Surface Topography as an Energy State: Hamiltonian Description of Functional Properties in Phase Space and Quantification via Optical Methods

The assessment of tribological processes necessitates comprehensive monitoring and interpretation of surface states, traditionally by topography height values and surface texture parameters. This paper proposes a phase space representation as generic interpretation of surfaces to enhance tribological assessments. By deriving distinctions between two-dimensional and three-dimensional manifolds from phenomenological thermodynamics, we demonstrate the existence of fractal dimensions on physical surfaces. Utilizing the smallest representable wavelength, a coordinate ensemble where each coordinate has a generalized degree of freedom and a differential amount across fractal dimensions is proposed. The metric is interpreted as a time coordinate, allowing the derivative to be seen as velocity. Through geometric dimension analysis, we derive a topographic Hamiltonian via generalized momentum. Each coordinate pair in the ensemble is assigned a location in phase space. Statistical considerations define a symplectic structure and phase space volume. As a use-case, a two-disc experiment demonstrates that topography changes under load can be understood as a self-organization process through thermodynamic reasoning. As a possibility for a direct assessment of the phase space of a surface for monitoring tribological processes, we propose the combination of topographic measuring systems with scattering light measurement. This multi sensor approach offers opportunities for optimizing performance in tribological applications.

Feature Characterization for Profile Surface Texture

Conventional field parameters for surface measurement use all data points, while feature characterization focuses on subsets extracted by watershed segmentation. This approach enables the extraction of specific features that are potentially responsible for the function of the surface or are a direct reflection of the manufacturing process, allowing for a more accurate assessment of both aspects. Feature characterization with the underlying watershed segmentation for areal surface topographies has been standardized for over a decade and is well established in industry and research. In contrast, feature characterization for surface profiles has been standardized recently, and the corresponding standard for watershed segmentation is planned to be published in the near future. Since the standards do not provide guidelines for implementation, this paper presents an unambiguous algorithm of the watershed segmentation and the feature characterization for surface profiles. This framework provides the basis for future work, mainly investigating the relationship between feature parameters based on feature characterization and the function of the surface or manufacturing process. For this purpose, recommendations for the configuration and extensions of the toolbox can also be developed, which could find their way into the ISO standards.