Learning Forum

[onedream97]

Hello!

For one of my FEA assignments, I have to model the Hertzian contact stress in two cylindrical elements that are in a line contact as can be seen on the picture below. The stresses have to be verified under two conditions, one is normal loading and the other one is tangential loading. Dimensions of the cylinder do not matter and the material to be used will be steel (AISI 52100).

 

We can simplify the problem to a 2D setting, so we can consider something like this:

Sadly, I have no idea on how to start this problem. I am not familiar with the different kinds of contacts in Ansys, since I am just a beginner ^^" Could you please help me out and tell me how to tackle this?

I'm also specifically interested into how to set the meshes, how to apply the force and support at just one point on the outer edge of the cylinder, how to set contact and analysis settings.

If I described something unclear, or if you need more details, please let me know
Thanks a lot in advance!

[peteroznewman]

Hertz contact stress is very localized, so you don't need a full cylinder, a half cylinder will do. That creates a new face to hold onto on the bottom and to push on the top.

A 2D plane strain model is a good idea, the half cylinders become half circles. Another good idea is to use symmetry. Cut the half circles vertically into quarter circles. Now the symmetry boundary condition will keep the two parts on the centerplane.

In Workbench, change the Analysis Type of the Geometry cell to 2D.  2D models must be drawn in the XY plane. Draw two quarter circles tangent to one another.

When you open the geometry in Mechanical, click on the Geometry branch of the outline and in the Details, choose Plane Strain.

Use a Displacement Y=0 on the bottom edge of the bottom quarter circle.  Use Displacement X=0 on the two vertical edges. This is the symmetry condition for this 2D model. Apply a Force on the top edge of the top quarter circle.

Add Frictionless Contact between the circular edges.

Use a very fine mesh to resolve the stress below the surface at the point of contact. There is a Mesh control called Sizing using Sphere of Influence. First create a Coordinate System at the point of contact (unless that is the Global Coordinate System).

[vkm120991]

Hello Peter. 

As always, thanks for your great contributions.

Just wanted to know your thoughts (with respect to my response in this thread) regarding 2D approximation for cylinder to cylinder finite contact length.

[onedream97]

Hello,

 

First of all, big thanks for the advice! I have tried implementing all you said, but somehow my cylinders seem to be sliding over each other... Any ideas how this is possible? Maybe a wrong contact?

 

Thanks a lot!

[peteroznewman]

Set the Result to 1.0 (True Scale)

[Niazi]

May you give me email please?

[marco.ballotta.2]

Hello,

I know it has passed some time, but I am also interested in this case.

Do you have an analytical solution to compare the Ansys results?

Thank you

[vkm120991]

I've been looking to understand Hertzian contact recently and here are my personal suggestions/thoughts: 1. Hertzian contact calculations depend on type of contact. Two spheres in contact have a point contact and have different contact area approximation and hence different analytical derivation. The contact area is an ellipse. Two cylinders in contact have line contact. The contact area approximation is a finite rectangle and this directly depends on length of contact. The contact pressure also depends on contact length (engagement length between cylinder, in case one cylinder is longer than other). As such, I'm thinking it may not be accurate to model a 2D problem for cylinders in contact. 2D approximation works well with spheres in contact though. 1. The most comprehensive analytical understanding on the subject is from "Boresi-Advanced Mechanics of Materials chapter 18". 2. A sample Hertz contact ansys problem with analytical validation is available free here: /courses/index.php/courses/hertz-contact-mechanics/ 3. There are many research papers which approximate Hertz theory for contact problems like gear teeth contact. I found them helpful. 4. Here is a direct useful calculator online: https://www.mesys.ag/?page_id=1220 [I verified this online calculator with research papers cited above and also with the example cited in #2 above. you can also verify how the output is different when you select 'sphere-sphere' and 'cylinder-cylinder' for same dia of spheres/cylinders. Hope you find this helpful.