A very simple solution to the rolling contact problem will falling friction

In rail-wheel contact modelling, there is a huge industrial interest to model accurately rolling contact of hard bodies with friction for predicting fatigue, squeal, noise, vehicle dynamics.     In the literature, the case of Carter 1926 has been extended with numerical codes known as FASTSIM and CONTACT which are based on algorithms by JJ Kalker.     However, there is a serious problem to model falling rate-dependent friction, which gives unexpected instabilities and unclear solutions.

FASTSIM in particular, being based on a Winkler elastic foundation model, has some unphysical predictions.

Hence, I gave a very simple solution which I recently submitted to a journal.   Any comment/discussion/possible extensions or testing with experiments/collaboration is welcome.

https://www.researchgate.net/publication/359730400_A_simple_solution_for...

Regards, Mike