COMBINED NUMERICAL AND STATISTICAL MODELLING FOR IN-DEPTH UNCERTAINTY EVALUATION OF COMPARATIVE COORDINATE MEASUREMENT

Quality assurance at low cost needs a tight interaction between machining and inspection. For this reason, the modern view of quality control (QC) requires highly repeatable coordinate measuring systems (CMSs) capable of being integrated into the manufacturing process for in-process feedback. Using this method, it becomes possible to reduce scrap levels and production costs while increasing part throughput. CMSs such as coordinate measuring machines (CMMs) have been used for decades in traditional manufacturing industry to ensure that the size and form of a part conform to design specifications. Although CMMs are considered as powerful and accurate measuring systems, most can only maintain or guarantee their measurement capability in quality control rooms typically having environmental temperature control systems set to maintain a nominal 20°C and maximum variation typically limited to ±2°C.However, shop floor environments have significant variability in ambient temperature. The need in manufacturing for dimensional inspection on the shop floor has led to many technological advancements in manufacturing metrology during recent years. In particular, a recent development includes a parallel kinematic machine (PKM)-based automatic flexible gauge, which is the system under investigation for this thesis. In order to be able to determine the measurement capability of a measuring or gauging machine to dimension a part reliably, it is necessary to evaluate the measurement uncertainties. This thesis first employs the design of experiments (DOE) approach to implement a practical analysis of measurement uncertainty of the automated flexible gauge. Several experimental designs are applied to investigate the influence of various key factors and their interaction on the uncertainty associated with coordinate measurement in comparator mode, in which the geometry of a part is compared with that of a calibrated master part nominally of the same shape. The ISO 15530-3 method is applied to derive uncertainty budgets for the flexible gauging system. A comparison is then made between typical shop floor measurement methods namely hard gauging, on-machine probing (OMP) and the automated flexible gauge. A set of identical test pieces was manufactured and then measured repeatedly using each method, with process and operator variability added as necessary to include typical industrial conditions. The measurement uncertainty is then calculated and compared for each of the measurements. The results show the measurement uncertainty of the comparator technique, which are lower than would be expected from an absolute measurement under workshop conditions. Finally, Markov chain Monte Carlo (MCMC) methods are applied to evaluate uncertainty associated with comparative coordinate measurement using a more realistic probability model to avoid repeating measurements. Samples are drawn from the unnormalized posterior using Gibbs sampling. Another feature of this thesis is the developed empirical method based on Bayesian regularized artificial neural networks (BRANNs) for estimating point coordinates and associated uncertainties when no satisfactory measurement model can be developed and large experimental designs are not practical. The effectiveness of the proposed method is demonstrated using two case studies

A novel method based on Bayesian regularized artificial neural networks for measurement uncertainty evaluation

Coordinate measuring machines (CMMs) are complex measuring systems that are widely used in manufacturing industry for form, size, position, and orientation assessment. In essence, these systems collect a set of individual data points that in practice is often a relatively small sample of an object. Their software then processes these points in order to produce a geometric result or to establish a local coordinate system from datum features. The subject of CMM evaluation is a broad and multifaceted one. This paper is concerned with the uncertainty in the coordinates of each point within the measuring volume of the CMM. Therefore, a novel method for measurement uncertainty evaluation using limited-size data sets is conceived and developed. The proposed method is based on a Bayesian regularized artificial neural network (BRANN) model consisting of three inputs and one output. The inputs are: the nominal coordinates; the ambient temperature; and the temperature of the workpiece. The output is the measured (actual) coordinates. An algorithm is developed and implemented before training the BRANN in order to map each nominal coordinate associated with the other inputs to the target coordinate. For validation the model is trained using a relatively small sample size of ten data sets to predict the variability of a larger sample size of ninety data sets. The calculated uncertainty is improved by more than 80% using the predicted variability compared to the uncertainty from the limited sample data set

Developments in automated flexible gauging and the uncertainty associated with comparative coordinate measurement

Traditional manufacturing uses coordinate measuring machines (CMMs) or component-specific gauging for in-process and post-process inspection. In assessing the fitness for purpose of these measuring systems, it is necessary to evaluate the uncertainty associated with CMM measurement. However, this is not straightforward since the measurement results are subject to a large range of factors including systematic and environmental effects that are difficult to quantify. In addition, machine tool errors and thermal effects of the machine and component can have a significant impact on the comparison between on-machine measurement, in-process measurement and post-process inspection. Coordinate measurements can also be made in a gauging/comparator mode in which measurements of a work piece are compared with those of a calibrated master artefact, and many of the difficulties associated with evaluating the measurement uncertainties are avoided since many of the systematic effects cancel out. Therefore, the use of flexible gauging either as part of an automated or manually-served workflow is particularly beneficial

Modelling uncertainty associated with comparative coordinate measurement through analysis of variance techniques

Over the last few years, various techniques and metrological instruments have been proposed to achieve accurate process control on the shop floor at low cost. An efficient solution that has been recently adopted for this complex task is to perform coordinate measurement in comparator mode in order to eliminate the influence of systematic effects associated with the measurement system. In this way, more challenging parts can be inspected in the shop floor environment and higher quality products can be produced while also enabling feedback to the production loop. This paper is concerned with the development of a statistical model for uncertainty associated with comparative coordinate measurement through analysis of variance (ANOVA) techniques. It employs the Renishaw Equator comparative gauging system and a production part with thirteen circular features of three different diameters. An experimental design is applied to investigate the influence of two key factors and their interaction on the comparator measurement uncertainty. The factors of interest are the scanning speed and the sampling point density. In particular, three different scanning speeds and two different sampling point densities are considered. The measurands of interest are the circularity of each circular feature. The present experimental design is meant to be representative of the actual working conditions in which the automated flexible gauge is used. The Equator has been designed for high speed comparative gauging on the shop floor with possibly wide temperature variation. Therefore, two replicates are used at different temperature conditions to decouple the influence of environmental effects and thus drawing more refined conclusions on the statistical significance

Evaluation of automated flexible gauge performance using experimental designs

An essential part of assessing whether a measurement or gauging system meets its intended purpose is to estimate the measurement uncertainties. This paper employs the design of experiments (DOE) approach to implement a practical analysis of measurement uncertainty of Renishaw Equator automated flexible gauge. The factors of interest are measurement strategy, part location, and environmental effects. The experimental results show the ability of the versatile gauge to effectively meet its measurement capability in both discrete-point probing and scanning measuring modes within its whole measuring volume and, in particular, at high scanning speeds and under workshop conditions

Uncertainty evaluation associated with versatile automated gauging influenced by process variations through design of experiments approach

Recent advances in versatile automated gauging have enabled accurate geometric tolerance assessment on the shop floor. This paper is concerned with the uncertainty evaluation associated with comparative coordinate measurement using the design of experiments (DOE) approach. It employs the Renishaw Equator which is a software-driven comparative gauge based on the traditional comparison of production parts to a reference master part. The fixturing requirement of each production part to the master part is approximately ±1 mm for a comparison process with an uncertainty of ±2 μm. Therefore, a number of experimental designs are applied with the main focus on the influence of part misalignment from rotation between master and measure coordinate frames on the comparator measurement uncertainty. Other factors considered include measurement mode mainly in scanning and touch-trigger probing (TTP) and alignment procedure used to establish the coordinate reference frame (CRF) with respect to the number of contact points used for each geometric feature measured. The measurement uncertainty analysis of the comparator technique used by the Equator gauge commences with a simple measurement task using a gauge block to evaluate the three-dimensional (3D) uncertainty of length comparative coordinate measurement influenced by an offset by tilt in one direction (two-dimensional angular misalignment). Then, a specific manufactured measurement object is employed so that the comparator measurement uncertainty can be assessed for numerous measurement tasks within a satisfactory range of the working volume of the versatile gauge. Furthermore, in the second case study, different types of part misalignment including both 2D and 3D angular misalignments are applied. The time required for managing the re-mastering process is also examined. A task specific uncertainty evaluation is completed using DOE. Also, investigating the effects of process variations that might be experienced by such a device in workshop environments. It is shown that the comparator measurement uncertainties obtained by all the experiments agree with system features under specified conditions. It is also demonstrated that when the specified conditions are exceeded, the comparator measurement uncertainty is associated with the measurement task, the measurement strategy used, the feature size, and the magnitude and direction of offset angles in relation to the reference axes of the machine. In particular, departures from the specified part fixturing requirement of Equator have a more significant effect on the uncertainty of length measurement in comparator mode and a less significant effect on the diameter measurement uncertainty for the specific Equator and test conditions