Avolio, Stefano (2025) Influence of the Height Distribution on Rubber Friction over Rough Surfaces. [Tesi di dottorato]

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Abstract

Tyre–road friction is a central phenomenon governing vehicle safety, performance, and energy efficiency. It defines the limits of braking and handling, influences the operation of driver assistance systems, and affects rolling resistance, wear, and overall tyre sustainability. Understanding its physical origin — and in particular how it depends on the viscoelastic behaviour of rubber and the topography of the road surface — is therefore of fundamental importance for both scientific and engineering perspectives. The present doctoral research was conceived to deepen the understanding of the mechanisms that govern rubber friction through a combined theoretical, numerical, and experimental approach. The work begins with a detailed study of contact mechanics and existing friction models, together with the extensive literature that has attempted to correlate surface roughness with grip and contact behaviour. From this analysis, it emerges that most established models are spectrum-based, relying on the surface power spectral density (PSD) to describe the multiscale distribution of roughness, whereas other studies highlight the potential role of statistical and functional parameters. This observation suggests that while the PSD remains essential, it may not fully capture all morphological information relevant to friction. Building on this insight, the research develops an original experimental methodology to investigate, in a controlled manner, the combined influence of spectral and statistical surface characteristics. Artificial surfaces were generated with identical PSDs but different height distributions, manufactured through high-resolution additive printing, and validated via optical profilometry. These surfaces were then employed in an extensive friction campaign conducted on two complementary linear friction testers — HiLiTe (Leibniz Universität Hannover) and GRIP (University of Naples ``Federico II'') — under equivalent load, speed, and temperature conditions, both in dry and lubricated regimes. In parallel, indentation and real-contact-area measurements were performed on the same surfaces to assess the validity and limits of spectrum-based contact models. The results show that, although the PSD remains a key descriptor for the hysteretic component of friction, significant variations occur between surfaces sharing the same spectral content. These differences are linked to the statistical morphology of the surface, indicating that parameters describing the height distribution and local topology also play a determining role in frictional behaviour and contact mechanics. Overall, the findings demonstrate that a comprehensive description of rubber friction must integrate both spectral and statistical aspects of surface roughness. The thesis is organised as follows: Chapter 1 introduces the scientific background of rubber friction, tracing the evolution from early viscoelastic approaches to modern multiscale theories. It explains how surface roughness became central to the understanding of friction and identifies the limitations of purely spectral frameworks, outlining the motivation for this research. Chapter 2 provides a systematic review of surface roughness descriptors and metrological standards, highlighting the transition from 2D to 3D areal characterisation and the introduction of ISO 25178-2. It discusses the challenges of applying industrial standards to road surfaces, where filtering, scale selection, and measurement procedures remain non-uniform, and concludes with a critical analysis of previous correlation studies between roughness parameters and frictional performance. Chapter 3 presents a comprehensive state of the art on rubber friction, combining an overview of experimental methodologies with a discussion of the most relevant friction models. The first part describes the evolution of friction testers, analysing their operating principles, capabilities, and limitations in reproducing tyre–road contact. The second part reviews the theoretical frameworks that have shaped the current understanding of rubber friction, from the classical works of Grosch to modern multiscale formulations. Particular attention is devoted to how the models relate friction to surface topography through spectral and statistical descriptors. This chapter establishes the conceptual basis that motivates the subsequent methodological development and the artificial surface approach. Chapter 4 presents the generation of artificial surfaces designed to decouple spectral and statistical effects. A hybrid numerical algorithm was developed to control both the spectral content and the statistical distribution of heights, producing seven surfaces with identical PSDs but different skewness and kurtosis. These surfaces, representative of real road conditions, were manufactured by high-resolution stereolithography and validated through 3D profilometric measurements, ensuring excellent morphological fidelity between numerical and physical models. Chapter 5 the chapter then details the compounds and the experimental campaign performed on the printed surfaces, carried out under equivalent normal pressure, sliding velocity, and temperature. The results show that while the hysteretic contribution correlates with the spectral content, systematic differences between surfaces with the same PSD confirm the influence of the statistical distribution of heights and other non-spectral morphological factors. Chapter 6 focuses on complementary indentation and real-contact-area tests conducted under controlled load and temperature. These experiments provide quantitative insights into the penetration behaviour of rubber and the evolution of real contact area, linking the topography of the artificial surfaces to the mechanical response of the material. Although simplified with respect to real tyre–road dynamics, these results serve as a bridge between surface metrology and contact mechanics, enabling a direct evaluation of spectrum-based contact models. Conclusions summarise and integrate the outcomes of this work. The results highlight that the frictional response of rubber cannot be fully captured through spectral parameters alone, as statistical and morphological features of the surface also exert a measurable influence. Together, these findings contribute to a more complete framework for understanding tyre–road friction and provide methodological tools for improving predictive models and surface characterisation strategies in the pursuit of safer, higher-performing, and more sustainable mobility. Summary. This doctoral research provides new insight into the relationship between surface roughness and rubber friction. By combining surface generation, advanced metrology, and controlled tribological testing, it demonstrates that friction depends not only on the spectral content of the surface but also on its statistical morphology. The developed methodology offers a reproducible way to disentangle these effects and contributes to the refinement of contact and friction models, enhancing both the scientific understanding and practical prediction of tyre–road interaction.

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