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I am working on designing a pressure cooker. I've have tried to find, using two different models, the wall thickness based on the following assumptions:

  • Cylindrically shaped container

  • Made of stainless steel

  • Internal pressure of 20 psi

  • The internal pressure is what sets a lower limit on the thickness

From the two aforementioned models I have found a wall thickness of 0.1mm and 0.05mm respectively.

The wall thickness I get seems to be very thin. My guess is that the internal pressure is not what makes ordinary pots thick but actually it's the resistance to impacts occuring during regular usage that sets the limit on how thin the walls can be. Is this correct? Is there a rigorous framework for estimating the required thickness from this criterion? I haven't been able to find litterature on this.


The models are as follows:

Simple pipe: $\sigma=\frac{pR}{t}$

Annaratone: $s=\frac{p D_e}{2f+p}$

$p$ - pressure $R$ - radius $t$ - thickness $D_e$ - Outer Diameter $f$ - basic allowable stress

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    $\begingroup$ Showing the equations you used & you calculation would improve your question $\endgroup$ – Fred Apr 21 '16 at 0:35
  • $\begingroup$ You will need to look at two types of failure, in structural (buildings) engineering we refer to ultimate limit state and serviceability limit state. Ultimate is where your material fails. On the stress-strain curve of your material your point where your material no longer behaves elastically and deforms permanently. The other is where it elastically deforms due to load (pressure), but the deformation is temporary while the load is applied. For a pressure cooker it would be where your metal deforms to such an extent that either your functionality is impaired or your seals become compromised. $\endgroup$ – NamSandStorm Apr 22 '16 at 10:42
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Those figures are about right for the bare minimum wall thickness for the walls of a cylinder however, as you say, this would be inadequate in practice for a number of reasons.

  • Safety concerns dictate that steam pressure vessels are designed with a large factor of safety. You certainly don't want any sort of pressure vessel to be operating anywhere near the yield stress of the material.
  • The hoop stress in an ideal cylinder is one thing but the design of the ends (ie lid and base) also have a significant effect on the stresses and pressure on the ends will introduce tensile as well as hoop stresses to the cylinder walls.
  • Stress raisers from fittings, catches etc and manufacturing artefacts may cause local stress concentrations well in excess of the calculated figures.
  • The pot needs to be robust enough to stand up to everyday use and handling.
  • Even when the stresses are at an acceptable level deflections may not be, especially in terms of sealing the lid. To put it another way being strong enough does not guarantee that something is rigid enough.
  • Depending on the material, fatigue, work hardening, corrosion embrittlement, thermal stresses, etc etc may be factors.
  • From a business perspective it may be preferable to adopt a more conservative design in order to simplify quality control, especially where material costs are a small proportion of overall costs and the risks associated with potential liability or loss of reputation are high.
  • A product made from heavier gauge material may be seen as better quality by consumers.

EDIT

The criterial I have listed are, by their nature, a bit fuzzy. The general approach to this sort of problem is to first do your best estimate based on calculations of the conditions you expect in normal use and then apply a factor of safety. This makes allowances for uncertainty in your calculations, variations in actual material properties and wear and tear over the life of the product as well as unforeseen conditions (to an extent).

In general a larger factor of safety is used where you are less certain about your model either because comprehensive calculations are impractical or conditions of use are difficult to predict. Larger factors of safety are needed when a failure would have safety implications (eg for pressure vessels, lifting equipment etc) but can be mitigated by more rigorous quality control.

It is also worth noting that factors of safety for aerospace are often significantly smaller than for general structures despite the fact that aerospace requires very high levels of reliability and redundancy. The reason for this is that weight/mass savings are so economically important that it is worth spending a lot of resources in the design stage to achieve reliability by testing and very detailed analysis rather than just being generous with loading calculations.

By contrast if you are designing a bridge it usually works out cheaper just to err on the side of caution, especially as you are often choosing between standardised parts, or at least parts fabricated from standard sections rather than designing every single component from scratch.

It is good practice for pressure vessels to be practically proof tested at a pressure in excess of their designed operating pressure. In many cases this is a regulatory requirement.

Finite element analysis software can be a useful tool for optimising designs but it needs to be treated with care and an understanding of its limitations.

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  • $\begingroup$ Thank you for the very useful answer. Do you have equations I can use to translate these criteria into quantitative requirements? $\endgroup$ – user6195202 Apr 22 '16 at 10:23
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Assuming it is a typical "kitchen-stove-sized" pressure cooker, your wall thicknesses seem to be the right order of magnitude, for the cylindrical part of the cooker, if your criterion is "what is the minimum thickness to withstand the pressure". The flat base will most likely need to be thicker, otherwise it would bulge outwards under the pressure and become unstable. You also need to consider the stress concentration where the flat base joins to the cylindrical sides.

But those are not the only criteria. As well as impact resistance, you should think about other issues like "what would happen if the all the water is boiled off", "what would happen if the safety valve sticks and doesn't open", "what thickness do you need to ensure a good seal between the pan and the lid", "what happens if the seal fails when the cooker is fully pressurised", "what happens if somebody tries to pressurize the cooker using oil instead of water", etc, etc, (Note: those are results of a couple of minutes brainstorming, not an exhaustive list!)

Googling "pressure cooker safety standard" threw up this standard, which doesn't actually cover your specification, but might point you in the right direction to search further: http://ulstandards.ul.com/standard/?id=136

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