Multiscale analysis of rough surfaces using the notion of 3D motifs

In this article, we present a 30 generalization of the standardized motif m ethod (ISO 12085),, used to characterize 2D profiles measured on engineerin g surfaces A 2D motif is defined as a portion of profile located between tw o maxima. The particular case of consecutive maxima corresponds to elementa ry motifs, which can easily be extracted from the profile. However, these e lementary motifs are not generally significant, on a morphological point of view. Thus, the main problem is the association of motifs to obtain signif icant ones. In the standardized method they are combined together; followin g empirical rules elaborated for a period of over 20 years of research in t his field. In the proposed method 30 surface motifs are considered as surface catchmen t basins, delimited by watershed lines. This definition is consistent with the previous one because a standardized 20 motif corresponds to the interse ction of a 30 mom with a vertical plane. To obtain all the catchment basins of the surface and the associated watershed lines, we use a powerful algor ithm based on immersion simulations. But as in the 20 case, these elementar y 30 motifs are not significant. To combine them, we use an indirect associ ation scheme. More precisely in a first stage bye fill all the motifs with a surface at their overflowing point greater than a threshold surface Delta . Then, in a second stage, watersheds of the modified surface are computed, giving rise to a new set of enlarged motifs. With this approach, we can pe rform multiscale analysis of surface motifs, examining the evolution of mot if number versus the threshold surface Delta. A flat section in this curve corresponds to a pertinent observation level of the surface. After the theoretical presentation of the method we set out the results obt ained applying it to a ground surface of ceramic and two steel surfaces, an end-milled one and a ground one. For the ground surfaces, the method leads to several pertinent observation levels associated with 30 motifs crossing over the whole surface or opened on one side only. This result was expecte d since this machining leads to scratches of finite length, depending on th e grindstone diameter: The final stage of our motif analysis systematically corresponds to a set of over crossing motifs. Let us remark that the prese nce of pores on ceramic surfaces do not lead to significant perturbation. T he case of ceramic surfaces is also interesting because a new problem arise beside the previous motif analysis : the determination of pore influence z ones, to separate them from the surface plateau. To solve this problem, we use first a specific method to compute the reference plane, in such a way t hat this plane corresponds exactly to the plateau. Then we choose a thresho ld level k.sigma, where k is a negative number and a the root mean square o f the positive distribution height function. The surface minima deeper than this threshold level are considered as pores at this scale or analysis, an d their influence zones are defined as the associated catchment basins. In fact, an intrinsic separation between plateau and pores cannot be obtained in this way because the number of pores varies continuously when increasing the threshold level k,a, Thus, the distinction between pores and plateau d epends on the choice of this level. A last aspect of our approach is the definition of parameters allowing a nu merical characterization of motifs. The first ones, corresponding to the 2D parameters generalization, are the motif width and the motif depth, which is defined as the difference between the mean height of the watershed surro unding it and the motif minimal height. However, other parameters can be us ed. For instance, considering the projection of the previous watershed on a horizontal plane as a cloud of paints, the motif direction can be defined as the direction of the associated principal inertia axis. The motif length and the motif width can be respectively defined as the length of the segme nts corresponding to the projection of this cloud of points on the previous axis and on a perpendicular axis. Of course, the motif length notion is on ly interesting for closed motifs. Then, mean values of the previous quantit ies leads to a statistical characterization of a motif set associated with a particular observation level.