FRICTIONAL BEHAVIOUR OF A BELT-DRIVEN AND PERIODICALLY EXCITED OSCILLATOR

A single-degree-of-freedom system with the parallel presence of a linear spring, a viscous damper and a contact dry friction device is studied here. The mass may slide or stick on the belt when the driver moves periodically or at a constant speed. We derive closed-form solutions according to a more complete two-phase formulation, and some interesting behaviours of the considered system are displayed. For the non-damping oscillator belt with fixed, we offer closed-form formulae for estimating the maximum displacement and the minimum driving speed amplitude needed to prevent sticking. Two friction laws are considered. For the Coulomb friction system, the positive damping term suffices to avoid the climb motion of the mass slider. We also investigate the friction behaviour of the mass slider under the influence of the friction force bound on mass speed, whose curve has negative slope when the mass speed is less than a certain value vmin. For the speed-dependent friction system we identify a critical speed denoted by v*. According to the qualitative analysis in the phase plane we give simple criteria of the parameter values for stable equilibrium point as well as for stable limit cycle. When v varies from vv* to v<v*, subcritical Hopf bifurcation occurs. For the latter case the mass slider undergoes a slide–stick motion, but by increasing the driving speed the slide–stick motion can be avoided.