A mathematical model describing the law of contact gliding friction, taking into account changes in the sliding contact states, is proposed for consideration. The generalization of classical linear models of contact friction is carried out by putting in more additive components allowing for new state transitions of frictional interaction. The developed mathematical model makes it possible to give analytic description of the schematic diagram of classical slip coefficient change depending on the load of B.I. Kostetsky and allows adding to
generalized friction law, mathematical model, sliding friction, transition, Fermi-Dirac integral
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