Stick slip and control in low-speed motion

Dimensional and perturbation analysis are applied to the problem of stick slip encountered during the motion of machines. The friction model studied is motivated by current tribological results and is appropriate for lubricated metal contacts. The friction model incorporates Coulomb, viscous, and Stribeck friction with frictional memory and rising static friction. Through dimensional analysis an exact model of the nonlinear system can be formed using five parameters rather than ten, 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.>