Buckling of rod with varying diameter (stepped)

[dubc4]

I would like to know the best method of calculating critical buckling force on a rod of varying diameters. I have a hydraulic cylinder rod that steps down to a smaller diameter (undercut) for the threaded end. Previously we have had rod failures at this undercut.

Currently I'm using the smallest diameter with the overall length of the rod (in Euler's buckling formula) to determine a conservative critical force. I'm not sure if this is the best approach.

Any suggestions would be appreciated.

Thank you

 

[racookpe1978]

Did you include the moment force as well? Or just a "pure" linear force down the whole piston as if there were no friction on both ends of the actuator?

 

[dubc4]

I did not include the moment force.

I basically used Euler's formula F = [n * (3.14^2) * E * I] / (L^2)

Where n = 2 for the fixed/pinned condition.

 

[robyengIT]

try Roark's formulas for stress and strain (7th edition) Chapter 15 Tables 15,1

 

[Tmoose]

Does it mount with a clevis or an eye at either or both ends?

Is the "threaded end" at the mounted end? Is the cylinder rated for that type of loading?

Or, is the "threaded end" inside where it might attach to a piston?

Do you have some pictures of the fialure fracture faces?

 

[Jboggs]

dub, My 41 years of experience tells me that this is almost surely a bending moment failure rather than a buckling failure. Is the cylinder horizontal or vertical? How is it mounted? Pivoted or fixed? What is the bending moment from its own weight on the rod connection? Is the load guided? If so, is the connection to the load floating or fixed? I have seen SO MANY cylinder failures over the years that were directly caused by improper initial design and incomplete understanding of the forces involved. A sketch might help.

 

[dubc4]

Thank you for all of the fast replies.

The cylinder end is mounted on a clevis. The rod end (threaded) is mounted with a rod eye/pin. The cylinder is mounted on a 5 degree incline from horizontal.

The rod end is pushing a lever so it is guided in that sense. However, the piston stroke is roughly 30mm and the arc diameter that is travelled is large in comparison, so I approximate it's condition as a linear motion (maybe an incorrect assumption?).

I can try and get a sketch tonight if this is unclear.

The force required to actuate and move the lever is small under normal conditions so the compressive force is not normally a concern. However, two factors come into play that I have to design around. First, our hydraulics engineer has advised me that he cannot limit the pressure in the cylinder too much. The application requires speed and if the set point for pressure is set too low, it affects how the pressure ramps and it will slow cycle times down. So naturally I would like the piston to bottom out on the end of its stroke and the compression will not be translated to the rod at the end of the stroke. However, if the lever becomes seized or stuck through it's travel, this is my concern. The full force will be transferred to the rod and we will have a potential failure from either buckling or bending as suggested.

 

[rb1957]

could it be a bending failure due to buckling (or extreme lateral displacement) of the column ? ... if the sections are co-axial then there`d be no bending in normal loading, but if the piston bows under compression load, then there'd be bending on the section.

another day in paradise, or is paradise one day closer ?

 

[desertfox]

Hi

Here is how the cylinder manufacturer recommends how to calculate cylinder buckling

http://www.boschrexroth-us.com/coun...ducts/02_cylinders/a_downloads/9535233846.pdf

See page 19

I think a sketch or photograph of your situation would help get better answers.

Do you have any parts of the previously ailed cylinder a photo of them would also help

 

[3DDave]

Two items pop out. The first is that buckling is an elastic failure mode that transitions to plastic failure/fracture. If it is breaking at the step before the rest of the rod is bent, then it's probably not buckling.

The second is the 30mm of travel. How small is this rod and what side loading is being placed on it? Even with no moment carrying attachments, there can be significant inertial loads.

 

[rb1957]

"So naturally I would like the piston to bottom out on the end of its stroke" ... that might make your component "work" better (ie easier to analyze) but i`m sure your hydraulics engineer will have a kerniption !

another day in paradise, or is paradise one day closer ?

 

[dubc4]

I've attached a picture and hopefully this will show the operating conditions more clearly.

The rod is 12mm in diameter and steps down to roughly 9.5mm at the undercut before the threaded section. The cylinder will see max 180 bar and the piston diameter is 25mm

We have not had any failures with this exact set up, however, in a similar application we have had rods break. The similar application actually had a shorter rod extension (different size rod/cylinder combination and longer travel, more of an arc). We are now reviewing this design to be sure it will not fail.

 

[boo1]

don't forget the stress concentrations

 

[Jboggs]

Misc. Thoughts: First, when I hear "high speed" I think high accel/decel and shock or impact loads. Two, bottoming out on the piston is RARELY a good idea. Does the cylinder have built-in cushions? Three, I see a long distance from the cylinder pivot to the lever connection. This is effectively a beam. As such it has a bending moment transmitted thru its full length. That means that the threaded connection at the rod end is indeed under a bending load, maybe a significant one. You have the weight of the cylinder plus the weight of the connecting tube all concentrated at that point.

One way to calculate that would be to visualize the cylinder and the tube connected and resting on a single support point right at the connection. How much moment is created at that point by the weight of the tube? How much moment is at that point from the weight of the cylinder? Add them together. Now throw in repetitive shocks from high speed stops and the effects of the stress concentrator at the thread root, and you have a recipe for eventual failure. Find a way to eliminate that moment and I think you might eliminate the problem.

 

[rb1957]

is it a fatigue failure ? or fracture ? where is it failing ? the rod at the uncut ? the tube section ? the clevis ends ??

is 180 bar a huge pressure ? it sounds huge to me ... 1 bar = 15psi (near enough) ... no, 2700psi isn't huge, about 2000 lbs load ...

another day in paradise, or is paradise one day closer ?

 

[desertfox]

Hi

Why does the pin at the cylinder rod end fasten with its pin at 90 degrees to all the other pins?

Whilst the link is a two force member as the cylinder operates I can see a bending moment occurring at the threaded end of the cylinder before the whole cylinder starts to rotate about the rear Clovis.
I think you should have the pins in the connections in the same orientation.

 

[rb1957]

i've seen this configuration before ... the strut on a Twin Otter wing; just saying that this isn't 'Rong.

another day in paradise, or is paradise one day closer ?

 

[Jboggs]

Except that the strut on a Twin Otter wing is in tension!

 

[rb1957]

the strut is in tension in-flight and compression on the ground (and some flight manoeuvres), but yes the maximum load is tension (and so fatigue allowables dictate the design)

another day in paradise, or is paradise one day closer ?

 

[dubc4]

Thanks again guys.

I was not very involved in the failure analysis of the similar application. I was told it failed in buckling so this is the information I initially used to approach this problem. Obviously there are many possibilities so I think the failure should be revisited.

desertfox, I'm not sure what you mean by the pin holding the cylinder being 90 degrees to the other pins. All of the pins that any of the components pivot about are all parallel.