The dependence of coordinate measurements error of the geometric elements shape characteristics of products on the control points number

Abstract

The issues of estimating the error of coordinate measurements of the shape characteristics of geometric elements of products depending on the number of control points, taking into account a given confidence probability, are considered. Analytical models are proposed for estimating the error based on a priori data, similar to estimating uncertainty by type B. The correspondence of model and experimental results is verified by the Monte Carlo method using a specially developed program in VBA and the library functions of the Statistical Analysis package of the Microsoft Excel program. Such a characteristic of the shape of the part as roundness is investigated. The influence of the parameters of regular structures associated with the features of the technological processes of manufacturing the part on the parameters of the distribution function of the coordinates of the control points is revealed. Fourier analysis is used to identify and quantify regular structures on the surface of the part. The sources of error that have a significant impact on the results of measurements of the shape characteristics of geometric elements of products are given. Based on the results of statistical calculations, the dependence of the measurement error of the shape characteristics on the number of control points is analyzed, the scope of application of analytical formulas for estimating the error of single measurements for a given confidence probability is determined. The article is intended for specialists in the field of practical coordinate metrology and related fields.