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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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AN APPROXIMATE METHOD FOR CALCULATING GRAIN FLOW IN A VERTICAL CYLINDRICAL VIBROSIEVE

DOI: 10.37128/2306-8744-2021-1-6
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Olshanskiy Stanislav Vasilyonych – Candidate of Physical and Mathematical Sciences (Ph. D.), Associate Professor, Associate Professor at the Department of Physics and Theoretical Mechanics Petro Vasilenko Kharkiv National Technical University of Agriculture, Alchevskikh str. 44, Kharkiv, Ukraine; 61022; OlshanskiyVP@gmail.com, тел.: (066) 0100955

Slipchenko Maksym Volodymyrovych – Candidate of Technical Sciences (Ph. D.), Associate Professor, Acting head of the Department of Physics and Theoretical Mechanics Petro Vasilenko Kharkiv National Technical University of Agriculture, Alchevskikh str. 44, Kharkiv, Ukraine; 61022; Slipchenko_M@ukr.net, тел.: (066) 7120989

Kharchenko Sergiy Oleksandrovych – Doctor of Technical Sciences, Full Professor, Professor at the Department of Optimization of Technological Systems named after T.P. Yevsukov Petro Vasilenko Kharkiv National Technical University of Agriculture, Alchevskikh str. 44, Kharkiv, Ukraine; 61022; kharchenko_mtf@ukr.net, тел.: (099) 1703477

Polievoda Yurii – candidate of technical sciences, associate professor of the department of technological processes and equipment for processing and food production, Vinnytsia National Agrarian University: Vinnytsia, st. Sonyachna 3, 21008, e-mail: vinyura36@gmail.com.

 

Annotation

A modified hydrodynamic model of a stable grain flow of an inhomogeneous mixture over the surface of a vertical cylindrical vibrating sieve is proposed under the assumption that the porosity of the mixture in the moving annular layer depends on the velocity of movement. A linear dependence of the porosity of the mixture on the velocity of movement are accepted, where higher speed corresponds to higher porosity.. The calculation of the velocity is reduced to solving an inhomogeneous differential equation of the Bessel type. Further, by "freezing" the variable coefficient of this equation, the problem has been simplified. This simplification is permissible due to the fact that the thickness of the moving layer of the mixture is much less than the radius of the vibrating sieve. As a result, the dependence of the velocity on the radial coordinate is expressed through the elementary functions. A compact formula for determining the maximum grain flow velocity is obtained. By integrating, in elementary functions, the formula for the average velocity in the layer is obtained. An approximate formula for the performance of the vibrating sieve by the mass of the exit fraction is derived. For this, it is proposed to calculate the corresponding integral approximately by the Simpson formula, so as not to calculate the values of special functions of large argument using the asymptotic formulas. It is shown that the named productivity significantly depends on the porosity of the grain mixture. In order to obtain information about the actual errors of the approximate formulas, we additionally carried out the numerical integration of the original non-simplified Bessel-type equation on a computer. A comparative analysis of the calculation results confirmed the small errors of the simplifications introduced into the equation of motion, as well as the adequacy of the theoretical results obtained.

By passing to a simplified differential equation, approximate formulas were derived and tested for calculating the main characteristics of the grain flow along a vertical cylindrical vibrating sieve, taking into account the change in porosity in the grain mixture layer from the velocity of movement. The work summarizes the known theoretical results obtained using hydrodynamic models of the motion of grain mixtures fluidized by vibrations. The generalization carried out slightly complicated the theory, because the final calculation formulas are quite compact and convenient in practical implementation.

 

 

Keywords: free oscillations, dissipative oscillator, quadratic viscous resistance, dry friction, Lambert function, identification of resistance characteristics, energy balance method.

List of references

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2. Tishchenko, L.N. (2004) Intensifikacija separirovanija zerna [Intensification of grain separation]. Kharkov : Osnova.. [In Russian].

3. Tishchenko, L.N, Mazorenko, D.I, Piven, M.V., Kharchenko, S.A., Bredikhin, V.V., & Mandryka A.V. (2010). Modelirovanie processov zernovyh separatorov [Modeling the processes of grain separators]. Kharkov : Miskdruk. [In Russian].

4. Tishchenko, L.N., Olshanskiy, V.P., Olshanskiy, S.V., Kharchenko, F.M., & Slipchenko, M.V. (2013) Dinamika vibrocentrobezhnoj zernoochistki [Dynamics of vibro-centrifugal grain cleaning]. Kharkov, Mіskdruk. [In Russian].

5. Tishchenko, L.N., Olshanskiy, V.P., & Olshanskiy, S.V. (2011) On velocity profiles of an inhomogeneonus vibrofluidized grain bed on a shaker. Journal of Engineering Physics and Termophysics. 84 (3), 509-514. doi.org/10.1007/s10891-011-0498-4.

6. Piven, M.V. (2004) Issledovanie processa segregacii zernovoj smesi pri vibrocentrobezhnom separirovanii. Vibracii v tehnike i tehnologijah. 4 (36), 23-26. [In Russian].

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8. Tishchenko, L.N., & Piven, M.V. (2003) Issledovanie processa segregacii zernovoj smesi pri vibrocentrobezhnom separirovanii [Investigation of the intra-layer motion of grain mixture particles during vibrocentrifugal separation]. Vibracii v tehnike i tehnologijah [Vibrating machines and technologies]. 4 (36), 23-26. [In Russian].

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12. Tishhenko, L.N., Karnodud, R.V., & Olshanskiy, V.P. (2012). Identifikacija koefficietnov vibrovjazkosti zernovyh smesej v cilindricheskih reshjotah vibrocentrifugi [Identification of the coefficient of vibration viscosity of grain mixtures in cylindrical sieves of a vibrocentrifuge]. Vіbracії v tehnіcі ta tehnologіjah [Vibrations in engineering and technology]. 3 (67), 134-137. [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.