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 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.

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.  

scholarly journals ДИФЕРЕНЦІЙОВАНИЙ ПІДХІД У НАВЧАННІ СТУДЕНТІВ АГРАРНИХ ВНЗ ОСНОВ МАТЕМАТИЧНОГО МОДЕЛЮВАННЯ З ВИКОРИСТАННЯМ MS EXCEL

2016 ◽  
Vol 54 (4) ◽  
pp. 165
Author(s):  
Leonid O. Flehantov ◽  
Yuliia I. Ovsiienko
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Information Technology ◽  
The Body ◽  
Dense Medium ◽  
Research Activities ◽  
Basic Concepts ◽  
Engineering Training ◽  
Mechanical Movement ◽  
Basic Level

The differentiated approach in teaching the students of engineering training areas of Agricultural Universities for the basics of mathematical modelling by information technology on the example of a mathematical model of the mechanical movement of the body in dense environments is proposed. We considered the phased construction, improvement and research of mathematical model of the three levels of difficulty: without the environment resistance, given the environment resistance, taking into account the effects arising from the forward-rotational motion of the body in dense medium. This approach provides successful mastering by students the basic concepts, methods and procedures of mathematical modeling at the basic level, the formation of representations about the application of mathematical models and basic skills for research activities.

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.

Application of the method of mathematical modeling for forecasting channel deformations at the underwater crossing of the main pipeline

2020 ◽  
Vol 10 (6) ◽  
pp. 599-609
Author(s):  
Valery А. Gruzdev ◽  
◽  
Georgy V. Mosolov ◽  
Ekaterina A. Sabayda ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Roughness Coefficient ◽  
Computational Domain ◽  
Channel Deformations ◽  
Geological Surveys ◽  
Kuban River ◽  
The Stability ◽  
Protective Structures

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

On the displacements of the contours of the optic-electronic space images. Mathematical modeling of displacement

2017 ◽  
Vol 992 (4) ◽  
pp. 32-38 ◽  
Author(s):  
E.G. Voronin
Keyword(s):  
Mathematical Modeling ◽  
Remote Sensing ◽  
Mathematical Model ◽  
Point Of View ◽  
Design Features ◽  
Space Images ◽  
Electronic Imaging ◽  
Measuring Accuracy ◽  
Physical Laws

The article opens a cycle of three consecutive publications dedicated to the phenomenon of the displacement of the same points in overlapping scans obtained adjacent CCD matrices with opto-electronic imagery. This phenomenon was noticed by other authors, but the proposed explanation for the origin of displacements and the resulting estimates are insufficient, and developed their solutions seem controversial from the point of view of recovery of the measuring accuracy of opticalelectronic space images, determined by the physical laws of their formation. In the first article the mathematical modeling of the expected displacements based on the design features of a scanning opto-electronic imaging equipment. It is shown that actual bias cannot be forecast, because they include additional terms, which may be gross, systematic and random values. The proposed algorithm for computing the most probable values of the additional displacement and ways to address some of the systematic components of these displacements in a mathematical model of optical-electronic remote sensing.

scholarly journals Mathematical Modeling and Numerical Simulation of Atherosclerosis Based on a Novel Surgeon’s View

2021 ◽  
Author(s):  
Meisam Soleimani ◽  
Axel Haverich ◽  
Peter Wriggers
Keyword(s):  
Mathematical Modeling ◽  
Inflammatory Response ◽  
Phase Field ◽  
Mechanical Response ◽  
Type Equation ◽  
The Body ◽  
Vasa Vasorum ◽  
Diffusion Reaction ◽  
Dust Particles ◽  
Driving Mechanism

AbstractThis paper deals with the mathematical modeling of atherosclerosis based on a novel hypothesis proposed by a surgeon, Prof. Dr. Axel Haverich (Circulation 135(3):205–207, 2017). Atherosclerosis is referred as the thickening of the artery walls. Currently, there are two schools of thoughts for explaining the root of such phenomenon: thickening due to substance deposition and thickening as a result of inflammatory overgrowth. The hypothesis favored here is the second paradigm stating that the atherosclerosis is nothing else than the inflammatory response of of the wall tissues as a result of disruption in wall nourishment. It is known that a network of capillaries called vasa vasorum (VV) accounts for the nourishment of the wall in addition to the natural diffusion of nutrient from the blood passing through the lumen. Disruption of nutrient flow to the wall tissues may take place due to the occlusion of vasa vasorums with viruses, bacteria and very fine dust particles such as air pollutants referred to as PM 2.5. They can enter the body through the respiratory system at the first place and then reach the circulatory system. Hence in the new hypothesis, the root of atherosclerotic vessel is perceived as the malfunction of microvessels that nourish the vessel. A large number of clinical observation support this hypothesis. Recently and highly related to this work, and after the COVID-19 pandemic, one of the most prevalent disease in the lungs are attributed to the atherosclerotic pulmonary arteries, see Boyle and Haverich (Eur J Cardio Thorac Surg 58(6):1109–1110, 2020). In this work, a general framework is developed based on a multiphysics mathematical model to capture the wall deformation, nutrient availability and the inflammatory response. For the mechanical response an anisotropic constitutive relation is invoked in order to account for the presence of collagen fibers in the artery wall. A diffusion–reaction equation governs the transport of the nutrient within the wall. The inflammation (overgrowth) is described using a phase-field type equation with a double well potential which captures a sharp interface between two regions of the tissues, namely the healthy and the overgrowing part. The kinematics of the growth is treated by classical multiplicative decomposition of the gradient deformation. The inflammation is represented by means of a phase-field variable. A novel driving mechanism for the phase field is proposed for modeling the progression of the pathology. The model is 3D and fully based on the continuum description of the problem. The numerical implementation is carried out using FEM. Predictions of the model are compared with the clinical observations. The versatility and applicability of the model and the numerical tool allow.

scholarly journals Simulation of Diffusion Processes in Chemical and Thermal Processing of Machine Parts

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 698
Author(s):  
Kateryna Kostyk ◽  
Michal Hatala ◽  
Viktoriia Kostyk ◽  
Vitalii Ivanov ◽  
Ivan Pavlenko ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Temperature Distribution ◽  
Thermal Treatment ◽  
Diffusion Processes ◽  
Nitrogen Concentration ◽  
The Body ◽  
Functional Dependencies ◽  
Technological Parameters ◽  
Gas Nitriding ◽  
Temperature State

To solve a number of technological issues, it is advisable to use mathematical modeling, which will allow us to obtain the dependences of the influence of the technological parameters of chemical and thermal treatment processes on forming the depth of the diffusion layers of steels and alloys. The paper presents mathematical modeling of diffusion processes based on the existing chemical and thermal treatment of steel parts. Mathematical modeling is considered on the example of 38Cr2MoAl steel after gas nitriding. The gas nitriding technology was carried out at different temperatures for a duration of 20, 50, and 80 h in the SSHAM-12.12/7 electric furnace. When modeling the diffusion processes of surface hardening of parts in general, providing a specifically given distribution of nitrogen concentration over the diffusion layer’s depth from the product’s surface was solved. The model of the diffusion stage is used under the following assumptions: The diffusion coefficient of the saturating element primarily depends on temperature changes; the metal surface is instantly saturated to equilibrium concentrations with the saturating atmosphere; the surface layer and the entire product are heated unevenly, that is, the product temperature is a function of time and coordinates. Having satisfied the limit, initial, and boundary conditions, the temperature distribution equations over the diffusion layer’s depth were obtained. The final determination of the temperature was solved by an iterative method. Mathematical modeling allowed us to get functional dependencies for calculating the temperature distribution over the depth of the layer and studying the influence of various factors on the body’s temperature state of the body.

Impact of Electric Vehicle Lateral Dynamics on the Battery Pack

2014 ◽  
Vol 590 ◽  
pp. 451-457
Author(s):  
Sen Nan Song ◽  
Fa Chao Jiang ◽  
Hong Shi
Keyword(s):  
Mathematical Model ◽  
Angular Acceleration ◽  
Simulation Software ◽  
The Body ◽  
Battery Pack ◽  
Vehicle Body ◽  
Rolling Motion ◽  
Rolling Angle ◽  
On The Road ◽  
The Mathematical Model

The present work is concerned with the rolling motion of the battery pack when EV travelling on the road. First McPherson suspension system was regarded as the research object with detailed analysis of its structural features and motion characteristics. Establish the mathematical model which could apply to calculating the rolling motion of the vehicle body. Through MATLAB/Simulink simulation software, we could calculate the rolling angle on passive suspension. On this basis, assume that the battery pack mounted on the vehicle body and make it passive connection and PID connection. When the body rolls, the battery pack will produce a certain angle then. Next establish the mathematical model to summarize the relationship between the two variables. Then we set the parameters and calculate the roll angle of battery pack in both cases for comparison. Simulation results show that road irregularities will make battery rotate an angle and PID controller can effectively reduce the angle, especially angular acceleration. This paper put forward a new idea that battery is connected with body by active control on EV, and proves the superiority in reducing the rolling angle.

Mathematical modeling of fluid movement inside the eyeball during intravitreal injection

2021 ◽  
pp. 106-109
Author(s):  
D.V. Lipatov ◽  
◽  
S.A. Skladchikov ◽  
N.P. Savenkova ◽  
V.V. Novoderezkin ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Residence Time ◽  
Complex Structure ◽  
Posterior Vitreous Detachment ◽  
Vitreous Body ◽  
Complete Removal ◽  
Intravitreal Injections ◽  
The World

Background. The avalanche-like growth of intravitreal injections in the world has significantly increased interest in the hemodynamics of the processes that occur in the eye when a drug is injected into the vitreous cavity. Every year, the number of intravitreally used drugs and promising areas in which they can be used is growing. This also applies to the creation of new combined medicines and the development of drugs with a long-term therapeutic effect. Aims. Create mathematical model of eyeball to evaluate the movement of the drug substance in it; to estimate the time of the drug's presence in the eye cavity before its complete removal, to characterize the ways of its removal from the eye cavity; to assess the significance of posterior vitreous detachment during the time when the drug is present in the eye cavity; to evaluate the effect on the hydrodynamics of the depth of drug administration. Results. When the drug is administered closer to the center of the eyeball, its residence time increases in comparison with the parietal administration. With a complete posterior detachment of the vitreous body, the time of finding the drug in the eye is prolonged compared to its absence. The obtained results of mathematical modeling of the movement of the drug administered intravitreally cannot be mechanically transferred to the human eye, due to the more complex structure of the latter. Key words: intravitreal injections, vitreous body, mathematic computing.

Sign in / Sign up

Export Citation Format

Share Document