I still remember all these pressure tables for the metric pipes that we used for our "hydraulic needs". Choosing the right pipe was a simple process of looking its rated pressure up. Very simple. But when I transitioned to hydraulic cylinders - I found it very strange that we didn't have similar tables for the honed tubes that we stocked.
I did talk to our designers about it, and I was shown a very old engineering standards book (yellowish pages and all) with some pressure charts, but... something was not adding up. At least in my head. For example - one of the tables indicated the max allowable pressure of 130 bar for the 80x90 metric cylinder tube, and yet I saw many "economically designed" log splitters push such tubes up to 200 bar, and the cylinders weren't exploding! Obviously, I wasn't seeing the whole picture.
So, this is what I will be talking about today - the definition of maximum allowable pressure for a given cylinder tube - a "simple" topic, that is, actually, not that simple at all, but I will "dumb it down" (to my level). Should be helpful to those who can relate to my "greenhorn doubts".
The idea is actually pretty straightforward - whatever material a tube may be made of, it will have the physical properties called yield strength (the maximum stress it will tolerate before plastic deformation) and ultimate tensile strength (the maximum stress before rupture). So, if you have a way of calculating the pressure-induced stress in the tube wall, you can figure out the pressure at which the deformation (ballooning) of the tube begins, and then get the maximum allowable pressure by applying a safety factor suitable for your application.
The biggest stress in a cylindrical pressurized vessel is the hoop (a.k.a. tangential) stress, and several generally accepted formulae are used for its estimation. But the two most common ones would be:
The Barlow's Formula:
P = 2ST/D
where S is the stress, T is the tube wall thickness, and D is the tube O.D.
and The Lame's Formula:
P = S((D2 - d2)/(D2 + d2))
where S is the stress, D is the tube's O.D., and d is the tube's I.D.
If you want to "dig deeper", you should look into the DIN 2413-1 and DIN 2413-3 standards for calculating working pressures for steel tubes in static and dynamic applications, and you will see that Barlow's formula is "slightly tweaked" for dynamic applications. Parker did a good job summing it up in their catalog on tubes ( CAT/4041-2/UK, page 7). Go through it when you have time, it's good stuff.
Now, to determine the strength of the material your tube is made of, you need to understand that the strength of a tube is defined not only by the steel grade but also by the mechanical and thermal processing it went through before shipping.
For example, the E235 steel (E for "engineering steel", 235 for 235 MPa yield strength), which is a common low-cost carbon steel used for hydraulic piping, can actually have its yield strength vary from 200MPa to 350MPa, depending on its delivery condition. The most common E235+N (normalized) pipe for hydraulic applications has a yield of 235MPa, but an E235+C (cold-drawn) pipe would be stronger (yield of 300MPa), but then also less ductile - something that is not very desirable for a pipe that is supposed to be bendable.
You can find nformation about the European steel grade standards (and what all the letters mean) here, and you can see how the steel properties vary according to their conditioning codes here (type in "E235", for example).
Your best reference for the strength is the catalog of your tube supplier, and you should always look it up. (You know what I think about catalogs and their value, right?).
Let's take a known European manufacturer - C.M.C. ITALIA S.r.l. Here's their product catalog. You can see that they manufacture their cold-drawn seamless tubes for hydraulic circuits from E235+N, which means that you would use 235MPa in your pressure calculations. Then you can see that they manufacture their H9/H10 honed tubes from E355+C (C for "cold worked"), with the declared yield of 540 MPa (!), and their H8 tubes from E355+SR (SR for "stress relieved"), with the declared yield of > 520 MPa. That is some strong tubing!
Let's take another manufacturer - ASO H&P. Here's their product catalog. One of the "nicer" things they manufacture is the O.D chrome plated and I.D skived and roller burnished tubes - something one would use in a telescopic cylinder - the type of cylinder with the biggest pressure concerns because most of the time these cylinders use sections with pretty thin walls.
You will see that they use the E355+SR (SR for "stress relieved") steel for these tubes, with a respectable yield of min. 420 MPa.
I guess what I am trying to say here is that the determination of the maximum allowable pressure for a cylinder tube is a three-step process, in which you:
1) Consider the tube material.
This is the step where you discover "what you paid for" by studying your supplier's tech docs (which is, once again, a great learning experience on its own).
2) Consider the application.
This is the step in which you carefully access the application and decide on the "pressure risks" that you are willing to take. Is it an outrigger of a stationary platform, of a log splitter, that will never go beyond the relief valve setting, or an excavator arm cylinder that will be subjected to all sorts of pressure spikes (and possibly direct impacts as well)? In other words - you determine the safety factor.
Other things to consider in this step:
Most tube batches have eccentricity, which means the wall may be thinner than you think. Check the specs and solve for the worst-case scenario.
A thinner cylinder wall, even if it's capable of taking the system pressure without permanent deformation, will still balloon out under pressure, and to a higher degree than a similar cylinder with a thicker wall. This means that this tube will have a bigger chance of fatigue failure, which can be an issue for cylinders with frequent cycling.
What should you do then?
You should apply what I like to call the "conservative safety factor". Three or more. The safer the better, in my opinion.
3) Do the math and get the numbers.
I built a small calculator for that. It uses both of the formulae. Do bookmark and use.