Math Check - Case Strength

[daveyfire]

Hey gang,

I'm fixing a 2550 case on the lathe (it's becoming a 1750, see here, it helps to remember the o-ring) and, in my excitement, brain farted and cut the groove 0.057 deep instead of 0.047 (the wall is 0.093).

To get a grasp on if it's usable or not, I figured that the cross-sectional area of the remaining aluminum wall "cylinder" (the part doing the holding) has been reduced from 0.300 in^2 to 0.236 in^2, leading to a reduction in yield strength from 12,000 lbf to 9440 lbf. Despite being a 20% decrease (in agreement with a quick FEA run), this is still a factor of safety of over 2.5 at 1200 psi chamber pressure, so I feel safe using it.

Where did I mess up?

[CarVac]

uhhh, the aluminum gets weaker as it gets hotter? Maybe? What is the safety factor with the intended cut depth?

[daveyfire]

The "normal" safety factor is 3.5. At ~400 F (roughly the external case temperature limit allowed by NFPA) the yield strength decreases to ~20ksi (from ~40 ksi) -- that makes the "normal" safety factor ~1.75 and mine ~1.38, using this math. But if the forward end of the case gets to 400 F during the high pressure portions of the motor operation, I think I've got bigger problems on my hands.

And this is all at 1200 psi, which is kind of an extreme case. I don't usually run hobby-grade stuff that high... heat transfer becomes a problem and whatnot. Derate these calcs to 800 or 600 psi for most cases and things get even better.

I guess I should mention that the "half the wall thickness" recommended groove depth was a rule of thumb that Frank Kosdon passed on to me... it's a pretty solid source, but I have no major reason to believe that it shouldn't work this way, too.

[tfish]

better safe then sorry..cut it down another 3" or so. I've got some 54mm tube I can send you for a new case. I might even have an un-used 2550 case not doing anything..PM if that helps.

Tony

[bobkrech]

Hey gang,

I'm fixing a 2550 case on the lathe (it's becoming a 1750, see here, it helps to remember the o-ring) and, in my excitement, brain farted and cut the groove 0.057 deep instead of 0.047 (the wall is 0.093).

To get a grasp on if it's usable or not, I figured that the cross-sectional area of the remaining aluminum wall "cylinder" (the part doing the holding) has been reduced from 0.300 in^2 to 0.236 in^2, leading to a reduction in yield strength from 12,000 lbf to 9440 lbf. Despite being a 20% decrease (in agreement with a quick FEA run), this is still a factor of safety of over 2.5 at 1200 psi chamber pressure, so I feel safe using it.

Where did I mess up?

You messed up by cutting the groove too deeo. (You didn't measure twice and cut once.)

The problem created by going too deep is that the snap ring wll not function as intended. I think the smap ring will release at a lower pressure. A safety feature by design with a Kosdon style casing is the snap ring will release the nozzle or the forward closure at about 2 x MEOP to prevent the casing from failing catostrphically at about 4X MEOP. When the groove is deeper than intended, the snap ring releases at a lower load.

Bob

[daveyfire]

You messed up by cutting the groove too deeo. (You didn't measure twice and cut once.)

The problem created by going too deep is that the snap ring wll not function as intended. I think the smap ring will release at a lower pressure. A safety feature by design with a Kosdon style casing is the snap ring will release the nozzle or the forward closure at about 2 x MEOP to prevent the casing from failing catostrphically at about 4X MEOP. When the groove is deeper than intended, the snap ring releases at a lower load.

Yea I know I messed up... I usually do thicker walled cases where the design drawing matches the "half the wall thickness" spec, so that's where the crossed wires come from.

I cut the groove as deep as McMaster asks for:

I don't get how making the groove deeper makes the snap ring release easier, though. Is it the wall tearing axially, or does the ring slip out of the groove easier, or does the deeper groove cause a shear failure in the tubing ahead of the groove? What's the mechanism for a "too deep" failure?

(BTW I've resigned myself to parting this one down 0.265" and redoing it. Womp womp, haha.)

[rocketsaway]

[bobkrech]

I don't get how making the groove deeper makes the snap ring release easier, though. Is it the wall tearing axially, or does the ring slip out of the groove easier, or does the deeper groove cause a shear failure in the tubing ahead of the groove? What's the mechanism for a "too deep" failure?

My bad. Too many 15 hour days at a customer site.

The snap ring casing design is interesting in that the closures will release at a nominal 2 x meop versus a casing failure at 4 x meop. A key design point is to make the snap ring groove depth 50% of the wall thickness.

This is a great range safety feature since the area under and above the rocket is alway cleared.

Bob

[Reinhard]

The 50% wall thickness rule does not refer to the total thickness of the casing or the actual dimensions of the snap ring. Therefore it is probably not a good general criteria to ensure the snap ring releases at a certain point, although it might be a good rule of thumb value for typical hobby rocketry casings.

There is probably another explanation: In a thin walled cylindrical pressure vessel, the hoop stress is about twice as high as the axial stress. Cutting a groove to at least 50% depth will equalize this difference, and considering that the sharp corner at the bottom of the groove will additionally additionally weaken the case by concentrating stress, this should be enough to ensure that the case fails axially (unless the snap rings yield first). AFAIK at least some CTI cases with strong threads (Pro75, Pro98) feature a groove for just that purpose.

Reinhard

[daveyfire]

There is probably another explanation: In a thin walled cylindrical pressure vessel, the hoop stress is about twice as high as the axial stress. Cutting a groove to at least 50% depth will equalize this difference, and considering that the sharp corner at the bottom of the groove will additionally additionally weaken the case by concentrating stress, this should be enough to ensure that the case fails axially (unless the snap rings yield first).

Oh, I like this explanation a lot. Thanks Reinhard!

[bjphoenix]

There is probably another explanation: In a thin walled cylindrical pressure vessel, the hoop stress is about twice as high as the axial stress. Cutting a groove to at least 50% depth will equalize this difference, and considering that the sharp corner at the bottom of the groove will additionally additionally weaken the case by concentrating stress

Well son of a gun...
I thought this was a strange relationship but I just checked the equations and through some quirk of algebra this is exactly right.

I was thinking about it a different way- the force on the snap ring is the same as the tension force in the tube, therefore if the snap ring groove is cut less than half the thickness then the compression stress of the snap ring on the tube material would be higher than the tension stress in the tube at the point where the groove is cut. The stress concentration at the bottom of the snap ring groove does make a difference though and if you wanted to equalize the strength of the snap ring bearing vs. the tension in the tube you would want the cut to be slightly less than 50% of the depth. I don't deal with stress concentration factors in my normal work so off the top of my head I don't know what the appropriate stress concentration factor would be.