Friction-induced sliding instability in a multi-degree-of-freedom system with oscillatory normal forces

A multi-degree-of-freedom (m.d.o.f.) system excited by a rough moving surface has been developed to study friction-induced oscillations. The normal degrees of freedom allow for oscillatory normal forces, while the normal–tangential coupling of friction produces parametric excitation in the slipping equations of motion. After a modal change of variables, first order averaging has been used to produce a set of autonomous equations of motion. Eigenvalue analysis of the averaged equations has produced stability predictions for the steady sliding position. Numerical integration of the original system of equations has verified the existence of locally unstable oscillations for a system excited by a rough surface input. The combination of velocity-dependent friction and a harmonically varying normal force have been shown to produce large-amplitude oscillations, in some cases leading to stick–slip responses.