Robin Guibert

Stitching de Topographies 3D Elémentaires pour l'Analyse Multi-Echelle de Rugosité : Développement, Optimisation et Applications: La rugosité de surface est liée à de nombreux phénomènes physiques, ayant des implications tant d’un point de vue industriel (frottement, aspect visuel ...) que quotidien (marche, préhension des objets ...). L’analyse multiéchelle de la rugosité est notamment un puissant outil permettant l’isolement des phénomènes physiques selon leur échelle d’application et la détermination de leurs lois de comportement. Cependant, l’analyse multiéchelle de rugosité nécessite de plus grands ensembles d’échelles étudiables que ce que procurent les profilomètres 2D ou 3D afin de détecter les échelles de rugosité pertinentes. Le stitching est une technique d’assemblage de topographies élémentaires permettant de pallier les limites intrinsèques des machines de mesure topographique, en proposant des topographies 3D haute précision sur large champ de mesure. Bien que les algorithmes de stitching fassent parti des algorithmes les plus utilisés en métrologie de surface, leur étude est un véritable challenge car il s’agit d’un problème fondamentalement multidisciplinaire, nécessitant notamment des connaissances en topographie, en science des matériaux, en métrologie, en mathématiques, en optimisation et en informatique. Cet aspect multidisciplinaire explique la collaboration entre les départements mécanique et informatique durant ces travaux de recherche. Pour répondre aux défis du stitching, une approche en deux axes est proposée. Le premier axe se concentre sur l’étude de la procédure de stitching et sur son intégration dans le flux de travail de l’équipe MorphoMeca du LAMIH, via la création d’une suite logicielle. De nouvelles méthodes d’évaluation des erreurs de repositionnement et de la qualité des procédures de stitching ont été développées, grâce à la création d’une base de données dédiée au test d’algorithmes de stitching. De nouveaux algorithmes de stitching sont également proposés, via l’utilisation du multimap et de processus d’optimisation. Enfin, ce premier axe se conclut par l’évaluation de la performance des algorithmes de stitching vis-à-vis de leur complexité algorithmique et de leur capacité d’ingestion de données pour des stitchings de grandes dimensions. Un second axe propose l’application du stitching à des cas d’études réelles. Des méthodes d’analyse multiéchelle ont ainsi pu être comparées, grâce au stitching et à l’étude de l’abrasion d’un polymère. Enfin, l’étude multiéchelle des phénomènes physiques impliqués dans l’abrasion de neufs polymères permet l’identification de quatre mécanismes d’abrasion. Ce deuxième axe met ainsi en lumière l’intérêt du stitching de topographie 3D, tant académique qu’industriel.

Friction braking is the most spread braking system in vehicles, where the morphologies of the disc and the braking pads are essential to ensure that friction reduces rotation speed efficiently. However, modern braking systems are submitted to a complex balance between functionalities: braking ability, resistance to wear, and limited noise emission, i.e., squealing. This article studies the evolution of the morphology of a braking pad in a pin-on-disc configuration to further understand its influence over surface functionalities. Data collected from a pin-on-disc tribometer, and topographies are coupled to perform a multiscale and multiphysics analysis of the braking pad surface. Relevancy of roughness parameters regarding braking ability, surface wear, pad temperature and noise emission is evaluated with a bootstrap-based relevancy analysis. Relevant scales of the pad morphological structures are identified for surface wear (446 µm), braking ability (19.5 µm), pad temperature (2717 and 446 µm) and squealing frequency (1720 and 15.7 µm). Correlations between test bench data and roughness parameters highlighted the role of wear plateaus on the braking pad surface. These plateaus are formed by the damaged surface peaks during braking or by compaction of the third body trapped across the braking pad surface.

Observation of physical phenomena and their expression on solids is a challenge, especially considering their coupling. As a privileged place of interaction between solids and the external environment, surface should be studied. Roughness analysis often relies on optical profilometers to provide detailed topographic maps of the solid. To facilitate the analysis of physical phenomena, multiscale analysis is used to separate each phenomenon at their scale of application. However, optical profilometers natively propose a limited scale range to observe. Stitching is an assembling technique of topographic map solving this problem, by generating high resolution over a large field of measurement. Stitching can be summed up as an optimization problem of the alignment of elementary maps, i.e., registration. Yet, the stitching optimization problem is not trivial to solve. This paper proposes a theoretical analysis of the algorithmic complexity of the stitching problem and provides an estimation of the stitching problem complexity, considering measurement uncertainties, which is lacking from literature. First, a simplified stitching problem is presented, based on the assumption that stitching in standard conditions is at least as algorithmically complex. Simulations of local stitching displacements are performed based on the simplified stitching problem. Modelling of stitching reveals that the stitching problem is in exponential time problem class. The complexity of the simplified stitching problem is then estimated to follow an evolution similar to 2 ⁿ by a theoretical analysis of the stitching problem complexity.

Surfaces are the privileged places of interaction between physical phenomena and objects. Roughness studies, especially when performing multiscale analysis, are tools of choice to understand physical phenomena and their scales of application. However, profilometers, especially optical systems, must compromise between field of measurement and resolutions. Stitching is an assembling technique aiming to solve this compromise by combining elementary maps, such as images or topographies. Stitching generates high resolution over a large field of measurement maps, which increases the measurable scale range and facilitates the correct identification of physical phenomena at their scales of application. This article proposes a review of 3D topography stitching algorithms. After explanations on the use cases of 3D topography stitching, the stitching procedure from elementary maps acquisition to the obtention of the stitched map is described step-by-step. Secondly, errors in measurement and stitching are presented with the sources of errors and the error evaluation methods. Lastly, the mathematical modelling of 3D topography is detailed to better understand the optimization process used in the in-plane and out-of-plane registration steps of the stitching algorithms. Comparison of algorithms involved in stitching are proposed so that researchers might find the most suitable algorithm to their needs. Overall, this work aims at introducing researchers and metrologists to important multidisciplinary notions for the use and design of 3D topography stitching algorithms and offers a tutorial-based approach.

Finding the relevant scale to observe the influence of a process is one of the most important purposes of multiscale surface characterization. This study investigates various methods to determine a pertinent scale for evaluating the relationship between the relative area and grit blasting pressure. Several media types were tested alongside two different methods for calculating the relative area and three bootstrapping approaches for scale determination through regression. Comparison with the existing literature highlights innovations in roughness parameter characterization, particularly the advantages of relative area over traditional parameters like Sa. This study also discusses the relevance of different media types in influencing surface topography. Additionally, insights from a similar study on the multiscale Sdq parameter and blasting pressure correlation are integrated, emphasizing a scale relevance akin to our Sdr method’s 120 µm cut-off length. Overall, our findings suggest a pertinent scale of 10,000 µm² for the Patchwork method and a 120 µm cut-off length for the Sdr method, derived from bootstrapping on residual regression across all media. At the relevant scale, every value of R² inferior to 0.83 is not significant with the threshold of 5% for the two methods of calculation of the relative area. This study enhances the understanding of how media types and blasting pressures impact surface topography, offering insights for refining material processing and surface treatment strategies.

Various methods exist for multiscale characterization of surface topographies, each offering unique insights and applications. The study focuses on fractal-based approaches, distinguishing themselves by leveraging fractals to analyze surface complexity. Specifically, the Richardson Patchwork method, used in the ASME B46.1 and ISO 25178 standards, is compared to the Sdr parameter derived from ISO 25178-2, with a low-pass Gaussian filter for multiscale characterization. The comparison is performed from the relative area calculated on topographies of TA6V samples grit blasted with different pressures and blasting materials (media). The surfaces obtained by grit blasting have fractal-like characteristics over the scales studied, enabling the analysis of area development at multiple levels based on pressure and media. The relative area is similar for both methods, regardless of the complexity of the topographies. The relevance scale for each calculation method that significantly represents the effect of grit blasting pressure on the increased value of the relative area is a tiling of 7657.64 µm² of triangle area for the Patchwork method and a 124.6 µm cut-off for the low-pass Gaussian filter of the Sdr method. These results could facilitate a standard, friendly, new fractal method for multiscale characterization of the relative area.

A new method is proposed to investigate the measurement variation of instruments and their ability to discriminate two TA6V surfaces obtained by grinding with SiC grit papers (80 and 120). Three optical measurement technologies included into a single apparatus, namely Confocal Microscopy (CM), Focus Variation (FV) and Coherence Scanning Interferometry (CSI), were used to measure both ground surfaces according to a specific experimental protocol (MorphoMeca Monitoring) based on measurement iterations and repetitions. From the measurements, four indices were built from the Sa roughness parameter to assess the Quality (ratio of the topographical variability over the measurement noise), the Drift (related to surface fluctuations) and the Stability (estimation of the temporal drift using a second order autoregressive model) of the three measurement technologies (modes), as well as their Relevance (computed from an analysis of variance) to discriminate ground surfaces with close roughness. For these investigated surfaces, it was especially highlighted that the Quality Index is four times higher for the CSI mode than for the FV and CM modes. All the used measurement modes experienced small drifting (Drift Index) during the measurements. The CSI mode was slightly more sensitive to drift than the FV and CM modes. The Stability Index indicated that there was no memory effect between two acquisitions for each measurement mode, i.e., the temporal drift did not depend on the measurement mode. Moreover, the three measurement modes are able to discriminate the two ground surfaces with the same accuracy through the Sa parameter. However, the Sa values may vary depending on the measurement modes, and it was finally shown that the Sa parameter is minimized by 0.03 μm for the FV mode compared with the CSI mode, due to its smoothing effect.

Identification of an individual artist’s touch on paintings is studied using surface metrology. Paintings’ topographies were measured using focus variation and stitching, creating 13 × 13 mm maps with 1 μm sampling intervals, and 169 megapixels, with a 10X objective lens. Topographic characterization parameters were analyzed for their ability to differentiate different painters’ renderings. Statistical treatments from data mining were used to discriminate, by optimization, multiscale topographic signatures characterized by a multitude of areal texture parameters. It appears that a fractal dimension can define 3 characteristic scale ranges. One from 3 to 70 μm corresponds to brushstroke details. Another, from 70 to 700 μm, corresponds to the topography of the material of the canvas fabric. Finally, scales greater than 700 μm correspond to undulations of the canvas. For scales less than 50 μm, the fractal structure of the topography left by brushstrokes follows a power law characterized by the slopes of the topography. The topography of the clouds painted on the canvas has an Sdq (topographic slopes) increasing with the clarity of the clouds at scales of 3–500 μm. According to the Torrance-Sparrow theory, the higher the Sdq, the more diffuse the light on the surface. The painter therefore wanted to show, by his brushstroke, that the light clouds diffuse more light giving an impression of local brightness. This study is confirmed by the analysis of the painting of Max Savy, a French painter from Carcassonne (1918–2009), which was measured with a white light interferometer Zygo NewView 7300, a X100 objective lens giving a 517 μm × 517 μm stitched surface, with a sampling interval of 0.109 μm. The box-counting method for estimating the fractal dimension of the topography of an oil painting appears optimal by the fact that it morphologically integrates scale variations of the local slopes of the surface morphology. This method thus characterizes the multiscale aspects, as well as the scale changes, of the topography.