FEM Contact Analysis Variables

[Stress_Eng]

Hi to all you FEA guys! Hoping you can shine some defining light onto an FEA aspect where I need to gain some more clarity.

The subject where I would appreciate your input is the FE analysis of pin loaded lug and clevis joints.

I've challenged myself to the task of creating a hand analysis template that calculates aspects such as the max principal and shear (tresca) stresses, and also the bearing contact loads for a lug. I would like to compare the output of my hand calculations to the results obtained from an FE analysis. This is a personal home project only, and as such I have no test data to compare to. My aim is to gain insight into the contact modelling of such joints, and to know that the approach I'm taking is relatively realistic.

Where I think I need more clarity is in the settings applied to the contact surfaces, in particular the pressure overclosure slope parameter 'k' given as N/mm^3 (surface contact stiffness). I'm using open source software to create the 3D model (FreeCAD) and to conduct the FE analysis (PrePoMax, version 2.2.0). The pictures shown are of the 3D model and the 1/4 FEM (grey lug, green clevis).



The FE models I've created consist of an Aluminum Alloy Lug and Clevis, with Steel or Titanium Pins. I'm also modelling different sized pins (same lug length). The pin diameter to lug width ratios are 0.25 (as shown), 0.50 and 0.75. PrePoMax uses the Calculix solver, and the 'k' values are based on the modulus factored by a value between 5 and 50. For the combination of materials, I'm using the analysis approach given in Roark, for two dissimilar materials in contact, to obtain a base-line modulus value. Some say to use a 'Hard' setting, although the 'k' value of which I don't know. Others say that a hard setting is too high and a lower value based on E should be used. In addition, some say that the 'k' value should be a function of E and thickness. I've tried a few variations. The max principal stress doen't seem to be too sensitive to the 'k' value, but the Tresca stress does vary somewhat.

Any input you can give would be much appreciated.

 

[FEA way]

There were some larger discussions about this parameter on the CalculiX forum. One good way to determine it is to use:

0.5*(E_stiff+E_less_stiff)/L_char

where L_char is the characteristic length (the typical length of the element edge at the contact boundary). This is usually adjusted in the case of convergence issues but it may affect the results significantly as well. Thus, it's good to have an analytical solution for reference.

 

[rb1957]

I think the idea to get FEA correlation with hand calcs (based on tests) is doomed to failure.

As a starting point I think the most critical dimension is the clearance gap between the pin and the hole, and I doubt if there is any data on this (recorded as part of the tests ... ie what is the exact dimension of the clearance (not what is could be based on tolerances)

Then there's local plasticity near the point of contact.

And all this for a very ideal load, so what about real world incidental loads ?

We have a reliable design guide now, based on previous testing. Sure we can get better at determining allowable lug loads ... but is this really where you want to improve the design ? Having a slightly overweight lug is in my mind a good thing (much better than a slightly under weight one !).

 

[Stress_Eng]

Thanks for your feedback.

Just some background info. Out of pure interest only, the task I set myself was to see if I could devise a hand analysis method from scratch that can estimate the kt factored max principal stress seen in a pin loaded lug. I must admit, the template has expanded somewhat. This was purely a personal investigative task only. These calculations are purely theoretical and doesn't include any test based information or any kt values from a book, etc. The approach is based on curved beam and non-prismatic beam theories. It includes calculating a displacement stiffness matrix (12x12 matrix, 12 placed point loads on hole surface with displacements at all other points), form which, when assuming the pin to lug hole contact displacement is sinusoidal in shape, I obtain a bearing pressure contact distribution. The displacement accounts for radial clearance between the pin and hole. I also use beam on elastic support foundation theory to calculate the non-uniform load distribution along the length of the pin, from the center of the lug to the end of the clevis. The max principal stress and shear are derived using a 3D stress tensor matrix approach. So, as you can see, the method is purely from 1st principals.

Bearing pressure distributions by hand analysis (shape functions). 0.02mm radial clearance affects contact, e.g. around 67, 75 and 83 degrees to end of contact for 0.25, 0.50 and 0.75 dW ratios (based on used geometry, materials and applied load).

Distributed loading by hand analysis along pin, dW = 0.25, Alu. Alloy lug and clevis, titanium pin.



For means of comparison, I decided to use FEA to model the same six lug joints (will adjust gaps, lug / clevis thicknesses, etc for variations later), to see how close my hand calculated kt factored stresses are to an alternative analysis. As you can see, the aspect within the FE modelling causing some confusion is the 'k' factor. Once I can calculate 'k' factors using recognized approaches, etc, I will then have more confidence in the comparisons.

 

[GregLocock]

I'm struggling with your 0.75 curve, why would a 'softer' foundation give higher peak stress bearing stress near the ends of the contact (ie at 80 degrees)? I'm guessing some sort of wedging action but it doesn't pass the sniff test. Or of course the lug itself is in tension at that point as shown in this random screenshot, but that is not the same as bearing pressure




To me the most interesting part of that pretty plot is the bulge in the outer profile. The same googleising gives me the impression that many people are assuming a cosine shape for the bearing pressure.

Of course if your FEA shows the same peaks as your hand analysis I'll have to eat my words.

Are you using this as a reference https://en.wikipedia.org/wiki/Bearing_pressure?

I'd have thought pin to lug bearing pressure distribution would have been measured long before FEA was around but must admit if there's any data it is hidden from me. Everyone seems more interested in rotating shafts. I guess that makes sense, static lifting lugs as rb1957 points out should be overspecced.

 

[rb1957]

Those bearing pressures ...

1) wow ! you can do that by a hand calc ? wow !
2) assume linear elastic material ? I'd've thought plasticity would rear it's ugly head pretty quickly ?

 

[Stress_Eng]

For the 0.75 dW lug, this is the contact bearing pressure I obtained. As you can see, it's relatively constant and locally peaks.




You can see the output for the bearing pressure calculated by the hand analysis method. It's taken to be uniform over the lug thickness.


It's just a confident 'k' factor would be good.

This is all based on linear elastic material.

 

[GregLocock]

I suggest you use much wider lugs (longer pins) to start with so you can ignore the funky end effects caused by pin bending in your FEA. Your FEA confirms the (in my initial opinion hard to believe) uniform pressure over much of the bearing, but does not agree with the spike at 78 degrees.

 

[Stress_Eng]

The FE model is 1/4 of the lug, so you're seeing 1/2 the lug thickness. This is the most current FE model version (done today with a revised 'k'). The position of the peak may be off, but the bearing stress level is quite close to the hand calc. The bearing pressure distribution for this dW ratio is a bit harder to profile, as the rate in change of bearing pressure is quite high over a relatively small angular range. My 12 x 12 stiffness matrix is based on 8 degree point loading steps. For more refinement, I'd need to reduce the angular step, giving a larger n x n stiffness matrix.



These are the Pmax and Tresca Shear FE results from the current version. With PrePoMax, the displayed Tresca Shear needs to be divided by 2. Below the two FE plots is the Pmax and the Shear from the hand analysis.





Hand analysis results for Pmax and shear stresses.

 

[SWComposites]

I have never seen a tested lug fail in bearing at the side of the hole. So a predicted peak bearing stress there makes no sense.

 

[Stress_Eng]

The purpose of my investigation is to try and predict the Pmax and to obtain the kt. I’m not trying to predict any failure mode, to do so would involve plasticity. A part of the approach was to first come up with the lug loading, just like a typical beam analysis. My investigation also involves 0.25 and 0.50 dW lug ratios, where the lug wall thickness is more significant. With a dW of 0.75, are we beginning to see a form of strap loading behaviour?

My interest now is to compare my hand calc results to an FE analysis. The aspect of the FE modelling causing some issues is the deriving of a confident ‘k’ factor.

Any help in calculating ‘k’ values involving 2 materials and lug geometry would be much appreciated.

 

[GregLocock]

You don't need k or thetamax if your FEA model is correct. They are outcomes, not inputs.


Typically a high dW lug would fail in tension at the end, Shirley?

Once the section 'thins' there's no load relief mechanism, the pin would just burst out like an alien out of an android.

Classic film night obviously.



And now Meatloaf joins in, 2 out of 3 ain't bad.

 

[Stress_Eng]

The k I’m referring to is the pressure overclosure slope factor (compression spring stiffness) used in FE contact analysis. I’m looking for an approach that will give more confident values.

When considering failure of a high dW lug, I would agree, you would expect tension failure.

 

[GregLocock]

Oh sorry, there's a k in bearing pressure distribution as well. Stuffing about with that penetration equation usually leads to tears.

 

[Stress_Eng]

Just as an indication, these are the current hand calc to FEA results (use of older FEA results).



The shear is seen to be more sensitive to the used k factor. At the end of the day though, all are affected by the k value.

 

[BlasMolero]

Hello!,
I have also "played" with a lug "invented" example using FEMAP trying to explain to our customers how to take advantage of the 2-D solid plane stress simplification in contact problems, also compare with GLUE effect:

• Tensión Plana (Plane Stress) con FEMAP y Simcenter NASTRAN

Cómo resolver un problema 2-D de Tensión Plana y comparar resultados entre GLUE vs. CONTACT No-Penetration En la vida real todo es en 3-D, cierto, pero mallar todo con elementos 3-D sólidos (tetrah…

iberisa.wordpress.com

Glue vs CONTACT, another world: this is to show FEM/FEA end user the effect of fully constraining holes, is the same ....

GLUE vs CONTACT resultant displacement results (mm) after performinn a linear static analysis using Nastran (SOL101):

And finally the vonMises stress results (MPa) in the LUG:

Best regards,
Blas.

 

[Stress_Eng]

Thanks for your interesting info Blas. The world of FEA seems to give you many ways to model lug joints!

 

[Stress_Eng]

Just as an update to what I've currently done to estimate a pressure over-closure spring stiffness value 'k', the info below is what I've come up with. There are a couple of aspects that I think has a big influence on the 'k' value. The 1st is the factor P_k. This is based on the assumed manner in which the compression field diminishes with radial distance through the lug and the pin. For both items, an enveloping radial length relative to the contacting surfaces is estimated (radially outward for the lug, and inwards for the pin from the surfaces). The 2.752 factor is the peak compression at the surface relative to the average. the l_lug and l_pin are the radial distances that are assumed effective in compression, for the lug and pin respectively (boundary conditions given). The R_jnt factors are the effectiveness of the pin in bending w.r.t the pin plus 1/2 the lug wall (fixed through vertical lug center plane) acting as a radially loaded cylinder (factor on distributed wall bending inertia, peak in axial direction (factor =1) and diminishing to zero at 90^o). A small flexible pin gives a low factor (< 0.3 / 0.4), from which the load in the lug wall is assumed to be highly concentrated at the lug walls. A large value (>0.75) indicates the lug wall loading will be more uniform through the thickness. R_e is an equivalent factor on the effective modulus. Well, that's as far as I've got so far. The results don't seem to look too bad (assumed hard for R_e > 50).