In fact, circular contacts are a special case of point contacts, when the surface of the pin in contact with the disk has a constant radius of curvature in all directions. In other words, when the end of the pin is comparable to a portion of a sphere.

If the end of the pin is flat, it is no longer possible to calculate the pressure using the classical Hertz formulas. The contact area presents a singularity on the circle that forms the boundary between the contact and the non-contact areas.

Philippe Vergne Nino Dakov

If the pin is flat the Hertz cannot be applied and the nominal contact pressure would be simple P = F_n/A_n with A_n = pi*d and F_n - normal force. In reality you will never have an ideal alignment of pin and the real contact area even for very flat surface will depend on the tilt angel of the pin relative to the disc plain. In the test the tilting of the pin would lead to the high wear in the beginning and will decrease with the time as the contact area grows and contact pressure drops. I would use FEA to analyze something like this. You can incorporate also elastic-plastic material model to account for plastic deformation for high pressures. With FEA you can also analyse the rough contact but to solve the problem you have to resolve the roughness and must account for plastic deformation. There are some efficient tools based on half-space like Tribo-X for example that can do the job as well.

Hello Pavel,

I agree that if pin is flat then hertz model can not ne used. Then, the contact pressure can be calculated as load/area. It comes into conclusion that modulus has no effect on pressure in flat on flat contact case i.e., flat pin of two different materials will have a same contact pressure under a constant load for a particular counter body? Also, why we dont consider modulus values in this case?

https://iopscience.iop.org/article/10.1088/1757-899X/1059/1/012020/meta

You can get the data automatically from the tribometer (wear device).