Shan Lou

Morphological method for surface metrology and dimensional metrology based on the alpha shape

Morphological filters are useful tools as they are commonly employed in surface metrology and dimensional metrology, serving for surface texture analysis and data smoothing, respectively. Compared to the mean-line filtering techniques, such as the Gaussian filter, morphological filters have the merits of compact support, no need to remove form and being relevant to geometrical properties of surfaces. This paper proposes a novel morphological method based on the alpha shape. The proposed method has the advantages over the traditional methods that it runs relatively fast, enables arbitrary large ball radii and applies to freeform surfaces and nonuniformly sampled surfaces. The theory of basic morphological operations and the alpha shape is introduced and the theoretical link between the alpha hull and the morphological closing and opening operation is presented. A practical algorithm is developed that corrects possible singularities caused by data spikes and reduces the amount of calculation for open profiles/surfaces. Computer simulation is used to compare the results from the traditional algorithm and the proposed one. Experimental studies are conducted to demonstrate the feasibility and applicability of using the proposed method.

Geometric computation theory for morphological filtering on freeform surfaces

Surfaces govern functional behaviours of geometrical products, especially high-precision and high-added-value products. Compared with the mean line-based filters, morphological filters, evolved from the traditional E-system, are relevant to functional performance of surfaces. The conventional implementation of morphological filters based on image-processing does not work for state-of-the-art surfaces, for example, freeform surfaces. A set of novel geometric computation theory is developed by applying the alpha shape to the computation. Divide and conquer optimization is employed to speed up the computational performance of the alpha-shape method and reduce memory usage. To release the dependence of the alpha-shape method on the Delaunay triangulation, a set of definitions and propositions for the search of contact points is presented and mathematically proved based on alpha shape theory, which are applicable to both circular and horizontal flat structuring elements. The developed methods are verified through experimentation.

Fast algorithm for Morphological Filters

In surface metrology, morphological filters, which evolved from the envelope filtering system (E-system) work well for functional prediction of surface finish in the analysis of surfaces in contact. The naive algorithms are time consuming, especially for areal data, and not generally adopted in real practice. A fast algorithm is proposed based on the alpha shape. The hull obtained by rolling the alpha ball is equivalent to the morphological opening/closing in theory. The algorithm depends on Delaunay triangulation with time complexity O(nlogn). In comparison to the naive algorithms it generates the opening and closing envelope without combining dilation and erosion. Edge distortion is corrected by reflective padding for open profiles/surfaces. Spikes in the sample data are detected and points interpolated to prevent singularities. The proposed algorithm works well both for morphological profile and area filters. Examples are presented to demonstrate the validity and superiority on efficiency of this algorithm over the naive algorithm.

Defining True Tribological Contact Through Application of the Morphological Method to Surface Topography

In tribological functions high peaks (summits) in the surface topography play a dominant role in that they determine the position of first contact and how the contact will occur. Both statistic-based methods and feature-based methods address the characterization of a single surface, while neglecting the interacting surface. A morphological method is proposed to simulate the contact of two mating surfaces. The surface under evaluation is rolled by a ball with radius meant to simulate the largest reasonable peak curvature at a contact. In such a situation the contact points of the rolling ball may serve as an identification of those surface portions that are in real contact. The morphological closing operation could then be applied to detect the contact points of the rolling ball, however, the traditional computation method does not lead to an accurate result. To overcome this deficiency, a geometrical computation approach has been developed to capture the contact points based on four searching procedures. The resulting method has been verified through experimentation and then applied to a case study in which the underlying form of the surface of a hip replacement taper junction is analyzed to remove the effect of the dominant threaded structure.

Applications of Morphological Operations in Surface Metrology and Dimensional Metrology

In contrast to the widely used mean-line based evaluation techniques, the capabilities of morphological methods are not fully recognized in practice. Morphological operations, e.g. dilation, erosion, closing and opening, are useful tools in surface metrology and dimensional metrology. This paper presents a variety of novel applications of morphological operations in association with several of existing critical cases to demonstrate their usability and capability. These applications include scanning process analysis, real mechanical surface reconstruction, freeform surface deviation evaluation, open surface and roundness filtration, form approximation, contact phenomenon simulation, establishment of uncertainty zone for continuous surface reconstruction and stratified functional surface evaluation.

An fast and efficient algorithm for spline filters

Filtration is very important for surface texture characterization. Spline filters that include linear and robust filters are recommended by ISO/TS 16610-22 and 32. In this paper, a general algorithm for both the linear and the robust spline filters is presented. The main advantage of the proposed algorithm is its ability to produce different types of filters only by choosing different M-estimators as shown in this note. This proposed algorithm relies on the Cholesky decomposition technique with an improved memory management procedure. Experimental and simulated results show that the proposed algorithm is fast, efficient and stable.

Morphological filters for functional assessment of roundness profiles

Filtration techniques are useful tools for analysing roundness profiles. The 2RC filter and Gaussian filter are commonly used to assess peripheral undulations of the roundness data. However they cannot do every aspect of functional prediction. Morphological filters are employed to characterize roundness profiles for functional assessment. Traditional computation methods for morphological filters are limited to planar surfaces and unable to be extended to roundness measurement. A novel method based on alpha shape theory is developed to break up the confinement. The morphological closing and opening envelopes are obtained by rolling a disk upon the roundness profile from the air and material side of the component respectively. They can be used to identify significant peaks and valleys on the profile respectively, which is vital to the functional performance of components, especially contact phenomenon. A case study is presented where various options of morphological filters and reference circles are applied to a roundness profile, delivering different functional meanings. An in-depth comparison of morphological filters and the Gaussian filter is followed to derive their pros and cons.