Hydraulics - Derive sideload from cylinder buckling under compression ?

[JMEthier]

Hello fellows, first post here so please be indulgent

I am working on a hydraulics calculation. The application is a compactor. The piston rod develops an axial force and sees a compressive load which creates buckling. The buckling generates a deflection, which in turn creates radial load at the cylinder head. See the attached sketch.

I'm trying to determine this radial reaction as a function of the compressive load (i.e. as a function of rod extension).

I know about Euler beam columns theory, but I just don't see how I can relate to it to calculate the reaction at the cylinder head. In my case, I am not so interested in the critical load Pcr, but more on the reactions generated on the piston rod, in the assembly...

I can determine the max deflection under the compressive load (which is known), and then what ? This is where I get lost.

Thoughts?

Many thanks

Jean-Michel

 

[desertfox]

Hi
Well you haven't supplied any forces or dimensions on your sketch, however the cylinders are two force members so draw a vertical load at the rod end of the cylinder which represents half the compacting block load or mass, draw a line from the end of the vertical line drawn previously at the angle of the cylinder, then complete the triangle with a horizontal line from the opposite end of the vertical load line, this triangle will give you all the forces acting at the rod end.
If you look up triangle of forces in any mechanics book you will understand what I mean.

 

[Dougt115]

side load = Compressive load / Tangent theta

Theta = atan (cylinder height/ witdth)

If you want the loads on the pistons use Compressive force/ sin theta then divide by 2.

 

[JMEthier]

Hi again,

Thanks fo the info. I realize my sketch was lacking some details, sorry for the confusion. I uploaded another sketch for your curiosity.

The assembly is viewed from the top. I added quick FBDs on page 2, and page 1 shows the forces I am trying to evaluate in a free body diagram of the piston rod alone.

@Desertfox, thank you, I am familiar with triangle of forces. However, I am interested in the reactions on the rod inside the piston assembly, not only at the blade attachment.

@Dougt115, Thanks for your insight, altought I am not quite sure how you got to these formulas.

Since the two reactions in X and Y at the blade attachment are equivalent to the axial force of the piston, they cannot create a bending moment at the cylinder head, right? Or I mean, their momennts will cancel each other, for any value of theta. That is what made me think about buckling generating sideload on the rod... I will look further into it, but if you see some basic flaw in my analysis, your comments are more than welcome.

Thanks

 

[JMEthier]

Forgot to mention the pistons are pinned at both ends. But you probably figured this

 

[desertfox]

Hi

Provided the cylinders pivots on the lower pin and the piston retracts into the full bored portion of the cylinder then I agree with you there can be no moment on the cylinder, again I don't know how much stroke of the cylinders are being used or the start nd finish position but there must be limit on he movement because the mechanicl advantage of the cylinders diminishes the closer they get to horizontal.

 

[Dougt115]

Use a free body diagram to get the forces.

Sum of the forces in the vertical direction are the cylinder and the pistons*sin of the angle. The angle can be determined from the width of the cylinder and the height of the piston above the bottom pins of the pistons.

The Fx force can be found from the Tangent of the angle (same angle as before).

Moments will occur in the pistons if there is any miss-alignment, which there will be some, because nothing is perfect. OR friction in the pivot pins.

Be careful of the buckling equations textbooks assume a flawless column and nothing is flawless.

 

[JMEthier]

Thank you for your answers, your help is much appreciated.

@Dougt115, You described the way to calculate the reactions Fx and Fy. These two are equal to the hydraulic force (in theory). So the radial loads in the piston assembly (on my previous sketch, F_head and F_piston) can only be caused by misalignment, friction in the pins, and buckling of the rod. Correct ?

I'm trying to figure those two forces, but I have a hard time wrapping my head around the link between deflection caused by buckling, and radial loads the cylinder gland.

Cheers

 

[desertfox]

Hi

What is the minimum and maximum angle the cylinders are operating over.

I think your attempting mission impossible but if you want to calculate misalignment then start looking at all the detail drawings and perform some tolerance stacks, that's the only way you will calculate misalignment.

We still have little to go on however looking at that plan view I think the design might be improved by placing one cylinder centrally and connecting to a scissor type mechanism to get your movement, that way the cylinder is merely extending and retracting.

 

[JMEthier]

The design of the application is fixed by the client, so I cannot change that.

The sketch is not to scale. The angle between the piston and the horizontal X axis varies from 45 deg to 65 deg from closed to fully extended position. The effective stroke lenght is 52 inches. Extension cycle time is about 9.5 seconds, and the operating pressure is 2500psi. The piston diameter is 4.5 inches, and rod diameter is 3 inches.

As you suggested, I already calculated a max rod misalignement of 0.25 deg, based on tolerance stacking (widest grooves in cylinder head, smallest diameter of wear bands, etc).

I agree with you that it might be mission impossible... Free Body Diagrams won't help me figure out the forces at the contact between the piston and the bore, and at the contact between the rod and cylinder head (sealpack).

I know I can get a max theoritical deflexion from Euler columns buckling. From this deflection then I may be able to calculate a localized stress at the cylinder head, since the rod is radially constrained at that point. Although I'm not sure how I would go about calculating that.

Thanks for your input.

 

[desertfox]

Hi

The misalignment you've calculated I presume that runs downwards in your plan view drawing by that I mean into the paper as you view from the top?

How are the cylindr controlled position wise and what does the compactor unit run on guides, rack and pinion?
The problem I see is the cylinders getting out of step so that one will drive till it gets stuck and then the will have to catch up with it, so I see that box shape unit staggering up into position instead of a nice smooth movement.

Just going back to the cylinder alignment have you contacted the cylinder manufacturers about alignment and offset loading?