Andreas Michael Müller

Industrial X-ray computed tomography is a relatively recent technology in the field of 3D coordinate metrology. The available technical solutions represent capable systems, which are continuously adapted for different applications. Nonetheless, some profound limitations and technical challenges remain (e.g. effects of the polychromatic X-ray spectrum and a strong correlation between image quality and measurement duration), which require continuous efforts in order to improve the accuracy of such systems in the context of dimensional metrology. Therefore, this contribution demonstrates the integration of CMM measurement data into a CAD model in order to generate full reference measurements, which can be used to evaluate the measurement accuracy of CT systems. Currently, much effort is being made in order to improve simulations of CT systems with the goal to realistically recreate real CT measurements. In order to validate the simulation model by comparison against physical CT measurements, the geometry of the measurement object has to be known as accurately as possible. The presented approach shows how to generate geometries from CMM reference data which are suited to be used as an input for CT simulation tools. Detailed technical descriptions of the algorithms are given and demonstrated based on real measurements.

The framework of the single point uncertainty developed at the Institute of Manufacturing Metrology (FMT) presents a methodology to determine and evaluate the local measurement uncertainty for a measurement setup by local comparison of a measurement series with an associated reference geometry. This approach, which was originally developed and optimized for the processing of complete areal measurements of work pieces using industrial X-ray computed tomography, was now also extended to line scans found in dimensional testing using tactile coordinate measuring machines (CMMs). The targets of the investigation are spur (involute) steel gear wheels, which can be dimensionally characterized by both helix and profile scans using a CMM in scanning mode in combination with a rotatory table. A second measurement procedure is characterized by a single scan of the complete gear profile without the usage of a rotatory table, using the “free-form scan” CMM functionality. The modification of the single point uncertainty framework in order to determine the single point precision of repeated gear wheel measurements was implemented successfully for gear measurements using the Zeiss Gear Pro evaluation software in combination with a rotatory table as well as unassisted free-form scans of the same gear. The examinations yielded abnormally high random measurement errors, which could not fully be explained within our examinations and was for the most part caused by the accuracy of the used rotatory table of the CMM. The alternative measurement method showed that the CMM system is capable of measuring very precisely in scanning mode if the changes in the curvature of the scan trajectory are favourable.

During the manufacturing of work pieces, geometrical deviations from the intended nominal geometry of the designer are inevitable. The procedure of conformance testing defined in ISO 14253-1:2018-07 is used to ensure the function of a work piece by verifying the geometrical compliance with pre-defined tolerance specifications. Depending on the measurement setup used for the validation step, it is possible that the local measurement uncertainty is too large in order to provide a meaningful conformance evaluation. This paper aims to demonstrate the complete workflow of the determination of the locally defined single point uncertainty and its components (systematic and random measurement error, respectively) for a given measurement task. It was shown for an optical measurement setup in combination with an industrial X-ray computed tomography reference measurement system that different necessary colouring methods of polymer (POM) gear wheels, which are required to enable measurements using structured-light scanning, have a measurable influence on the local distribution of the measurement uncertainty. Because of the fact that the presented method is dependent on a discrete surface sampling, the effects of different polygonization settings during the creation of the areal measurement result were evaluated in order to rate the reduced data complexity against the hereby possibly increased measurement uncertainty. The gained information regarding the local measurement uncertainty of a measurement setup can then be used for downstream processes in various use cases, e.g. for the improvement of holistic tolerance simulation models or the improvement of geometrical measurements using weighted regression analysis. Additionally, the visualization of the areal distribution of the measurement uncertainty enables a powerful tool to optimize the used measurement setup.

In the field of industrial Computed Tomography (CT), the orientation of the workpiece influences the local quality of the reconstructed volume data and therefore dimensional measurements. In the literature, different a priori criteria for an optimal orientation are proposed, which are purely based on the part and setup geometry. However, it is not evident to which extent they correlate with the measurement accuracy or how different quality parameters should be weighted, especially if a wider range of materials and therefore different artefact contributions should be covered. In this work, existing methods and criteria are compared and extended. In contrast to most existing investigations, different quality parameters are evaluated not only globally, but also restricted to relevant regions of interest (ROI). A straightforward derivation for an analytical determination of surface areas affected by cone-beam artefacts is presented. Results show that an ROI-based evaluation is important to find an optimal orientation for single measurands. The investigated quality parameter based on the prediction of surface areas which are affected by cone-beam artefacts was found to be applicable as exclusion criterion. This only holds true if the evaluation is restricted to relevant ROI surface areas, which should also be considered when evaluating the maximum X-ray penetration length as quality parameter. The correlation of the latter with resulting measurement deviations was found to depend on the measurement task.

X-ray computed tomography (CT) enables dimensional measurements of numerous measurands with a single scan, including the measurement of inner structures. However, measurement artefacts complicate the applicability of the technology in some cases. This paper presents a methodology to assess the surface point quality of computed tomography measurements without the requirement of a CAD model. Measurement artefacts lowering the surface point quality can therefore automatically be detected. The correlation of quality values with the random measurement error is demonstrated. The presented method can in principle be used to weight single fit points to reduce the measurement uncertainty of CT measurements.

Zusammenfassung: In dem folgenden Artikel konnte anhand verschiedener Messreihen gezeigt werden, dass die optische Erfassung von Bauteiloberflächen unter verschiedenen Betrachtungswinklen auch zu unterschiedlichen Oberflächentexturkennwerten führt. Die Ergebnisse rechtfertigen die Entwicklung einer daraufhin angepassten messtechnischen Erfassung von Zahnradflanken mit Hilfe einer optischen Strahlumlenkung.

Geometrical work piece deviations are unavoidable and directly affect the function and quality of technological products. Tolerance management is regarded as a crucial subtask of the development of technological products, because it ensures the function as well as a sufficient product quality while maintaining reasonable production costs. That means, that geometric tolerances as an essential part of the product description greatly affect the functional capability, manufacturability, mountability, verifiability and the costs of the final product. The research group FOR 2271 was founded to enable the computer-aided specification of tolerances, which meet the requirements of production, assembly, verification and function by close cooperation between the departments responsible for product design, assembly and metrology. The aim of this contribution is to determine the manufacturing process scatter as well as the measurement uncertainty and establish ways and means to include that information into efficient meta-models, ultimately enabling improved and accurate tolerance analyses.

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As the experimental measurement uncertainty evaluation for computed tomography is currently an expensive and timeconsuming task, numerical uncertainty evaluation (according to GUM Supplement 1) using a virtual CT is a promising alternative. For this digital twin to simulate accurate measurement results, the virtual CT system needs to be modelled as reallistically as possible using adequate input parameters for the simulation. This paper describes a method for the separated determination of two significant input parameters: focal spot size and detector unsharpness. The method is tested using a wide range of measurement parameters on a Zeiss Metrotom 1500 with different test specimen. It could be shown that the method yields reasonable results for most parameters. In addition, there is a dependence of the focal spot size on the ratio of tube voltage and tube current at constant power. This contradicts the wide-spread rule of thumb that the spot size depends on the tube power only. Indications of a changing focal spot shape at high powers could be detected.