Redirected stresses on steel rings

[GEGibson]

This should be easy but my brain is locked. Ok, to set the stage picture three cylinders that are nested inside one another...for instance:

Cyl A: Ø5.000" x Ø6.500" x 3"
Cyl B: Ø4.995" x Ø4.006" x 2"
Cyl C: Ø3.000" x Ø4.000" x 3"

Now I nest all three of these cylinders, put a plunger on Cyl B, and place into a hydraulic press.

What I am trying to do, as a rough calculation, is to see how much pressure I can apply to the center ring without failure occurring on the inner or outer ring. I am looking at thick walled pressure vessel calcs but for that would need to assume tranference of load from the axial direction to the radial direction. Any ideas (or questions on the setup)?

Thanks!

 

[desertfox]

Hi GEGibson

Please provide a sketch I cannot see at present how the plunger only contacts cylinder B witout interfering with cylinder C.

desertfox

 

[GEGibson]

I will attach a sketch this afternoon when i get home. In the mean time, picture a plunger that is shaped like a cylinder with dimensions of:

Plunger: 4.950" OD; 4.050" ID

Thanks

 

[zekeman]

I don't see any interference fits so I'll call it zero.

 

[Cockroach]

oh Zekeman, you're killing me man. LOL!

Regards,
Cockroach

 

[GEGibson]

With no radial deformation of the center ring, i would agree. That is not the assumption here though. There are metallics, composites, and/or thermoplastics.

Thanks

 

[dhengr]

Nice sketch and problem description. Now we can see and understand your entire problem. But, I still have some “ questions on the setup.”

 

[GEGibson]

Here is a rough MSWord sktch to show the relationship of the cylinders. There is deformation of the intermediate cylinder depending on material.

@dhengr: What questions do you have on the setup?

Thanks

 

[telecomguy]

I'm guessing cylinder B is made of a non-compressible material so you have to assume compression in the axial direction will result in an expansion in the radial dimensions. So at some point B will fill the gap(s) and become an interference fit. (ie. constant material volume; no change in density of cylinder B). This interference results in strain in the adjacent cylinder. You should be able to then evaluate the stresses for cylinder failure.
<tg>

 

[dhengr]

GEGibson:
What is your engineering background? Who assigned you this problem? What exactly are you trying to do with this system of concentric cylinders, what does this arrangement do in the real world, and what are you trying to prove? How does this arrangement apply to thick walled pressure vessels? What materials are the cylinders made of, with all of their mechanical properties? How do you suppose the middle cylinder will deform and apply load or stress to the other two cylinders? What are the possible failure modes of each of the cylinders? What means do you use to be sure that you apply your compressive loading uniformly to the center cylinder, and how do you apply and measure this load and any deflections? Assuming the middle cylinder is made of the right kind of material how do you suppose stresses might be converted from axial to radial? You called it “tranference of load from the axial direction to the radial direction.” How many courses have you had in Strength of Materials or Theory of Elasticity?

If you can’t explain your question and problem in sufficient detail so some pretty experienced engineers understand what you are doing and what you want, you might do better by talking this over with your Professor. You’ve got the problem and we don’t usually play 20 questions to solve other’s problems, we have enough of our own problems.

 

[GEGibson]

Real life application: lantern ring component within a packing setup

TWPV idea? This is due to the load that could potentiall be aplpied to the ineer wall of the outer cylinder. Incorrect assumption?

Failure modes: Central ring - Delamination, yield, cold flow, shear, transverse shear, compression
Outer ring - Tensile, compressive, bending (due to stress concentrations that will eventually be explored)
Inner ring - This will be changed to a solid shaft and therefore wil not be as concered, although the probable failure mode will be compressive

There is no professor involved here and this is not an elementary problem assigned just to practice theory.
I am an engineer with 25+ years in the HPI and CPI arena for operations and reliability that has been away from this for almost 20 yrs. I left it fairly generic as I was looking for advice not for someone to solve it as I am still looking at the properties of our composite materials with classical laminate theory.

My apologies to you dhengr for wasting your time and pulling you away from your own problems.

Best Regards

 

[Cockroach]

Hit the nail on the old perverbial head, DHengr. Great points. I'm just not following the problem, too obtuse.

Regards,
Cockroach

 

[GEGibson]

Problem:
1. Apply load to central ring
2. Deformation/ compressive failure of central ring which then applies load to outer ring and inner ring

 

[zekeman]

Yeah Cockroach, I finally got it and agree with you.
To get a handle on this one would need too many dubious assumptions and
so, I'll pass.