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.
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