The assessment and application of form evaluation algorithms in coordinate metrology
Three-dimensional coordinate measurements present a range of new challenges to measurement instruments and to the numerical algorithms, which significantly determine the performance of the measurements. Advanced measurement techniques provide a means of obtaining the data points that are accurately representative of the inspected surfaces. Numerical form evaluation algorithms characterize geometric dimensions and verify the conformance to a given tolerance from the 3D measurement data, which is linked the design process and dimension inspection. This thesis addresses mainly the form evaluation algorithms. Generally, two types Qf algorithms are employed in the form evaluation software of coordinate measurements: the least squares methods and the Mini-max methods. Other methods, such as minimum average deviation method, error curve analysis methods have also been proposed and employed. Different algorithms are based on different mathematical principles and may provide different form evaluation parameters on the same data set. This inconsistency is a significant issue and is a focus of current research. This thesis examines the present controversy to help users to select and employ appropriate form evaluation algorithms. For these purposes, taking spheres as an example, a set of criteria has been drawn up for comparing the existing form evaluation algorithms and selecting a proper algorithm for a specific measurement case. The criteria aim to control and minimize the influence of the measurement error, form errors and the evaluation algorithms on the inspection results. Based on these criteria, appropriate procedures for comparison and selection of the algorithms, such as computer simulation and experimental methods have been developed. General recommendations for the use of these algorithms have been given. From the conclusions of comparison and selection of the algorithms, it is found that the non-linear least square method (NLS) can derive a random measurement uncertainty on the estimated radius of a sphere which is independent of the form error of the measured spheres. Therefore, the random error propagation model of the estimated radius derived by the NLS method has been formulated, which can be used to provide a measurement uncertainty for any single measurement and applied to predict the random errors of a CMM. Also, by analysing the estimated parameters of the calibrated sphere, such as the deviation of the estimated radius, sphericity and residual error, the squareness errors of a CMM has been modelled mathematically and predicted. The criteria for judging the algorithms are concerned with the accuracy indices of the estimated geometric parameters. For any algorithm, it is assumed that data points are reasonably accurate and representative of the geometric elements concerned. To obtain a reliable assessment of geometric form, data pre-processing is necessary. In this thesis, an approach of data pre-processing by operating on the data according to the functional requirements of nominally spherical objects has been introduced and applied. Taking eroded electrical contacts as examples, an approach to pre-processing data, referred to as the Defect Removal Method, is proposed and developed.