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.