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.

已知模式耦合不稳定性会触发滑动触点中的自激振动。在这里，研究了球形振荡器和移动粘弹性基底之间接触中模式耦合（或“颤振”）不稳定性的条件。这项工作扩展了经典的 2 自由度传送带模型，并考虑了基底中的粘弹性耗散、界面处的粘附摩擦和非线性法向接触刚度，这些都是从基于能够考虑线性的边界元方法的数值模拟得出的粘弹性效应。线性稳定性边界在非常低和非常高的基板速度范围内通过分析估计，而在中间速度范围内，特征值问题以数值方式解决。\(\tau _{0}\)和粘弹性摩擦系数。特别是，对于给定的衬底速度，存在临界剪切强度\(\tau _{0,crit}\)和法向载荷\(F_{n,crit}\)，这会触发模式耦合不稳定：对于剪切应力大于\(\tau _{0,crit}\)或正常负载小于\(F_{n,crit}\)，必须预期自激振动。