scholarly journals INVESTIGATION CASES OF ROLLING STOCK DERAILMENT USING MATHEMATICAL MODELING

2019 ◽  
Vol 20 (2) ◽  
pp. 340-350
Author(s):  
А. Batig ◽  
A. Kuzyshyn
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Technical Condition ◽  
The Body ◽  
Object Oriented Programming ◽  
Rolling Stock ◽  
Highly Qualified ◽  
Rolling Surface ◽  
Computer Environment

The purpose of this article is to analyze the need to apply the methods of mathematical modeling when performing examinations of rolling stock derailment. The description of the dynamic behavior of rolling stock when moving on the track is a rather complicated, time-consuming process, which requires highly qualified expert and time-consuming. The presence of detailed mathematical models of the constituent units of the rolling stock would greatly facilitate the study of cases of their derailment. At present, a significant number of scientific papers are devoted to the study of the dynamics of rolling stock movement using mathematical models. In Lviv NDISE, investigations of such railway accidents as rolling stock derailment from the rails are performed by experts according to the methods developed by the doctor of technical sciences Sokol E. M., allowing to take into account a certain number of parameters of wagon running gears. At present, when experts examine the cases of rolling stock derailment, there is a need to develop new methods that would allow to take into account more parameters of the undercarriage parts of the wagons, such as: parameters of the damping system, spring suspension, bolster, node of the body-bogie bolster center plates, etc. P. There are also cases of railway accidents, in which one of the reasons may be the presence of defects on the rolling surface of the wheels of the rolling stock. In this regard, experts of Lviv NDISE to take into account the above-mentioned parameters of the running gears and to identify the most significant for rolling stock derailment, it was developed object-oriented programming in the computer environment Maple. At present, have developed a mathematical model of a passenger car of a diesel train, the DPKr-2, and an improved mathematical model of a freight wagon. The authors of the article came to the conclusion that the use of mathematical models and their computer solution can facilitate the process of researching rolling stock cases from the rails, as it allows automating and speeding up the study of dynamic indicators of rolling stock, facilitating the process of establishing the limiting values of its technical condition parameters and assessing the consequences changes in these parameters in certain working conditions.

scholarly journals Dynamic Loading Research of the Gondola car Supporting Structure with an Elastic-Viscous Filler in a Center Sill

2021 ◽  
pp. 59-66
Author(s):  
A. O Lovska ◽  
O. V Fomin ◽  
A. V Rybin
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Dynamic Loading ◽  
Equations Of Motion ◽  
Resistance Coefficient ◽  
The Body ◽  
Rolling Stock ◽  
Friction Forces ◽  
Supporting Structure ◽  
Modeling Methodology

Purpose. The work aims to investigate dynamic loading of the supporting structure of a gondola car with an elastic-viscous filler in the center sill by means of mathematical modeling. Methodology. Mathematical modeling of the dynamic loading of the supporting structure of a gondola car with a closed center sill filled with a filler with elastic-viscous properties has been carried out. The case of the highest load on the supporting structure of the gondola car in operation is taken into account – a shunting collision, taking into account the action of a load of 3.5 MN on the rear stop of the automatic coupler. To determine the dynamic loading of a gondola car, a mathematical model formed by prof. G. I. Bohomaz was used. However, within the framework of this study, the model was refined by adapting it to the determination of the dynamic loading of a gondola car. It also takes into account the friction forces arising between the center plates of the body and the center pivots of the bogies, as well as the properties of the energy-absorbing material. The solution of the mathematical model was carried out in the MathCad software package. In this case, the differential equations of motion were reduced to the Cauchy normal form, and then integrated using the Runge-Kutta method. Initial displacements and speeds are taken equal to zero. The calculation was carried out on the example of a universal gondola car model 12-757 built by Kriukivskyi Carriage Works PJSC (Kremenchug) on standard bogies 18-100. Findings. Accelerations are obtained as components of a dynamic load acting on a gondola car with a closed center sill structure filled with an elastic-viscous filler. It was found that with the stiffness of the center sill filler of 82 kN/m, as well as the viscous resistance coefficient of -120 kN∙s/m, the maximum accelerations of the gondola car supporting structure is about 37 m/s2 (0.37g). Originality. A mathematical model is proposed for determining the dynamic loading of a gondola car with a closed structure of a center sill filled with an elastic-viscous filler. The model makes it possible to obtain accelerations as the components of the dynamic loading acting on the supporting structure of the gondola car, taking into account the improvement measures during a shunting collision. Practical value. The results of the research will help to reduce the damage to the supporting structures of gondola cars in operation, reduce the cost of their maintenance, create developments in the design of innovative structures of rolling stock, as well as increase the efficiency of its operation.  

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

scholarly journals World Experience in Creating Mathematical Models of Air Springs: Advantages and Disadvantages

2021 ◽  
pp. 25-42
Author(s):  
A. Y Kuzyshyn ◽  
S. A Kostritsia ◽  
Yu. H Sobolevska ◽  
А. V Batih
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Mathematical Models ◽  
Dynamic Behavior ◽  
High Speed ◽  
Vertical Direction ◽  
Rolling Stock ◽  
Air Spring ◽  
Advantages And Disadvantages ◽  
Mechanical Models

Purpose. Taking into account the production and commissioning of modern high-speed rolling stock, the authors are aimed to analyze the currently created mathematical models describing the dynamic behavior of the air spring, systematize them and consider the advantages and disadvantages of each model type. Methodology. For the analysis, a comparative chronological method was used, which makes it possible to trace the development of several points of view, concepts, theories. In accordance with the adopted decision equations, the existing models of air springs were divided into three groups: mechanical, thermodynamic and finite-elements. When analyzing mathematical models, the influence of a number of parameters on the dynamic behavior of the air spring, such as disturbing force frequency, heat transfer, nonlinear characteristics of materials, the shape of the membrane, etc., was considered. Findings. A feature of mechanical models is the determination of input parameters based on the analysis of experimental results, requires access to complex measuring equipment and must be performed for each new model of an air spring separately. Unlike mechanical models, which allow taking into account the damping effect of an air spring in the horizontal and vertical direction, thermodynamic models are mainly focused on studying the dynamic behavior of an air spring in the vertical direction. The use of the finite element method makes it possible to most accurately reproduce the dynamic behavior of an air spring, however, it requires significant expenditures of time and effort to create a finite element model and perform calculations. Originality. Mathematical models of the dynamic behavior of an air spring are systematized, and the importance of their study in conjunction with a spatial mathematical model of high-speed rolling stock is emphasized. Practical value. The analysis of the mathematical models of the dynamic behavior of the air spring shows the ways of their further improvement, indicates the possibility of their use in the spatial mathematical model of the rolling stock in accordance with the tasks set. It will allow, even at the design stage of high-speed rolling stock, to evaluate its dynamic characteristic and traffic safety indicators when interacting with a railway track.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

scholarly journals RESEARCH OF VIBRATION MACHINES DYNAMICS FOR PRODUCT SURFACES PROCESSING BY MATHEMATICAL MODELING

2020 ◽  
pp. 35-43
Author(s):  
Volodymyr Topilnytskyy ◽  
Yaroslav Kusyi ◽  
Dariya Rebot
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Surface Treatment ◽  
Lagrange Equation ◽  
The Body ◽  
Technological Problem ◽  
Surface Processing ◽  
Approximate Methods ◽  
Vibration Machine ◽  
Working Chamber

The article describes the methodology for the study of the dynamics of vibrating machines for surface processing of products by mathematical modeling, which is presented in four main stages. The first stage: analysis of classes of vibrating machines for surface treatment of products, choice of basic for solving the technological problem, project of a unified calculation scheme of the machine. The second stage: development of a nonlinear mathematical model for describing the dynamics of the vibration machine working body and its filling, development of elements of automated calculations of the machine. The third stage: the study of the influence of the parameters of the vibrating machine, product sets and tools (with their various combinations) on the factors of the intensity of products surface processing. The fourth stage: recommendations for choosing vibrating machine parameters and machining bodies that will maximize the processing performance of products with the selected intensity criterion. A mathematical model for describing the motion of a vibrating machine for surface treatment of articles by a set of unrelated bodies of small size is created. It has two unbalance units that generate oscillations of its working body and a spring suspension-mounting of the working chamber (container). The model is parametric and nonlinear, incorporating key dynamic, kinematic and geometric parameters of the vibrating machine in symbolic format. It is constructed by: descriptions of the plane-parallel movement of the mechanical system, the rotational motion of the material point and the body; second-order Lagrange equation; asymptotic (approximate) methods of nonlinear mechanics. With the help of the model it is possible: to describe the oscillatory movement of the working chamber (container) of the vibrating machine; to study the influence of the machine parameters on the efficiency of performance of the set technological task, the conditions of occurrence of non-stationary modes of operation of the vibrating machine and the ways of their regulation.

scholarly journals Diagnostics of supercapacitors

2018 ◽  
Vol 182 ◽  
pp. 01009 ◽  
Author(s):  
Valeriy Martynyuk ◽  
Oleksander Eromenko ◽  
Juliy Boiko ◽  
Tomasz Kałaczyński
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Methodological Approach ◽  
Frequency Dispersion ◽  
Technical Condition ◽  
Transient Processes ◽  
Nonlinear Frequency ◽  
Diagnostic Reliability ◽  
General Reliability ◽  
The Mathematical Model

The paper represents the mathematical model for diagnostics of supercapacitors. The research objectives are the problem of determining a supercapacitor technical condition during its operation. The general reliability of diagnostics is described as the methodological and instrumental reliabilities of diagnostics. The instrumental diagnostic reliability of supercapacitor includes the probabilities of errors of the first and second kind, α and β respectively. The methodological approach to increasing the reliability of supercapacitor diagnostic has been proposed, in terms of multi-parameter supercapacitor diagnostic by applying nonlinear, frequency dependent mathematical models of supercapacitors that take into account nonlinearity, frequency dispersion of parameters and the effect of transient processes in supercapacitors. The more frequencies, operating voltages and currents are applied in the supercapacitor diagnostics, the more methodological reliability of diagnostics will increase in relation to the methodological reliability of supercapacitor diagnostics when only one frequency, voltage and current are applied.

scholarly journals Mathematical modeling in economics for selection of optimum investment solution

2021 ◽  
Vol 273 ◽  
pp. 08003
Author(s):  
Arthur Alukhanyan ◽  
Olga Panfilova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Linear Programming ◽  
Mathematical Models ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Target Function ◽  
Investment Portfolio ◽  
Monetary Relations ◽  
Selection Of

This work is devoted to development of economic and mathematical models for selection of the optimum investment solution. Moreover, it states the basis for development of model examples and correction of the model considering the results obtained in the examples. In the work the problem is set for selection of the investment sources and objects, which is limited to the linear programming problem. The controlled variable and basic limitations simulating real credit and monetary relations are distinguished in the provided model. The discounted profit obtained from implementation of the optimum investment portfolio is considered as a target function. The economic and mathematical model presented in the article allows finding the optimum investment solution within the limits of the credit and monetary relations taking place both at the micro- and macroeconomic level.

scholarly journals X-ray densitometric indices of proximal phalanx, medial phalanx and ungular pelvic limb bones as criteria for age diagnosis of cattle in forensic veterinary expertise

2019 ◽  
Vol 10 (2) ◽  
pp. 197-202
Author(s):  
I. V. Yatsenko ◽  
S. A. Tkachuk ◽  
L. V. Busol ◽  
M. M. Bondarevsky ◽  
I. V. Zabarna ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Proximal Phalanx ◽  
The Body ◽  
Heterogeneous Structure ◽  
Tubular Bone ◽  
X Rays ◽  
X Ray ◽  
Limb Bones ◽  
Pelvic Limb

Morphological parameters of biological material are extremely informative in diagnostic studies, in particular, to determine the species, sex, time of death, the term of burial. The most informative object for these tasks is the skeleton, because changes in the bones are stored for a long time, while soft tissue is subjected to rotting. Bone tissue is the most durable, but at the same time, it is very labile and reacts to all metabolic processes in the body. The object of the study was proximal phalanx, medial phalanx and ungular bone of the pelvic limb of cattle ranging in age from newborn to 12 years old. Radiography of the proximal phalanx, medial phalanx and ungular bones of the pelvic limb was performed on the Arman apparatus. The bones were subjected to X-ray in the lateromedial projection. The inner and outer sections of the tubular bone were determined. The mathematical modeling of the interaction of X-rays and the cortical layer of bones of fingers (proximal phalanx, medial phalanx and ungular) of cattle was carried out in this work. It is established that this process is described by Bouger's law. The physico-mathematical model of proximal phalanx, medial phalanx and ungular bones has been calculated, on the basis of which it was possible to calculate the X-ray densitometric indices of these bones of cattle. The age features of dynamics of X-ray densitometric indices of the proximal phalanx, medial phalanx and ungular bones were established and a method of determining the age of cattle according to this criterion was proposed. A mathematical model for the proximal phalanx, medial phalanx and ungular bones of the pelvic limbs of cattle that can be applied in X-ray densitometry uses: for the average third proximal phalanx – section of heterogeneous tubular structure modeled by a semicircle; for a medial phalanx bone – a section of a triangular shape; for the ungular bone – a heterogeneous structure, the plantar surface is inscribed in a rectangle. The process of interaction of X-rays with the bone structure of the examined pelvic limb bones can be described by Bouguer's law. The developed mathematical modeling of this interaction and the algorithm for its analysis is the basis for determining the age of cattle for X-ray densitometric indices of the proximal phalanx, medial phalanx and ungular bones of pelvic limbs. By X-ray densitometry of the proximal phalanx and medial phalanx bones of the pelvic limbs extremities one can diagnose the age of bovine animals from birth to 5 years, but according to ungular bones – from birth to 10 years. X-ray densitometry of medial phalanx and ungular bones of pelvic limbs can be used for diagnosing bovine cattle in a complex with other morphological, chemical and physical methods of investigation.

INFLUENCE OF DYNAMIC LOADING ON THE CHARACTERISTICS OF POLYMER IMPACT DAMPERS

2020 ◽  
Author(s):  
Vladimir Altuhov ◽  
Aleksey Boldyrev ◽  
Pavel Zhirov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Ambient Temperature ◽  
Dynamic Loading ◽  
Loading Rate ◽  
Rolling Stock ◽  
Wear Factor ◽  
Shock Absorbers ◽  
Draft Gear ◽  
Freight Car

The article is devoted to the study of the influence of dynamic loading on the characteristics of polymer elements of shock absorbers of the rolling stock of railways and to the description of the creation of a mathematical model of their work. The results of mathematical modeling are further used to solve problems of the longitudinal dynamics of rolling stock. In the study, the initial loading rate varied, the ambient temperature and the influence of the wear factor remained unchanged. For the operating speeds of a freight car, a mathematical model of the PMKP-110 draft gear was determined.

Mathematical Modeling of the Anaerobic Filter Process

1983 ◽  
Vol 15 (8-9) ◽  
pp. 197-207 ◽  
Author(s):  
M Lindgren
Keyword(s):  
Mathematical Modeling ◽  
Waste Water ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Efficient Tool ◽  
Anaerobic Filter ◽  
Filter Process

A dilute synthetic waste water was anaerobica1ly treated in a filter. A mathematical model of the anaerobic filter process was also developed and analyzed. Analysis showed that mathematical models are an efficient tool for system understanding and design.

Sign in / Sign up

Export Citation Format

Share Document