Model of a Tribological Sensor Contacting Rotating Disc

Abstract

We study mechanical oscillations of a sensor, forming a friction pair with the rotating disc. In the absence of friction the model is described by a two-dimensional hamiltonian system of ODE’s which is completely integrable. As the Coulomb-type friction is added, the regimes appearing in the modelling system become more complicated. They are investigated both by the qualitative methods and the numerical simulation. With such a synthesis we obtain a complete global behavior of the system, within the broad range of a driven parameter values, for two principal types of the modeling function, simulating the Coulomb friction. A sequence of bifurcations (limit cycles, double-limit cycles, homoclinic bifurcations and other regimes) are observed as the the driven parameter changes. The pattern of bifurcations depends in essential way upon the model of friction force employed and this dependence is analyzed in detail. Much more complicated regimes appear as we incorporate into the model the one-dimensional oscillations of the rotating element. The system possesses in this case quasiperiodic, multiperiodic and, probably, chaotic solutions.