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.

The relationship of the parameters of the optical density of the sample and the absorbance of the sample material is studied, which is relevant for the analysis and differentiation of measurement results by devices with light flux filtration and spectral devices (densitometers and spectrophotometers). To identify the analytical dependence of the obtained values of the optical density of the sample and the absorbance of the sample material, a formula is derived for calculating the diffuse optical transmittance density if the detected radiation contains directional and diffuse components. The first term in the obtained formula characterizes the absorbance of the sample material, the second is a correction due to the diffuse component of the radiation, and is a function of the ratio of the diffuse and regular transmittances. Expressions are obtained that allow functional and quantitative determination of the relationship of the absorbance of the sample material and the parameters of the optical transmittance density of the sample. The results of calculating the absorbance of the sample material, the component of diffuse radiation, diffuse optical transmittance density and corrections of these values are presented.

The problem of reducing magnetic losses (no-load losses) in the steel of the magnetic cores of electrical machines is investigated. The tasc of determining the optimal thickness of steel sheets of the magnetic circuit of an electric machine is considered. The criterion for optimality is the minimum power of magnetic losses in steel. Currently, this problem does not have an exact solution due to the fact that the exact ratio of the hysteresis and eddy current components of magnetic losses in steel is unknown. Analyzed the power of magnetic losses in modern electrical machines and devices, depending on the thickness of the sheets of electrical steel. A method is proposed for determining the optimal thickness of steel sheets of the magnetic circuit of an electric machine based on the wattmeter method. In the course of the experiment, two identical magnetic circuits were selected from steel sheets of different thicknesses, for which the losses in steel were measured at different frequencies of magnetization reversal and the optimal thickness of the sheets was calculated. The proposed formula for calculating the thickness of the sheets is valid for both isotropic and anisotropic steel. The proposed technique can be used for both transformers and electric motors and generators.

The paper presents the results of experimental research for the quantitative chemical analysis procedures using the robust parameter design methodology. There is an example of the parameter design in development of the measurement procedure for the mass fraction of chlorine in dusty waste in the ferronickel production. Results of experiment analysis has provided an information about the optimal conditions for sample preparation procedure.