Papers by Keyword: Mathematical Model

Abstract: A segmented 3-D coupled electromagnetic-thermal solute transportation model, aimed to better understand the macro-segregation formation in the strand during a popular continuous casting (CC) process, has been developed. Based on the model validation by industrial tests, the effect of M-EMS and F-EMS running parameters on the segregation distribution were subsequently carried out. It is shown that the simulated solute segregation profile in the W-shape along the casting thickness direction is in a good agreement with the measured profile. In the initial solidification shell with thickness in 0.020 m, the solute segregation degree changes from a positive value to a negative with the increasing distance from strand surface because of the washing effect induced by the impact flow from the nozzle side port and M-EMS. Here, the minimum degree of carbon segregation decreases from 0.976 to 0.875 with the increasing stirring current from 100A to 550A. As the stirring current of F-EMS decreases from 630A to 200A, the minimum segregation degree locating at 0.109 m distance from strand surface increases from 0.805 to 0.967. The carbon segregation degree at the strand center first decreases from 1.10 to the minimum value of 1.06 at the case of 350 A/4 Hz because of the concentration equilibrium for the local decreasing negative segregation induced by F-EMS, and then increases to 1.16 due to the local poor stirring.

Abstract: The process of producing a composite material hybrid powder-laser-casting method. Developed new design of the mixing reactor. On the basis of mathematical methods of modeling examined of hydro-and gas-dynamic conditions for obtaining the suspension of the aluminum melt. Investigated the trajectory of moving particles in gas and liquid flows. Comprehensively studied the regularities of formation and stability of structural phase components in the composite material of aluminum alloy, which was obtained hybrid powder-laser-casting method. We show the possibility to control the porosity of the obtained composite material using the process parameters of the developed hybrid method.

Abstract: In this paper, we develop a mathematical and physics model or formula of displacement-time dependent, velocity-time dependent, acceleration-time dependent, kinetic energy-time dependent and mechanical power-time dependent for Usain Bolt in the 100 m sprint at Beijing olympic games 2008. We use data of distance, velocity, time for Usain Bolt from Mackata Krzysztof and Antti Mero analysis kinematic parameter of Usain Bolt to compare the mathematical and physics model. The mathematical and physics model corresponding velocity, and acceleration as shown in the book entitled Introduction to sport biomechanics of Roger Bartlett(pp.83-92).

Abstract: In this study, target size effects in the low energy impact response of plain CFRP plateswere investigated. It was found that increase the target size leads to a reduction in the maximumimpact force recorded during the test. This is due to the reduction on flexural rigidity of the largerpanels. The experimental results indicated that at energies above the first failure threshold, themaximum impact force does not coincidence with the predicting value. Two mathematical modelswere used to predict the maximum impact force including single degree of freedom (SDOF)spring-mass model and Energy-Balance (E-B) model. The predicting results were then comparedwith the experimental results, and both of the two models show good agreement with theexperimental results in elastic deformation region. In addition, the level of agreement between thepredictions and the experimental results indicate that both models are capable of modelling theimpact response of these CFRP panels at elastic regime.

Abstract: Mathematical models of a suspension strut such as an aircraft landing gear are utilized by engineers in order to predict its dynamic response under different boundary conditions. The prediction of the dynamic response, for example the external loads, the stress and the strength as well as the maximum compression in the spring-damper component aids engineers in early decision making to ensure its structural reliability under various operational conditions. However, the prediction of the dynamic response is influenced by model uncertainty. As far as the model uncertainty is concerned, the prediction of the dynamic behavior via different mathematical models depends upon various factors such as the model's complexity in terms of the degrees of freedom, material and geometrical assumptions, their boundary conditions and the governing functional relations between the model input and output parameters. The latter can be linear or nonlinear, axiomatic or empiric, time variant or time-invariant. Hence, the uncertainty that arises in the prediction of the dynamic response of the resulting different mathematical models needs to be quantified with suitable validation metrics, especially when the system is under structural risk and failure assessment. In this contribution, the authors utilize the Bayesian interval hypothesis-based method to quantify the uncertainty in the mathematical models of the suspension strut.

Abstract: A mathematical model for analysis of features of the drug release , previously introduced into a polymer implant, into a biological tissue is proposed. A carbon nanolayer obtained as a result of plasma-immersion ion implantation was created to improve biocompatibility with biological tissue on the surface of the implant. The medicine can go through micro-ruptures in this layer. Calculations show that the carbon layer allows a uniform release of the drug.

Abstract: The work is devoted to the discussion of hypotheses that are put forward to explain the processes occurring during ion-plasma treatment of polyurethane. A carbonized layer forms on the surface of the polymer as a result of ion-plasma treatment. However this layer is not even. Wavy relief, the geometric features of which depend on the fluence (the number of ions entering the unit surface of the sample) and the energy of ions, is formed. It is shown that a simple explanation related to material heating and subsequent shrinkage does not allow explaining the cause of the phenomenon. The second hypothesis can be the pressure of the ion flow on the surface of the sample. It causes deformation and subsequent changes in the stress-strain state after the irradiation is stopped. Calculations show that this mechanism cannot explain the formation of the folded relief of the layer. A hypothesis, based on information about a significant material change, is expressed in the article. Polymer chains under ion-plasma treatment are broken into atoms. After striking ions move deep into the material causing the polymer to swell in the near-surface layer. This swelling can cause material to move close to the sample boundary and leads to the formation of a wavy surface.

Abstract: Polymer coatings are widely used for effective vibration damping of sheet or hull structures of different engineering systems. The article presents a calculation and experimental technique that enables improved accuracy and validity of damping properties determination of polymer coatings. Mathematical models to determine the parameters of the experimental specimen having a homogenous strain state of the polymer coating are obtained. Experimentally confirmed that the use of coatings based on adhesive compositions such as "Sprut" increases by 18...28 times the damping capability in metal structures. An addition of fillers in adhesive compositions "Sprut" type in a proportion of 30...50% of its weight reduces by 2.4 times the damping properties of metal structures.

Abstract: The development of woodworking and furniture industry in the past twentieth century was largely due to the launch of the production of a large group of artificial materials, now classified as wood-polymer composites. Diversity and renewability of the resource base, convenience and cost-effectiveness of wood-polymer composites (WPC) are the main prerequisites for the development of this group of materials. Fillers in thermoplastic wood-polymer composites may be present in a variety of forms. At this stage industrial WPCs are manufactured mainly from small fractions - wood flour and sawdust. This provides a high technological plasticity of production, namely - the possibility of manufacturing products by extrusion and casting methods, a variety of geometric shapes and even with a small thickness of the walls of the structures. However, this is true if we focus on the maximum possible mechanical properties and accuracy of geometric shapes of finished products. If we focus production on the manufacture of sound-proofing WPC, then almost any wood waste can be used for the filling of such composites. To study and predict sound-proofing properties of wood polymer-sand composite (WPSC), a corresponding mathematical model was developed. It is found that with an increase in the thickness of the polymer-sand coating, the coefficient of sound proof significantly increases. For example, a coating thickness of only 4 mm, increases the sound-proofing properties of a wood sample from 16 to 35 dB, thus the sound-proofing properties of the WPSC are improved by half compared to pure wood.

Abstract: The geometrical interpretation of the transformation of cylindrical milling of products into profile milling by shaping cutters with a convex and concave cutting profile is considered. A mathematical model of geometric errors of profile surfaces processed with tools with the specified cutting profiles is developed. On the basis of the model and the results of its analysis, scientifically based recommendations for designing a technological operation for profile milling of products have been developed. When processing a product with a contoured cutter with a concave profile, it is recommended to calculate the geometric errors formed in the transverse plane of the shaping cutter, and when machining with a shaping cutter with a convex cutting profile - in the planes of both its ends. The calculated values of the above geometric errors should be compared with the values limited by the work drawing of the product. The implementation of these recommendations will reduce the labor costs for experimental research and control operations associated with ensuring a given geometric accuracy of products.