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Vibrations in engineering and technology

space SCIENTIFIC JOURNALS OF VINNITSA NATIONAL AGRARIAN UNIVERSITY

Issue №: 4(91)

Published: 2018.09.26
DOI: XXXXX.XXXXXXXX


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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THE GENERALIZED PROBLEM OF A MECHANICAL IMPACT IN THE HERZ THEORY

DOI: XX.XXXXX/XXXXXXXXXXXXX
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Olshanskiy Vasiliy Pavlovich – Doctor of Physical and Mathematical Sciences, Professor, Kharkiv Petro Vasylenko National Technical University of Agriculture, Kharkov.

(e-mail: OlshanskiyVP@gmail.com).

 

Olshanskiy Stanislav Vasilevich – PhD in Physics and Mathematics, Kharkiv Petro Vasylenko National Technical University of Agriculture, Kharkov; (e-mail: stasolsh77@gmail.com).

 

Annotation

The generalization of the well-known classical Hertz problem of the impact of two solids, taking into account contact deformations, was achieved by introducing into consideration the internal hysteresis energy losses, accompanying the dynamic deformation of bodies upon impact. In contrast to the classical version of the theory, in the generalized problem they do not coincide, but the graphs of the dependence of the impact force on the convergence of the centers of mass of the bodies at the stages of their compression and stretching differ. Therefore, the differential equations of motion at these stages have different values of the coefficients. They also correspond to different durations in time of the mentioned stages, and the duration of compression is longer than the duration of decompression. The first integrals of the nonlinear differential equations of motion are expressed in elementary functions and the second integrals are expressed through periodic Ateb-functions. Compact formulas have been derived for calculating the maxima: the convergence of the centers of mass of the bodies, the impact force, the dimensions of the contact area, the pressure at the center of this area. A compact expression was also obtained for the coefficient of speed recovery for a direct central impact, moreover, its value is less than unity and does not depend on the speed of the collision and the masses of the bodies subjected to the impact. This is consistent with the well-known Newton hypothesis, which is traditionally used in the theory of partially elastic stereomechanical shock.

Keywords: mechanical shock, contact deformation, impact force, compression and decompression stages, hysteresis energy loss, speed recovery factor.

List of references

1. Pisarenko G.S., Kvitka A.L., & Umansky E.S. (2004) Opir materialiv [Materials Resistance]. – Kyiv: Vyshcha shkola.

2. Gurniak L.I., Gutsulyak Yu.V., & Yuzkiv T.B. (2005) Opir materialiv [Materials Resistance]. – Lviv: Novyi svit.

3. Goldsmith W. (1965) Udar. Teoriya i fizicheskie svojstva soudaryaemyh tel [Impact. Theory and physical properties of the colliding bodies]. – M.: Stroyizdat.

4. Kilchevsky N.A. (1976) Dinamicheskoe kontaktnoe szhatie tverdyh tel. Udar. [Dynamic contact compression of solids. Blow]. – Kiev : Naukova Dumka.

5. Panovko Y.G (1977) Vvedenie v teoriyu mekhanicheskogo udara. [Introduction to the theory of mechanical shock] – M.: Nauka.

6. Timoshenko S.P., Yang D.H., & Weaver U. (1985) Kolebaniya v inzhenernom dele [Fluctuations in engineering] – M: Mashinostroenie.

7. Naduty V.P., Yagnyukov V.F., & Yagnyukova I.V. (2014) Vzaimodejstvie kuskov materiala s futerovannym valkom vibracionnogo klassifikatora [Interaction of pieces of material with a lined roll of a vibration classifier]. Vibracii v tekhnike i tekhnologiyah, 1, 94-99 [in Russian].

8. Olshanskiу V.P., Olshanskiу S.V., & Tishchenko L.M. (2012) Kolebaniya sterzhnej i plastin pri mekhanicheskom udare [Oscillations of rods and plates during a mechanical shock] – Kharkov: Miskdruk.

9. Larin A.А. (2013) Ocherki istorii razvitiya teorii mekhanicheskih kolebanij [Essays history of development theory of mechanical oscillations] – Sevastopol: Weber.

10. Olshanskiy V.P., & Olshanskiy S.V. (2018) Ateb-sy`nus u rozvyazku zadachi Gercza pro udar [Ateb-sin in solving the Hertz problem]. Visnyk NTU «KhPI». – Kharkiv : NTU «KhPI», Seriia : Matematychne modeliuvannia v tekhnitsi ta tekhnolohiiakh. 3 (1279), 98-103 [in Ukrainian]. 

11. Gricik V.V., Nazarkevich M.A. (2007) Matematichnі modelі algoritmіv і realіzacіja Ateb-funkcіj [Mathematical models of algorithms and implementation Atte functions] Dopovidi Natsionalnoi akademii nauk Ukrainy, 12, 37-42 [in Ukrainian]. 

 

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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, 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.