MATHEMATICAL MODEL OF THE OPTICAL-MECHANICAL SENSOR FOR MEASURING OF GEOMETRIC CHARACTERISTICS OF FIREARMS BORES

Abstract

The work is devoted to the study of the characteristics of the optical-mechanical sensor for the measurement control of geometric characteristics of firearms bores.

The results of the analysis of publications devoted to the structure and application of measuring devices based on the triangulation method of distances determining are given. The limited possibility of applying of the results obtained in known works in the creation of an optical-mechanical sensor for diagnosing of firearms bores was noted.

Features of construction and basic geometric parameters of the optical-mechanical sensor are considered. A description of the measurement method is given, which provides for the calculation of the desired distance using the known parameters of the optical scheme of the optical-mechanical sensor and the linear and angular parameters of the triangles consisting of the elements of the optical scheme of the sensor.

An expression for the dependence of the angle between the optical axis of the receiving lens and the light-sensitive detector from other basic geometric parameters of the optical-mechanical sensor was obtained using the basic formula for a thin lens. The expression determines the angular position of the light-sensitive detector in relation to the main optical axis of the receiving lens and should be taken into account as a limitation in the practical implementation of the sensor.

The conversion function of the optical-mechanical sensor is determined, which establishes the dependence between the increment of the coordinate of the light spot on the surface of the light-sensitive detector of the sensor and the increment of the radius of the bore. An expression for solving the inverse problem – calculating the value of the input value based on measurement information about the output value – was obtained. Graphs of these functions for typical combinations of optical-mechanical sensor parameters are given. A study of the linearity of the conversion function of the optical-mechanical sensor and the nature of its sensitivity change within the range of measurement was conducted.