24th International Colloquium Tribology - January 2024 211 Unveiling the Butterfly Effect in Tribology: The Impact of Surface Profile Yulong Li 1,2 , Nikolay Garabedian 1,2 , Johannes Schneider 1,2 , Christian Greiner 1,2* 1 Institute for Applied Materials (IAM), Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131 Karlsruhe, Germany 2 KIT IAM-ZM MicroTribology Center (µTC), Str. am Forum 5, 76131 Karlsruhe, Germany * Corresponding author: christian.greiner@kit.edu 1. Introduction In many tribological studies, a surface that seems homogenous is, in reality, a planar anomaly riddled with inconsistencies. Even surfaces refined to a mirror-like polish manitain microscale undulations and deviations, characterized by pronounced, coarse, or jagged protrusions termed “asperities” (derived from the Latin word “asper”, meaning “rough”). These asperities have various scales, displaying self-affine or fractal patterns. The intricate configuration of the interface between a substance and its external environment critically influences the tribological characteristics of that surface [1-3]. Usually, surface deviations are quantified using mean roughness and waviness metrics, typically represented as simple scalar values (for example, roughness R a and waviness W t as per ISO-4287 standards). These metrics for roughness and waviness are not directly derived from the primary surface profile. Instead, they are from their respective roughness and waviness profiles after the primary profile undergoes filtering in line with prevailing standards (e.g., ISO- 116610 or ASME-B46.1), as illustrated in Figure 1. Roughness pertains to the minor, closely spaced deviations observable at the microscopic scale on a surface. These deviations commonly arise from the manufacturing process and can include characteristics such as scratches, indents, and others. Conversely, waviness denotes the more pronounced, broadly spaced deviations visible at the macroscopic scale on a surface. Such irregularities frequently arise from processes like machining or assembly, encompassing features such as undulations, bumps, and other substantial surface anomalies. [4] The impact and control of roughness parameters on friction and wear have been thoroughly explored in the literature. However, achieving a perfectly flat surface or replicating the same surface consistently remains an unachievable goal. As a result, each tribological experiment is conducted on a distinct surface, even if certain parameters (such as R a ) deem them similar. On the one hand, the subtle surface deviations in experimental conditions may exert a surprisingly significant and yet unknown influence on tribological behavior. On the other hand, the effects of these minor surface deviations on tribo-logical behavior could potentially shed light on unre-solved questions that continue to perplex the tribological community. Figure 1: (a) Roughness and waviness on a surface [5]; (b) Schematic of arithmetical mean deviation of roughness profile R a [6]. 2. Results and discussion The tribological experiments in this contribution were carried out using a pin-on-disk configuration with pins and disks made from bearing steel (100Cr6, AISI 5210). Maximum efforts were made to control the surface topography of the disk, maintaining its roughness within a range from R a = 0.08 to 0.11 µm. The radial height discrepancy along the frictional track was kept under 2-µm, as depicted in Figure 2. Ensuring that the height variation of the 132-mm disk’s sliding track stays within 2-µm, representing the minimum achievable value in our laboratory. Figure 2: Extracting the surface profile from chromatic profilometry data. The height difference of the 132-mm sliding track is below 2-µm [7]. 212 24th International Colloquium Tribology - January 2024 Unveiling the Butterfly Effect in Tribology: The Impact of Surface Profile However, when comparing the average friction coefficient along the entire disk’s sliding track with the roughness distribution (as shown in Figure 3a) and the waviness profile (presented in Figure 3b), we observe no discernible correlation between the friction coefficient and roughness. In contrast, a partial correlation exists between the friction coefficient and the disk’s waviness profile, as illustrated in Figure-3b. The friction coefficient peaks where the waviness profile reaches its maximum height. A “hill” with an approximate height of 2-µm elevates the friction coefficient by 91%. The influence of this mere “2-µm” is remarkable, especially considering our rigorous efforts to regulate waviness, ensuring it remains below 2 µm over such an extended sliding track (132-mm). Even in precision semiconductor manufacturing, exemplified by the 7-nm node lithography process, the permissible height variance on a 300 mm wafer is just under 5-µm [8]. Thus, a 132-mm sliding track with a height differential of only 2 µm is conventionally deemed “flat” within tribological studies. However, this research has unveiled that even such a tiny difference can significantly dictate tribological behavior, which is a point often overlooked by tribologists and deserves broader attention in the future. Figure 3: Comparing friction coefficient with roughness distribution(a) and waviness profile(b) [7]. 3. Conclusion This research unveils the “butterfly effect” in tribology, where even minute surface topographical variations can exert a decisive influence on frictional performance. The insights presented in this thesis offer a lucid explanation for why frictional behavior is impossible to repeat. Even when surface topography is minimized and controlled, there exists a significant and hitherto unrecognized impact on tribological behavior. Given that the surface topography is distinct in each experiment, achieving absolute consistency in frictional behavior is inherently unattainable! References [1] Jacobs T. D. B., Pastewka L. Surface topography as a material parameter. MRS bulletin 12 (2022) 1205-10. [2] Hanaor D. A., Gan Y., Einav I. Contact mechanics of fractal surfaces by spline assisted discretisation. International Journal of Solids and Structures (2015) 121-31. [3] Aghababaei R., Brink T., Molinari J.-F. Asperity-Level Origins of Transition from Mild to Severe Wear. Physical review letters 18 (2018) 186105. [4] Aghababaei R., Brodsky E. E., Molinari J.-F., Chandrasekar S. How roughness emerges on natural and engineered surfaces. MRS bulletin (2023). [5] American Society of Mechanical Engineers. Surface texture: Surface roughness, waviness, and lay. New York: American Society of mechanical engineers; 2020. [6] DIN EN ISO 4287: 2010-07, Geometrische Produktspezifikation (GPS)_- Oberflächenbeschaffenheit: Tastschnittverfahren_- Benennungen, Definitionen und Kenngrößen der Oberflächenbeschaffenheit. Berlin: Beuth Verlag GmbH. [7] Li Y., Garabedian N., Schneider J., Greiner C. Waviness affects friction and abrasive wear (2022). [8] Iida S., Nagai T., Uchiyama T. Standard wafer with programed defects to evaluate the pattern inspection tools for 300-mm wafer fabrication for 7-nm node and beyond. Journal of Micro/ Nanolithography, MEMS, and MOEMS 02 (2019) 1.