Critical thresholds for mode-coupling instability in viscoelastic sliding contacts

Mode-coupling instabilities are known to trigger self-excited vibrations in sliding contacts. Here, the conditions for mode-coupling (or “flutter”) instability in the contact between a spherical oscillator and a moving viscoelastic substrate are studied. The work extends the classical 2-Degrees-Of-Freedom conveyor belt model and accounts for viscoelastic dissipation in the substrate, adhesive friction at the interface and nonlinear normal contact stiffness as derived from numerical simulations based on a boundary element method capable of accounting for linear viscoelastic effects. The linear stability boundaries are analytically estimated in the limits of very low and very high substrate velocity, while in the intermediate range of velocity the eigenvalue problem is solved numerically. It is shown how the system stability depends on externally imposed parameters, such as the substrate velocity and the normal load applied, and on contact parameters such as the interfacial shear strength τ and the viscoelastic friction coefficient. In particular, for a given substrate velocity, there exist a critical shear strength τ,crit and normal load Fn,crit, which trigger mode-coupling instability: for shear stresses larger than τ,crit or normal load smaller than Fn,crit, self-excited vibrations have to be expected.