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Vibrations in engineering and technology

space SCIENTIFIC JOURNALS OF VINNITSA NATIONAL AGRARIAN UNIVERSITY

Issue №: 1(100)

Published: 2021.03.23
DOI: 10.37128/2306-8744-2021-1


Description:
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.

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DEVELOPMENT OF A MATHEMATICAL MODEL FOR THE RESEARCH OF THE DYNAMICS OF VIBRATION MILL WITH TWO DRIVES FOR BULK MATERIALS FINE GRINDING

DOI: 10.37128/2306-8744-2021-1-9
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Topilnytskyy Volodymyr – PhD, Associate Professor of the Department of Designing and Operation of Machines of the Lviv Polytechnic National University (S. Bandery str., 12, Lviv, Ukraine, 79013, e-mail: topilnvol@gmail.com).

Rebot Dariya – PhD, Assistant of the Department of Designing and Operation of Machines of the Lviv Polytechnic National University (S. Bandery str., 12, Lviv, Ukraine, 79013, e-mail: dasha_kotlyarova@ukr.net).

 

 

Annotation

Reducing by grinding the size of various materials as raw materials for its further use is an urgent applied task. The requirements for the final product obtained by fine grinding are its homogeneity in shape and size of individual parts. It is necessary to reduce the time of the grinding operation, reduce energy consumption to obtain a unit of product of the required quality.  One way to solve the problem is to use high-tech universal equipment, namely mills for fine grinding of materials. One way to solve the given problem is to use high-tech universal equipment, namely mills for fine grinding of materials. Their optimal design, construction, manufacture and operation are ensured by studying their dynamics at the stage of their development. In particular, such a study of the dynamics can be carried out on the basis of previously created mathematical models of these mills. The use of computer technology and appropriate mathematical CAD systems will speed up and optimize the process of studying the dynamics of the corresponding mill of fine grinding of materials. The purpose of the research is to build a mathematical nonlinear parameterized model of vibrating mill with two drives for bulk materials fine grinding for further study on its basis the dynamics of the mill with the development of optimal designs for mills with similar structure and the principle of operation and selection of optimal modes of operation. 

The mathematical model is presented as a system of expressions describing the of the mill points motion, which will include in the form of symbolic symbols all its parameters (kinematic, geometric, dynamic, force). This model is constructed using the Lagrange equation of the second kind and asymptotic methods of nonlinear mechanics. The mathematical model for studying of the dynamics of vibration mill with two drives for bulk materials fine grinding is nonlinear and universal. The non linearity of the model makes it possible to adequately determine of the above parameters influence on the amplitude of oscillations of the  mill working chamber as the main factor in the intensity in the technological process of the fine grinding bulk materials fine grinding. The possibility of a wide range of changes in the parameters of the mill in the obtained models makes it universal based on the possibility of application for the study of dynamic processes in vibrating mills of different types with two or one drive which are different by shape, size, location of the suspension and more. This model can also be used to develop optimal designs for vibrating mills for different industries, which will be used to grind different types of materials in different volumes and productivity.

 

Keywords: vibrating mill, mathematical model, nonlinear equations, fine grinding, bulk material, unbalance drive, working chamber, elastic suspension.

List of references

1. Dzhedzhula,  О.М. (2019). Osobluvosti konstryjuvannja vibracijnuch zmischuvachiv [Features of vibration mixers design]. Vibratsiyi v tekhnitsi ta tekhnolohiyakh − Vibrations in engineering and technology, 4 (95), 24−30. [in Ukrainian].  

2. Lawinska, K. and Modrzewski, R. (2017). Analysis of sieve holes blocking in a vibrating screen and a rotary and drum screen. Journal «Fizykochemiczne Problemy Mineralurgii – Physicochemical Problems of Mineral Processing», 53, 812–828.

3. Zhou, N. (2015).  Dynamic characteristics analysis and optimization for lateral plates of the vibration screen. Journal of Vibroengineering (J. VIBROENG), 17(4), 1593–1604. 

4. Subach A.P. (1991). Dynamica processov i mashyn obyemnoy obrobotky [Dynamics of processes and machines of volumetric processing]. Riga: Zinatne [in Russian].

5. Symonenko T. E. (2011). O razrabotke matematycheskoi modely dlia obrabotky nezakreplennykh detalei [The development of a mathematical model for processing loose parts].  Visnyk Donbaskoi derzhavnoi mashynobudivnoi akademii − Bulletin of Donbass State and Maschine-Building Academy, 2 (23),  201–205 [in Russian].

6. Oryshchenko S.V. and Matsiuk B.V. (2013). Doslidzhennia dynamiky vibratsiinoho hrokhota ta otsinka yoho efektyvnosti [Research of the dynamics of vibrating screen and evalution of its effectiveness].  Vibratsiyi v tekhnitsi ta tekhnolohiyakh − Vibrations in engineering and technology, 3 (71), 120−125. [in Ukrainian].  

7. Ivanov, K. and Vaisberg, L. (2015). New Modelling and Calculation Methods for Vibrating Screens and Separators. Journal «Lecture Notes in Control and Information Sciences», 22, 55–61. 

8. Topilnytskyy. V., Rebot. D., Sokil. M., Velyka. O., Liaskovska S., Verkhola. I., et al. (2017).  Modeling the dynamics of vibratory separator of the drum type with concentric arrangement of sieves. Eastern-European Journal of Enterprise Technologies. Applied Mechanics, 2, 7 (86), 26–35.

9. Mitropolskii Yu. A. (1997). Nelineynaya mekhanika. Odnochastotnye koljebaniya  [Nonlinear mechanics. Single frequency oscillations]. Кyiv: Ins.matematiki NAN Ukrainy [in Russian].

 

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About journal

Topics of the journal:

The journal "Vibrations   in engineering  and technology" presents materials on the following issues

• Theory of processes and machines
• Mechanical Engineering and materialprocessing
• Processing and food production

Key information:
ISSN (print): 2306-8744
DOI: 10.37128/2306-8744

The certificateof massmediaState registration:kv no 16643-5115 from 30.04.2010 .
Founder of the journal: Vinnytsia National Agrarian University

Kind of publication: journal
Type of publication : Scientific
Publication status: Domestic
Year of founding:
Periodicity: 4 times a year
Extent: 18.75 nominal printed pages
ISSN: 2306-8744 (printed version), (online)
Language of edition  : (mixed languages) Ukrainian, Russian, English
The scope of the distribution and the category of readers: national, foreign, teaching staff, scientists, businessmen.
Periodical is included in the list of scientific professional editions of Ukraine approved by the Order of Ministry of Education and Sciences of Ukraine from 21.12.2015 No. 1328.
The journal "Vibrations in engineering and technology" is included in the "Catalogue of periodicals of Ukraine".
Journal subscription can be executed in each post office department.
 Subscription Index is  99720.

 

Old version of site: http://vibrojournal.vsau.edu.ua/

History of journal:

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  94 issues wherestudy of vibration effects, the creation of progressive energy saving technologies and equipment for their implementation were highlighted.
Currently Kaletnik H.M  PhD , professor, academician NAAS 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.