Papers by Keyword: Mathematical Model

Abstract: This article describes the problems of deterioration of the quality of processed raw materials due to depletion of mineral resources. It is proposed to use nitric acid for the processing of complex refractory low-grade concentrates containing non-ferrous and noble metals. It was found that the studied concentrate contains: sphalerite (26.9 %), pyrite (22.0 %), chalcopyrite (19.9 %), silica (13.9 %), alumina (5.5 %), galena (1.7 %), oxidized forms of iron (Fe₂O₃) (12 %). Gold and silver are associated with sulfide minerals. Typical reactions of interaction of these minerals with nitric acid are considered. A sufficiently high thermodynamic probability of these reactions in a wide temperature range is established. With the use of mathematical methods, the optimal conditions of the process of nitric acid leaching are selected: the ratio of L:S = 5:1; the concentration of nitric acid 10 mol/L; the duration of the process is 60 minutes. In this case, the extraction of copper, zinc, iron and sulfur into the solution was 99.00 %, 99.84 % 98.60 %, 88.51 %, respectively.

Abstract: The article presents the mathematical model worked out for calculating the operating force of the wire drawing. The solution of the problem was achieved by dividing the wire work piece material in the deformation zone into an infinitely small finite elements ij; and, by parting the working area of the die geometry, consisting of crimping cone, drawing cylinder and the radius of curvature between them into infinitely small linear sections. The authors described the conditions for continuity at the finite element line, the dependencies required to determine the geometric grid sizes. To determine the total modified draw force, the authors obtained formulas to describe the stress condition at each point of the finite element, based on the motion equations, equations of velocity fields, the incompressibility condition, the deformation rate intensity, taking into account the speed factor and viscoplastic properties of the work material. The article presents the adequacy of the proposed model.

Abstract: The aim of this article is to develop the mathematical model to describe response of endodontic file in curved root canal during the preparation of root canal using fracture mechanics approach. Any obturation process involves the filling of prepared root canal using bio-compatible materials like gutta-percha. During preparation of infected root canal, substrate, dead tissue and pulp is removed and tapered shape is formed so that any practitioner can fill it effectively. During preparation process of root canal, the canal wall applies locking action and causes resistance to motion of endodontic file, finally resulting into fatigue failure. This article described plastic behavior of endodontic file in curved root canal, mathematical model describing the necessary condition for crack growth in endodontic file, a mathematical model describing plastic zone size for crack on surface of endodontic file, a mathematical model describing crack tip opening displacement for crack on surface of endodontic file and mathematical model for pure-combined torsion and bending consideration for design of endodontic file. The mathematical model described is helpful for the Endodontic experts, researchers, design engineers. However the applicability of the described mathematical model limited to assumption of study. The gap between root canal to be prepared and endodontic file is zero while preparation. The endodontic file weight, speed of rotation and substrate removal rate is assumed to be constant. The mathematical model for endodontic file discussed above proved to be efficient tool for studying the root canal preparation.

Abstract: The mathematical modeling of wildland fires impact on buildings have been carried out to study the effects of fires at different conditions of buildings ignition. The forest is modeling as a porous reactive medium. The formulation of this problem was developed using standard nonstationary three-dimensional Reynolds equations for flow in a multiphase reactive medium. These equations are solved numerically using finite volume method. The influence of meteorological conditions, properties of the forest and its state on the possibility of ignition of buildings located near forests is studied.

Abstract: The paper studies the influence of various constructive factors on the parameters of design reliability and bearing capacity of span prestressed reinforced concrete structures. With the help of experimental design techniques and an effective software package, 12 adequate mathematical models have been developed and brought to the level of practical use. They allow to predict the reliability and bearing capacity of normal and oblique sections of specified structures for any combinations of concrete class, reinforcement class and reinforcement ratio. These models also allow to investigate both the direction of the change in bearing capacity and reliability index of prestressed reinforced concrete elements with the change of the above-mentioned factors, which is useful in solving some optimization problems at the design stage.

Abstract: Electrical and thermal processes, occurring while heating materials in metallic capacities of cylindrical form, are examined. The peculiarities of those processes are defined, and it is shown that their essence is in the way of distributing the sources of heat, while using different methods of electrical heating, in the change of properties of the heated material under varying temperature and in the course of the process in time. Mathematical model to calculate the thermal process, taking place in the heated material, taking into consideration the changes of its thermal parameters, as well as the character of the controlling electrical actions, is developed. On the basis of differential equation of the process of heating and boundary conditions, difference equations are formed, which allow to solve the task by numerical method. The solution is carried out by the method of passing. Analytical dependences to determine the coefficient of the method of passing, and temperature in the random point of the heated material are obtained. It is proposed to carry out the correction of the thermal parameters of the heated material while calculating the coefficients in the process f the “direct” course of the method of passing. The values of temperature of the material, obtained in the period of the preceding “reverse” course of passing, are taken into consideration with that. The opportunity to concentrate the sources of heat both in the internal and external covers of the installation is realized. The change of intensity of their action in time is possible, and that allows to reproduce a wide range of the controlling actions. Algorithm for task solution on the electronic computer is developed. The example for calculating the thermal process of concrete heating in winter time is considered.

Abstract: This work presents a theoretical and experimental study of drying of sisal fibers. The fibers were submitted to drying in oven with forced air circulation at temperatures ranging from 50°C up to 90°C. Drying and heating lumped models were proposed and fitted to the experimental data. Non-linear regression analyzes were performed to verify the consistency of the models to predict the experimental data. It was verified that the curves of moisture loss and temperature of the sisal fibers were influenced by the drying-air temperature, showing a gradual variation with the drying time, being more accentuated in the higher temperatures of the drying-air. The fitted models presented good agreement with the experimental data.

Abstract: This article describes a method for the hydrochemical dissolution of a sulfide gold-bearing raw material from the Uderey’s deposit using nitric acid. The chemical and phase compositions of the studied material, mainly represented by compounds of silicon, sodium, arsenic, iron and sulfur, are investigated. Phase composition: pyrite, arsenopyrite, quartz, thenardite. The dependences of the influence of temperature, time, and the liquid to solid ratio on extracting the main components in the solution were determined by methods of mathematical experiment planning. The calculated values ​​of the determination coefficients testify to the adequacy of the chosen two-level model. The optimum parameters of the process were obtained: L/S ratio = 8; the nitric acid concentration was 6 M; experiment duration was 75 minutes.

Abstract: The process of a eutectic alloy crystallization is considered when the eutectic alloy is instantly cooled from the liquid state to below the eutectic transformation temperature. The features of such crystallization are considered. The mathematical model of the process is constructed that takes into account the nucleation of new phases particles, their growth and the associated change the concentrations of the melt components. The nuclei of new phases are supposed be spherical. As they grow, they come into contact and become lamellar. The developed approach was applied to the amorphization process of the eutectic alloys. An amorphous state has been reached if the clusters of solid phases can’t grow above nanosize. The model allows researching the necessary amorphization conditions.

Abstract: A mathematical model of the overall material and thermal balance of the ferromanganese smelting in blast furnaces of JSC "Satka Iron Smelting Works" is presented. Completeness of chemical reactions was taken into account in calculations based on thermodynamic analysis and technological data. Data on the thermochemical properties of substances; on the thermal effects of chemical reactions; on the degree of carbon graphitization in coke; on the heats of formation of metallic and slag solutions; on the thermochemical characteristics of ferromanganese, slag and gas phase were systematized and corrected. Heat losses for a particular type of blast furnaces are taken into account. The mathematical model is implemented in the computer program environment Lazarus. Test calculations of material and heat balances of ferromanganese blast furnace smelting were carried out. The calculation results correspond to the technological data. The developed software allows you to manage quickly the production process, to predict the optimal composition of charge materials for obtaining a product of a specific composition without experimental smelting. The software is used in the "consultant" mode at the JSC "Satka Iron Smelting Works".