Frictional lag and stick-slip

Dimensional and perturbation analyses are applied to the problem of stick-slip encountered during the motion of machines with nonlinear low-velocity friction. The friction model studied incorporates kinetic, viscous and Stribeck friction with frictional lag. Through dimensional analysis an exact model of the nonlinear system can be formed in four parameters rather than nine, greatly facilitating study and explicitly revealing the interaction of parameters. By converting the system of differential equations into a set of integrations, the perturbation technique makes approximate analysis possible where only numerical techniques had been available before. The analysis predicts the onset of stick-slip as a function of plant and controller parameters. These results are compared with experimental data