Mathematical Model For Calculation Research Articles

Modeling of nitrogen oxides emission in the cylinder of tractor gas-diesel engine

The article is devoted to the modeling of process of nitrogen oxides formation in the cylinder of diesel engine operating on compressed natural gas. The combustion of methane-air mixture, ignited by atomized pilot oil that is injected through multijet nozzle, in the cylinder of gas-diesel engine increases the rate of turbulent fluctuations, which leads to intensification of heat and mass exchange in the plume, and significantly increases the rate of formation and decomposition of nitrogen oxides. The calculation of expected emissions of nitrogen oxides in the cylinder of diesel engine and their content in the exhaust gases is carried out. It is done on the basis of the results of kinetic systems modeling for calculation of the kinetics of nitrogen oxides formation during combustion of natural gas and diesel fuel, taking into account the influence of turbocharging, intermediate cooling of charged air and exhaust gas recirculation. In the mathematical modeling of nitrogen oxide formation in the cylinder of diesel engine, the combustion process is divided into two zones, namely the zone of fresh mixture and the zone of combustion products. First zone is a mixture of fresh air with recycled gases (if there is a process of recycling) and residual gases. Before combustion starts, this zone occupies the whole cylinder. During combustion, the volume of zone of combustion products increases. Theoretical researches are carried out on the basis of developed mathematical model for calculation of nitrogen oxides in the cylinders of 4Ch 11.0/12.5 and 4ChN 11.0/12.5 diesel engines. The high precision of theoretical calculations of volumetric content and mass concentration of nitrogen oxides is confirmed, compared to the results of experimental researches (the difference does not exceed 5%).

Mathematical model of kinetostatithic calculation of flat lever mechanisms

Currently widely used graphical-analytical methods of analysis largely obsolete, replaced by various analytical methods using computer technology. Therefore, of particular interest is the development of a mathematical model kinetostatical calculation mechanisms in the form of library procedures of calculation for all powered two groups Assyrians (GA) and primary level. Before resorting to the appropriate procedure that computes all the forces in the kinematic pairs, you need to compute inertial forces, moments of forces of inertia and all external forces and moments acting on this GA. To this end shows the design diagram of the power analysis for each species GA of the second class, as well as the initial link. Finding reactions in the internal and external kinematic pairs based on equilibrium conditions with the account of forces of inertia and moments of inertia forces (Dalembert principle). Thus obtained equations of kinetostatical for their versatility have been solved by the Cramer rule. Thus, for each GA of the second class were found all 6 unknowns: the forces in the kinematic pairs, the directions of these forces as well as forces the shoulders. If we study kinetostatic mechanism with parallel consolidation of two GA in the initial link, in this case, power is the geometric sum of the forces acting on the primary link from the discarded GA. Thus, the obtained mathematical model kinetostatical calculation mechanisms in the form of libraries of mathematical procedures for determining reactions of all GA of the second class. The mathematical model kinetostatical calculation makes it relatively simple to implement its software implementation.

Mean Stress in Algorithms Estimating Fatigue Life of Selected Structural Materials

The paper presents comparison of the mathematical models for fatigue life calculations including influence of the mean load value. Several model based on stress analysis on the critical plane and energy density parameter were investigated. In this paper three types of materials were tested and subjected to bending, torsion and combination of bending with torsion loading with the participation of mean value of the load. It was found, that the best fatigue life estimations obtained by models taking into account changes of the material behavior under fatigue loading related to the specified numbers of cycles of the load.

Mathematical model for calculation of the heat-hydraulic modes of heating points of heat-supplying systems

The mathematical model and calculation method of the thermal-hydraulic modes of heat points, based on the theory of hydraulic circuits, being developed at the Melentiev Energy Systems Institute are presented. The redundant circuit of the heat point was developed, in which all possible connecting circuits (CC) of the heat engineering equipment and the places of possible installation of control valve were inserted. It allows simulating the operating modes both at central heat points (CHP) and individual heat points (IHP). The configuration of the desired circuit is carried out automatically by removing the unnecessary links. The following circuits connecting the heating systems (HS) are considered: the dependent circuit (direct and through mixing elevator) and independent one (through the heater). The following connecting circuits of the load of hot water supply (HWS) were considered: open CC (direct water pumping from pipelines of heat networks) and a closed CC with connecting the HWS heaters on single-level (serial and parallel) and two-level (sequential and combined) circuits. The following connecting circuits of the ventilation systems (VS) were also considered: dependent circuit and independent one through a common heat exchanger with HS load. In the heat points, water temperature regulators for the hot water supply and ventilation and flow regulators for the heating system, as well as to the inlet as a whole, are possible. According to the accepted decomposition, the model of the heat point is an integral part of the overall heat-hydraulic model of the heat-supplying system having intermediate control stages (CHP and IHP), which allows to consider the operating modes of the heat networks of different levels connected with each other through CHP as well as connected through IHP of consumers with various connecting circuits of local systems of heat consumption: heating, ventilation and hot water supply. The model is implemented in the Angara data-processing complex. An example of the multilevel calculation of the heat-hydraulic modes of main heat networks and those connected to them through central heat point distribution networks in Petropavlovsk-Kamchatskii is examined.

A mathematical description of the separation of gas mixtures generated by the thermal utilization of waste

The study focuses on the problems of the mathematical description of separating the flows of gas mixtures in the technological process of an environmentally-friendly utilization of waste. The devised mathematical calculation models use the conventional ratios of thermodynamics and the heat-and-mass exchange, including the Peng-Robinson equation of state (PR EOS) for describing the coefficients of thermal and physical properties of the working media. These models represent systems of equations that allow determining the temperatures of the coolant and the cooling air at the outlet of the heat exchanger with predetermined ratios of the mass of coolant and the air flow. In addition, the suggested equation systems allow determining the component composition of the product that is a part of the rectifying column and its output final products. The calculation shows that the rectifying column generates two flows of a gas mixture. The first flow is a gas mixture with a methane content of 89.2% and, therefore, is a valuable motor fuel for vehicles or a fuel for household purpose. The second flow of the gas mixture, given its high hydrogen content (about 34.0%), may be used as a source of energy for maintaining the gasification of waste during its utilization. The preparation of such energy sources makes the waste utilization process cost-effective. Establishing links between the functional elements that are used in a power technology plant allows devising a system of equations for the entire plant. The subject of further research is the mathematical description of the entire system and the selection of an acceptable option of the PTP arrangement that would facilitate its practical implementation.

CALCULATIONS FOR THE STRENGTH OF CASTING AT THE FORMATION OF ITS CAVITY BY CYLINDRICAL ROD

The mathematical model of stress calculation of casting at forming of its cavity by cylindrical rod has been analyzed in the paper. The dependencies of arising radial and tangential stresses were determined, as well as distributed contact pressure predicting force interaction of the “casting-rod” system in various combinations of stiff ness expressed by modulus of elongation. It is shown that the highest stresses occur in the layers of casting adjacent to the rod surface. The infl uence of the temperature gradient, the rigidity of the casting and sand-clay molding sand, casting geometric para meters displayed wall thickness and the outer radius, on the value of appearing in the casting of radial, tangential and equivalent stresses, as well as the distribution of contact forces has been considered. The impact of these factors on the strain-stress state of the casting wall, expressed in terms of equivalent stress obtained using the second hypothesis strength has been estimated.

Program realization of mathematical model of kinematic calculation of flat lever mechanisms

Calculation of kinematic mechanisms is very time-consuming work. Due to the content of a large number of similar operations can be automated using computers. Forthis purpose, it is necessary to implement a software implementation ofthe mathematical model of calculation of kinematic mechanisms of the second class. In the article on Turbo Pascal presents the text module to library procedures all kinematic studies of planar lever mechanisms of the second class. The determination of the kinematic characteristics of the mechanism and the construction of its provisions, plans, plans, speeds and accelerations carried out on the example of the six-link mechanism. The beginning of the motionless coordinate system coincides with the axis of rotation of the crank AB. It is assumed that the known length of all links, the positions of all additional points of links and the coordinates of all kinematic pairs rack mechanism, i.e. this stage of work to determine the kinematics of the mechanism must be preceded by a stage of synthesis of mechanism (determining missing dimensions of links). Denote the coordinates of point C and considering that the analogues of velocities and accelerations of this point is 0 (stationary point), appeal to the procedure that computes the kinematics group the Assyrians (GA) third. Specify kinematic parameters of point D, taking the beginning of the guide slide E at point C, the angle, the analogue of the angular velocity and the analogue of the angular acceleration of the guide is zero, knowing the length of the connecting rod DE and the length of link 5, refer to the procedure for the GA of the second kind. The use of library routines module of the kinematic calculation, makes it relatively simple to organize a simulation of the mechanism motion, to calculate the projection analogues of velocities and accelerations of all links of the mechanism, to build plans of the velocities and accelerations at each position of the mechanism.

Analysis and Evaluation of Interface Mechanics for Thin Films using the Method of Image

The evaluation of interface mechanics was very useful for the design of thin solid film. According to the method of image, interface stresses and deformations of coating-substrate system were gained. Using this mathematical calculation model, the indentation test data was carried out and the results were analysed. Based on the mechanical model and test, the critical state of interface stresses from elastic deformation to plastic yield was evaluated. From experimental and calculating results, interface shear stress and normal stress had different affecting level for the coating failure under the same surface load. And a fitting relationship equation for the two stresses was also gained to determining the failure value in designing. The method of this paper could be used for thin film interface mechanics design and evaluation.

ВЛИЯНИЕ ТЕХНОЛОГИЧЕСКИХ ФАКТОРОВ НА ЛОКАЛЬНЫЕ ТЕМПЕРАТУРЫ ПРИ ШЛИФОВАНИИ С НАЛОЖЕНИЕМ УЛЬТРАЗВУКОВЫХ КОЛЕБАНИЙ

The application of ultrasonic vibrations (USV) power is one of the means for heat depression of the grinding process. However, the existing studies do not reveal the mechanism of USV influence on the local temperatures. To identify the significance of technological factors influencing the temperature of ultrasonic assisted grinding process, it is necessary to develop physical and mathematical models for heat-transfer factor calculation, the methodology, the algorithm and the software for the local temperatures calculation, and to carry out the numerical simulation of temperatures. The author specified the factors having prevalent influence on the local temperatures during ultrasonic assisted grinding and gave the dependencies for calculation of the lubricating-cooling fluid motion speed in the area of contact of a grinding wheel with a workpiece, lubricating-cooling fluid consumption through the area of contact and the heat-transfer factor of work piece, abrasive grains and wheel bond to the lubricating-cooling fluid. The paper presents the results of numerical simulation of the local temperatures in the area of contact of a grain with a workpiece and a chip during micro-cutting by the first of the subsequently working grains. When applying USV, the temperatures reduce mostly in the result of the change of the strain-stress state in the treatment area due to the strength characteristics degradation including the tensile strength of a workpiece material and the change of kinematics of the workpiece material micro-cutting by the single abrasive grains of a grinding wheel. The increase of consumption of lubricating-cooling fluid through the treatment area and the intensification of its cooling action influence the local temperatures insignificantly. The author identified the influence of the USV parameters (amplitude and phase) on the local temperatures change depending on the duration of contact of a grain with a workpiece. As a result, the degree of technology factors influence on the local temperatures during the ultrasonic assisted grinding was established analytically for the first time. The author determined that the USV application allows reducing local temperatures by a mean of 12 … 24 %.

Program realization of mathematical model of kinetostatical calculation of flat lever mechanisms

Global computerization determined the dominant position of the analytical methods for the study of mechanisms. As a result, kinetostatics analysis of mechanisms using software packages is an important part of scientific and practical activities of engineers and designers. Therefore, software implementation of mathematical models kinetostatical calculating mechanisms is of practical interest. The mathematical model obtained in [1]. In the language of Turbo Pascal developed a computer procedure that calculates the forces in kinematic pairs in groups Assur (GA) and a balancing force at the primary level. Before use appropriate computational procedures it is necessary to know all external forces and moments acting on the GA and to determine the inertial forces and moments of inertia forces. The process of calculations and constructions of the provisions of the mechanism can be summarized as follows. Organized cycle in which to calculate the position of an initial link of the mechanism. Calculate the position of the remaining links of the mechanism by referring to relevant procedures module DIADA in GA [2,3]. Using the graphics mode of the computer displaying on the display the position of the mechanism. The computed inertial forces and moments of inertia forces. Turning to the corresponding procedures of the module, calculated all the forces in kinematic pairs and the balancing force at the primary level. In each kinematic pair build forces and their direction with the help of simple graphical procedures. The magnitude of these forces and their direction are displayed in a special window with text mode. This work contains listings of the test programs MyTеst, is an example of using computing capabilities of the developed module. As a check on the calculation procedures of module in the program is reproduced an example of calculating the balancing forces according to the method of Zhukovsky (Zhukovsky lever).

The Non-contact Method of Assessing the Quality of the Road Surface with the Rubber Crumb in the Construction Process

Process of cooling of a paving of hot asphalt concrete mixes containing a rubber crumb at construction of highways is considered. The article presents the description of the mathematical model of calculation of temperature fields of pavement. One-dimensional unsteady heat conduction equations for each layer consist in a mathematical model. The boundary conditions on the surface of the top layer consider the heat transfer by convection and radiation. The boundary conditions of the fourth kind are between the layers. The temperature boundaries of the lower layer are constant. Testing the model is performed for limited and semi-infinite rods. The article presents the results of testing the mathematical model. Numerical solution of heat conduction equations held by the implicit scheme. Results of an experimental study of the thermal conductivity of asphalt concrete containing crumb rubber are listed in this article. In article the method of calculation of temperature of a surface of a paving is offered. The calculated values of temperature of a paving depending on the speed of a wind, solar radiation, thickness of a coat layer, a difference of thickness of a layer of hot asphalt concrete containing a rubber crumb, and reference temperature of a layer are presented. It is established that under identical conditions porosity of material of a layer has the greatest impact on change of temperature.

Models of Reliability Prediction of Electric Machine Taking into Account the State of Major Structural Units

It is shown that conventional mathematical models for calculation of the reliability of electric machine structural units, based on the theory of planning an experiment, do not take into account the peculiarities of their properties variation during the process of manufacture and long-term operation. Taking into consideration the multiple factors of the assigned problem, the prospect of the use of fuzzy logic postulates in the creation of models for calculation of reliability is substantiated. An approach to such models building is formed.

Calculation of hydraulic parameters of copper crystallizers with a complex connection of channels

A mathematical model and algorithm of the hydraulic calculation of the crystallization wall with a complex connection of a periodically repeated system of horizontal and vertical channels are considered. A computer program allowing one to perform the hydraulic calculation of the crystallizer plate having an arbitrary number of channels of various forms and sizes is created based on the developed mathematical model. The possibilities of this software product when designing copper crystallizes to select their geometric parameters and rational regimes of hydraulic operation are shown.

Математическая модель для расчета характеристик термоэлектрических модулей охлаждения

Математическая модель для расчета характеристик термоэлектрических модулей охлаждения

EXPERT SYSTEM OF BAR ROLLING TECHNOLOGY

The Expert System (ES) was developed at the Ural Federal University for the analysis and design of bar rolling technologies and it can be used in the optimization of existing and design of new processes of bar rolling. For the operation of the ES a knowledge base was created about the subject area, based on theoretical and experimental studies, as well as generalizations of experience in the production of rolled bars at existing mills. A comprehensive mathematical model of calculation of rolling passes and technological rolling, created on the basis of modern ideas about the mechanics of deformable bodies, allows the calculation of a full range of technological and energy-power parameters of the simulated process. The ES software was developed for operational system Windows using the visual programming environment of Borland C++ Builder.

Calculation of hydraulic parameters of copper crystallizers with a complex connection of channels

A mathematical model and algorithm of the hydraulic calculation of a crystallization wall with a complex connection of a periodically repeated system of horizontal and vertical channels are considered. A computer program allowing one to perform the hydraulic calculation of the crystallizer plate having an arbitrary number of channels of various forms and sizes is created based on the developed mathematical model. The possibilities of this software product in the design of copper crystallizers to select their geometric parameters and rational regimes of hydraulic operation are shown.

The study of pituitary-thyroid hormones ratio based on regression analysis

Aim. To work up a mathematical model for calculation of the levels of pituitary-thyroid hormones system by least squares method in rats with experimental hypothyroidism.
 Methods. To study the relationship of hormones levels regression analysis was used. The search of coefficients was performed using the least squares method. Investigations were carried out on rats, which were divided into six groups of 12 rats each: the first group was control, in the animals of second, third, fourth, fifth and sixth groups hypothyroidism was induced by daily intragastric administration of tiamazol in following doses: 2.5; 20.0; 10.0; 5.0 and 1.0 mg per 100 g of rat body weight for 3 weeks.
 Results. Regression analysis was carried out, the type of regression as well as parameters were chosen; statistical analysis of the relationship of hormones was conducted based on the obtained results. By comparing the calculation results of the laboratory analysis sufficiently high reliability of the developed model was set up. The deviation of the arithmetic mean value of the level of thyroid stimulating hormone, produced on the basis of experimental and calculated data, is 2.7%. The accuracy of thyroid stimulating hormone levels calculations increased with the decrease of thyrostatic medication dose. The relative error while calculating the free thyroxine levels in the same groups of rats did not exceed 2.15%, accounting for 1.64; 1.34; 0.36 and 2.15%, respectively, when administered daily 20.0; 10.0; 5.0 and 1.0 mg of antithyroid drug per 100 g body weight. One can argue about the reliability of the constructed model to reproduce the performance levels of the hormones of the pituitary-thyroid system.
 Conclusion. In the absence of modern high sensitive immunochemiluminescent diagnostic methods the results can be used for thyroid-stimulating hormone levels calculation as one of the major markers of the thyroid gland functional state.

Some properties of man-made Dnieper Steppe ecosystems

Physico-chemical and hydrogeological properties of technogenic ecotope landscapes are unique in the world. Their development has created a new, completely unexplored problem of recultivation of disturbed lands. The ecological and biological evaluation of ecotypes is the leading place because it is the basis of targeted restoration of fertility of such anthropogenic tumors. As tests for the development of waste quarry sectors in the long-term stationary trials there were tested 23 species of higher plants. In the steppe of Ukraine the greatest ecological and biological according to technogenic ecotopes showed alfalfa and sainfoin. They are plant-dominants, accumulate large quantities of biomass, creating pockets of concentrations of elements in soil fertility, improve the sanitary conditions of the surrounding area. The nature translocational process in higher plants was identified. It completely depends on their biological features and is the creation of their root systems with the same structure and therefore their distribution in the thickness of elafotopos who are able to provide plants with nutrients and to produce the maximum possible efficiency in data soil-ecological conditions. Alfalfa and sainfoin showed great ecological plasticity of root systems. On the poverty of ecotopes batteries they reacted by increasing the surface and length of roots. It is established that the saturation of ecotopes roots is directly proportional to their mass, and the surface root system and its length are values associated with root mass. With the depth of the absorbing working surface root systems increases. The mathematical model of calculation of the ecological and biological characteristics of root systems of plants and progressive framework method of selection of soil monoliths with roots. After washing, the roots are reported to air-dry state and are distributed through the thickness of 4 factions: more than 5 mm, 5–1, 1–0,5 and less than 0.5 mm. This allows you to get an idea about the structure of the root system and its distribution in the thickness of ecotopes, as well as to determine the portion of the roots through which the greatest absorption of water and food items. The features of the development of the underground part of plants that is the basis for the development of practical methods of influence on ecotopia. For example, alfalfa is useful for sodding slope plots dump pits or eroded fields, and sainfoin – to create water-stable structural units. It is shown that the qualitative indicators of ecotopes strictly determine the morphology and aboveground and underground parts, as well as the number and weight of nodules in legumes. In the thickness of ecotopes man-made landscapes is the basis for the creation of primary consorting relations are root systems of perennial leguminous grasses. They determine the structure of microbial cenosis and regulate the number of microorganisms. Adaptation of perennial legumes and soil microorganisms to the variability of environmental conditions in the deep ecotypes reflects their close interaction with the factors of this unique environment. Overburden, the unconsolidated rocks have a high stimulatory effect on the development of microorganisms. In 10–15 years after the removal of the "day" the surface sets up a pool of microorganisms and is manifested microbiological profile, the pattern of which reflects the diversity of ecotopia. There was determined the intensity of decomposition of roots in a layer of technogenic ecotopes landscapes. It falls in the direction from the zonal soil to gray-green clay. For the year transformed to 80 % of the roots of alfalfa and to 66 % in winter wheat. First of all the thin roots of the legumes were destroyed in the spring. It was shown increased sidorovskaya role of kulturpflanzen, especially species of alfalfa and sainfoin. They are plant-dominants and create pockets of concentration of the soil platoro-Diya. Soil formation begins with the surface, gradually spreading to the lower layers of ecotopes.

Calculation of Thermodynamic Properties in Solid-Liquid, Solid-Gas and Liquid-Gas Region

The paper features the mathematical model of analytical calculation of thermodynamic properties like viscosity, speed of sound and thermal conductivity for fluids in one and two-phase region (fluid-solid, fluid-gas) on the basis of statistical mechanics. For the calculation of thermal conductivity and viscosity for fluids will be presented Chung-Lee-Starling model Equations for the thermal conductivity are developed based on kinetic gas theories and correlated with the experimental data. The low-pressure transport properties are extended to fluids at high densities by introducing empirically correlated density dependent functions. These correlations use acentric factor, dimensionless dipole moment and an empirically determined association parameters to characterize molecular structure effect of polyatomic molecules. The calculation of thermodynamic properties for fluids was developed under the theory of statistical thermodynamics and statistical associated fluid theory. For the calculation of thermal conductivity of solids are the most important two contributions: the heat transport by electrons (el) and by phonons (ph). In our model we have made the assumption that heat transport by electrons and by phonons is independent and the thermal conductivity is than a sum of both terms.

Critical Mach Number for Flow around Circular-Arc Airfoil

An approximate method for the account of compressibility, which was successfully applied earlier for airfoil with subsonic-type edge, was used for airfoil with supersonic-type edge in the present paper. Calculations of the critical Mach number of free-stream flow around circular-arc airfoil are considered. This method allows defining the parameters of a compressible fluid through the flow characteristics of an incompressible fluid. The method to account of compressibility of a flow does not depend on mathematical model of calculation of incompressible flow. Calculations of the velocity field for incompressible flow on the basis of Theory Function of Complex Variable (TFCV) have been accomplished. It has been shown that the value of critical Mach number decreases with increasing the relative thickness of the circular-arc airfoil.