Prediction of tribological properties of structural steels using artificial neural networks

https://doi.org/10.23939/ujmems2019.01.045
Надіслано: Червень 12, 2019
Переглянуто: Червень 25, 2019
Прийнято: Червень 26, 2019

V. Uvarov, S. Bespalov, "Prediction of tribological properties of structural steels using artificial neural networks", Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 5, no. 1, pp. 45-60, 2019.

1
G.V. Kurdyumov Institute for Metal Physics of the NAS of Ukraine
2
Presidium of NAS of Ukraine, Technical Center of NAS of Ukraine

The effect of quenching temperature on wear resistance of 40Kh steel after tempering has been investigated. It was found that compared to standard heat treatment, quenching from 1050 °С and high temperature tempering increase its tribological characteristics. The character of fracture of the contacting surfaces was studied. It was shown that in the specimens quenched from 860 °С and tempered, the fracture of the contact surface occurs by the mechanisms of smooth splitting and delamination with plastic deformation. Increasing the quenching temperature to 1050 °С along with high temperature tempering changes the character of the contact surface destruction. The areas with a distinctive microstructure appear on the surface exhibiting substantially higher wear resistance during friction as compared to the surrounding volume. The structural-geometrical parameters characterizing the roughness and bearing capacity of the contact interaction surface were analyzed. It was found that increasing the quenching temperature to 1050 °С allows to reduce the surface roughness and increase the bearing capacity. Using the methods of optical and transmission electron microscopy, the peculiarities of forming the microstructure of the investigated steel were studied, depending on the temperature conditions of the thermal treatment. It was shown that raising the quenching temperature to 1050 °С increases the austenitic grain size, enhances non-uniformity of carbon distribution, which leads to the formation of large needle-shaped crystals of lath martensite with microtwin boundaries inside. This, in turn, promotes the formation at high tempering of non-uniformly distributed aggregates of coarse carbides at these microtwin boundaries. The aggregates form areas of microstructure with increased resistance to plastic deformation processes. That is, the morphology of the carbide phase is one of the main factors that determine the tribological characteristics of steel, namely roughness, structural-geometrical parameters and bearing capacity of the surface. The expediency of using artificial neural networks for prediction of tribological properties of structural steels was shown. According to the results of modeling the structural-geometrical parameters of the surface and the roughness characteristics, the bearing capacity of the 40Kh steel surface during friction was predicted.

[1] I. V. Kragelskii, Trenie i iznos [Friction and wear]. Moscow, Russia: Mashinostroenie Publ., 1968. [In Russian].

[2] D. N. Garkunov, Tribotekhnika (konstruirovanie, izgotovlienie i ekspluataciya mashin) [Tribotechnics (design, manufacturing and operation of machines)]. Moscow, Russia: MSKhA Publ., 2002. [In Russian].

[3] Yu. M. Pleskavskii, et al., “Belorusskaya nauchno-tekhnicheskaya programma “Tribotechnika” [“Belarusian scientific and technical program “Tribotechnology”], Trenie i iznos [Friction and wear], vol. 16, no. 3, pp. 404-415, 1995. [in Russian].

[4] V. P. Kogaev, Prochnost’ i iznosostoikost’ detalei mashin [Strength and wear resistance of machine parts]. Moscow, Russia: Vystshaya Shkola Publ., 1991. [in Russian].

[5] P. Jost, “Mirovyie dostizheniya v oblasti tribologii” [“World achievements in the field of tribology”], Trenie i iznos [Friction and wear], vol. 7, no. 4, pp. 593-603, 1986. [in Russian].

[6] A. S. Pronikov, Parametricheskaya nadiozhnost’ mashin [Machine parametric reliability]. Moscow, Russia: MGTU im. N.E. Baumana Publ., 2002. [in Russian].

[7] V. M. Pavlis’kyi, “Doslidzhennia prypratsiuvannia i znosu tsylindriv ta porshnevykh kilets’ v period obkatky dvyhuniv” [“Investigation of the pre-working and wear of cylinders and piston rings during the run-in period of engines”], Naukovyi visnyk NAU [Scientific bulletin of NAU], vol. 4, pp. 160-164, 1998. [in Ukrainian].

[8] K. B. Katsov, and R. A. Khrunyk, “Novyie malonikelevyie vysokoprochnyie stali dlia burovykh dolot” [“New low nickel high strength steels for drill bits”], Fiziko-khimicheskaya mekhanika materialov [Physicochemical mechanics of materials], vol. 5, pp. 90-92, 1979. [in Russian].

[9] I. S. Kernytskyi, V. V. Kozub, and M. I. Pashechko, “Abrazyvna znosostiykist’ evtektychnykh pokryttiv” [“Abrasive wear resistance of eutectic coatings”], Visnyk Derzhavnoho universytetuLʹvivsʹka politekhnika” “Optymizatsia vyrobnychykh protsesiv i tekhnichnyi kontrol’ u mashynobuduvanni i pryladobuduvanni” [Bulletin of State University “Lviv Polytechnic” “Optimization of production processes and technical control in mechanical engineering and instrumentation”], vol. 371, pp. 93-96, 1999. [in Ukrainian].

[10] R. A. Khrunyk, “Rozrobka novykh oshchadnolehovanykh stalei dlia sharoshkovoho porodoruinuval’noho instrumentu” [“Development of new low-alloyed steels for conical rock-breaking tools”], Fizyko-khimichna mekhanika materialiv [Physicochemical mechanics of materials], vol. 36, no. 3, pp. 102-107, 2000. [in Ukrainian]. https://doi.org/10.1007/BF02769608

[11] A. V. Chichinadze, et al., Osnovy tribologii (trenie, iznos, smazka) [Fundamentals of tribology (friction, wear, lubrication)]. Moscow, Russia: Mashinostroenie Publ., 2001. [in Russian].

[12] S. Bakhodur, “Ekonomicheskoe znachenie iznosa materialov v sovremennom obshchestve” [“The economic importance of material wear in modern society”], Problemy treniya i smazki [Friction and lubrication problems], vol. 2, pp. 1-4, 1978. [in Russian].

[13] P. Jost, “Budushchee tribologii” [“The future of tribology”], Trenie i iznos [Friction and wear], vol. 12, no. 3, pp. 10-15, 1991. [in Russian].

[14] O. P. Datsyshyn, and V. V. Panasyuk, Kontaktna dovhovichnist’ i ruinuvannia elementiv konstruktsii za tsyklichnoho navantazhennia [Contact durability and fracture of structural elements under cyclic loading]. Kyiv, Ukraine: Naukova Dumka Publ., 2018. [in Ukrainian].

[15] K. E. Aliyev, “Metody i sredstva modelirovaniya slabostrukturirovannykh informatsionnykh protsessov” [“Methods and tools for modeling poorly structured information processes”], M.S. thesis, Azerbaijan State Economic University, Baku, Azerbaijan, 2018. [in Russian].

[16] S. V. Aksenov, and V. B. Novoseltsev, Organiztsia i ispol’zovanie neyronnych setei (metody i technologii) [Organization and use of neural networks (methods and technologies)]. Tomsk, Russia: NTL Publ., 2006. [in Russian].

[17] S. Khaikin, Neyronnyie seti: Polnyi kurs [Neural networks: Full course]. Moscow, Russia: OOO “I. D. Williams” Publ., 2006. [in Russian].

[18] The basics of ANN. Neural networks. Electronic resource. Log access mode: https://neuralnet.info/book/.

[19] A neural network based on the “Functionality on multiple table functions” model. Electronic resource. Log access mode: http://www.uatur.com/html/neural_nets/Lecture4.htm#base/.

[20] N. S. Liesna, Intelektual’nyi analiz danych [Intelligent data analysis]. Kharkiv, Ukraine: KhNURE Publ., 2003. [in Ukrainian].

[21] S. V. Pronin, “Primenenie iskusstvennykh neyronnykh sistem dlia modelirovania transportnykh sistem” [“Application of artificial neural systems for modeling of transport systems”], Avtomobil’nyi transport [Road transport], vol. 18, pp. 123-125, 2006. [in Russian].

[22] B. N. Bublik, Osnovy teorii upravleniya [Fundamentals of management theory]. Kyiv, Ukraine: Vyshcha Shkola Publ., 1975. [in Russian].

[23] T. Kvater, Neyromerezhevi informatsiyni tekhnologii kontroliu ta diahnostyky dynamichnykh obyektiv v umovakh nevyznachenosti [Neural network information technologies for control and diagnostics of dynamic objects in the face of uncertainty]. Lviv, Ukraine: Taras Soroka Publ., 2005. [in Ukrainian].

[24] V. I. Komashinskii, and D. A. Smirnov, Neyronnyie seti i ikh primenenie v sistemakh upravlenia i sviazi [Neural networks and their application in control and communication systems]. Moscow, Russia: Goriachaia Liniya – Telekom Publ., 2003. [in Russian].

[25] V. A. Terekhov, D. V. Yefimov, and I. Yu. Tyukin, Neyrosetevye sistemy upravlenia [Neural network management systems]. Moscow, Russia: Radiotechnika Publ., 2002. [in Russian].

[26] P. G. Krug, Neyronnyie seti i neyrokompyutery [Neural networks and neurocomputers]. Moscow, Russia: MEI Publ., 2002. [in Russian].

[27] D. Forsait, and J. Pons, Kompyuternoe zrenie. Sovremennyi podkhod [Computer vision. Modern approach]. Moscow, Russia: OOO “I. D. Williams” Publ., 2004. [in Russian].

[28] V. P. Boyun, “Intelektual’ni video systemy ta prystroi real’noho chasu” [“Intelligent real-time video systems and devices”], in Proc. Int. Conf. “Intelligent decision-making systems and applied aspects of information technologies”, Evpatoria, Ukraine, May 15-18, 2007, pp. 101-107. [in Ukrainian].

[29] D. E. Bestens, V. M. Vandenberg, and D. Vud, Neyronnye seti i finansovyie rynki: priniatie reshenii v torgovykh operatsiyakh [Neural networks and financial markets: decision making in trading]. Moscow, Russia: TVP Publ., 1997. [in Russian].

[30] A. A. Yezhov, and S. A. Shumskii, Neyrokompyuting i yego primenieniya v ekonomike i bizniese [Neurocomputing and its applications in economics and business]. Moscow, Russia: MIFI Publ., 1998. [in Russian].

[31] K. H. Davies, R. Biddulph, and S. Balashek, “Automatic speech recognition of spoken digits”, J. Acoust. Soc. Am., vol. 24, no. 6, pp. 637-642, 1952. https://doi.org/10.1121/1.1906946

[32] U. Li, Metody avtomaticheskogo raspoznavaniya rechi [Automatic speech recognition techniques]. Moscow, Russia: Mir Publ., 1983. [in Russian].

[33] V. V. Berehovs’kyi, “Matematychne ta programne zabezpechennia avtomatyzovanoho proektuvannia system “Intelektual’noho budynku” [“Mathematical support and software for automated design of Intelligent Home systems”], Ph.D. dissertation, Lviv Polytechnic National University, Lviv, Ukraine, 2017. [in Ukrainian].

[34] N. Kasabov, “Introduction: Hybrid intelligent adaptive systems”, International Journal of Intelligent Systems, vol. 6, pp. 453-454, 1998. https://doi.org/10.1002/(SICI)1098-111X(199806)13:6<453::AID-INT1>3.3.CO;2-I

[35] V. V. Yemelyanov, V. V. Kurieychik, and V. M. Kurieychik, Teoriya i praktika evoliutsionnogo modelirovaniya [Theory and practice of evolutionary modeling]. Moscow, Russia: FIZMATLIT Publ., 2003. [in Russian].

[36] Y. Shoham, and K. Leyton-Brown, Algorithmic, game-theoretic, and logical foundations. London, UK: Cambridge University Press, 2009.

[37] S. Ossovskii, Neyronnyie seti dlia obrabotki informatsii [Neural networks for information processing]. Moscow, Russia: Finansy i Statistika Publ., 2002. [in Russian].

[38] V. Chaban, T. Kvater, and Ya. Bartman, “Diagnostyka elektromagnetnoho kola za dopomohoyu shtuchnoi neyronnoi merezhi” [“Diagnosis of electromagnetic circuit using artificial neural network”], in Proc. of the Scientific and Technical Conference on the 100th Anniversary of T. Gubenko “Electromechanics. Theory and practice”, Lviv-Slavske, Ukraine, September 25-28, 1996, pp. 191-193. [in Ukrainian].

[39] A. Chaban, “Zastosuvannya shtuchnykh neyronnykh merezh dlia analizu elektromekhanichnykh system” [“Application of artificial neural networks for the analysis of electromechanical systems”], Elektrotekhnika i elektromekhanika [Electrical engineering and electromechanics], no. 1, pp. 57-59, 2008. [in Ukrainian].

[40] Artificial neural networks. Electronic resource. Log access mode: http://masters.donntu.org/2007/fvti/yemeliyanenko/library/3.htm/.

[41] Z. Duriagina, and P. Tkachenko, “Vykorystannya shtuchnykh neyronnykh merezh dlia prohnozuvannya vlastyvostei poverkhni konstruktsiynykh materialiv” [“The use of artificial neural networks to predict the surface properties of structural materials”], Mashynoznavstvo [Mechanical Science], vol. 56, no. 2, pp. 29-31, 2002. [in Ukrainian].

[42] Z. Duriagina, P. Tkachenko, and T. Ivashko, “Neyromerezheve modeliuvannya vlastyvostei zakhysnykh poverkhnevykh shariv, stvorenykh lazernym lehuvannyam” [“Neural network modeling of properties of protective surface layers created by laser alloying”], Fizyko-khimichna mekhanika materialiv [Physicochemical mechanics of materials], vol. 38, no. 3 (special issue), pp. 585-588, 2002. [in Ukrainian].

[43] E. V. Kozlov, et al., “Vliyanie skorosti zakalki na strukturu i kolichestvennyie parametry martensitnogo prevrashcheniya v litoi konstruktsionnoi srednelegirovannoi stali” [“Effect of quenching rate on the structure and quantitative parameters of martensitic transformation in cast structural middle alloyed steel”], Fundamental’nyie problemy sovremennogo materialovedeniya [Fundamental problems of modern materials science], vol. 2, no. 1, pp. 118-123, 2005. [in Russian].

[44] Yu. F. Ivanov, and E. V. Kozlov, “Izotermicheskii otpusk zakalennoi sredneuglerodistoi malolegirovannoi stali. Kinetika obrazovaniya chastits tsemenita pri temperature 200 °C” [“Isothermal tempering of quenched medium-carbon low alloyed steel. Kinetics of the formation of cementite particles at a temperature of 200 °C”], Fundamental’nyie problemy sovremennogo materialovedeniya [Fundamental problems of modern materials science], vol. 3, no. 3, pp. 61-68, 2006. [in Russian].

[45] M. A. Tylkin, Spravochnik termista remontnoi sluzhby [Repair service thermist reference]. Moscow, Russia: Metallurgia Publ., 1981. [in Russian].

[46] Izmenenie mikrotviordosti tsarapaniyem almaznymi nakonechnikami [Change in microhardness by scratching with diamond tips], GOST 21318-82, 1983. [in Russian].

[47] P. V. Diachenko, Sovremennyie napravlienia v oblasti obespechenia vysokogo kachestva poverkhnosti detalei [Modern trends in the field of providing high quality surface parts]. Moscow, Russia: AN SSSR Publ., 1960. [in Russian].

[48] N. K. Myshkin, and M. I. Petrokovets, Trenie, smazka, iznos. Fizicheskie osnovy i tekhnicheskie prilozheniya tribologii [Friction, lubrication, wear. Physical foundations and technical applications of tribology]. Moscow, Russia: FIZMATLIT Publ., 2007. [in Russian].

[49] N. S. Pienkin, A. N. Pienkin, and V. M. Serbin, Osnovy tribologii i tribotekhniki [Fundamentals of tribology and tribotechnology]. Moscow, Russia: Mashinostroenie Publ., 2012. [in Russian].

[50] Surface roughness. Part 1: Surface and its parameters, ISO 4287/1, 1984.

[51] Rules and procedures for the measurement of surface parameters, ISO 4288, 1985.

[52] S. P. Yakovlieva, et al., “Povyshenie iznosostoikosti i relief poverkhnosti treniya ferritno-perlitnoi stali, nanostrukturirovannoi megaplasticheskoi deformatsiyey” [“Improving the wear resistance and friction surface relief of ferritic-pearlite steel, nanostructured by megaplastic deformation”], Fundamental’nyie issledovaniya. Razdel “Tekhnicheskiye nauki” [Basic research. Section “Engineering”], vol. 15, no. 10, pp. 3451-3455, 2013. [in Russian].

[53] N. A. Morozova, “Povyshenie iznosostoikosti tsilindricheslikh poverkhnostei detalei mashin vibroudarnym plasticheskim uprochneniem” [“Improving the wear resistance of cylindrical surfaces of machine parts by percussion plastic hardening”], Ph.D. dissertation, Siberian State University of Railway Engineering, Novosibirsk, Russia, 2005. [in Russian].

[54] P. Yu. Volosievich, and S. A. Bespalov, “Strukturoobrazovaniye i iznosostoykost’ stali 40Kh” [“Structuring and wear resistance of 40Kh steel”], Metallofizika i noveyshiye tekhnologii [Metallophysics and advanced technologies], vol. 26, no. 5, pp. 691-701, 2004. [in Russian].

[55] A. A. Zhukov, G. I. Silman, and L. Z. Epshtein, “Struktura stali i chuguna i printsip Sharpi” [“Steel and cast iron structure and Charpy principle”], Izvestiya AN SSSR. Metally [Proceedings of the USSR Academy of Sciences. Metals], vol. 2, pp. 145-152, 1971. [in Russian].

[56] Metallurgical dictionary. Electronic resource. Log access mode: http://metallurgy_dictionary.academic.ru/.

[57] V. V. Iliushin, B. A. Potiekhin, and A. S. Khristoliubov, “Napravlieniye sozdaniya splavov skol’zheniya s povyshennymi tekhnologicheskimi svoystvami” [“Direction of creation of slip alloys with enhanced technological properties”], Lesa Rossii i khoziaystvo v nikh [Forests of Russia and the economy in them], vol. 44, no. 1, pp. 169-171, 2013. [in Russian].

[58] G. G. Mukhin, et al., “Materialy v mashinostroenii” [“Materials in mechanical engineering”], in Mashinostroenie. Entsiklopediya v 40 tomakh, [Engineering. Encyclopedia in 40 volumes], vol. 2. Moscow, Russia: Mashinostroenie Publ., 2001. [in Russian].

[59] K. V. Frolov, Sovremennaya tribologiya: Itogi i perspektivy [Modern tribology: Results and prospects]. Moscow, Russia: LKI Publ., 2008. [in Russian].

[60] V. V. Iliushin, and B. A. Potiekhin, “Al’ternativnyi antifriktsionnyi material” [“Alternative antifriction material”], Lesa Rossii i khoziaystvo v nikh [Forests of Russia and the economy in them], vol. 44, no. 1, pp. 166-168, 2013. [in Russian].

[61] A. I. Shpagin, Antifriktsionnyie splavy [Antifriction alloys]. Moscow, Russia: Metallurgizdat Publ., 1956. [in Russian].

[62] Yu. K. Mashkov, Tribologia konstruktsionnykh materialov [Tribology of engineering materials]. Omsk, Russia: OmGTU Publ., 1996. [in Russian].

[63] L. S. Rapoport, and L. M. Rybakova, “Vliyaniye strukturnogo sostoyaniya poverkhnostnykh sloyev na protsessy treniya i iznashivaniya” [“The influence of the structural state of surface layers on the processes of friction and wear”], Trenie i iznos [Friction and wear], vol. 8, no. 5, pp. 888-893, 1987. [in Russian].

[64] L. S. Rapoport, and L. M. Rybakova, “Vliyaniye strukturnogo sostoyaniya poverkhnostnykh sloyev na protsessy treniya i iznashivaniya” [“The influence of the structural state of surface layers on the processes of friction and wear”], Trenie i iznos [Friction and wear], vol. 8, no. 6, pp. 1038-1043, 1987. [in Russian].

[65] O. Yu. Yelagina, Tekhnologicheskiye metody povysheniya iznosostoikosti detalei mashin [Technological methods for increasing the wear resistance of machine parts]. Moscow, Russia: Universitetskaya Kniga Publ., 2009. [in Russian].

[66] M. L. Bernshtein, and V. A. Zaymovskii, Mekhanicheskiye svoistva metallov [The mechanical properties of metals]. Moscow, Russia: Metallurgia Publ., 1979. [In Russian].

[67] K. H. Zum Gahr, Microstrure and wear of materials. Amsterdam-Oxford-New York-Tokyo: Elsevier Science Publishers, 1987.

[68] B. N. Arzamasov, Tsirkuliatsionnyi metod polucheniya zharostoikikh i iznosostoikikh diffuzionnykh pokrytii [The circulation method of obtaining heat-resistant and wear-resistant diffusion coatings]. Moscow, Russia: Mashprom Publ., 1980. [In Russian].

[69] M. V. Belous, and V. T. Cherepin, “Izmenieniya v karbidnoi faze stali pod vliyaniyem kholodnoi plasticheskoi deformatsii” [“Changes in the carbide phase of steel under the influence of cold plastic deformation”], Fizika metallov i metallovedenie [Metal physics and metals science], vol. 12, p. 685, 1961. [in Russian].

[70] M. V. Belous, and V. T. Cherepin, “Izmenieniya v karbidnoi faze stali pod vliyaniyem kholodnoi plasticheskoi deformatsii. Raspad i grafitizatsiya vysokootpushchennoi stali” [“Changes in the carbide phase of steel under the influence of cold plastic deformation. Decomposition and graphitization of high tempered steel”], Fizika metallov i metallovedenie [Metal physics and metals science], vol. 14, no. 1, p. 48, 1962. [in Russian].

[71] N. A. Popova, “Evolutsia dislokatsionnogo ansamblia, vnutrennie polia napriazhenii i fazovyie prevrashchenia pri plasticheskoi deformatsii stalei s razlichnoi strukturoi” [“The evolution of a dislocation ensemble, internal stress fields, and phase transformations during plastic deformation of steels with different structures”], Ph.D. dissertation, Tomsk State University of Architecture and Civil Engineering, Tomsk, Russia, 2005. [in Russian].

[72] V. V. Matveyev, “Naplavka grebnei vagonnykh koles posle otzhiga poverkhnosti kataniya na vagonoremontnykh zavodakh Ukrainy” [“Repair flange surfacing of railway wheels after annealing of the tread surface at railway repair plants in Ukraine”], Avtomaticheskaya svarka [Automatic welding], vol. 6, pp. 42-48, 2005. [in Russian].

[73] P. Yu. Volosievich, and S. A. Bespalov, “Mikrotviordost’ poverkhnostei i yeyio sviaz’ s temperaturoi zakalki i raspredeleniyem ugleroda v staliakh 40Kh i 40KhNM” [“Microhardness of surfaces and its relationship with quenching temperature and carbon distribution in steels 40Kh and 40KhNM”], Metallofizika i noveishiye tekhnologii [Metallophysics and advanced technologies], vol. 28, no. 12, pp. 1629-1638, 2006. [in Russian].

[74] V. M. Uvarov, and S. A. Bespalov, “Vykorystannia shtuchnykh neyronnykh merezh dlia vyrishennia trybolohichnykh zadach” [“Using artificial neural networks to solve tribological tasks”], Metaloznavstvo ta obrobka metaliv [Metals science and treatment of metals], vol. 90, no. 3, pp. 1-10, 2019. [in Ukrainian].

[75] A. A. Mukhammedov, “Prochnost’ i iznosostoikost’ v zavisimosti ot velichiny austenitnogo zerna i tonkoi struktury stali” [“Strength and wear resistance depending on the size of austenitic grain and the fine structure of steel”], Metallovedenie i termicheskaya obrabotka metallov [Metals science and heat treatment of metals], vol. 7, pp. 31-34, 1968. [in Russian].

[76] V. V. Tikhonovich, and V. N. Uvarov, “Vliyaniye aktivnykh elementov rabochei sredy na elektronnuyu strukturu i mekhanism deformatsii poverkhnostnykh sloyev metalla pri trenii” [“The influence of active elements of the working medium on the electronic structure and mechanism of deformation of the surface layers of metal during friction”], Uspekhi fiziki metallov [Advances in metal physics], vol. 12, no. 2, pp. 209-239, 2011. [in Russian]. https://doi.org/10.15407/ufm.12.02.209

[77] V. M. Uvarov, et. al., “Atomne rozuporiadkuvannia ta elektronna budova splavu Heuslera CoTiSb” [“Atomic disorder and electron structure of Heusler alloy CoTiSb”], Ukrains’kyi fizychnyi zhurnal [Ukrainian journal of physics], vol. 62, no. 2, pp. 106-111, 2017. [in Ukrainian]. https://doi.org/10.15407/ujpe62.02.0106