Advances in Large-Scale Metrology – Review and future trends

https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1467&context=mechengfacpub

Task Specific Uncertainty in Coordinate Measurement

Thirty years since their invention, laser trackers are now recognized as the measurement tool of choice in the manufacture and assembly of large components. The general design of laser trackers, i.e., a ranging unit on a two-axis gimbal, has not changed significantly over the years. However, innovations in ranging technology, for example, the emergence of increasingly accurate absolute distance meters (ADMs), are providing users with an alternative to interferometers (IFMs). Hand-held accessories such as touch probes and line scanners are expanding the scope and applicability of laser trackers. In this paper, we survey the literature in all areas of laser trackers as applied to large-scale dimensional metrology (LSDM), with emphasis on error modeling, measurement uncertainty, performance evaluation and standardization.

Laser trackers for large-scale dimensional metrology: A review

X-ray computed tomography (CT) is uniquely suited for dimensional measurement of components having internal geometry, difficult-to-reach part features, and easy-to-deform or flexible structures. Through the development of standards it is also becoming accepted as a metrology tool. The objectives of this study are to compare dimensional measurements on artifacts containing internal structures and mechanically compliant features using current state-of-the-art CT and coordinate measure machine (CMM) techniques. It also aims to discuss some of the issues with recently developed standards for CT measurement uncertainty estimation. To illustrate the challenges of CMM and the potential of X-ray CT for reliable dimensional inspection, two different problems are presented: 1) characterization of internal geometry in a metallic artifact that has features inaccessible to tactile or vision-based measurement techniques; and 2) evaluation of dimensional measurement of diameters, form, and relative distances in the components of a flexible object with stems that bend due to mechanical contact by tactile instruments, e.g., CMM. In addition, some issues with the direct application of the ISO 15530 series for the estimation of CT measurement uncertainties are discussed, and a generalized formalism for uncertainty budgeting in CT metrology (still based on the ISO 15530 guidelines but with some differences) is applied to the measurements presented throughout this paper. For dimensions of geometric features ranging from 0.6 mm to 65 mm, a comparison between CT and CMM measurements typically resulted in differences of approximately 5 μm or less for most of the measurements, while expanded uncertainties computed for the CT measurements ranged from 1 to 20 μm. CT measurements on the internal geometries resulted in uncertainties comparable to CMM data that were obtained with the metallic artifact disassembled. However, in the particular case of measuring compliant structures, the conventional CMM strategies led to large systematic errors in the measurements. It is demonstrated that using extrapolation methods, measurements from these two systems converged to within ±2 μm.

Dimensional metrology with X-ray CT: A comparison with CMM measurements on internal features and compliant structures

The substitution method—an empirical approach for uncertainty assessment (adapted from the ISO 15530-3 guidelines) that is based on a comparison between repeated measurements of a calibrated standard workpiece and measurements of a test (uncalibrated) sample—has been the approach most adopted over the past decade for estimation of measurement uncertainties in dimensional metrology with X-ray computed tomography (CT). However, questions about how to apply the substitution (or use calibrated workpieces) for X-ray CT metrology persist because the substitution method does not always encompass all the most relevant CT measurement influencing factors. This paper discusses some issues with the direct application of the ISO 15530 series for the estimation of CT measurement uncertainties and reviews other empirical methods that can be applied in uncertainty analyses in CT metrology. Special attention is placed to the treatment of uncertainties in the case of ‘uncorrected’ measurement results (i.e., not compensated for bias), which for X-ray CT has traditionally been limited to the use of the root-sum-of-squares of standard uncertainties (RSSu) approach. This article investigates other possibilities for uncertainty estimation of ‘uncorrected’ results that could be applied to CT measurements, namely the root-sum-of-squares of expanded uncertainties (RSSU), the algebraic sum of expanded uncertainty with the signed bias (SUMU), the enlargement of the expanded uncertainty by adding the absolute value of the bias (SUMUMAX), and the so-called Ue method that sums the expanded uncertainty with the absolute value of the bias scaled by a factor e assigned for a 95% distribution coverage. In addition, the alternative of using a maximum permissible error ( M P E ) statement—typically specified by the manufacturer of the CT instrument—to generate a rough estimate of the expanded uncertainties of CT measurements is considered. Through two examples using dimensional X-ray CT data, these possibilities are analyzed. From all the possibilities for estimation of uncertainties associated with CT dimensional measurements that are not compensated for bias, the RSSu method produced the largest uncertainty estimates and thus seems to be the most conservative approach. For dimensioning geometric features mostly ranging between 10 mm and 60 mm, the expanded uncertainties ( k = 2 ) computed with the RSSu method ranged from 0.6 μm up to 72.7 μm. It was with the asymmetrical SUMU approach that the smaller uncertainty intervals were generated. On the other hand, uncertainty bounds estimated with the M P E based approach changed little from a constant value (around ±9.5 μm), and, therefore, risk creating significant under- or over-estimation of the uncertainty intervals.

Empirical approaches to uncertainty analysis of X-ray computed tomography measurements: A review with examples

We present a detailed model of dimensional changes in long length artifacts, such as step gauges and ball bars, due to bending under gravity. The comprehensive model is based on evaluation of the gauge points relative to the neutral bending surface. It yields the errors observed when the gauge points are located off the neutral bending surface of a bar or rod but also reveals the significant error associated with out-of-straightness of a bar or rod even if the gauge points are located in the neutral bending surface. For example, one experimental result shows a length change of greater than 1.5 µm on a 1 m ball bar with an out-of-straightness of 0.4 mm. This and other results are in agreement with the model presented in this paper.

/pdf/a-model-for-geometry-dependent-errors-in-length-artifacts-1e1vvmo4g3.pdf

A Model for Geometry-Dependent Errors in Length Artifacts.

: This paper proposes a method to extend the current ISO Guide to the Expression of Uncertainty in Measurement to include the case of known, but uncorrected, measurement bias. It is strongly recommended that measurement results be corrected for bias, however in some situations this may not be practical, hence an extension of the Guide is proposed to address this special situation. The method keeps with the spirit of the Guide in maintaining the link between uncertainty and statistical confidence. Similarly, the method maintains the transferability of one uncertainty statement to be included as a component in another uncertainty analysis. The procedure involves modifying the calculation of the expanded uncertainty, allowing it to become asymmetric about the measurement value. The method is compared to other alternative procedures, and an illustration of how it affects tolerance zones is presented.

/pdf/guidelines-for-expressing-the-uncertainty-of-measurement-j3r43r8bwz.pdf

Guidelines for Expressing the Uncertainty of Measurement Results Containing Uncorrected Bias.

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A Model for Geometry-Dependent Errors in Length Artifacts.

Guidelines for Expressing the Uncertainty of Measurement Results Containing Uncorrected Bias.