On the effect of planar dynamics and resonance on vibration-induced friction modulation

Numerous theoretical and experimental studies have explored the effect of external excitation in modulating friction forces. To align with experimental findings, various friction models have been employed, with dynamic constitutive laws of friction often showing better correlations, though parameter tuning is always required for each different case. In this work, the focus is on enhancing the overall system dynamics rather than increasing the complexity of the friction law, with the aim of providing a better understanding of how system dynamics influence friction modulation under vibration. Specifically, two cases are investigated. A first one-degree-of-freedom case explores a resonant (and nearby resonance) case with a weak and strong friction force, for which an enhanced implicit expression for the velocity response (needed to compute the modulated friction quantity) is provided. The second case investigates the influence of transverse stiffness on friction modulation in a two-degree-of-freedom system subjected to combined longitudinal and transverse loading. On a qualitative basis, this study indicates that the results obtained using dynamic friction laws can also be obtained by employing Amonton-Coulomb’s law, provided the system’s dynamics is captured at a more detailed level.