New Method for Free-Form Surface Fitting in Precision Metrology

Precision Engineering, 1997

We describe an algorithm that can achieve exact self-calibration for highprecision two-dimensional (2-D) metrology stages. Previous attempts to solve this problem have often given nonexact or impractical solutions. Selfcalibration is the procedure of calibrating a metrology stage by an artifact plate whose mark positions are not precisely known. By assuming rigidness of the artifact plate, this algorithm extracts the stage error map from comparison of three different measurement views of the plate. The algorithm employs the orthogonal Fourier series to expand the stage error map, which allows fast numerical computation. When there is no random measurement noise, this algorithm exactly calibrates the stage error at those sites sampled by the mark array. In the presence of random measurement noise, the algorithm introduces a calibration error of about the same size as the random measurement noise itself, which is the limit to be achieved by any self-calibration algorithm. The algorithm has been verified by computer simulation with and without random measurement noise. Other possible applications of this algorithm are also discussed.

International Journal of Modeling and Optimization, 2017

This paper deals with the manner on which a cloud of points should be generated when measuring a part surface and with the processing procedures needing to be applied in order to characterize the geometry of addressed surface. More precise, an algorithm for surface geometry identification has been developed and implemented by MatLab applications. It finds the necessary number of measuring points, according to surface precision requirements, and their distribution, conform to surface functional role. Basic geometrical features of the surface are assessed by using the coordinates of the resulted cloud of points. A numerical simulation has been performed for sampling the algorithm application.

There is a constant search for more accurate measurement, which generally leads to higher cost, greater complexity, or devices that do not lend themselves to manufacturing environments. For example, surface metrology can be accomplished by a number of methods, ranging from rulers and visual estimation (cheap, fast, and inaccurate) up to fixed Coordinate Measurement Machines (expensive, slow, and accurate). The tradeoffs involved in selecting metrology methods generally involve these three parameters of cost (initial and operation), measurement speed, and accuracy. We present a method of adding one more tradeoff: measurement precision (perpendicular to the surface) vs. sampling resolution (along the surface). Through application of statistical sampling and curve fitting, we can improve precision by approximately the square root of the amount that we decrease resolution. We applied this technique to a number of known and unknown targets, using the Cognitens WLS400 by Hexagon Metrology...

International Journal of Metrology and Quality Engineering, 2012

This research work describes a novel approach for comparing different technologies for free form surface metrology: computerized tomography (CT), photogrammetry and coordinate measuring machines (CMM). The comparison has the aim of providing relevant information for the selection of metrology equipment when measuring free form components. Results demonstrate that there is the imperative need to assess the uncertainty and reproducibility of CT and photogrammetry measurements by applying some calibration procedures taking into account some recommendations for work piece alignment. This article also deals with costs issues, required standards, and necessary additional information when selecting inspection equipment.

Computer-Aided Design, 2014

h i g h l i g h t s • A method is developed for predicting variances of localized measurement points. • Robust rough localization is conducted by matching various geometric properties. • Robust fine localization is conducted by selecting the optimal coordinate system.

Procedia CIRP, 2013

Tolerances for freeform surfaces are specified using profile tolerance that controls form or combination of size, form, orientation and location of a feature(s) relative to a true profile. Freeform surfaces are generally inspected by using fixtures on a coordinate measuring machine (CMM). The combination of fixtures and the CMM enables the establishment of correspondence between points on the machined and nominal surface for tolerance verification. To respond to the market quickly, it has become inevitable to use 3D scanners that can scan an object rapidly and provide dense unorganized points as an output without maintaining any correspondence with the nominal CAD model. Current state of art uses the shortest distance criterion to establish correspondence and verify the profile tolerances. This results in acceptance of parts that ought to be rejected and vice versa. A novel, alternative approach is proposed to overcome this deficiency and verify tolerances specified on a free-form surface. The technique establishes the correct one to one correspondence between the machined surface and CAD model using the Medial axis transform (MAT). The MAT of both the nominal surface and the measured points respectively, are discretised to obtain grids. Corresponding points on the two grids are then used to verify the deviation of the machined surface from the nominal surface. Results of preliminary experiments with simulated data are presented.

Advances in Science and Technology Research Journal, 2017

A difficulty of freeform surfaces evaluations lies in a setup of a coordinate measuring system in general, when it is not possible to use the standard system of alignment by a point, a line, and a surface. An algorithm for the measurement adjustment using a small workpiece coordinate system movement and rotation to achieve a smaller least square error of the produced surface for a given freeform surface defined by the function of two variables is considered. The algorithm uses the Newton method for calculation of the orthogonal distance of a measured point to a given surface and also for minimization of the sum of the distance squares. Numerical results for an example are given.

2001

The ability to construct CAD or other object models from edge and range data has a fundamental meaning in building a recognition and positioning system. While the problem of model fitting has been successfully addressed, the problem of efficient high accuracy and stability of the fitting is still an open problem. In the past researchers have used approximate distance functions rather than the real Euclidean distance because of computational efficiency. We now feel that machine speeds are sufficient to ask whether it is worth considering Euclidean fitting again. This paper address the problem of estimation of elliptical cylinder and cone surfaces to 3D data by a constrained Euclidean fitting. We study and compare the performance of various distance functions in terms of correctness, robustness and pose invariance, and present our results improving known fitting methods by closed form expressions of the real Euclidean distance.

Computer Aided Geometric Design, 2002

In spite of extensive research on fitting parametric surfaces, the published 'standard' solutions often fail, when data points are irregularly distributed over topologically irregular domains, high accuracy is required and the free quantities of least squares fitting-such as the number and placement of knots, the weights of the smoothing functionals and the best parametrisation of the data points-must be set without user assistance. Further difficulties arise when the fitted surface needs to be extended in a natural way and hole loops without underlying point data need to be covered smoothly. This paper attempts to analyse the above difficulties and provide practical solutions to overcome these. Main results include algorithms to compute a good initial parametrisation, a fitting strategy to maintain tight tolerances and smoothness simultaneously, to handle weakly defined control points and a shape dependent knot refinement procedure. A few examples and suggestions for future work conclude the paper.

Procedia CIRP, 2017

3D surface metrology scanners are primarily used for surface reconstruction in reverse engineering and for off-line inspection of parts but, their application potential for in-line process control remains largely unexplored. The lack of usage of 3D surface metrology scanners for in-line process control can be attributed to the large processing time of metrology equipment compared to the cycle time of automotive assembly systems. To overcome this challenge, a novel methodology for adaptive measurement and modelling of data captured by in-line 3D surface measurement systems is proposed in this paper. The methodology models part deviations by augmenting the scanner data with spatio-temporal correlations in deviation field and enables efficient implementation of in-line part shape measurement for process control. The proposed methodology consists of two steps: (i) modelling deviations to enable prediction of entire part deviations with partial measurements, and; (ii) adaptively selecting part regions to be measured by taking into account the measurement data available from the scanner up to current time-step. The partial measurement strategy based on deviation modeling and adaptive region selection results in maximum information gain within the given assembly system cycle time. The prediction of entire part surface deviation with higher confidence leads to effective identification of part-to-part defect variation patterns. The proposed methodology is demonstrated on an automotive door component.