A new method for aspherical surface fitting with large-volume datasets

In the framework of form characterization of aspherical surfaces, European National Metrology Institutes (NMIs) have been developing ultra-high precision machines having the ability to measure aspherical lenses with an uncertainty of few tens of nanometers. The fitting of the acquired aspherical datasets onto their corresponding theoretical model should be achieved at the same level of precision. In this article, three fitting algorithms are investigated: the Limited memory-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), the Levenberg–Marquardt (LM) and one variant of the Iterative Closest Point (ICP). They are assessed based on their capacities to converge relatively fast to achieve a nanometric level of accuracy, to manage a large volume of data and to be robust to the position of the data with respect to the model. Nev-ertheless, the algorithms are first evaluated on simulated datasets and their performances are studied. The comparison of these algorithms is extended on measured datasets of an aspherical lens. The results validate the newly used method for the fitting of aspherical surfaces and reveal that it is well adapted, faster and less complex than the LM or ICP methods.EMR

Reconstruction of freeform surfaces for metrology

The application of freeform surfaces has increased since their complex shapes closely express a product's functional specifications and their machining is obtained with higher accuracy. In particular, optical surfaces exhibit enhanced performance especially when they take aspheric forms or more complex forms with multi-undulations. This study is mainly focused on the reconstruction of complex shapes such as freeform optical surfaces, and on the characterization of their form. The computer graphics community has proposed various algorithms for constructing a mesh based on the cloud of sample points. The mesh is a piecewise linear approximation of the surface and an interpolation of the point set. The mesh can further be processed for fitting parametric surfaces (Polyworks® or Geomagic®). The metrology community investigates direct fitting approaches. If the surface mathematical model is given, fitting is a straight forward task. Nonetheless, if the surface model is unknown, fitting is only possible through the association of polynomial Spline parametric surfaces. In this paper, a comparative study carried out on methods proposed by the computer graphics community will be presented to elucidate the advantages of these approaches. We stress the importance of the pre-processing phase as well as the significance of initial conditions. We further emphasize the importance of the meshing phase by stating that a proper mesh has two major advantages. First, it organizes the initially unstructured point set and it provides an insight of orientation, neighbourhood and curvature, and infers information on both its geometry and topology. Second, it conveys a better segmentation of the space, leading to a correct patching and association of parametric surfaces.EMR

Fast B-Spline 2D Curve Fitting for unorganized Noisy Datasets

In the context of coordinate metrology and reverse engineering, freeform curve reconstruction from unorganized data points still offers ways for improvement. Geometric convection is the process of fitting a closed shape, generally represented in the form of a periodic B-Spline model, to data points [WPL06]. This process should be robust to freeform shapes and convergence should be assured even in the presence of noise. The convection's starting point is a periodic B-Spline polygon defined by a finite number of control points that are distributed around the data points. The minimization of the sum of the squared distances separating the B-Spline curve and the points is done and translates into an adaptation of the shape of the curve, meaning that the control points are either inserted, removed or delocalized automatically depending on the accuracy of the fit. Computing distances is a computationally expensive step in which finding the projection of each of the data points requires the determination of location parameters along the curve. Zheng et al [ZBLW12] propose a minimization process in which location parameters and control points are calculated simultaneously. We propose a method in which we do not need to estimate location parameters, but rather compute topological distances that can be assimilated to the Hausdorff distances using a two-step association procedure. Instead of using the continuous representation of the B-Spline curve and having to solve for footpoints, we set the problem in discrete form by applying subdivision of the control polygon. This generates a discretization of the curve and establishes the link between the discrete point-to-curve distances and the position of the control points. The first step of the association process associates BSpline discrete points to data points and a segmentation of the cloud of points is done. The second step uses this segmentation to associate to each data point the nearest discrete BSpline segment. Results are presented for the fitting of turbine blades profiles and a thorough comparison between our approach and the existing methods is given [ZBLW12, WPL06, SKH98]

Integrated training in using different Coordinate Measuring Systems to support Digital Manufacturing

Highly qualified labour force is a key resource for growth. In modern manufacturing, the competent use of advanced measuring equipment for inspection and digitization of parts is an essential competence that is needed for both advanced product/process engineering and quality control. Coordinate Metrology (including 3D digital measuring technologies) is by far the most important tool for these specialized activities. As widely reported, the individuals operating the measuring systems - with their decisions - are frequently one of the most relevant error sources in Coordinate Metrology operations, especially when dealing with new measuring technologies supporting Digital Manufacturing (e.g. Computed Tomography, Fringe-projection, Reverse Engineering). The paper reports the intermediate results of an initiative aiming at innovating training in Coordinate Metrology, focused on supporting the needs of SMEs in the supply chain of the automotive industry. The main target group are industry employees operating in SMEs that are newcomers on 3D measuring technologies. An integrated concept for training in Coordinate Metrology has been developed using a blended learning approach, based on a 10-steps structure and incorporating the learning outcomes required to operate different measuring systems in a consistent way

Integrated training in using different Coordinate Measuring Systems to support Digital Manufacturing

International audienc

Design of an ultra-high precision machine for form measurement

International audienceIn today's business environment, the trend towards more product variety and customization is unbroken. Due to this development, the need of agile and reconfigurable production systems emerged to cope with various products and product families. To design and optimize production systems as well as to choose the optimal product matches, product analysis methods are needed. Indeed, most of the known methods aim to analyze a product or one product family on the physical level. Different product families, however, may differ largely in terms of the number and nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production system. A new methodology is proposed to analyze existing products in view of their functional and physical architecture. The aim is to cluster these products in new assembly oriented product families for the optimization of existing assembly lines and the creation of future reconfigurable assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the similarity between product families by providing design support to both, production system planners and product designers. An illustrative example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach

STEP-NC based optimization and smart industrialization of NC machining in the context of the factory of the future

L'article propose un nouveau concept pour assurer le retour d'information depuis les Machines-Outils à Commandes Numériques vers les systèmes FAO et la simulation d'usinage. Le but principal de la proposition est de gérer les connaissances d'usinage extraites de la machine pour les réutiliser au niveau de la simulation d'usinage et ainsi fournir une aide à la décision pour la réalisation de futur programme d'usinage. Pour assurer la capitalisation des connaissances d'usinage, la proposition s'appuie sur une structure basée sur les entités d'usinage. Bien que la structure du standard STEP-NC permette l'exploitation d'une telle structure, son utilisation est impossible du fait de sa faible implémentation. C'est pourquoi la proposition se base sur la chaîne numérique actuelle et propose une reconnaissance des entités d'usinage directement depuis les fichiers STL extrait de la simulation d'usinage et propose une conversion des programmes de Code-G en STEP-NC. Cela permet alors d'interagir avec l'implémentation d'OntoSTEP-NC, une ontologie basée sur STEP-NC, comme base de connaissance

Assembly Based Methods to Support Product Innovation in Design for Additive Manufacturing: An Exploratory Case Study

Additive manufacturing (AM) is emerging as an important manufacturing process and a key technology for enabling innovative product development. Design for additive manufacturing (DFAM) is nowadays a major challenge to exploit properly the potential of AM in product innovation and product manufacturing. However, in recent years, several DFAM methods have been developed with various design purposes. In this paper, we first present a state-of-the-art overview of the existing DFAM methods, then we introduce a classification of DFAM methods based on intermediate representations (IRs) and product's systemic level, and we make a comparison focused on the prospects for product innovation. Furthermore, we present an assembly based DFAM method using AM knowledge during the idea generation process in order to develop innovative architectures. A case study demonstrates the relevance of such approach. The main contribution of this paper is an early DFAM method consisting of four stages as follows: choice and development of (1) concepts, (2) working principles, (3) working structures, and (4) synthesis and conversion of the data in design features. This method will help designers to improve their design features, by taking into account the constraints of AM in the early stages

Comparison of tactile and chromatic confocal measurements of aspherical lenses for form metrology

Both contact and non-contact probes are often used in dimensional metrology applications, especially for roughness, form and surface profile measurements. To perform such kind of measurements with a nanometer level of accuracy, LNE (French National Metrology Institute (NMI)) has developed a high precision profilometer traceable to the SI meter definition. The architecture of the machine contains a short and stable metrology frame dissociated from the supporting frame. It perfectly respects Abbe principle. The metrology loop incorporates three Renishaw laser interferometers and is equipped either with a chromatic confocal probe or a tactile probe to achieve measurements at the nanometric level of uncertainty. The machine allows the in-situ calibration of the probes by means of a differential laser interferometer considered as a reference. In this paper, both the architecture and the operation of the LNE’s high precision profilometer are detailed. A brief comparison of the behavior of the chromatic confocal and tactile probes is presented. Optical and tactile scans of an aspherical surface are performed and the large number of data are processed using the L-BFGS (Limited memory-Broyden-Fletcher-Goldfarb-Shanno) algorithm. Fitting results are compared with respect to the evaluated residual errors which reflect the form defects of the surface.EMR