Papers by Keyword: Mathematical Modeling

Abstract: Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

Abstract: In this paper the methods of mechanical testing of metal and the possibility of their implementation, using mathematical modeling by the finite element method in Deform software package, are considered. As the studied parameters, both the strength indicators (yield strength, tensile strength, Brinel micro-hardness), and the plasticity indicator (the number of kinks before the crack is formed), were studied. The values obtained in the simulation have a very high convergence with the real data.

Abstract: The article presents the results of experimental studies to determine the relationship between the electrolysis modes and the properties of electroplating coatings for mathematical modeling of the dynamics of the electrolytic process (MDEP), described by a system of ordinary differential equations due to the complex relationship of the kinetics of chemical reactions, hydrodynamics and mass transfer in the electrolyte flow, the kinematics of electrode plates, and the influence of the electric field of the "anode-cathode" pair on all these processes. At the same time, the experimental base was a series of full-scale experiments to restore the seats of the root supports of cylinder blocks with electroplated coatings. The final result of the research is the procedure for constructing an optimal resource-saving mode of electroplating, which is a zinc-iron alloy.

Abstract: The aim of the study is to construct a mathematical model to describe the effect of a magnetic field on the melt crystallization, in particular cast iron. The authors’ research is based on the hypothesis of the certain energy function existence in the short-range order region, which describes the equilibrium state of the "fluid - short-range order" thermodynamic system. Using the hypothesis, we simulated the effect of a magnetic field on the melt crystallization process, which is based on the fundamental laws of statistical physics and thermodynamics and includes four components: a model of the stationary state of the short-range order region, a model for determining the energy function of the short-range order region, a model of the effect of a proportional magnetic field, a model the effects of a commensurate magnetic field on the crystallization of molten iron. Being based on the simulation results, test calculations were performed, the results of which are confirmed by previously known studies. The simulation results showed that the influence of a magnetic field on the crystallization of melts is insignificant in comparison with thermal motion. The authors of the work believe that the magnetic field acts on the region of short-range order at the formation time at a fluctuation temperature that is much lower than the equilibrium one.

Abstract: The main problem with creating compressed air systems is to properly regulate the flow of water and the flow of air that is fed into the mixing chamber so as to continuously provide a foam that must have adequate fire-fighting properties and remain stable over time. The process of obtaining compression foam is a thermodynamic process, which depending on the specified technological factors can be both isothermal and adiabatic. The nature of the process determines both the geometric and physical properties of the foam, and its possible fluctuations can lead to changes in the physical characteristics of the foam. The work provides recommendations for determining the type of thermodynamic process, which makes it possible to improve the accuracy when creating mathematical models of mobile plants for the production of CAF.

Abstract: This article discusses the possibility of using an unconventional method of heat treatment of a wall structure in winter. The methods of introducing concrete work at a negative outside temperature are analyzed. The basis of the article is the derivation of systems of differential equations characterizing thermal processes during concreting of a wall fragment to previously constructed sections and floor slabs. A mathematical model has been developed that describes heat transfer processes based on the differential heat equation. In compiling the mathematical model, the classical equations of thermophysics are used, which do not require proof of reliability. The article also discusses the classical boundary conditions of the first, second, third, and fourth genera. The reliability of the calculation results was estimated by the experimental method on a fragment of a concrete wall with a given shape thickness. Processing of experimental data was performed using standard methods of mathematical statistics.

Abstract: For optimal experimental design and development of a mathematical model of the relationship between the technological parameters of synthesis and the properties of foam glass materials, statistical methods were used to design an experiment with a mathematical description in the form of a polynomial. A fractional factorial experiment was carried out, multivariate regression models of linear structure were constructed and analyzed, the Pareto model for standardized model variables, the Pareto curve of the dependence of the response function on independent variables, a histogram of the predicted values of the independent variables and their influence on the effective factor, the dispersion model of the indicator values, the projection of the relationship of factors with a dependent variable, the mathematical equation of the relationship of factors and the effective indicator of the response function.

Abstract: Developed was a computer model of temperature field in the tool and parts in the process of their friction stir welding (FSW). Modeling of the temperature field was carried out for both successive stages of welding process, i.e. plunging of pin of tool working element into the part (1^st stage) and progressive motion of plunged pin in the part (2^nd stage). The mathematical model represents a nonlinear equation of transient heat conduction, which takes into account progressive pin movement during the 2^nd stage of welding. Two constituents describe the heat sources, appearing in welding. The first one considers power of heat sources, caused by friction of the tool with the parts on contact surfaces, the second one takes into account heat generation, promoted by mechanical deformation of the part material. Mathematical modeling and experimental examination of temperature field were carried out for tool from cubic boron nitride (cubonit) and hard alloy in copper parts during FSW. Adequacy of the developed model was determined based on correlation of numerical and experimental results.

Abstract: Silicon production by silica-containing raw material reduction by carbon in ore-smelting furnaces (OSF) is a complex pyro-metallurgic process. Silicon is produced in a system consisting of charge, furnace electrodes, air, melt, slag, and gases at temperatures above 2000°C, which generates silicon monoxide and carbide unavoidably. The finished product contains impurities (Fe, Ca, Al, Ti, etc.) in small amounts; however, it is still unknown for sure how impurities, contained in raw materials, behave and interact with each other and with silicon. To analyze the distribution of charge components during smelting, the research team used thermodynamic (mathematical) modeling in Selector software. The constructed four-tank silicon production model describes adequately the process. The assumed tank temperatures correspond to the OSF reaction zones (400°C, 1530°C, 2200°C, and 2000°C). Modeling involves 15 charge-carried elements: quartzite from the Cheremshanskoye deposit, charcoal and black coal, petroleum coke, wood chips, and OSF coal electrodes. According to the model, silicon recovery (with a 97.15 wt% silicon content in the melt) is 75%, which is consistent with literature and production data (AO Kremniy, Shelekhov, Irkutsk Oblast).

Abstract: The paper considered the peculiarities of the numerical mathematical modeling of gradient hardening processes under conditions of complex local loading of the center of deformation. The authors described the mathematical model. They presented the results of modeling in the form of a picture of the change in Odkvist parameter with an increase in the number of passes. Data were given on the comparison of the results of experimental work and mathematical modeling.