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 Modeling of anisotropic base plate of a ballastless railway track under dynamic influences

Vestnik MGSU ◽  
2020 ◽  
pp. 1105-1114
Author(s):  
Lilia A. Illarionova ◽  
Alexey A. Loktev
Keyword(s):  
Mathematical Model ◽  
Dynamic Behavior ◽  
High Speed ◽  
Vertical Component ◽  
Base Plate ◽  
Railway Track ◽  
Rolling Stock ◽  
Cylindrical Anisotropy ◽  
Concrete Plate ◽  
Shock Impact

Introduction. Due to dynamic loading, the upper structure of the railway track is subject to deformation over the entire construction and operation period. This paper focuses on the development of a mathematical model of the base plate of a general-type ballastless railway track structure without relying on specific existing technological solutions used for such elements. The effect of the actually given vertical component of the rolling stock velocity arising from the deviation from the design position of the long-welded rails on the dynamic deflection of the plate and the contact force of cylindrical anisotropy and the initial rate of dynamic interaction is studied. The proposed model makes it possible to take into account the effect of elastic waves originating in the contact area between the wheel and the rail that move at their final speeds after contact. The actual issue researched in this paper is the reinforcement of the ballastless railway base plate for the prevention of severe damage in the base plate. Materials and methods. A mathematical model has been developed to describe the dynamic behavior of a reinforced concrete plate of a ballastless railway track taking into account the specifics of load application from rolling stock wheel sets. Results. Detailed presentation of the research results in the form of analytical expressions and dependence diagrams of dynamic and kinematic parameters of the structure behavior can have practical application when designing rapid transit and high-speed railway lines both in Russia and abroad. Conclusions. The obtained results can be used for carrying out full-fledged research of dynamic behavior of the track bed under mobile loading, for checking the local durability of plates under shock impact, for researching and selecting optimal rigidity parameters for the track bed.

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 A Grey-BPNN Model for Evaluating the Competitiveness of Chinese Contractors in the High-Speed Rail Market in Europe

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Yi-Hsin Lin ◽  
Biling Shi ◽  
Po-Han Chen ◽  
Zhao Xu ◽  
Huimin Liu
Keyword(s):  
High Speed ◽  
Rolling Stock ◽  
High Speed Rail ◽  
The Sustainable Development ◽  
Advantages And Disadvantages ◽  
Management Ability ◽  
Study Results ◽  
Grey Relational ◽  
Technology Level ◽  
Bpnn Model

With the planning and progress of the construction of the trans-Eurasian high-speed rail (HSR) network, it becomes an important issue for Chinese contractors to enter the European HSR market. Facing the world’s most competitive contractors and their high technology levels, Chinese contractors will need to know their advantages and disadvantages, so as to make necessary improvements. In this study, contractors for HSR are divided into two groups: construction contractors and rail equipment suppliers. In order to evaluate the competitiveness of HSR contractors, a Grey-BPNN model that combines the grey relational analysis and backpropagation neural network (BPNN) is proposed. The Grey-BPNN model is expected to analyze the overall competitiveness of Chinese contractors in the European HSR market and provide informative decision support for them. The study results show the following: (1) in the field of HSR construction, the competitiveness gap between the top-tier Chinese contractors and the most competitive international contractors is small. Chinese contractors’ competitive advantages lie in medium- and low-technology-level projects, with a strong development potential. However, they highly depend on Chinese domestic market and lack in intangible resources, like management ability and market development ability; (2) for rail equipment suppliers, China Railway Rolling Stock Corporation (CRRC) ranks among the top-tier leaders of the international market. CRRC’s greatest competitor in the European HSR market is Siemens, and CRRC is much more competitive than others in the sustainable development capability. However, CRRC needs to increase the quantity of patents and Research and Development (R&D) expenditures in transportation. As a weak transportation patent holder, CRRC has a potential risk of getting intellectual property litigations in the European HSR market.

APPLICATION OF THE JUMPING FROGS METHOD FOR THE OPTIMIZATION OF THREE-LEVEL PLANS OF A MULTIPLE FACTOR EXPERIMENT

2019 ◽  
pp. 35-42
Author(s):  
N. Koshevoy ◽  
E. Kostenko ◽  
V. Muratov
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
High Speed ◽  
Minimum Cost ◽  
Optimization Method ◽  
Experimental Designs ◽  
Minimal Cost ◽  
Taboo Search ◽  
Time Costs ◽  
The Cost

he planning of the experiment allows us to solve the problem of obtaining a mathematical model with minimal cost and time costs. The cost of implementing an experiment is significantly affected by the order of alternating levels of change in factors. Thus, it is required to find a procedure for the implementation of experiments that provides the minimum cost (time) for conducting a multivariate experiment. This task becomes especially relevant when studying long and expensive processes. The purpose of this article is the further development of the methodology of optimal planning of the experiment in terms of cost (time), which includes a set of methods for optimizing the plans of the experiment and hardware and software for their implementation. Object of study: optimization processes for the cost of three-level plans for multivariate experiments. Subject of research: optimization method for cost and time costs of experimental designs based on the use of the jumping frog method. Experimental research methods are widely used to optimize production processes. One of the main goals of the experiment is to obtain the maximum amount of information about the influence of the studied factors on the production process. Next, a mathematical model of the object under study is built. Moreover, it is necessary to obtain these models at the minimum cost and time costs. The design of the experiment allows you to get mathematical models with minimal cost and time costs. For this, a method and software were developed for optimizing three-level plans using the jumping frog method. Three-level plans are used in the construction of mathematical models of the studied objects and systems. An analysis is made of the known methods for the synthesis of three-level plans that are optimal in cost and time costs. The operability of the algorithm was tested when studying the roughness of the silicon surface during deep plasma-chemical etching of MEMS elements. Its effectiveness is shown in comparison with the following methods: swarm of particles, taboo search, branches and borders. Using the developed method and software for optimizing three-level plans using the jumping frog method, one can achieve high winnings compared to the initial experimental plan, optimal or close to optimal results compared to particle swarm, taboo search, branches and borders methods, and also high speed of solving the optimization problem in comparison with previously developed optimization methods for three-level experimental designs.

Research and Analysis of Dynamic Behaviour in the Mathematical Models of the 6-Axle Locomotive

2011 ◽  
Vol 105-107 ◽  
pp. 541-544
Author(s):  
Van Tham Mai ◽  
Shi Jing Wu ◽  
Xiao Sun Wang ◽  
Jie Chen ◽  
S. A. K. S. Jafri
Keyword(s):  
Differential Equations ◽  
Mathematical Models ◽  
Dynamic Behavior ◽  
Dynamic Behaviour ◽  
Computer Software ◽  
Rolling Contact ◽  
Rolling Stock ◽  
Vertical Movements ◽  
Dynamic Behaviors ◽  
Second Order Differential Equations

With the aiming of mathematically modeling dynamic behavior in latitudinal and vertical movements of the 6-axle locomotive, this paper introduces the Kalker’s Wheel-Rail Rolling Contact Theories and their implementation in multibody codes. This paper also highlights methodology for solving inhomogeneous linear second-order differential equations with MATLAB computer software aided. The calculation has reported that the dynamic behaviors of Diesel-Electric 6-axle locomotive are significantly demonstrated. The calculation has reported that the dynamic behaviors of Diesel-Electric 6-axle locomotive are significantly demonstrated the requirements on Rolling stock Dynamic behaviors of Vietnam Railways.

scholarly journals Modeling of Self-Vibratory Drilling Head-Spindle System for Predictions of Bearings Lifespan

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
F. Forestier ◽  
V. Gagnol ◽  
P. Ray ◽  
H. Paris
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Dynamic Behavior ◽  
Potential Risk ◽  
Feed Rate ◽  
High Speed ◽  
Element Model ◽  
Experimental Measurements ◽  
Alternative Response ◽  
Tool Breakage

The machining of deep holes is limited due to inadequate chip evacuation, which induces tool breakage. To limit this drawback, retreat cycles and lubrication are used. An alternative response to the evacuation problem is based on high-speed vibratory drilling. A specific tool holder induces axial self-maintained vibration of the drill, which enables the chips to be split. The chips are thus of a small size and can be evacuated. To anticipate the potential risk of decreased spindle lifespan associated with these vibrations, a model of the behavior of the system (spindle—self-vibrating drilling head—tool) is elaborated. In order to assess the dynamic behavior of the system, this study develops a rotor-based finite element model, integrated with the modelling of component interfaces. The current results indicate that the simulations are consistent with the experimental measurements. The influence of spindle speed and feed rate on bearing lifespan is highlighted.

Modelling Approach for a High Speed Machine Tool Spindle-Bearing System

2005 ◽  
Author(s):  
Vincent Gagnol ◽  
Belhassen C. Bouzgarrou ◽  
Pascal Ray ◽  
Christian Barra
Keyword(s):  
Finite Element ◽  
Dynamic Behavior ◽  
High Speed ◽  
Modal Identification ◽  
Coordinate Frame ◽  
Mass Unbalance ◽  
Spindle Bearing ◽  
Milling Forces ◽  
Bearing System ◽  
Modelling Approach

This paper presents a modelling approach of a high-speed spindle-bearing system based on a finite-element model analysis coupled to an experimental modal identification. Dynamic equations of the rotating entity are obtained using Lagrangian formulation associated with a numerical finite element method based on Timoshenko beam theory. Element kinematics is formulated in a co-rotational coordinate frame. A method for the experimental characterization of the dynamic behavior of a High Speed Machining (HSM) spindle is proposed. The goal of this method is to understand the influence of spindle structure elements on overall dynamic behavior. Each element is individually characterized and is integrated or not into the global model depending on the results. The choice of the finite element type for generating the numeric model is carried out on the basis of modal and harmonic experimental results. High-speed rotational effects including gyroscopic coupling and spin softening effects are investigated. The Campbell diagram indicates the potential critical speed for mass unbalance response and for synchronous excitation representative of the milling forces at tooth impact frequency. Excessive vibration levels at specific node location enable spindle component stress or failure during manufacturing processes to be predicted. The model is a useful tool for qualifying spindles in the manufacturing process and predicting their reliability. The proposed modeling approach can be transferred to other type of spindle.

Simulation of reciprocating gas compressors with automatic reed valves

SIMULATION ◽  
1967 ◽  
Vol 8 (4) ◽  
pp. 209-214 ◽  
Author(s):  
M.W. Wambsganss ◽  
Donald Coates ◽  
Raymond Cohen
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Steady State ◽  
Dynamic Behavior ◽  
High Speed ◽  
Experimental Results ◽  
The Other ◽  
Reciprocating Compressor ◽  
Trial And Error ◽  
State Tests

The simulation of high-speed reciprocating refrigeration compressors was motivated by the needs of design engi neers. In this paper a mathematical model describing the dynamic behavior of a reciprocating compressor is pre sented. The model is semianalytic in that two types of empirical factors are required to relate phenomena not yet analytically predictable. One type is obtained from steady- state tests and the other by trial and error based on com parison with experimental results. Both analog and digital computers were considered as means of simulating the model. Due to nonlinearities in the model, the digital com puter, using Fortran IV, was selected. To evaluate the sim ulation, a one-quarter horsepower 3600-rpm stock com pressor was modified and used as a laboratory vehicle. A typical correlation between the computer simulation and experimental results is given. In general, good correlation was achieved.

Stress Analysis of Underground Arch Structure

2011 ◽  
Vol 243-249 ◽  
pp. 938-941
Author(s):  
Bin He ◽  
Jun Long Lu
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Structural Analysis ◽  
Finite Element Model ◽  
Mathematical Models ◽  
Stress Analysis ◽  
Element Model ◽  
Arch Structure ◽  
The Impact ◽  
Actual Stress

To research the safety of an underground defense project and the impact to other buildings, applying basic mechanics principles, established two types of mathematical model for arch about the project, and analyzed stress in different directions of ground arch structure. The data shows that the results were very different in different mathematical models, and mathematical models should be considered as close to actual stress situation in structural analysis. In the structural analysis involved soil, spatial finite element model is more accurate and reasonable than truss finite element model.

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