Load Shoulder Pressure Stress Calculations (Sketch Attached)

[thereddevil]

I'm in the process of designing a part which must be submerged down to 2000m (200 bar/20 MPa/ 2900 psi). A sketch of the part has been attached. The outer housing will be titanium and the inner part aluminium. I've carried out the calcs for the outer part to withstand the external pressure, but am stuck a little with the internal part.

My understanding of the stresses acting on this part are:
- Compressive stress on the load shoulder
- Shear stress acting across at roughly a 45° angle (assuming this angle and not a straight line across)
- Stress concentration on the corner (blend rad to be added)

Both these stresses at present are below the material yield (quick bonus question: I'm assuming that the shear stress for aluminium is 60% of the yield - is this a correct assumption?). I'm thinking I can't just leave it here and that I should be working out principal stresses and max shear stresses etc. Can anyone provide guidance on this? Is this required? What should I be looking for (Mohr's circle to calculate P1/P2/shear max, Rankine's theory, von Mises etc.).

http://pasteboard.co/HFxzoE3mw.jpg
http://pasteboard.co/HFxzoE3mw.jpg

 

[Nidum]

Is this an academic exercise or a real world design project ?

 

[thereddevil]

Real world - it will be a component within the housing of an underwater sensor.

 

[Nidum]

I see several potential problems with the design as shown . I suggest that you seek assistance from a professional engineer with appropriate experience .

 

[thereddevil]

Haha well I am the professional engineer, just lacking the experience... It is quite a common concept (seen quite often for pressure rated plugs/connectors etc.). I'm just curious as to the theory behind it and was hoping someone could help expand on my initial thoughts.

Out of curiousity, what potential problems do you see?

 

[JBA]

Yes this is a common configuration for pressure applications and assuming your compressive contact stress on the plug shoulder face is within the yield strength of the aluminum alloy (including a reasonable safety factor), then a more exotic stress analysis should not be required. As for the shearing stress this is generally calculated as being straight back through the plug at the i.d. of the plug shoulder rather than as a 45° cone as you show , so if your calculation indicates that the shear on that cone is acceptable then you should be fine in that respect.

What I don't see is any provision for sealing on your drawing. If there is some element of this associated with your plug/body connection in the area of the shoulder this could impact how that joint should be analyzed.

As a side question, why are you choosing to use aluminum for the plug as opposed to the same titanium material as the body. If this instrument is to be used in a saltwater environment then aluminum is a poor choice from a corrosion resistance standpoint. It is true that coatings or anodizing can help with its corrosion resistance, however, any damage to that coating due to handling can result in rapid corrosion particularly if your sealing method could allow accumulation in a crevice such as the cylindrical joint gap between the plug and body where moist salt can accumulate.

It may be a bit more expensive to use titanium for the plug but corrosion in this joint could impact its integrity and in the long run it could be offset by maintenance issues if this assembly will potentially need to be opened for repair to the instrument.

 

[thereddevil]

Wow, thanks! You seem to know your stuff so I'd like to pick your brains a bit more if that's OK. May I ask your background?

It passes compression and shear with the shear length being at a 45° angle. I've had doubts about calculating shear length as being a straight back through the plug as I don't feel that's how it would necessarily shear. Take a look at this pressure-rated connector, for example:
http://www.kemlon.com/catalogs/multipin/pmdm/diagram.jpg
The connector looks to have a load shoulder where dimension B ends. Therefore, would the shear length be to the o-ring or to the end of the connector and why? What if the o-ring gland was larger in diameter, when would you stop considering the o-ring gland as the shear path?

Since we've agreed that the two stresses are through compression and shear, surely this requires a compound analysis? Perhaps max principal/shear is not releveant for aluminium part (ductile), and a von Mises analysis required instead?

Other answers:
Sealing is done on an acrylic part further down the line - aluminium part won't see saltwater.
Aluminium chosen for anodising purposes - contacts electronic components.

 

[JBA]

I am familiar with connector designs from a period as a manufacturer of electrical control systems and multi-wire cable assemblies for oil well servicing companies.

Beyond that, the most pertinent segment of my background that applies to your application is the 20 years I spent in new product development and engineering for pilot operated high pressure relief valves for ASME Section VIII Pressure Vessel code services. During that time, a wide range of valve and their accessories were designed for system pressures up to 15,000 psig for service fluids ranging from corrosive fluids and gases to 10,000 psig systems for cryogenic LOX and liquid hydrogen for rocket engine test stands and 1000 psig, 1000° F service valves for super heated steam power generating plant systems.

For a connector with o-ring seals as shown in your diagram the shear length for the plug would be from the shoulder face to o-ring groove.

At the same time, the length of plug shoulder between the two o-ring grooves must also be analyzed for shearing stress based upon the pressure exerted by the first o-ring on the area from the o-ring groove I.D. to the body bore diameter as this is the pressure area that section of the plug will result in direct shearing from the o-ring pressure loading.

As to the need for a more rigorous analysis method, this simple loading configuration of this design reduces the need for the more rigorous approaches; however, if it makes you more confident in your design then you should perform any of those analyses you prefer. On the other hand, if there were an 0-ring groove a short distance behind the plug shoulder face; then, a more rigorous analysis would be justified (including FEA) because there is a potential for a contact loading gradient on the plug contact ring face that could result in an elastic radial bending stress on the ring from the shoulder I.D. to its O.D.

 

[thereddevil]

Thanks - you seem well qualified!

I do have good understanding of o-ring grooves and shear, the comment was more on what if the gland diameter was larger than the load shoulder bore diameter where the shear path would be at an angle, rather than straight through. What point would you include it as part of the shear path (up to 20°?) and what point would you just go straight through the back? Also, if we had an infinite length part, would you assume that the shear stress is 0, or would you look to angle as I have done? In this case I could increase the shear path to be significantly longer.

The shear question feels important here as this has a lot to do with the vector in which it acts. If I was to do compound analyses such as max principal, using a lower shear stress would reduce values significantly... Perhaps I need to take a look at FEA and see what I can get out.

 

[JBA]

A classic shear theory requires two stress vectors to determine the shearing stress, i.e a shaft with combined torsion and and tensile stresses as is often used for the illustrate the Mohr's Circle method . Since there is only one load vector longitudinal to the plug centerline then using an allowable shearing stress of 60% of the material's yield strength along the longitudinal plug axis is all that is required. From a practical standpoint, in your case, where the end of the plug at the shoulder is effectively constrained by the surrounding body counterbore, an angular shearing failure as you view it cannot occur.

If there is an offset in the o-ring I.D. as you describe there is still no discontinuity along the contact face as long as the body face remains solid so providing an adequate face bearing area and acceptable longitudinal shearing length from the shoulder face to the plane of the ring grove face should be all that is required; and, that length will also provide an adequate length for load transfer from the outer region of the plug face to the groove I.D.

 

[thereddevil]

Ahh OK, makes more sense now - I had assumed that because the part was sitting on a shoulder and subject to shear, you could use that as one of the load vectors, with compression the other. Is this 100% not the case then?

 

[JBA]

That is correct, there is only one load vector and it is longitudinal along the plug centerline.