Skip to main content
main-content
Top

Hint

Swipe to navigate through the articles of this issue

Published in: Measurement Techniques 9/2021

08-02-2022 | LINEAR AND ANGULAR MEASUREMENTS

Dependence of the Coordinate Measurement Error of Geometric Elements’ Shape Characteristics on the Control Point Number

Authors: M. F. Danilov, A. P. Ivanova

Published in: Measurement Techniques | Issue 9/2021

Login to get access
share
SHARE

Abstract

This article presents issues in estimating the coordinate measurement error of geometric elements’ shape characteristics of products depending on the control point number, taking into account a given confidence probability. Analytical models are proposed for estimating the error based on a priori data, similar to estimating uncertainty by type B. The correspondence of the model and experimental results are verified by the Monte Carlo method using an especially developed program in VBA and the library functions of the Statistical Analysis package of the Microsoft Excel program. The roundness characteristic is also investigated. The influence of the parameters of regular structures and the aspects of the technological processes of manufacturing of control point coordinates is revealed. Fourier analysis is performed to identify and quantify regular structures on the surface. This article also presents error sources that have a significant impact on the measurement results of the shape characteristics of products’ geometric elements. Based on the statistical calculation results, the dependence of the measurement error of the shape characteristics on the control point number is analyzed, and the scope of the application of analytical formulas for estimating the error of single measurements for a given confidence probability is determined. This study can be of use by specialists in the field of practical coordinate metrology and related fields.
Literature
2.
go back to reference A. O. Cheveleva and M. A. Bolotov, “Investigation of the influence of technological heredity on the formation of a measurement technique on a coordinate measuring machine when detecting non-flatness of aircraft parts,” Vest. Samarsk. Gos. Aerokosm. Univ., No. 5 (36), 118–124 (2012). A. O. Cheveleva and M. A. Bolotov, “Investigation of the influence of technological heredity on the formation of a measurement technique on a coordinate measuring machine when detecting non-flatness of aircraft parts,” Vest. Samarsk. Gos. Aerokosm. Univ., No. 5 (36), 118–124 (2012).
3.
go back to reference M. N. Selivanov, A. E. Fridman, and Zh. F. Kudryashova, Measurement Quality. Metrological Reference Book, Lenizdat, Leningrad (1987). M. N. Selivanov, A. E. Fridman, and Zh. F. Kudryashova, Measurement Quality. Metrological Reference Book, Lenizdat, Leningrad (1987).
4.
go back to reference D. Flack, CMM Measurement Strategies, NPL Measurement Good Practice Guide, No. 42, National Physical Laboratory, UK (2001). D. Flack, CMM Measurement Strategies, NPL Measurement Good Practice Guide, No. 42, National Physical Laboratory, UK (2001).
5.
go back to reference N. Maheshwari, On the Selection of CMM Based Inspection Methodology for Circularity Tolerances, Elseiver (2001). N. Maheshwari, On the Selection of CMM Based Inspection Methodology for Circularity Tolerances, Elseiver (2001).
6.
go back to reference P. S. Serenkov, “Application of nonparametric models for evaluating the uncertainties of measurement results,” Vestn. Beloruss.-Ross. Univ. Priborostr., No. 3 (48), 109–115 (2015). P. S. Serenkov, “Application of nonparametric models for evaluating the uncertainties of measurement results,” Vestn. Beloruss.-Ross. Univ. Priborostr., No. 3 (48), 109–115 (2015).
8.
go back to reference S. A. Kononogov and V. G. Lysenko, Coordinate Metrology: Monograph, ASMS, Moscow (2010). S. A. Kononogov and V. G. Lysenko, Coordinate Metrology: Monograph, ASMS, Moscow (2010).
9.
go back to reference L. Zachs, Statistical Estimation, Statistika, Moscow (1976). L. Zachs, Statistical Estimation, Statistika, Moscow (1976).
11.
go back to reference G. B. Dwight, Tables of Integrals and Other Mathematical Formulas, Nauka, Moscow (1977). G. B. Dwight, Tables of Integrals and Other Mathematical Formulas, Nauka, Moscow (1977).
Metadata
Title
Dependence of the Coordinate Measurement Error of Geometric Elements’ Shape Characteristics on the Control Point Number
Authors
M. F. Danilov
A. P. Ivanova
Publication date
08-02-2022
Publisher
Springer US
Published in
Measurement Techniques / Issue 9/2021
Print ISSN: 0543-1972
Electronic ISSN: 1573-8906
DOI
https://doi.org/10.1007/s11018-022-01993-x