Analysis of multiscale theories for viscoelastic rubber friction

Rubber friction plays a fundamental role in the study of the tire-road interaction and still represents a topic of discussion for both academics and manufacturing companies, especially with the introduction of the concept of multiscale roughness [1, 2]. Taking into account that the road surface is a hard substrate, the two contributions to rubber friction can be considered to be (i) hysteretic phenomena deriving from time dependent viscoelastic deformations of the rubber due to the substrate asperities and (ii) adhesive effects. From the modelling point of view, the estimation of each contribution represents a great challenge, and both formulations are inevitably affected by the presence of empirical constants. For example, hysteretic friction could be in principle computed by a full multiscale Persson’s theory [1, 3], but the latter one ultimately embraces an arbitrary choice of the cutoff frequency value, and, furthermore, the full multiscale theory can be in most cases simplified [4]. The adhesive contribution, instead, remains fundamentally empirically described by fitting functions and parameters, and, despite considerable progress and huge effort in this research field, it continues to represent the greatest challenge as well as to recognize the relative importance of the two contributions [5]. In this work, an analysis of the results obtained with the different formulations available in literature is proposed with particular reference to the empirical constants variability.