Torsional vibrations in systems with combined dry friction

We consider an example of torsional vibrations of a vertically located cylindrical rod one of whose ends is elastically fixed and the other end rests on an infinite band moving at a constant velocity. We compare the main models of dry friction, such as “pure” dry friction and “viscous” friction, and the models based on the Padé expansions of the corresponding order. We show that the model based on linear-fractional Padé expansions of the exact integral model, which is written under the assumption that the Coulomb law in differential form is true, is the simplest form of the model of combined dry friction, which gives correct results, while the models of pure dry and viscous friction cannot provide correct descriptions of the effects of combined dry friction.