Decaying law for the free oscillating response with a pseudo-polynomial friction law: Analysis of a superlow lubricated friction test

Friction is an important phenomenon in various dynamic systems. In order to understand the physical behavior of such systems, it is crucial to choose a friction law that can correctly model the mechanical system. This paper aims to study the dynamic responses of a new tribometer, based on a single degree-of-freedom (sdof) mass-spring system having a sliding contact. We introduce a velocity-dependence friction law in order to understand the dynamic system. The model is studied numerically and experimentally. In this paper, the friction law has been carefully investigated using a linear model (Coulomb and viscous friction) and a quadratic velocity-dependence model, introduced as a power series of the sliding velocity. Results demonstrate that when the decaying envelope is described by both concave and convex forms, a linear friction law could not properly model the system. It is shown that in some cases, a more refined friction law with higher order than quadratic expansion should be introduced to precisely model the dynamic system. In addition, some experimental results are presented using the tribometer, showing a good agreement with the numerical results. The results are then discussed in terms of different lubrication regimes.