Papers by Keyword: Mathematical Model

Abstract: The urgency of a new process development of cold forming of high-strength flange bolts has been shown in the article. It also points out some shortcomings of existing technologies. To improve the quality of bolts a new instrument design was developed. The research of the working tool identification impact on its resistance and stress-strain state of the workpiece was carry out. The software package DEFORM, designed for process simulation of metal forming is used in the article. The mathematical and computer modeling technology bolt stamping with flange was applied to carry out the study. Based on the conducted theoretical and experimental studies a new technology for manufacturing the flange bolts is patented.

Abstract: The article examines the history of development and state-of-the-art of the design theory of structures of filled shells delivered in “Civil Engineering” specialist, MSc, and postgraduate engineering disciplines courses. The analysis of the engineering design methods based on the theory of shells propositions has been performed. Structural numerical model field of application expansion has been proved. The obtained parameters and proposed methods can be used in numerical simulations using finite element method to analyze and design the thin shell structures with soil infill. The propositions reflecting state-of-the-art of the design theory of the structures under consideration have been set; their place in the logic of delivering engineering disciplines taught to civil engineering students has been designated.

Abstract: This paper presents a mathematical model of the maximum thickness and the chip area for the processes of cylindrical and profile milling of various materials, including wood. The analytical dependences connecting the geometry of the shear layer with the elements of the milling mode and cutter design parameters are determined. Also, a model of the volume of material removed from the surface of the workpiece during the milling profile is presented. The comparative calculations of the previously known models and the models developed by the author were done. It was found that the models of the geometric parameters of cutting layer presented in the article are adequate and can be used to calculate the energy performance of the wood milling process with cylindrical and shaping cutters. These models are suitable for use in the calculations of the processing parameters for a wide range of material: metals, wood, plastic, glass and others.

Abstract: The paper presents a non-isothermal model of the initial stage of ion implantation process. The model takes into account the existence of internal interfaces. The model assumes that the implantable impurity generates mechanical perturbations. These disturbances can propagate at different speeds before and after internal boundary. The examples of the waveform evolution in transition across the border are shown.

Abstract: From the viewpoint of control theory is given the synthesis of building materials. A control of structure and properties of the material is carried by changing the relevant technological parameters. Material is regarded as an object of control in mathematical modeling. The model is presented as a solution to the Cauchy problem for an ordinary differential equation fourth-order. The synthesis is based on parametric identification of mathematical models. The parameters are typical points of the kinetic processes of the formation of physical and mechanical characteristics of the material. Among them: roots of the characteristic polynomial; inflection points; the extreme points, etc. Applications of this approach to the synthesis of building materials for special purposes are given.

Abstract: This project aims to study the factors causing moisture migration and moisture loss of grain in storage grain that subsequently affect production costs by compensating lost weight due to its moisture. From reviewing a related mathematical model, it is found that physical changes of grain in silo, both the temperature and moisture, are caused by its oxidation during storage and aeration. Therefore, suitable grain storage can reduce its weight loss. To control storing process, the numerical solution of the model, a system of partial differential equations, is obtained by finite difference method. Moreover, a Java program has developed based on overall processes of the model as an information for decision making in grain production and storage.

Abstract: Crack resistance is an important parameter determining the carrying capacity and durability of composite materials in which as a binding element apply adhesive compositions. Estimation of crack resistance is usually carried out using an energy criterion – specific energy of crack propagation. Existing mathematical models to determine the value of crack resistance do not always give reliable results, because they can contain several dependent variables. In the article the mathematical models of the two types for calculation of crack propagation energy, which includes only one independent parameter, which needs to be defined experimentally are received. For the mathematical model of type I on the experimental setup it is necessary to define value of bending moment at which the formation of crack. Use of mathematical model of II type does not demand experimental setup as independent parameter is the radius of curvature of the bent beams.

Abstract: In this research paper, we will develop a theory about the mathematical and physics models for the velocity-time of Usain Bolt in the 100 metres sprint during the Beijing olympic games 2008, Berlin world championships in Athletics 2009, and London olympic in 2012. We will use data from Usain Bolt’s distance, velocity and time as shown in K. Mackata and M. Antti research study of Usain Bolt’s kinematic parameter and will analyze them using mathematical and physics models in order to formulate a theoretical equations showing the power vitality of the sprinter value and his speed endurance as well. We will also use the Introduction to Sport Biomechanics by Roger Bartlett (pp.83-92) which covers the study of the hypothetical center of mass velocity time-dependent. And the comparison of the applied force is time-dependent oscillator which are all obtained from the mathematical and physics models1 and the applied force is time-dependent oscillator in mathematical and physics models2 and the experimentation done by in figure (1)-(3)

Abstract: This paper presents the experiment-based mathematical modelling of fluidized bed carbonitriding process for 1C 25 steel meant to optimize this type of thermochemical processing.Based on experimental results, the mathematical model was developed, which is a second order equation with three unknown terms (parameters): temperature, depth of carbonitrided layer, the percentage of ammonia.The mathematical model allowed the simulation of the fluidized layer carbonitriding process according to its parameters and the thermal energy optimization for obtaining HV hardness values in the range 300-400 MPa.Using the software package Matlab a graphical interface was done, through which all the combinations of technological parameters of the carbonitriding process are determined, leading to obtaining values of microhardness between 300 and 400 MPa, as well as the amount of energy consumed for each variant. The variant consuming the lowest energy is considered optimal.

Abstract: The paper presents a formulation of the problem for choosing an optimal size range of technical products and a mathematical model for solving of the said problem. Particular attention is paid to the ways for satisfying the types of demand for the size ranges’ elements. Two ways are proposed, and they are formalized as constraints in a mathematical model. Methods are proposed for solving the problem in accordance with the chosen way of satisfying the demand, and an algorithm is developed. The methods and the algorithm are approbated by solving a particular problem.