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 tau(0) and the viscoelastic friction coefficient. In particular, for a given substrate velocity, there exist a critical shear strength tau(0,crit) and normal load F-n,F-crit, which trigger mode-coupling instability: for shear stresses larger than tau(0,crit) or normal load smaller than F-n,F-crit, self-excited vibrations have to be expected.

Automated summary

This study investigates the conditions for mode-coupling instability in the contact between a spherical oscillator and a moving viscoelastic substrate, taking into account various factors such as viscoelastic dissipation, adhesive friction, and nonlinear normal contact stiffness. The stability of the system is shown to depend on externally imposed parameters and contact parameters, such as substrate velocity, normal load applied, shear strength, and viscoelastic friction coefficient. The critical shear strength and normal load that trigger mode-coupling instability are identified, indicating that self-excited vibrations can be expected under certain conditions.