The conditions for the appearance of instability have been analyzed in solving typical problems of coordinate measurements of the geometric parameters of products. The connection is shown between unstable problems of coordinate measurements and ill-conditioned systems of linear equations, and also with the parameters of the geometric elements that show signs of degeneracy. Formulas have been derived for estimating measurement error of the parameters of a circle, coaxiality of cylinders, and parallelism of planes. It has been established that the experimental results are consistent with the theoretical ones.
Similar content being viewed by others
References
V. P. Suslin and A. V. Dzhunkovskii, “Application of the method of regularization to solve ill-conditioned problems of coordinate measurements,” Izmer. Tekhn., No. 7, 23–26 (2009).
A. E. Umnov, Analytical Geometry and Linear Algebra: Textbook, MFTI, Moscow (2011).
I. B. Petrov and A. I. Lobanov, Lectures on Computational Mathematics: Textbook, Internet University of Information Technologies, BINOM, Moscow (2006).
GOST P 53442–2015, Characteristics of Geometric Products. Establishment of Geometric Tolerances. Tolerances for Form, Orientation, Location, and Runout.
M. F. Danilov, A. P. Ivanov, and A. A. Savel’eva, “Evaluation of the error of coordinate measurements of the geometric parameters of a component based on a priori data,” Izmer. Tekhn., No. 3, 23–27 (2018).
Ya. S. Bugrov and S. M. Nikol’skii, Higher Mathematics. Elements of Linear Algebra and Analytical Geometry, Nauka, Moscow (1980).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izmeritel’naya Tekhnika, No. 6, pp. 41–45, June, 2018.
Rights and permissions
About this article
Cite this article
Danilov, M.F., Savel’eva, A.A. Analysis of Basic Data of Unstable Problems of Coordinate Measurements of Geometrical Parameters of Products. Meas Tech 61, 588–594 (2018). https://doi.org/10.1007/s11018-018-1469-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11018-018-1469-3