you can find a short description about this concept in the paper 'USE OF “CONTACT” IN MULTI-BODY VEHICLE DYNAMICS AND PROFILE WEAR SIMULATION: INITIAL RESULTS'. Hope it is helpful.

Thank you, Mr. Liu. In that paper just it is indicated that the equivalent elastic method is based on the work of Kik and Piotorowski. I am looking just for some detail, but it seems that I can not find.

Thank you, Mr. Burgelman. I have already looked at your PhD thesis.  Actually, I was looking for the details of the contact search method used in Simpack. The only thing that I can find is the paper that Mr. Liu indicated. There is written that Simpack contact search is based on Kik-Piotrowski method. I have already applied it (rescaling Hertzian contact based on virtual penetration) and the results I found are closer than before. However there is still some difference in the results. I think it is caused because Simpack uses different contact locus search and there is no detail how Simpack finds contact locus.

I am comparing the results for zero yaw angle.

Dear Mr. Burgelman,

Thank you for your intererst and concern.

Actually , I am not using penetration zone during contact search. I am using the quasi-elastic contact search method. Details of the method already reported in "Modelling the Contact between Wheel and Rail within Multibody System Simulation". After obtaining Hertzian contact (meanwhile I am calculating the penetration by using theory of Hertz), I am rescaling the contact by using Kik and Piotorowski method.

Overlay is not problem as I am adjusting the origins of the wheel and rail profiles as speciified in the UIC and EU standarts (S1002-UIC60E1). I am sampling the profiles wıth a 0.01 mm discretisation and then I apply the quasi-elastic contact search. I think 0.01 mm is a fine grid. The main problem is in the width I found that near origin Simpack finds slightly higher contact width than I found. I could not solve what causes this situation. You can find the comparison in the pdf files I have added.

Dear Altan,

I don't know if this is of concern anymore, but I came across the question and may be of help. Whereas our paper says that the equivalent elastic method originates from an approach by Kik and Piotrowski, it is in a number of ways different from what's known as "the Kik-Piotrowski approach".

The method starts for the wheel and rail in a state with a certain amount of interpenetration, as opposed from the state of making precise contact at a single point. The program computes the depth of interpenetration along the lateral y-coordinate as shown in Figure 1, left. From there, it takes the length and width of the interpenetration area, and defines an equivalent ellipse. This ellipse is shifted such that the center occurs at the "center of gravity" of the interpenetration area.

Then there's some magic about the penetration or equivalent penetration, and Hertz' solution is used to arrive at the normal force and corresponding pressures on the contact area.

Best wishes, Edwin

Dear Mr. Vollebregt,

First of all, thank you very much for the answer. It is still a concern for me since I am planning to code a multibody simulation tool for reseach purposes.

I think that Simpack uses "the Kik-Piotrowski approach" along with the "Quasi-Elastic Contact Search" method. They are combining these two approaches and name it "Equivalent-Elastic Contact Search", but I do not know how and there is no information about it. I interpreted this situation like this, since my results for contact area dimensions are especially different near nominal wheel position.

In order to validate my results in my PhD thesis, I have used Gensys results. My results are in a very good agreement with Gensys results which are provided graphically in its website.

I should say that I may have used Contact software since it is accepted as a reference in the literature. However, my main research area is not contact mechanics, so I needed a quick validation approach during my PhD studies and I preferred such a way. Another factor is that when I saw the user manual of Contact software, I was a little bit scared.

Again thank you very much for the explanation.

With my kind regards.

Altan.