, reminded me that HPA can be dangerous.  I was wondering if there were tools that could help us analyze things like this, and could be used by folks that hadn't done this kind of work for a living.  I'm thinking in terms of people that want to make or machine items for airguns.

Many CAD packages have some level of finite element analysis tools.  Ones that have these FEA packages include Fusion360, SolidWorks, FreeCAD, and I'm sure others.  The question I had was how hard is it to actually do this analysis.  Turns out, it's not too hard, at least in FreeCAD to do FEA.  FreeCAD being non-commercial, isn't quite as slick as the other tools, but, it seems to work ok, once you figure out a few quirks.  Now I am not a mechanical engineer, nor have I done this professionally, but I have had exposure to FEA for solving electromagnetic problems.

The basic steps are as follows

• Create a model of the structure under test
• Add any fixed constraints
• Apply pressure constraints
• Apply the material
• Mesh the model
• Set up the Solver and run the Solver
• View the results

Here's a simplified model, hey we have to start somewhere.  It's 38.5mm OD with 3mm walls.  It has a horrible sharp inside corner, which we know is not good for a pressure vessel.  Lets say it is made of 6061-T6 and we charge it to 300 MPa.  To the right side of the line is pressurized.  Then we put some constraints.  We mesh the model.  At least in FreeCAD, it's a good idea to constrain the maximum element size.  Since this model is roughly 150 mm long, I chose a max element size of 1.5 mm.  The meshing takes a little bit. Then one runs the solver.  At least on my PC, it uses all the CPU cores for solving.  On an i7 it took 30 seconds.
We can show various results including von Mises Stress, Max Shear Stress, and displacement.

What I am trying to learn still is where and how to constrain the model.  This took me a couple of days to figure out so far.  Have a lot more to learn.  I can post the model if anyone is interested.  My original model had the vessel threads in it, but I stripped them out, since they were not in the pressure region.

[WobblyHand]

As you practice a bit, it gets a little easier.  (Instead of being clueless, I have progressed to slightly befuddled  )Here's the interior view of a pressure cylinder made of 7075-T6 running at 105 MPa, 3.5 x its working load.  You can see the stress induced by the sharp interior edge.  Had to play with some of the defaults in FreeCAD to get this to render correctly.  The default is no anti-aliasing, which is a poor choice.  I set the anti-aliasing setting to MSAA-4x, and the formerly gray interior now seems to be rendered better.  In a while, I will radius that inside corner, because we all know that is the right way to do it.

Been interesting doing this.  Makes me leery of using aluminum pressure cylinders...  Wonder what titanium would be like?  (A devil to machine!) 

[sb327]

I’ve no input here but enjoy your explanations. Very interesting subject for sure. Keep us updated.

Dave

[Privateer]

Interesting thread for the software your using.
Can't say that I really care for the programs being used by Marco or Ed.
And I have to wonder IF both are using the exact same 3D mesh and how accurate the mesh is to the final produced part.

[WobblyHand]

Interesting thread for the software your using.
Can't say that I really care for the programs being used by Marco or Ed.
And I have to wonder IF both are using the exact same 3D mesh and how accurate the mesh is to the final produced part.

I think Marko uses Fusion360, not sure about Ed.  Unlikely they are using the same mesh.  Ed, unlike Marko has the original drawings.  Marko is measuring "used equipment".  Not sure if that is good or bad.  Perhaps you could say Marko is using "as built".

The meshing on FreeCAD is sort of ok.  I simply controlled the maximum cell size and let it figure it out from there.  Fusion360 and all the other packages may have smarter routines.  All meshers will fill the model.  There will not be any unmeshed areas - that would trigger a meshing error.  It's possible to zoom in on the mesh and verify full coverage.

I'm so far from being expert at this...  But it has been interesting working on FEA.  I'm now trying a cylinder with a rounded bottom.  Having trouble with FreeCAD meshing and constraining, due to me not understanding some key point.  I'll figure it out eventually. 

[WobblyHand]

Was having a little trouble with meshing the cylinder, and found I had an old version of the mesher.  Updated the mesher and it easily did the cylinder with rounded inside corners.  The solver had fewer issues with the mesh and was quicker as well, so that's a win win.  The stresses are a bit more spread out over a larger area, primarily over the fillet area.  Material: 7075-T6, 3mm wall thickness, 105 MPa.  (3.5X operating pressure)  Peak von Mises Stress is still high at 639 MPa.  I used a 1.200 mm largest element size for the mesh.  Curiously a 1.250 mm mesh had errors in it.  Running at a 1mm mesh gave the same peak stress, to within 0.1%, but took more than twice as long to run.  Not going to lie, the application tends to favor server grade computation and memory sizes.  Peak memory consumption was around 28 GB, for the 1mm mesh, so it was getting close to the limit on my laptop with only 32 GB RAM.  But running at finer and finer mesh only seems to refine the answer by a minuscule amount - and is usually only used as a sanity check.  Most of the time a coarser mesh is perfectly acceptable.  Or simplifying the model.  I put in threads in the model, which strictly speaking, is not required, since they are out of the HPA zone.  Lots of ways to make the model fit, if required.

[WobblyHand]

Turns out the meshing was a little coarse in the example above.  Went to a finer mesh, which does stress memory constraints, on my 32GB system.  Went to a 0.990mm mesh, which guaranteed there were at least 3 elements in the thickness of the pressure tube.  Probably should make the cell smaller, but that's pushing it on my laptop.  But now we can see the stresses in the cylinder, which seem to make some sense.  In the curved region (5mm radius) the stresses are moderate.  The peak stresses are on the inner surface where the HPA resides.  There's clearly an art to this - as well as the science.  First picture is with 50% transparency, so you can see through the part.  Second picture is 0% transparent, but the cylinder has been cut in half lengthwise so you can see inside.  The second picture shows the maximum stress is on the inner surface.

[WobblyHand]

At 105 MPa, (3.5x operating pressure) the von Mises stress (638 MPa) is well over the typical yield strength of 7075-T6 (503 MPa).  The von Mises stress is also greater than the ultimate strength of 572 MPa.  Doesn't seem like a safe area to operate...

At 90 MPa (3x operating pressure) the von Mises stress is 547 MPa, which is still higher than the typical yield strength of 7075-T6 and somewhat close to the typical ultimate strength of 572 MPa.  Still not quite a happy place to be, if I am understanding correctly.  I think this means there will be permanent deformation of the cylinder at 90 MPa, but I'm just a dabbler at this.

At 75 MPa (2.5x operating pressure) the maximum von Mises stress is 456 MPa, which is under both the typical yield strength and the ultimate strength.  So not likely to have an issue, he naively thinks.  So roughly speaking, this design has about a 2.5x safety factor.
Please don't design to this and think it is safe - this is merely an engineering exercise - make sure you verify any of your designs to make sure they are safe!  I am not a professional mechanical engineer, I do not have access to the minimum values of the material properties, nor have I learned all the rules of thumb, so take all my comments above with a grain of salt.  Merely the ramblings of an amateur.

[Privateer]

How accurate is the scale of your Model? I mean is it to scale of the Real World part?
Not trying to start a problem just want to understand.

[WobblyHand]

How accurate is the scale of your Model? I mean is it to scale of the Real World part?
Not trying to start a problem just want to understand.

Don't honestly know Jeff.  I looked at the photos in the epic thread, and estimated values based on a couple of measured values that Marko showed, and the proportions relative to those measurements.  So it's a WAG, but not too far off.  The model above I used a 5mm radius on the end, rather than a sharp inside corner.  Within the guide lines Marko mentioned for a 3mm wall.  As far as I know, Marko didn't publish that many dimensions, perhaps not to publicly show the dimensions (as a courtesy?).  If I had better dimensions, of course the model and results would be better.

I simulated 7075-T6 above.  That is what I am guessing that has 2.5x safety factor.  Not 2024 (D16T) which is the material for the actual tube.

2024-T4 is not as strong...  Yield strength of 2024-T4 is 324 MPa, but 7075-T6 is 503 MPa.  Ultimate strength 2024-T4 469 MPa vs 7075-T6 572 MPa.  https://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA2024T4
https://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA7075T6

I'm not a professional ME.  Just dabbling in this, because it really caught my attention.

BTW, I agree, Ansys is a professional grade simulator.  We used HFSS (an Ansys product) for RF simulations for quite a while.  We found it didn't scale well for the really huge problems we wanted to simulate for millimeter wave radar, so we transitioned to a different technology using GPU's.  This was because the new technology could use/exploit massive parallelism and use GPU's for computation.  We achieved 30-100x faster solutions than using HFSS, which didn't exploit parallelism.  This meant simulations that took days the old way now took under an hour.  The new method called Finite Difference Time Domain, allowed us to see electromagnetic waves as they were propagating and how they interacted with the structure.  HFSS in contrast was a steady state solution.  We were able to massively increase our understanding and throughput using the new system.  I don't know if HFSS has been updated to use GPU's.  It was a rough transition at our company, with the HFSS guys having to learn new ways...  We also had to install huge fast disk farms - if I recall correctly, we had 1 Exabyte capacity.  It was a major problem just shuttling data around, due to the puny 10GbE networks we had, because moving 10TB files took a significant amount of time!  These are typical problems with high performance computing - there are bottlenecks in the most unforeseen places.

Anyways, this is a mechanical FEA thread, not electromagnetic one, sorry for the digression.

[Privateer]

I totally understand. I think that's where people went all crazy on me. I believe to fully understand a problem people need to share data.
It's called Peer Review. I bet you'd LOVE my friends HOME system! That thing is CRAZY beyound belief!

[WobblyHand]

I totally understand. I think that's where people went all crazy on me. I believe to fully understand a problem people need to share data.
It's called Peer Review. I bet you'd LOVE my friends HOME system! That thing is CRAZY beyound belief!

I agree.  Peer review is indeed a good thing.  WAGging the dimensions, is not so good, but all I have. 

Sound like a very cool computer setup.  Would be neat to see.  Of course, I'd want to see what it could do!  Always testing the limits!

I'm going to do a 2024 simulation using the identical mesh, at 2.5x rated pressure for giggles.  I'm sure I will have to back off the pressure, at least not to have it yield on me.  Unfortunately, my SW won't tell me something is about to explode, but it will give me the stresses, and I can compare them to the published material properties.  Best I can do.

[Privateer]

He's stepping up to an Epyc before long. 128 core 256 thread, with 256 GB of ECC RAM (4TB max)!

[WobblyHand]

Looks like the same design in 2024, has a safety factor (no yield, well under ultimate tensile stress) of a smidge under 2:1, best I can tell.  This is assuming 2024T4.
I get von Mises stress = 365 MPa.  This compares to UTS (ultimate tensile stress) 427, so we are good there, and yield stress of 305 min, 324 MPa typical.  The simulation shows the tube grows by 91um.  I don't know how much of that is permanent - that's beyond my pay grade.  This is a static simulation (linear).  Perhaps the answer is different using a non-linear sim.

7075T6 is definitely superior, allowing a 2.5x no yield margin.

Without radiusing the corner, 2024 doesn't seem like a very good choice, at least to my inexpert opinion.  The radiused corner doesn't even make 2x yield safety factor.  Seems like trouble waiting to happen.  But that's only my inexpert opinion, based on swag numbers from crooked pictures... 

[Privateer]

I have to wonder something.
That area is supported somewhat.
So how likely would that support hold that area from catastrophic failure as seen in the pictures?
That may be why there was no sever injuries.

[WobblyHand]

I have to wonder something.
That area is supported somewhat.
So how likely would that support hold that area from catastrophic failure as seen in the pictures?
That may be why there was no sever injuries.

Have a picture of that?  Not really that familiar with how that AG is setup.
I did model this once, but it was a pain in the neck.  I had to fuse two pieces together and it was tough to edit afterwards.  If I had known it was tough to edit, I would have modeled it differently.  The pitfalls of modeling - there are many ways that work, but some are way better to use!

[WobblyHand]

He's stepping up to an Epyc before long. 128 core 256 thread, with 256 GB of ECC RAM (4TB max)!

What does he do with the old computers?

[Privateer]

Here's a quick image.
The Red arrow is where the failure was.
The Blue arrow is the brace.
So I suspect a sideways rupture after the end failed near the red arrow area.
Being covered by the neoprene? That burst of air is what shredded it.

[Privateer]

He's stepping up to an Epyc before long. 128 core 256 thread, with 256 GB of ECC RAM (4TB max)!

What does he do with the old computers?

He runs them as backup for now. He is a Operating Systems Programmer.
Just his network in his home is near to a PetaByte of data storage!
His home Network operates at 20 Gigabyte times 2!
All fiber Optics.

[WobblyHand]

Here's a quick image.
The Red arrow is where the failure was.
The Blue arrow is the brace.
So I suspect a sideways rupture after the end failed near the red arrow area.
Being covered by the neoprene? That burst of air is what shredded it.

Thanks for that.  I didn't model that area.  Looking at the dimensions, it looked beefy.  And it is pretty clear the fracture was not in that area.  I modeled the versions with a fixed constraint pushing against the bottom of the cylinder.  I also have a high uncertainty of the dimensions there.  Apparently there is a threaded hole there, and possibly a narrow diameter hole into the cylinder?  Happen to know the diameter of the threaded hole?  (M6? M8?) The tiny through hole diameter, if it indeed goes through?  To be honest, those details seem pretty far removed from the explosion zone.  The fracture looks like it is at the base of the main diameter, which is roughly 5mm away from the rest of the area.  Hard to say what the actual sequence of events was during the rupture - outside of my experience.