Abstract
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,crit}, which trigger mode-coupling instability: for shear stresses larger than tau _{0,crit} or normal load smaller than F_{n,crit}, self-excited vibrations have to be expected.
Highlights
Friction-induced vibrations (FIVs) are an incredibly widespread phenomenon, where friction plays an unexpected role: instead of acting as a damping source, attenuating the system dynamics, dissipative forces are the original cause that triggers this class of vibrations
Among these: (i) the “sprag-slip effect”, pioneeringly investigated by Spurr in Ref. [19], was related to “jamming” phenomena at the interface level, (ii) the “Stribeck’s effect”, which is due to a falling characteristic of the friction law [20,21,22,23,24,25] and (iii) the “mode-coupling” instability, which is the result of the coupling of two stable vibrational modes that originates one stable and one unstable mode [26]
To better understand the importance of accounting for the effect of a time varying contact area in determining the dynamical response of a mechanical system in relative motion with a viscoelastic substrate, here we focus on the post-instability response of the dynamical system by means of time integration results
Summary
Friction-induced vibrations (FIVs) are an incredibly widespread phenomenon, where friction plays an unexpected role: instead of acting as a damping source, attenuating the system dynamics, dissipative forces are the original cause that triggers this class of vibrations. Notice that both μvisc (vrel , y) and A (vrel , y) are time varying quantities that depends at every time instant on the indentation of the spherical punch and on the relative horizontal velocity between the punch and the moving substrate [44,45,47,48,49] This is briefly recalled in Appendix A, where the main peculiarities of viscoelastic materials and the Boundary Element Method implemented to study the viscoelastic contact mechanics are summarized. We have implemented the following fitting equation: choice is consistent with the approach adopted in the entire paper: the simple one-relaxation time material allows us to clearly see which are the possible mechanisms of instability in a viscoelastic material and how these depend on the relative velocity between the oscillator and the moving substrate, including the correct elastic limits at low and high relative speed. The elastic reaction force increases moving from the rubbery to the glassy region, i.e., from low to high velocity
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