Search

The article discusses the potential of mathematical modeling in understanding the impact of vibrations and seismic waves, aiming at enhancing the sustainability of systems within the mining industry. It explores the dynamic response of a tall, elastic structure with a uniform cross-section and a fixed cylindrical fluid reservoir, subject to various complex boundary conditions. The study delves into the vibrational behavior of the structure when exposed to seismic and harmonic forces, calculating frequency, vibration periods, and deriving formulas for stress, tension, deformation, bending moments, and shear forces in different parts of the structure through both theoretical and experimental approaches. Additionally, the article derives the differential equation for the free oscillation of a tall hydraulic structure in pure bending with an incorporated mass load under appropriate boundary conditions, identifying specific vibration frequencies and periods. The forced vibration scenario is also examined, focusing on the structure's foundation movement due to external harmonic forces. Numerical computation technology is utilized to analyze the change laws of principal quantities that describe both free and forced vibrational movements of the hydraulic structure, showcasing the applicability of these models in predicting and mitigating the effects of seismic activities on mining infrastructure.

This article provides for the possibility of manufacturing crown cutters from foreign-made high-speed steel HSS, which is not inferior to other similar alloys. The article presents the geometric parameters for the manufacture of a new crown cutter and its use in the field of mechanical engineering for cutting holes in the manufacture of machine parts and rolled products. An example is also given of connecting new pipeline lines to an existing pipeline, which is under pressure up to 2.5 MPa, in heat supply and water supply networks. Methods for eliminating vibration when cutting holes on pipes and rolled products using special lubricating coolants are considered. An example of an invented device design is given that cuts holes in pipeline networks used under pressure up to 25 MPa in hydrometallurgical plants for gold mining and in the chemical and oil industries. A practical example of replacing expensive (tungsten) carbide alloys with foreign highspeed alloys HSS is also presented.

In this article, mathematical modeling of quantitative changes in hydrogen and oxide inclusions in aluminum alloys is justified, developed, and analytically implemented. Usually, the methods of linear algebra are mostly used; in particular, the solutions of systems of inhomogeneous algebraic equations are obtained based on the method of Gauss, Cramer, and inverse matrices using the Maple 13 software package. Quantitative changes in hydrogen and oxide inclusions in the alloy are determined by a change in the average dispersion of the loaded flux. The connectivity functions of the change of oxide aluminum in the alloy β (%) with an increase in temperature Т (0С) during the loading of the charge into the liquid bath are obtained. The connectivity functions to determine the change quantity of hydrogen λ (cm3/100 g) in the alloy depending on the time t (minute) holding of the heated charge in the period of research is obtained. Based on functional dependencies, graphs of changes in the mainly desired parameters and numerical indexes in tabular form for engineering and applied calculations are constructed. In particular, graphs of the change quantity of hydrogen and oxide inclusions in the alloy with an increase of average dispersion of the flux d, graphs of change quantity of hydrogen with an increase in temperature during loading of the charge into the liquid bath, changes of the quantity of oxide aluminum in the alloy β (%) with an increase in temperature Т ( 0С), patterns of change quantity of hydrogen in the alloy λ (cm3/100 g) and quantity of oxide η (%) were plotted depending on the time of holding the heated charge in period research.

The article substantiates the relevance and necessity of developing mathematical models in foundry production, as well as the problems and prospects of their use. Based on an analytical review of the world literature on foundry production, it was emphasized that in many studies of the authors and literary sources, not enough attention is paid to the development of mathematical models of the technological process of extracting non-ferrous metals from slag and industrial waste. A brief description of the developed technologies for the high-temperature treatment of industrial slags and waste, separation treatment in electric furnaces, and metals extracted from liquid slag is given. During the development and analytical implementation of the mathematical model, the developed technology for extracting copper from slags is presented as an research object. Based on the study of the dynamics of changes in the thermophysical properties of the components as a function of temperature, a mathematical model of high-temperature treatment of slags is compiled. This will allow you to predict the process of processing slags and the results obtained. Also, a mathematical model of the extraction of copper from the slag is compiled, taking into account the chemical properties of metal inclusions in the slag. This serves as the basis for automating the process of extracting copper from slags and waste products.

In the article, the object of research is the development of a technology for improving the operational properties of cast parts from steel 45, obtained by the method of electroslag remelting. Based on the research results, the modes of heat treatment of the shaft-gear part in an aqueous medium water-oil, heat treatment to increase the service life of the product, and energy-saving melting technology by the method of electroslag remelting were developed. Particular attention is paid to the development and analytical implementation of the mathematical model of the developed technologies by the methods of linear algebra by drawing up the Lagrange interpolation polynomial. Functional dependencies have been obtained for determining the amount of oxygen in the melt depending on the diameter of the electrode and the aluminum content in this electrode for any diameter of the mold, the hardness of the shaft surface depending on its diameter, the oxygen content (amount) in the melt depending on the aluminum content in the electrode for different mold diameters. Based on the developed and analytically implemented mathematical models of the investigated technological process, it seems possible to simplify experimental studies. In other words, based on analytical studies, it is possible to predict the results of subsequent experiments. Based on the developed and analytically implemented mathematical models of the investigated technological process, it seems possible to simplify experimental studies. In other words, based on analytical studies, it is possible to predict the results of subsequent experiments.

The topic of the article is modeling fluid outflow from a channel consisting of three different segments. The subject of research is the outflow of fluid from a channel consisting of three different sections. The article discusses the parameters of the fluid flow in the channel segments of the converging flow section, the section of a constant radius and expanding flow section. Research methods are based on Newton's rheological law; the continuity equation and the Navier-Stokes equation, which are the basic equations of fluid flow; and on the method of mathematical modeling and analytical method of solution. Expressions of hydrodynamic parameters for each segment, with a successively located converging section, a section of a constant radius, and expanding flow sections, are determined in the article by analytical method. Analytical expressions are obtained for the pressure and average flow rate of the fluid in the channel where there are converging rectilinear inlet flow area, cylindrical average area, and expanding rectilinear outlet flow area. The solutions obtained make it possible to determine the flow parameters in the zone of the vibration baffle of pipeline transport of such a geometry that damps vibrations caused by the flow; in the transition sections of the channels of hydraulic drives and in other channels of the fluid flow, which are set to improve the hydrodynamic parameters of the flow.