TEMPERATURE ERROR OF THE MEANS OF MEASURING THE GEOMETRIC CHARACTERISTICS OF BORES OF FIREARMS: MATHEMATICAL MODEL AND QUANTITATIVE EVALUATION

Abstract

The work is devoted to the construction of mathematical models and quantitative assessment of the components of the temperature error of a laser triangulation sensor for measuring the geometric characteristics of bores of firearms. The existence of problematic issues in the field of evaluating the metrological characteristics of laser triangulation means for technical diagnostics of firearms barrel channels is highlighted. An analysis of publications on the evaluation of the error of a laser triangulation sensor caused by the influence of ambient temperature is carried out, and known approaches to their mathematical modeling are considered. The need to develop mathematical models of the components of the temperature error of a laser triangulation sensor and to quantify this error is substantiated. The parameters of the optical scheme of the laser triangulation sensor, whose deviation from their nominal (calculated) values will affect the conversion function, are determined. It is shown that the presence of a temperature error during the processing of measurement information will be perceived as an apparent change in the measured value with a constant input signal. On the basis of algebraic transformations of expressions reflecting the relationship between the output value of a laser triangulation sensor and deviations of the optical circuit parameters from their nominal values, mathematical models of the temperature error components are obtained and presented in the form of error component limits at the input of the measuring instrument. The expressions for determining the confidence limits of the total temperature error, taking into account the correlation between its components, are substantiated. A quantitative assessment of the temperature error for the characteristic combinations of weapon parameters (for four ranges of barrel calibers) in the range of ambient temperature variations inherent in the region where measurements are made is carried out. The results of the quantitative evaluation are presented in the form of graphs of the dependence of the limits of relative and absolute temperature errors on temperature and on the increase in the bore radius in the measurement range. The data obtained were analyzed, the peculiarities of the dependencies were determined, and conclusions were drawn about the compliance of the temperature error characteristics of the measuring instrument with the requirements for its accuracy.