Bifurcational Dynamics of a Two-Dimensional Stick-Slip System

A two degree of freedom plane disk, performing one-dimensional translational and rotational motion, placed on the moving belt, is mathematically modelled and numerically analysed. The friction model for sliding phase is developed assuming classical Coulomb friction law, valid for any infinitesimal element of circular contact area. As a result, the integral expressions for friction force and torque are obtained. The exact integral model is then approximated by the use of different functions, like Pade approximants or their modifications. Some generalizations of the approximate functions used by other authors are proposed. The special event-driven model of the investigated system together with numerical simulation algorithm is developed, where in particular the transition conditions between the stick and slip modes are defined. Some examples of numerical simulation and analysis by the use of Poincare maps and bifurcational diagrams are presented. It has been shown, that for certain parameter sets, the investigated system exhibits very rich multi-periodic stick-slip oscillations.