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Join Date: Mar 2007
Location: Glasgow
Posts: 14

### Calculating the Thickness of a Hydraulic Cylinder

04/07/2007 4:36 PM

hi

i want to design a piston pump, i want to know how i can get the thickness of cylinder, i have got the differential pressure in piston pump, and i know what the diameter of my bore is, would u please tell me the proper formula for getting the external stress on that is exerted on cylinder for getting the thickness of cylinder?

Best regards

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Guru

Join Date: Feb 2007
Location: Cairo, Egypt
Posts: 1746
#1

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/08/2007 3:54 AM

You can use the following equatin with a good accuracy:

t = P D / (2 S E) + CA

Where,

t = Nominal Cylinder Wall Thickness, Inch

P = Internal Design Pressure, PSI (at the most severe condition)

D = Cylinder Inside Diameter, Inch

S = Allowable Tensile Strength of Cylinder Material, PSI (at Design Temperature)

E = Joint Efficiency, dimensionless (E=1 in case of Seamless Cylinder)

CA = Corrosion,Erosion, Wear, .... etc. tolerances, Inch

Note : If the Cylinder is subjected to external pressure, you have to check the calculated thickness at that pressure using another technique)

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Guru

Join Date: Mar 2007
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#5

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/08/2007 12:25 PM

The equation you suggest is valid for "thin wall" tubes (ratio D/t>20) without axial load.

Depending on the pressure used and on the internal diameter the errors can be important especially if one will neglect the stress due to axial forces. For the allowable stress level one should consider the "transverse" value since tubing is not equal in axial and tangential directions.

There is one value I do not understand = the E-joint efficiency it is usually used for the computation of the diameter but not for the wall thickness. What do you mean by its effect?

In general you equation is used for low pressures and in (mostly) reservoirs for pneumatic systems thus the CA since humidity leads to corrosion.

It can be also considered for rams in agricultural environments but is not usual in einteg civil eng. or industrial systems.

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Join Date: Feb 2007
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#7

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/09/2007 1:43 AM

Dear nick name,

The equation shown is for longitudinal joints (circumferential or what we called "hoop stresses" resulting due to internal pressure) which are the most severe stresses compared with longitudinal stresses.

Note : In case of circumferential joints (longitudinal stresses) : t1 = P D /4 SE + CA, and it is easy to find that t = 2 t1 by neglecting CA.

According to ASME Code, Section VIII, Division 1, the equation can be applied up to : t <= D/2 (not D/20 as you mentioned), or P <= 1.25 SE.

Otherwise the equation for "thick wall tubes", can be applied in accordance with ASME Code.

Can you please provide me the name of Code which states the condition of D/t > 20?

I prefer to select a Design Code and apply its rules and recommendations. For E, refer to ASME Code. Also refer to ASME Code to find S (allowable tensile strength of tube material).

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#10

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/09/2007 8:04 PM

Dear Mr. Galala,

I understand your position and it is some times better to use codes. But as you very well know codes are for specific applications and not always extrapolable. I never saw in a code for stress calculation the mention that the gap in apump can be so big due to pressure that the seal will be extruded. This a specific requirement for stiffness calculations. Being a designer in hydraulics for many many years I came, due to own expereince to some results. I use usually codes there wher my experience is not good enough and need a solution even if not optimal. Codes are recommended to avoid errors and are very good in fields where they are thought for and guide lines in other simmilar fields but not always optimal.

I use this opportunity to make some comments on the efficiency problem made by a guest. I do not know where the cylinders he gets come from but during last 10 years due to research efficiency went bery high even in high pressure applications. Sealing is no more a problem with compounds very performant and as well low wear as low friction. Stick-slip is in many servocylinders not any more present.

By the way you did not explain (or I did not notice it) why you introduce an efficiency factor in the wall thickness equation. I would very much like to understand it.

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Join Date: Feb 2007
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#12

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/11/2007 6:48 AM

Dear nick name

Thank you for your question related with factor E.

E is a Joint Efficiency multiplied by S (allowable tensile strength) to lower the allowable tensile strength of cylinder material. E depends on if there is a seam weld (longitudinal weld) in the cylinder or not. If yes, did you radiographed that weld or not. For each case there is a different value for E, but in no case E >1.

Also E may be specified as Casting Quality Factor with a symbol "F" (instead of E) which depends on the type of cylinder material and its procedure of production.

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Guru

Join Date: Mar 2007
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#13

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/11/2007 7:02 AM

Ok

It was a misunderstanding since efficiency has different meanings. I agree that for tubes a sensitivity factor for the stress calculation has to be considered. I call it differntly but the meaning is the same. In general cyliders have welded bottoms but are not made from welded tubes. On the contrary reservoirs with exeption of accumulators are made from welded steel plates. It is interesting to notice that when the standard for "pressure vessels" it was a discussion which lead (at least in europe) to the result that cylinders should not be designed according to same rules.

The trend is to use DOM tubes for tighter tolerances and a more uniform structure. In fact as long as one is concerned by cylinders there are all over suppliers for already honned tubes at standard diameters or able tu supply honned tubes at special diameters.

Thank you for the details.

Commentator

Join Date: Sep 2006
Location: Wimborne, Dorset. UK.
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#14

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/11/2007 8:26 AM

Just for reference, Roark's Formulas for Stress and Strain, 6th edition, article 12.6, states the following:

"Thick Shells of Revolution. If the wall thickness of a vessel is more than about one-tenth of the radius, the meridional and hoop stresses cannot be considered uniform throughout the thickness of the wall and the radial stress cannot be considered negligible. These stresses in thick vessels, called wall stresses, must be found by formulas that are quite different from those used in finding membrane stresses in thin vessels."

I know that Roark's is not a code in the same way as the ASME B&PV code is, but it is a recognised source and illustrates the point being made in #5

Participant

Join Date: Feb 2010
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#20

### Re: Calculating the Thickness of a Hydraulic Cylinder

02/27/2010 10:30 PM

Dear Mr. Galala,

Could you, please, send me the allowable stress for the SAE 1026 steel

(Yield strength=74,800 psi; Ultimate strength = 93,500 psi)

Best regards

Commentator

Join Date: Feb 2008
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#17

### Re: Calculating the Thickness of a Hydraulic Cylinder

08/11/2008 6:46 AM

Huh? You got it all wrong. This is only for thin walled cylinders like pipes!

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Anonymous Poster
#18

### Re: Calculating the Thickness of a Hydraulic Cylinder

01/05/2010 1:07 AM

hi dear

i want this formula in (SI)

thank you alot.

best regards.

Anonymous Poster
#22

### Re: Calculating the Thickness of a Hydraulic Cylinder

10/15/2010 2:12 AM

could you plz tell me is there any reference book is there book hydraulic design components like cylinder,pumps etc. because i hav searched but still i m not getting it. so help me out. from bgmpraveen@gmail.com

Off Topic (Score 5)
Guru

Join Date: Mar 2007
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#2

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/08/2007 6:15 AM

Look for the Lammé formulas (use google for it). Take care to consider the equivalent von Mises stress and allow a safety coeff. of at least 2 to the yield limit of the material you use. Depending on your concept it could be needed to design the wall not for stress but for stiffness. That means that under pressure you have to limit the radial expansion of the cylinder. The same series of formula give also a relationship between expansion (radial) and pressure. Do not forget to consider the axial force as well it has an increasing effect on stress and decreasing on expansion. The above mentioned formulas are only for the elastic domain and materials with a symmetrical behavior in tension and compression (same Young modulus).

Power-User

Join Date: Feb 2007
Posts: 274
#3

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/08/2007 10:25 AM

Why is everyone trying to re-invent the wheel? Or in this case the pump?

"GOOD GRIEF!" as Linus would say.

There are over 10,000 existing pump designs out there. Instead of wasting time and money use your brain, your computer and a "Search Engine" like Google, MetaSearch, etcetera, and look for the pump you need.

Try being a little self-sufficient.

Guru

Join Date: Oct 2006
Location: Philippines
Posts: 2021
#6

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/08/2007 10:09 PM

He didn't say, specifically.

Perhaps as an exercise? A hobby? A brain challenge? He wants to make his own product? Maybe he's got no money to buy an off-the-shelf piston but he's got a solid piece of metal, a lathe or CNC machine and he wants to do it himself. Or he just wants to learn how it's done.

There are all sorts of reasons. Who are we to judge them?

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Anonymous Poster
#8

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/09/2007 11:25 AM

Because

1. Cylinders and pumps are more complex machines then wheels.

2. The current cylinders are not efficent enough.

3. New materials and processes are now avalible to increase efficiency.

4. That is what engineers do. If you are satisfied with the current state of technology then being an engineer is a poor career choice. Mabey you should be a truck driver of fireman or something.

5. The question was not "find me a catolog of pumps", it was "what is the design criteria for a cylinder/pump".

Guru

Join Date: Oct 2006
Location: Philippines
Posts: 2021
#11

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/09/2007 10:45 PM

That's not what I meant.

If a guy wants to build his own equipment, learning as he goes, he still needs to know certain things and he would be right to ask help. If he wanted to buy it, he wouldn't ask how to build it.

Some people learn how to assemble their own cars with or without an engineering degree. Some of them do it well, and some of them make a mess of it. That's how they want to learn.

Telling him to go and just buy the thing is okay. Telling him how to do it is okay too. Have you helped him to learn?

'Careful about what you say about truck drivers and firemen. There may be a couple of them here.

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Associate

Join Date: Dec 2006
Posts: 48
#4

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/08/2007 12:10 PM

this is a simple problem, which can be addressed by referring to Strength Of Materials Book by Morley or Timoshenko.

If the diameter is small and pressure is not too high (say 100- 200psi), than it can be treated as a Thin cylinder and if the pressure is high enough (say in excess of 500 and above psi.) than this can be treated as Thick cylinder. The pressures given are approx. only for guidance which you should take from the books given as above.

You refer to the above books or any other known text books, which should cover above topics in detail. Here, in case of Thick cylinder is required, you have to calculate with Lame's formula with appropriate units, or you may use a suitable selection chart for a given material of construction required, which the manufacturer can help. Hope this will be a help in someway towards your exercise at hand. In some cases there are ready-made Nomograms available, for such solutions which are quick to use and good enough for the answer.

Anonymous Poster
#9

### Re: Calculating the Thickness of a Hydraulic Cylinder

04/09/2007 11:43 AM

It may seem simple enough, but by using a mechanics of materials "simplified and idealized" method your error can be relativley high. I think that mabey the Theory of Elasticity would be a good place to start. If this theory is used "thick" and "thin" wall sections are absorbed into the whole equation. This is how Lame first came up with the equations that he did. Most basic Strengths of Materials text do not include anything on the theory of elasticity. I would recommend Advanced Mechanics of Materials By Cook and Young.

Anonymous Poster
#15

### Re: Calculating the Thickness of a Hydraulic Cylinder

10/13/2007 6:31 AM

hello sir

i want to know that if id & od are given and also pressure , then how will we able t calculate the wall thichness

Anonymous Poster
#16

### Re: Calculating the Thickness of a Hydraulic Cylinder

10/13/2007 6:43 AM

hello sir

we have to design a cylnder of working prsssure 250 bar , cylinder id is 200, cylinder od is 245 , load on cylinder is 80 ton , holding time of cylinder whle working is 12min to 15 min

sir plz advice us that will a thickness of 22.5mm will be workable(material is st52)

thanx regards

Anonymous Poster
#19

### Re: Calculating the Thickness of a Hydraulic Cylinder

01/20/2010 7:29 AM

shigyld book explained this problem for either thick or thin walled cylinders :)

Anonymous Poster
#21

### Re: Calculating the Thickness of a Hydraulic Cylinder

09/07/2010 4:29 AM

Hi

MY NAME IS RAJ AND I AM IN HYDERABAD INDIA. WE MANUFACTURE HYDRAULIC PRESSES. I GOT AN ENQUIRY TO MANUFACTURE A 750 TONS HYDRAULIC PRESS. I INTEND TO USE A 600MM BORE CYLINDER AND WORK AT 250 BAR. FOR SAFETY ASPECT TAKE 300BAR (4500PSI). I WOULD LIKE TO KNOW WHAT SHOULD BE THE WALL THICKNESS OF THE TUBE AND WHAT SHOULD BE THE THICKNESS OF THE CAP OF THE HYDRAULIC CYLINDER. PLEASE HELP ME IN THIS REGARD.

Thanking you and warm regards

raj

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Guru

Join Date: May 2008
Posts: 1667
#23

### Re: Calculating the Thickness of a Hydraulic Cylinder

08/22/2014 1:08 PM

Dear Mr.mrezazaeemi,

During our Engineering College studies, in Applied Mechanics subject, we studied that the formula for calculating thickness for a cylinder is (p x d)/ x 2t = Fs

where p = pressure in psi, d = dia of cylinder in inches, t = thickness of cylinder, Fs = stress permissible.

DHAYAYANANDHAN.S

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