critical buckling stress for cylinder

[cylseal]

Can anyone give me the calculations (or send me to a site) necessary to compute the critical buckling stress for the piston rod of a hydraulic cylinder. I know I'll probably use Euler's formula, but I don't know what to substitute for the "effective length" and "k" values. I've looked in Machinery's Handbook and on the web - neither have proved to be very helpful.

Thanks,
Calman

 

[JStephen]

If the cylinder is fully extended, and if the top of the cylinder (IE, at the bottom of the ram) is laterally supported, you should be able to use the effective length as the actual length of the rod, with K = 1.

If the cylinder is partially extended, and if the top of the cylinder is laterally supported, you should be able use the effective length as the larger of the rod lengths outside or inside the cylinder.

If the cylinder is pinned at the bottom, ram is pinned at the top, and the top of the cylinder is unsupported, you'd need to consider the whole cylinder as a unit for the buckling analysis, and it won't be as simple as plugging numbers into a formula.

In either of the first two cases, Euler's equation may not do much for you. It is applicable to "long" columns, and hydraulic cylinders tend to be shorter. There are various sources for shorter column design loads, one source being a good Strength of Materials textbook.

In either of the first two cases, the design of the piston itself may allow you to consider one end of the ram as fixed or partly fixed, which would reduce the effective length.

 

[desertfox]

Hi calcultr

If you have a suppliers catalogue for the hydraulic cylinder they usually have a section on calculating their actuators buckling load. Failing that you could try contacting other suppliers by phone and asking them.
Last but not least with the cylinder fully extended I would assume an effective length of 2 this would be equalivant to one end fixed and the other pinned.


regards desertfox

 

[cylseal]

Desertfox,
When you say an effective length of 2, do you mean 2 times the cylinder stroke distance? Or 2 times the length of the rod?

 

[desertfox]

Hi calcultr

Provided that the cylinder is externally supported against lateral movement then I am talking about twice the rod length. Remember also to include a good safety factor as Eulers is only approximate and it assumes perfectly straight struts.

regards desertfox

 

[zekeman]

You have two ends pin connected, so the effective length is the rod length,i.e. conservatively the distance between the pivot points. The Euler formula is then
Pcritical=(pi)^2*I*E/L^2
where:
L=length
E= modulus
Pcritcal=minimum force in lbs for buckling

 

[Cockroach]

I just completed a 4.0 diameter hydraulic cylinder to 5.0 ksi maximum operating pressure. This gave an effective load of 55.3 kips forward, 46.7 kips in return, it was a bi-directional piston. Noting stability for the shaft at full extension, JStephen is bang on the mark. DesertFox is also correct with the end conditions as noted. The pin-pin condition implies an effective length equivalent to the unsupported extended length.

This isn't a particularly challenging problem. Keep it simple and carry a factor of safety over two (2). I found that making the shaft out of a super hard material, like chrome steel would allow for the end cap to be composed of and L80 type steel like AISI 4140/4130 HRc 18-22. This will reduce material transfer from pickup if the shaft is truly unguided, as in my case. I decided to case harden all wetted components by liquid nitration, keeping the free iron away from the fluid interface. This may or may not be important for you if you're going the stainless steel route.

Good luck with it. Oh yeah, my shaft was 1 1/2 diameter with a 12 inch stroke.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada