Issue №: 4 (103)
The journal deals with the problems of vibration technologies and machines, mathematical methods of vibration process studies, information on design and technological development, presents teaching and methodological aspects of teaching in the Higher School of Applied Sciences, where vibration machines and technologies are studied.
STUDY OF THE KINEMATICS OF PLASTIC FLOW OF A METAL USING THE EULER AND LAGRANGE VARIABLES
Sivak Roman – Doctor of Technical Sciences, Associate Professor of the Department of General Technical Disciplines of Vinnytsia national agrarian university (st. Soniachna, 3, Vinnytsia, Ukraine, 21008, e-mail: sivak_r_i@ukr.net)
Zalizniak Roman – graduate student (st. Soniachna, 3, Vinnytsia, Ukraine, 21008, e-mail: pacifistroma@gmail.com)
In continuum mechanics, two equivalent points of view on the flow of a metal in the process of deformation - Euler and Lagrange - have found application. When attention is focused on a given point in space, where different particles of a continuous medium come in the process of deformation, this is the essence of Euler's point of view on the studied motion of a continuous medium. From the point of view of Lagrange, the motion is considered known if the speed, acceleration, temperature and other quantities are given as functions of the coordinates of a point in space and time. The essence of Lagrange's view of the studied motion lies in the fact that they focus on a specific particle of a continuous medium and investigate the history of its deformation and motion. The coordinates that individualize the points of the continuous medium are called Lagrange variables. Lagrange's view on the study of the motion of a continuous medium underlies physical laws, since it is associated with the motion of individual particles. At the initial moment, the coordinates of a certain point according to Euler and Lagrange coincide.
The article discusses the possibility of using mixed Euler and Lagrange coordinates to determine the component of the strain rate tensor in plastic deformation processes. The expediency of the approach of Lagrange and Euler is clarified in specific problems. It should be borne in mind that in the Euler coordinates, the equilibrium equations have a simpler form (they are linear), and the boundary conditions are more complex due to the fact that it is impossible, without solving the problem, to determine the displacement components that are usually included in the boundary conditions. In Lagrange coordinates, the boundary conditions, as a rule, are written easier, and the equilibrium equation is more complicated.
When processing metals by pressure, the metal undergoes significant deformation. However, it is convenient to consider each process at each fixed moment of its course, therefore, it is necessary to know the basic provisions and dependencies related to small deformations.
1. Аlіevа L. І., Аlіeв І. S., Grudkіnа N. S., Маlіy H. V. Моdеliuvаnnia prоtsеsu kоmbіnоvаnоgо rаdіаlnо-zvоrоtnоgо vydаvliuvаnnia dеtаlеy z flаntsеm. Оbrаbоtkа маtеriаlоv dаvlеniеm. Krаmаtоrsk. 2019. № 1 (48). S. 23-34.
2. Маtvіychuk V. А., Bubnоvskа І. А. Оtsіnkа dеfоrmоvаnоstі mаtеrіаlu kryvоlіnіynyh zаgоtоvоk pry hоlоdnоmu vаltsuvаnnі. Теhnіkа, еnеrgеtykа, trаnspоrt АPК. Vіnnytsia. 2017. Vypusk 4. S. 92-97.
3. Мyhаlеvych V. М., Dоbrаniuk Iu. V., Кrаevskyi V. О. Pоrіvnialnе dоslіdzhеnnia mоdеlеy grаnychnyh plаstychnyh dеfоrmаtsіy. Vіsnyk mаshynоbuduvаnnia tа trаnspоrtu. Vіnnytsia. 2018. № 2. S. 56-64.
4. Grushkо О. V., Оgоrоdnіkоv V. А., Slоbоdianiuk Iu. О. Dеfоrmоvnіst malоvuglеtsеvоgо drоtu v prоtsеsі yоgо bаgаtоstupіnchаstоgо hоlоdnоgо vоlоchіnnia. Vіsnyk Vіnnytskоgо pоlіtеhnіchnоgо іnstytutu. Vіnnytsia. 2019. №3. S. 103-110.
5. Sivak R. Evaluation of metal plasticity and research of the mechanics of pressure treatment processes under complex loading. Eastern-European Journal of Enterprise Technologies. Kharkiv. 2017. №6/7 (90). P. 34-41.
6. Rekechynskyi V. І. Zastosuvannia metody funktsiy toku v statsionarnyh protsessah plastychnogo deformuvannia. Vibratsii v tehnitsi і tehnologiah. Vinnytsia. 2020. №2 (97). S. 157-163.
7. Syvаk R. І., Gunkо І. V., Zаlіzniak R. О. Zаstоsuvаnnia lіnіy tоku pry vyznаchеnnі kіnеmаtychnyh hаrаktеrystyk v stаtsіоnаrnyh prоtsеsаh plаstychnоy tеchiy mеtаlu. Vibratsii v tehnitsi і tehnologiah. Vinnytsia. 2021. №2 (97). S. 157-163.
About the journal
The journal "Vibrations in Engineering and Technologies" is included in the list of technical scientific publications of Ukraine
(Category "B", Order of the Ministry of Education and Science of Ukraine dated July 2, 2020 No. 886)
Old version of the site: http://vibrojournal.vsau.edu.ua/
The journal "Vibrations in Engineering and Technology" is indexed by the following databases and catalogs:
The certificateof massmedia State registration:kv no 16643-5115 from 30.04.2010 .
Founder of the journal: Vinnytsia National Agrarian University
The journal is devoted to highlighting current issues in engineering, mechanical engineering, and technological processes, including the study of dynamic and oscillatory phenomena in technical systems, the application of mathematical methods for process modeling and analysis, as well as the presentation of results of design-engineering and technological developments. Particular attention is given to the study of vibration processes and their application in modern technologies.
The purpose of the scientific journal “Vibrations in Engineering and Technologies” is to disseminate the results of fundamental and applied research in the field of engineering sciences aimed at developing theoretical foundations and practical approaches to the design, analysis, and improvement of machines, materials, and technological processes, including the use of vibration and oscillatory effects in various sectors of production.
The publication is focused on the formation of a modern scientific and informational environment for the effective exchange of research results, support of innovative development, and implementation of advanced technical solutions in industry, agro-industrial production, and related fields.
The journal promotes the development of interdisciplinary research, the integration of modern engineering approaches, and the enhancement of the efficiency of technological processes and technical systems, including through the rational use of vibration phenomena.
Objectives of the Scientific Journal
To achieve its stated purpose, the journal addresses the following key objectives:
dissemination of results of fundamental and applied scientific research in the fields of mechanics, mechanical engineering, technological processes, machine dynamics, and equipment, as well as in areas related to the application of vibration phenomena in engineering and technologies;
promotion of research aimed at the creation and improvement of machines, mechanisms, and technological equipment based on oscillatory and vibration processes;
support for the implementation of modern technological solutions focused on improving productivity, energy efficiency, and reliability of technical systems;
обеспечение scientific exchange of research results among research institutions, higher education establishments, and industrial enterprises;
development of interdisciplinary cooperation among researchers in the fields of mechanics, materials science, material processing technologies, and automation of technological processes;
dissemination of modern scientific achievements and advanced technologies related to the application of vibration processes in production and technical systems.
Publisher Vinnytsia National Agrarian University
In June 1994 the 2nd International Scientific and Technical Conference "Application of vibrations for technological purposes" was organized on the basis of Vinnytsia State Agricultural Institute. Leading experts in this field, noting the significant contribution to the school of Vibration Engineering under the leadership of P. S. Bernyk, proposed to create a professional all-Ukrainian scientific and technical journal "Vibration in engineering and technology..The journal was foundedat Vinnytsia State Agricultural Institute and P.S. Bernyk was elected to be the chief editor .
For all these years (since 1994) theJournal "vibration in engineering and technology" published 119 issues wherestudy of vibration effects, the creation of progressive energy saving technologies and equipment for their implementation were highlighted.
Currently Ihor Kupchuk, Candidate of Technical Sciences, Associate professor, Associate Professor of the Department of Engineering Mechanics and Technological Processes in the Agricultural Industry Faculty of Engineering and Technology Vinnytsia National Agrarian University is the chief editor of the "Vibrations in engineering and Technology"
The journal "Vibration in Engineering and technology", which has no analogues on the territory of Ukraine, is well known abroad.
