Papers by Keyword: Mathematical Model

Abstract: The paper presents the results of the computer modelling of the stressed state and relative density when burnishing a porous hollow cylinder, made from copper sintered powder material. The mathematical model, based on the theory of porous bodies’ plasticity, is used for the analysis. The paper researches the impact of the initial porosity of the material on the effective stresses distribution, relative density and force change when free burnishing of hollow cylinders. It is ascertained that with the decrease of the initial porosity of the sintered material there is the increase of the burnishing force, stresses rate and relative density on the inner sur-face of a hollow cylinder. For porous materials at a certain stage of burnishing, the deformation zone is transformed into the compaction zone with a high relative density which de-creases while moving away from the inner surface of hollow cylinders. The maximum value of the relative density is implemented directly on the inner surface of hollow cylinders; along with this the density value is evenly distributed on the inner wall.

Abstract: The possibility of obtaining multilayer cylindrical waveguides by explosion welding is investigated. The fact that the technological welding scheme has a significant impact on the shaping of workpieces and the value of edge effects was established. The studies demonstrated that the nature of wave formation during the manufacture of multilayer cylindrical waveguides from a homogeneous material by explosion welding using a central rod is identical to the wave formation when welding flat multilayer compositions on a rigid base.

Abstract: The paper reviews and develops the mathematical model of plastic flow during the hot-forming processes. A flat non-stationary temperature problem for a cross-section of a long solid (rolled product) of arbitrary shape with different heat transfer conditions along the perimeter of the cross-section was considered. Equations for calculation of the thermal conductivity coefficient and heat capacity of tungsten billets were obtained in the temperature range of 700 - 1500°C, based on the literature data. Analytical dependences in form of regression equations were obtained, allowing for computer calculations of physical specifications of 11x11 mm VA grade tungsten billets in form of temperature functions with accuracy sufficient for practical calculations.

Abstract: In this study, a structural-deformation analysis of the process of crack development is performed, on the basis of which an engineering methodology is developed for assessing the endurance limit and resource of large-sized structures. A simple analytical dependence (correlation аналитическая зависимость) was obtained, which allows one to determine the critical size of macrocracks for ferritic-pearlitic steels without using the well-known Griffith formula. The results of calculating the cracks critical lengths of various steels depending on their yield strength are presented. The analytical dependence of the calculation of the fatigue limit for the most dangerous symmetric loading cycle according to the standard set of mechanical characteristics of ferrite-pearlite steel is presented. The obtained results make it possible to calculate the endurance limit of structural elements of marine equipment and other structures subject to cyclic loads

Abstract: The paper presents the studies on the compositions selection and properties of polymer-bitumen binders obtained using the viscous petroleum bitumen, styrene-butadiene-styrene polymer and plasticizer according to the experimental planning method. Regression equations of the polymer-bitumen binders processing and performance properties, which make it possible to optimize the compositions and predict their properties taking into account the operating conditions, were obtained. Polymer-bitumen binders in comparison with the properties of viscous road bitumen have the increased indicators of heat resistance, crack toughness, ductility and elasticity. To obtain the adequate mathematical model, the experimental data were processed, compositions were optimized and dependence diagrams were constructed by using the Maple software package. The software for a personal computer including the algorithm and program for selecting the polymer-bitumen binders has been developed. When using the software it is possible to automate the calculation of the polymer-bitumen binders compositions with a given set of technical properties.

Abstract: Developed a mathematical model, which makes it possible to optimize, from the point of view of defect formation, the parameters of stress concentration in a deformable elastic body of the materials being processed, destruction is considered as a method for creating defects at a submicroscopic level in various media. Getting expressions of conformal reflection of single circle on an arbitrary area, using a conformal reflection and transformation of Laplace, it is possible to design behavior of a tensely deformed state of solid at the arbitrary loading.

Abstract: This study demonstrates application of mathematical techniques such as modeling, inverse analysis, and numerical simulation to biodegradation of xenobiotic polymer. In particular, this paper presents results of numerical simulation based on experimental results. Numerical results and experimental results show the behavior of microbial population in exogenous type depolymerization processes.

Abstract: The paper presents the results of studies of the reaction of the interaction of phenol with cyclohexene (CH) in the presence of a Zeolite-Y catalyst impregnated with phosphoric acid and studying the dependence on the yield and selectivity of the target product on various parameters. As a result of the study of the phenol cycloalkylation by cyclohexene, optimal conditions were found, the yield of which is 81.6 % of theory for the taken CH, and the selectivity is 94.0 % for the target product. The developed mathematical model of the processes of the interaction of phenol with cyclohexene in the form of a regression polynomial made it possible to find the optimal values ​​of the input variables.

Abstract: Refinement and uniform austenite grains are essential to obtain excellent and homogenous properties for non-quenched and tempered steel, which is mainly affected by static recrystallization of the rolling process. Using the Gleeble-3500 thermal simulation test machine, 20% compression test was carried out for two passes at 850~1050 °C (interval of 50 °C) and different pass interval time conditions to study the static softening and recrystallization behavior of 38MnSiVS non-quenched and tempered steel during deformation process. The effects of strain rate, deformation temperature and interval time on static softening rate and austenite recrystallization fraction were analyzed. The results showed that the increase of deformation temperature and the increase of pass interval time had more significant impact on the static recrystallization volume fraction of 38MnSiVS steel, while the influence of strain rate was relatively smaller. When the deformation temperature was 950 °C or higher, the non-conditioning steel 38MnSiVS could undergo complete recrystallization, and partial recrystallization occurred in the temperature range of 850-950 °C. A static recrystallization volume fraction model of non-regulatory steel 38MnSiVS was established. The static recrystallization activation energy was 296.7 kJ·mol^-1, and the static recrystallization volume fraction model had a relative error of 2%.

Abstract: In this article, mathematical models and processes of introducing homogeneous ultrasonic oscillations and mechanical stresses into silicon wafers in the direction of their thickness are developed and investigated, and mathematical models of the movement of interstitial defects in silicon wafers created by the processes of ion-beam transients at the transitions of ion-beam transitions and hidden dielectric layers using the action of ultrasound oscillations and mechanical stresses, both in the process of implantation of impurities and before the annealing of plates upon activation of the impurities are developed and investigated.