Skip to content
Licensed Unlicensed Requires Authentication Published by Oldenbourg Wissenschaftsverlag January 27, 2021

Analysis of the random measurement error of areal 3D coordinate measurements exclusively based on measurement repetitions

Analyse der zufälligen Messabweichungen bei flächenhaften 3D Koordinatenmessungen allein aus Messwiederholungen
  • Andreas Michael Müller

    Since 2016, Andreas Müller has been a research associate at the Institute of Manufacturing Metrology. His main fields of research are applications of GPU computing and efficient computer vision algorithms for dimensional metrology, industrial X-ray computed tomography and measurement uncertainty analysis. He is the scientific coordinator of the research group for X-ray computed tomography.

    EMAIL logo
    and Tino Hausotte

    Tino Hausotte has been professor and head of the Institute of Manufacturing Metrology at the Friedrich-Alexander-University Erlangen-Nuremberg since 2011. Under his management, the institute specialises in research about the topics X-ray computed tomography, surface and coordinate metrology, micro- and nanometrology, photogrammetry and measurement uncertainty evaluation.

From the journal tm - Technisches Messen

Abstract

The measurement uncertainty characteristics of a measurement system are an important parameter when evaluating the suitability of a certain measurement system for a specific measurement task. The measurement uncertainty can be calculated from observed measurement errors, which consist of both systematic and random components. While the unfavourable influence of systematic components can be compensated by calibration, random components are inherently not correctable. There are various measurement principles which are affected by different measurement error characteristics depending on specific properties of the measurement task, e. g. the optical surface properties of the measurement object when using fringe projection or the material properties when using industrial X-ray computed tomography. Thus, it can be helpful in certain scenarios if the spatial distribution of the acquisition quality as well as uncertainty characteristics on the captured surface of a certain measurement task can be found out. This article demonstrates a methodology to determine the random measurement error solely from a series of measurement repetitions without the need of additional information, e. g. a reference measurement or the nominal geometry of the examined part.

Zusammenfassung

Die Messunsicherheit ist ein wichtiger Parameter zur Bewertung der Eignung eines bestimmten Messsystems für eine spezifische Messaufgabe. Die Messunsicherheit kann aus den beobachteten Messabweichungen berechnet werden, welche sich sowohl aus systematischen als auch zufälligen Anteilen zusammensetzt. Während die systematischen Anteile durch Kalibrierung kompensiert werden können, können die zufälligen Anteile grundsätzlich nicht korrigiert werden. Die Messabweichungen verschiedener Messprinzipien können abhängig von den spezifischen Eigenschaften einer Messaufgabe durch verschiedene Effekte beeinflusst werden, z. B. die optischen Oberflächeneigenschaften des Messobjekts bei einer Messung mittels Streifenlichtprojektion oder die Materialeigenschaften bei der Nutzung industrieller Röntgencomputertomografie. Somit kann es unter Umständen hilfreich sein, wenn die räumliche Verteilung der Aufnahmequalität und der Messunsicherheit auf der gemessenen Oberfläche bestimmt werden kann. Dieser Artikel zeigt eine Methodik zur Bestimmung der zufälligen Messabweichungen allein auf Basis von Messwiederholungen ohne dass zusätzliche Informationen, wie z. B. eine Referenzmessung oder die Nominalgeometrie des untersuchten Werkstücks, benötigt werden.

Award Identifier / Grant number: 324672600

Funding statement: The authors would like to thank the German Research Foundation (DFG) for supporting the research project FOR 2271: process-oriented tolerance management based on virtual computer-aided engineering tools under grant number HA 5915/9-2 and for the financial support of the acquisition of the CT system Zeiss Metrotom 1500 through Grant No. 324672600.

About the authors

Andreas Michael Müller

Since 2016, Andreas Müller has been a research associate at the Institute of Manufacturing Metrology. His main fields of research are applications of GPU computing and efficient computer vision algorithms for dimensional metrology, industrial X-ray computed tomography and measurement uncertainty analysis. He is the scientific coordinator of the research group for X-ray computed tomography.

Prof. Dr.-Ing. habil. Tino Hausotte

Tino Hausotte has been professor and head of the Institute of Manufacturing Metrology at the Friedrich-Alexander-University Erlangen-Nuremberg since 2011. Under his management, the institute specialises in research about the topics X-ray computed tomography, surface and coordinate metrology, micro- and nanometrology, photogrammetry and measurement uncertainty evaluation.

Acknowledgment

The authors thank the anonymous reviewers whose comments helped to improve and clarify this manuscript.

  1. Author contributions: “CRediT (Contributor Roles Taxonomy) is high-level taxonomy, including 14 roles, that can be used to represent the roles typically played by contributors to scientific scholarly output. The roles describe each contributor’s specific contribution to the scholarly output.” [4]

    AMM contributed to Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualisation, Writing – original draft and Writing – review & editing. TH contributed to Funding acquisition, Project administration, Resources, Supervision and Writing – review & editing.

References

1. Guide to the expression of uncertainty measurement (GUM:1995): Guide pour l’expression de l’incertitude de mesure (GUM:1995), volume 98-3 of ISO-IEC guide. ISO copyright office, Geneva, first edition 2008, corrected version 2010 edition, 2010.Search in Google Scholar

2. M. Bartscher, U. Neuschaefer-Rube, J. Illemann, F. Borges de Oliveira, A. Stolfi, and S. Carmignato. Qualification and Testing of CT Systems. In S. Carmignato, W. Dewulf, and R. Leach, editors, Industrial X-Ray Computed Tomography, pages 185–228. Springer International Publishing, Cham, 2018. ISBN 978-3-319-59571-9. 10.1007/978-3-319-59573-3_6.Search in Google Scholar

3. G. Berndt, E. Hultzsch, and H. Weinhold. Funktionstoleranz und Meßunsicherheit. Wissenschaftliche Zeitschrift der Technischen Universität Dresden, 17(2):465, 1968.Search in Google Scholar

4. CASRAI. CRediT: CRT, accessed 2020-11-15. URL https://www.casrai.org/credit.html.Search in Google Scholar

5. DIN EN ISO 14253-1:2018-07. Geometrical product specifications (GPS) – Inspection by measurement of workpieces and measuring equipment – Part 1: Decision rules for verifying conformity or nonconformity with specifications (ISO 14253-1:2017).Search in Google Scholar

6. DIN EN ISO 15530-3:2018-09. Geometrical product specifications (GPS) – Coordinate measuring machines (CMM): Technique for determining the uncertainty of measurement – Part 3: Use of calibrated workpieces or measurement standards (ISO 15530-3:2011).Search in Google Scholar

7. B. Heling, A. M. Müller, B. Schleich, T. Hausotte, and S. Wartzack. Consideration and impact assessment of measurement uncertainty in the context of tolerance analysis. In The American Society of Mechanical Engineers, editor, Proceedings of the International Mechanical Engineering Congress and Exposition, 2019.10.1115/IMECE2019-11328Search in Google Scholar

8. F. Härtig and M. Krystek. Berücksichtigung systematischer Fehler im Messunsicherheitsbudget. In 4. Fachtagung Messunsicherheit Messunsicherheit praxisgerecht bestimmen, 2008.Search in Google Scholar

9. W. Knapp. Tolerance and uncertainty. In Laser Metrology and Machine Performance V, pages 357–366. 2001. ISBN 1853128902.Search in Google Scholar

10. A. M. Müller and T. Hausotte. Data fusion of surface data sets of X-ray computed tomography measurements using locally determined surface quality values. Journal of Sensors and Sensor Systems, 7: 551–557, 2018. 10.5194/jsss-7-551-2018.Search in Google Scholar

11. A. M. Müller and T. Hausotte. Comparison of different measures for the single point uncertainty in industrial X-ray computed tomography. In 9th Conference on Industrial Computed Tomography. e-Journal of Nondestructive Testing, 2019a.Search in Google Scholar

12. A. M. Müller and T. Hausotte. Utilization of single point uncertainties for geometry element regression analysis in dimensional X-ray computed tomography. In 9th Conference on Industrial Computed Tomography. e-Journal of Nondestructive Testing, 2019b.Search in Google Scholar

13. A. M. Müller and T. Hausotte. Determination of the single point precision associated with tactile gear measurements in scanning mode. Journal of Sensors and Sensor Systems, 9(1):61–70, 2020d. 10.5194/jsss-9-61-2020.Search in Google Scholar

14. A. M. Müller and T. Hausotte. Improving geometry element regression analysis for dimensional X-ray computed tomography measurements using locally determined quality values. In 10th Conference on Industrial Computed Tomography (iCT2020), 10, 2020b.Search in Google Scholar

15. A. M. Müller, B. Heling, B. Schleich, T. Oberleiter, K. Willner, S. Wartzack, and T. Hausotte. Methoden zur Reduzierung und Berücksichtigung der Unsicherheiten von dimensionellen Messgrößen in der Toleranzanalyse. In S. Wartzack, editor, Industriekolloquium der Forschergruppe FOR 2271, pages 64–73, Stamsried, 2019c. Druck+Verlag Ernst Vögel GmbH. ISBN 978-3-89650-477-7.Search in Google Scholar

16. A. M. Müller, T. Oberleiter, K. Willner, and T. Hausotte. Implementation of Parameterized Work Piece Deviations and Measurement Uncertainties into Performant Meta-models for an Improved Tolerance Specification. Proceedings of the Design Society: International Conference on Engineering Design, 1(1):3501–3510, 2019d. 10.1017/dsi.2019.357.Search in Google Scholar

17. A. M. Müller, L. Butzhammer, F. Wohlgemuth, and T. Hausotte. Automated evaluation of the surface point quality in dimensional X-ray computed tomography. tm - Technisches Messen, 87(2):111–121, 2020a. ISSN 0171-8096. 10.1515/teme-2019-0116.Search in Google Scholar

18. A. M. Müller, D. Schubert, D. Drummer, and T. Hausotte. Determination of the single point uncertainty of customized polymer gear wheels using structured-light scanning with various polygonization settings. Journal of Sensors and Sensor Systems, 9(1):51–60, 2020c. 10.5194/jsss-9-51-2020.Search in Google Scholar

19. T. Oberleiter, A. M. Müller, T. Hausotte, and K. Willner. Surrogate modeling considering measuring data and their measurement uncertainty. In M. Papadrakakis, V. Papadopoulos, and G. Stefanou, editors, Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019), Athens, 2019. Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece.10.7712/120219.6347.18786Search in Google Scholar

20. S. D. Phillips and M. Krystek. Assessment of conformity, decision rules and risk analysis. tm - Technisches Messen, 81(5), 2014. ISSN 0171-8096. 10.1515/teme-2014-1007.Search in Google Scholar

21. VDI/VDE 2630-1.3. Computed tomography in dimensional measurement: Guideline for the application of DIN EN ISO 10360 for coordinate measuring machines with CT sensors, Dec. 2011.Search in Google Scholar

22. VDI/VDE 2630-2.1. Computed tomography in dimensional measurement: Determination of the uncertainty of measurement and the test process suitability of coordinate measurement systems with CT sensors, Jun. 2015.Search in Google Scholar

Received: 2020-11-20
Accepted: 2021-01-14
Published Online: 2021-01-27
Published in Print: 2021-02-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 7.2.2023 from https://www.degruyter.com/document/doi/10.1515/teme-2020-0087/html
Scroll Up Arrow