RESEARCH OF METHODS OF DISCRETE INTEGRATION OF DYNAMICS OF MECHANICAL ENGINEERING DESIGNS

DOKUKOVA Nataliya A., Ph. D. in Phys. and Math., Associate Professor of the Department of Theoretical and Applied Mechanics, Belarusian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

NOVIK Mariya G., Undergraduate Student, Belarusian State University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

Innovative methods and algorithms of numerical calculations of big systems of the differential equations, to which problems of dynamics of multibody element mechanical engineering designs are given, are rather simple in use, standardized by types and classes of mathematical models, presented by the closed modules in different packages of application programs. Similar ready means save time of modeling and calculation. At the same time the reliability of the received results turns out to be approximate confirmed by the authors’ calculation model for calculating the dynamics of the crank gear mechanism with elastic-damping coupling by classical methods and the NSTIFF method of MATLAB package.

design elements, discrete integration, crank gear mechanism

1. Negrut D., Jay L.O., Khude N. A Discussion of low-order numerical integration formulas for rigid and flexible multibody dynamics. Journal of Computational and Nonlinear Dynamics, 2009, vol. 4, iss. 2.
2. Shabana A.A. Dynamics of Multibody Systems. Cambridge, Cambridge University Press, 2005.
3. Brenan K.E., Campbell S.L., Petzold L.R. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. New York, North-Holland, 1989.
4. Lubich C., Hairer E. Automatic integration of the Euler–Lagrange equations with constraints. Journal of Computational and Applied Mathematics, 1989, vol. 12, pp. 77–90.
5. Hairer E., Wanner G. Solving ordinary differential equations II. Stiff and differential-algebraic problems. Berlin, Springer, 1991.
6. Potra F., Rheinboldt W.C. On the Numerical Solution of Euler–Lagrange Equations. Mechanics of Structures and Machines, 1991, no. 19(1), pp. 1–18.
7. Rheinboldt W.C. Differential-algebraic systems as differential equations on manifolds. Mathematics of Computation, 1984, no. 43, pp. 473–482.
8. Wehage R.A., Haug E.J. Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems. ASME Journal of Mechanical Design, 1982, no. 104, pp. 247–255.
9. Liang C.D., Lance G.M. A Differentiable null space method for constrained dynamic analysis. ASME Journal of Mechanisms, Transmission, Automation, 1987, no. 109(3), pp. 405–411.
10. Yen J. Constrained equations of motion in multibody dynamics as ODE’s on manifolds. SIAM Journal on Numerical Analysis, 1993, no. 30(2), pp. 553–558.
11. Lunk C., Simeon B. Solving constrained mechanical systems by the family of Newmark and methods. Zeitschrift für Angewandte Mathematik und Mechanik, 2006, no. 86(10), pp. 772–784.

ABOUT THE ROLE OF GRAPHENE-LIKE CARBON IN THE FORMATION OF COATINGS BY THE METHOD OF MICROARC OXIDATION

KOMAROV Alexander I., Ph. D. in Eng., Head of the Laboratory of Modification Techniques of Structural Materials, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

ZOLOTAYA Polina S., Junior Researcher, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

GORBACHUK Nikolay I., Ph. D. in Phys. and Math., Associate Professor of the Department of Physics of Semiconductors and Nano-Electronics, Belarusian State University, Minsk, Republic of Belarus

Based on the provisions of the discharge percolation theory, an interpretation is given for the mechanism of the effect of carbon nanoparticles introduced into the electrolyte on the microarc oxidation process. The effect of graphene-like carbon particles (GC) on the main characteristics of the formed coating is studied using the D16 alloy as an example. It is established that GC introduced in silicate-alkaline electrolytes at a concentration of 250–1000 mg/l intensifies microplasma processes, which is directly evidenced by an increase in the coating thickness by 1.3–2.2 times. At the same time, the participation of graphene particles in the process of coating formation leads to an increase in the content of corundum in it and, as a result, to an increase in microhardness up to 25 GPa relative to 15 GPa for unmodified coatings.

microarc oxidation, modification, aluminum alloys, graphene, shungite, phase composition, microhardness

1. Komarov A.I., Vityaz P.A., Komarova V.I. Sozdanie iznosostoykikh uprochnyayushchikh pokrytiy mikrodugovym oksidirovaniem, neposredstvennoy i posleduyushchey modifikatsiey uglerodnymi nanomaterialami [Creation of wear-resistant hardening coatings by microarc oxidation with direct and subsequent modification by carbon nanomaterials]. Perspektivnye tekhnologii [Advanced technologies], 2011, ch. 6, pp. 114–148.
2. Vityaz P.A., Ilyushchenko A.F., Zhornik V.I. Nanoalmazy detonatsionnogo sinteza: poluchenie i primenenie [Nanodiamonds of detonation synthesis: production and application]. Minsk, Belaruskaya navuka, 2013. 381 p.
3. Komarov A.I., Vityaz P.A., Komarova V.I. The role of fullerene soot in structure formation of MAO-coatings. Nanomechanics Science and Technology, 2013, vol. 4, no. 4, pp. 289–297.
4. Vityaz P.A., Komarov A.I., Komarova V.I., Kuznetsova T.A. Osobennosti formirovaniya iznosostoykikh sloev na poverkhnosti modifitsirovannogo fullerenami MDO-pokrytiya pri trenii [Features of the formation of wear-resistant layers on the surface of the microarc oxidation coating modified by fullerenes in friction]. Trenie i iznos [Friction and wear], 2011, vol. 32, no. 4, pp. 313–325.
5. Vityaz P.A., Komarov A.I., Komarova V.I., Zhukov B.G., Sedov A.I., Ponyaev S.A., Dubovskiy A.L. Rol fullerensoderzhashchikh sazh v strukturoobrazovanii MDO-pokrytiy [The role of fullerene-containing soot in the formation of microarc oxidation coatings]. Nanostruktury v kondensirovannykh sredakh [Nanostructures in condensed media], 2014, pp. 3–12.
6. Vityaz P.A., Komarov A.I., Komarova V.I. Vliyanie nanorazmernykh chastits ugleroda na formirovanie struktury i svoystv mikrodugovykh keramicheskikh pokrytiy na splavah alyuminiya [Influence of nanosized carbon paticles on the formation of the structure and properties of microarc ceramic coatings based on aluminum alloys]. Doklady NAN Belarusi [Reports of the National Academy of Sciences of Belarus], 2013, vol. 57, no. 2, pp. 96–101.
7. Vityaz P.A., Komarov A.I., Komarova V.I. Rol nanougleroda v formirovanii struktury i svoystv mikrodugovykh keramicheskikh pokrytiy na splavah [Role of nanocarbon in the formation of the structure and properties of microarc ceramic coatings on aluminum alloys]. Doklady NAN Belarusi [Reports of the National Academy of Sciences of Belarus], 2013, no. 5, pp. 96–101.
8. Borisov A.M., Crete B.L., Ludin V.B., Morozova N.V., Suminov I.V., Epelfeld A.V. Mikrodugovoe oksidirovanie v elektrolitakh-suspenziyakh (obzor) [Microarc oxidation in electrolyte suspensions (review)]. Elektronnaya obrabotka materialov [Electronic processing of materials], 2016, vol. 52, no. 1, pp. 50–77.
9. Rocca E., Veys-Renaux D., Guessoum K. Electrochemical behavior of zinc in KOH media at high voltage: Micro-arc oxidation of zinc. Journal of Electroanalytical Chemistry, 2015, vol. 754, pp. 125–132.
10. Xiaopeng L., Mohedano M., Blawert C. Plasma electrolytic oxidation coatings with particle additions (A Review). Surface and Coatings Technology, 2016, vol. 10, 307 p.
11. Novikov V.P., Kirik S.A. Nizkotemperaturnyy sposob polucheniya grafena [Low-temperature method for the production of graphene]. Pisma v Zhurnal tekhnicheskoy fiziki [Letters to the Journal of Technical Physics], 2011, vol. 37, iss. 12, pp. 44–49.
12. Rozhkova N.N. Nanouglerod shungitov [Shungite nanocarbon]. Petrozavodsk, Karelskiy nauchnyy tsentr RAN Publ., 2011. 100 p.
13. Shklovskiy B.I., Efros A.L. Elektronnye svoystva legirovannykh poluprovodnikov [Electronic properties of doped semiconductors]. Moscow, Nauka Publ., 1979.

MICROARC OXIDATION OF THE GAS-THERMAL ALUMINUM COATINGS DEPOSITED ON POLYMERIC MATERIALS

BELOTSERKOVSKY Marat A., D. Sc. in Eng., Prof., Head of the Laboratory of Gas-Thermal Methods of Machine Components Hardening, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

SOSNOVSKY Aleksey V., Ph. D. in Eng., Leading Researcher, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

TARAN Igor I., Senior Researcher, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

KOT Pavel I., Deputy Head of Operation and Maintenance of Dormitories, Belarusian National Technical University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

The modes of hypersonic metallization for the formation of coatings of aluminum on polymeric materials are selected. An empirical dependence of the sputtered aluminum particles size and the thermal-oxidative degradation temperature of the polymer is obtained. The microarc oxidation equipment has been developed for the formation of ceramic oxide coatings on the surface of aluminum gas-thermal coatings. It is found that the largest thickness of ceramic-oxide coatings is achieved when the ratio of air and propane in the atomizing air-propane mixture is from 15:1 to 18:1. The material of the sublayer (Ni) is determined, which ensures the maximum adhesion of aluminum coatings to polymers.

polymers, hypersonic metallization, microarc oxidation, ceramic oxide coatings

1. Suminov I.V., Belkin P.N., Epelfeld A.V., Lyudin V.B., Krit B.L., Borisov A.M. Plazmenno-elektroliticheskoe modifitsirovanie poverkhnosti metallov i splavov. Tom 2 [Plasma-electrolytic modification of the surface of metals and alloys. Volume 2]. Moscow, Tekhnosfera Publ., 2011. 512 p.
2. Kolomeychenko A.V. Tekhnologii povysheniya dolgovechnosti detaley mashin vosstanovleniem i uprochneniem rabochikh poverkhnostey kombinirovannymi metodami s primeneniem mikrodugovogo oksidirovaniya
   [Technologies for increasing the durability of machine parts by restoring and hardening work surfaces with combined methods using microarc oxidation]. Orel, Orel GAU Publ., 2012. 255 p.
3. Dudareva N.Yu., Butusov I.A., Kalshchikov R.V. Vliyanie rezhimov mikrodugovogo oksidirovaniya na mekhanicheskie svoystva obraztsov iz alyuminievogo splava [Influence of microarc oxidation regimes on the mechanical properties of aluminum alloy samples]. Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika [Bulletin of Perm National Research Polytechnic University. Mechanics], 2014, no. 4, pp. 102–117.
4. Shatalov V.K., Shtokal A.O., Rykov E.V., Dobrosovestnov K.B. Primenenie metodov mikrodugovogo oksidirovaniya pri sozdanii konstruktivnykh elementov kosmicheskikh apparatov [Application of microarc oxidation methods to create structural elements of spacecraft]. Nauka i obrazovanie [Science and Education], 2014, no. 6, pp. 183–194.
5. Belotserkovsky M.A., Sosnovsky A.V., Taran I.I., Trusov D.I. Formirovanie metallicheskikh pokrytiy na polimernykh materialakh metodom giperzvukovoy metallizatsii [The formation of metal coatings on polymeric materials by means of hypersonic metallization]. Aktualnye voprosy mashinovedeniya [Topical issues of mechanical engineering], 2018, iss. 7, pp. 366–368.
6. Vityaz P.A., Zhornik V.I., Belotserkovsky M.A., Levantsevich M.A. Povyshenie resursa tribosopryazheniy aktivirovannymi metodami inzhenerii poverkhnosti [Increasing the life of tribocouplings by activated surface engineering methods]. Мinsk, Belaruskaya navuka Publ., 2012. 452 p.

STRUCTURE OF GRAIN BOUNDARIES AND MECHANISM OF STABILIZATION OF THE GRAIN STRUCTURE OF STEELS BY STEP HEATING TO AUSTENIZATION TEMPERATURES

KUKAREKO Vladimir A., D. Sc. in Phys. and Math., Prof., Head of the Center of Structural Research and Tribo-Mechanical Testing of Materials and Mechanical Engineering Products of Collective Use, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

GRIGORCHIK Aleksandr N., Ph. D. in Eng., Deputy Head of the Center of Structural Research and Tribo-Mechanical Testing of Materials and Mechanical Engineering Products of Collective Use, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus

CHICHIN Aleksey N., Process Engineer, OJSC “Minsk Tractor Works”, Minsk, Republic of Belarus

An analysis of the existing information on the structural state of grain boundaries in metals and the effect of impurities on grain growth during high-temperature heating is carried out. It is established that the heating rate in the interval of phase α→γ transformation has a great influence on the kinetics of growth of austenitic grain. Based on experimental and published data, a model is proposed that describes the mechanism of formation and growth of austenitic grains in steels upon heating at different speeds. It is concluded that slow heating of steel in the interval of phase α→γ transformation leads to the formation of grains with predominantly high-angle misorientation and adsorption at the boundaries of impurity atoms, which contributes to the stabilization of the grain structure.

grain boundaries, structure, impurity atoms, growth of austenitic grain, step heating

1. Kukareko V.A. Zakonomernosti rosta austenitnogo zerna v stali 18KhNVA [Regularities of growth of austenitic grain in steel 18KhNVA]. Metallovedenie i termicheskaya obrabotka [Metal science and heat treatment], 1981, no. 9, pp. 15–17.
2. Kukareko V.A., Valko A.L., Chichin A.N. Vliyanie skorosti tsementiruemykh konstruktsionnykh staley na rost austenitnogo zerna pri vysokotemperaturnoy vyderzhke [The influence of the heating rate of cemented constructional steels on the growth of austenitic grain in the process of high-temperature holding]. Vestsi Natsyyanalnay akademii navuk Belarusi. Seryya fizikatekhnichnykh navuk [Proceedings of the National Academy of Sciences of Belarus. Physical-technical series], 2018, vol. 63, no. 4, pp. 399–406.
3. Kukareko V.A., Valko A.L., Chichin A.N. Vliyanie rezhima nagreva konstruktsionnykh staley pri vysokotemperaturnoy tsementatsii na velichinu austenitnogo zerna [Impact of the mode of construction steels heating at high-temperature cementation on the amount of austenite grain]. Aktualnye voprosy mashinovedeniya [Topical issues of mechanical engineering], 2017, iss. 6, pp. 372–375.
4. Gulyaev A.P., Leshchinskaya R.P. Naftalinistyy izlom bystrorezhushchey stali [Naphthalene fracture of high-speed steel]. Metallovedenie i termicheskaya obrabotka metallov [Metal science and heat treatment of metals], 1963, no. 9, pp. 22–27.
5. Novikov I.I. Defekty kristallicheskogo stroeniya metallov [Defects in the crystal structure of metals]. Moscow, Metallurgiya Publ., 1983. 232 p.
6. Grabski M.W. Struktura granic ziarn w metalach. Katowice, Śląsk, 1969.
7. Mott N.F. Slip at Grain Boundaries and Grain Growth in Metals. Proceedings of the Physical Society, 1948, vol. 60, no. 4, pp. 391–394.
8. Smoluchowski R. Theory of Grain Boundary Diffusion. Physical Review, 1952, vol. 87, pp. 482–487.
9. Li J.C.M. High-Angle Tilt Boundary – A Dislocation Core Model. Journal of Applied Physics, 1961, vol. 32, no. 3, pp. 525–534.
10. McLean D. Grain boundaries in metals. Oxford, Clarendon Press, 1957.
11. Gleiter H., Chalmers B. High-Angle Grain Boundaries. Oxford, Pergamon Press, 1972.
12. Read W.T., Shockley W. Dislocation Models of Crystal Grain Boundaries. Physical Review, 1950, vol. 78, pp. 275–289.
13. Read W.Т. Dislocations in Crystals. London, McGraw-Hill, 1953. 256 p.
14. Gjostein N.A., Rhines F.N. Absolute interfacial energies of [001] tilt and twist grain boundaries in copper. Acta Materialia, 1959, vol. 7, pp. 319–330.
15. Cahn R.W. Physical metallurgy. 1st ed. New York, Wiley, 1965. 1100 p.
16. Bokshteyn S.Z. Diffuziya i struktura metallov [Diffusion and structure of metals]. Moscow, Metallurgiya Publ., 1973. 208 p.
17. Lukke K., Detert K. A quantitative theory of grain-boundary motion and recrystallization in metals in the presence of impurities. Acta Materialia, 1957, vol. 5, pp. 628–637.
18. Cahn R.W., Haasen P. Physical metallurgy. 3rd ed. New York, North-Holland Physics Pub., 1983. 2050 p.
19. Gorelik S.S. Rekristallizatsiya metallov i splavov [Recrystallization of metals and alloys]. Moscow, Metallurgiya Publ., 1978. 568 p.
20. Leslie W.C., Michalak J.T., Aul F.W. Iron and its dilute solid solutions. New York, Interscience Publ., 1963. 119 р.
21. Burke J.E., Turnbull D. Recrystallization and grain growth. Progress in Metal Physics, 1952, vol. 3, pp. 220–244.
22. Gulyaev A.P. Metallovedenie [Metal science]. Moscow, Metallurgiya Publ., 1986. 647 p.
23. Vinokur B.B., Pilyushenko V.L., Kasatkin O.G. Struktura konstruktsionnoy legirovannoy stali [Structure of structural alloyed steel]. Moscow, Metallurgiya Publ, 1983. 216 p.
24. Zagulyaeva S.V., Vinograd M.I. Rost austenitnogo zerna v konstruktsionnoy stali [Austenitic grain growth in structural steel]. Metallovedenie i termicheskaya obrabotka metallov [Metal science and heat treatment of metals], 1971, no. 7, pp. 2–7.
25. Van Vlack L. Elements of Materials Science and Engineering. Addison-Wesley, 1989. 598 p.
26. Li J.C.M. Possibility of Subgrain Rotation during Recrystallization. Journal of Applied Physics, 1962, vol. 33, no. 10, pp. 2958–2965.
27. Hu H. Annealing of Silicon Iron Single Crystals. Recovery and Recrystallization of Metals, 1963, pp. 311–378.
28. Vinograd M.I., Ulyanina L.Yu., Fayvilevich G.A. O mekhanizme rosta zerna austenita v konstruktsionnoy stali [On the mechanism of austenite grain growth in structural steel]. Metallovedenie i termicheskaya obrabotka metallov [Metal science and heat treatment of metals], 1975, no. 2, pp. 5–9.
29. Gulyaev A.P., Serebrennikova L.N. Vliyanie raznozernistosti na mekhanicheskie svoystva stali 18Kh2N4VA [Effect of grain size on the mechanical properties of steel 18Kh2N4VA]. Metallovedenie i termicheskaya obrabotka metallov [Metal science and heat treatment of metals], 1977, no. 4, pp. 2–11.
30. Li Y.J., Kostka A., Choi P., Goto S., Ponge D., Kirchheim R., Raabe D. Mechanisms of subgrain coarsening and its effect on the mechanical properties of carbon-supersaturated nanocrystalline hypereutectoid steel. Acta Materialia, 2015, vol. 84, pp. 110–123.
31. Kukareko V.A., Gatsuro V.M., Grigorchik A.N., Chichin A.N. Matematicheskoe modelirovanie i mekhanizm polucheniya austenitnogo zerna pri vysokotemperaturnom nagreve legkikh konstruktsionnykh elementov [Mathematical modeling and mechanism of coarsening of austenitic grain at hightemperature heating of alloyed structural steels]. Mekhanika mashin, mekhanizmov i materialov [Mechanics of machines, mechanisms and materials], 2019, no. 3(48), pp. 58–68.
32. Novikov I.I. Teoriya termicheskoy obrabotki metallov [Theory of heat treatment of metals]. Moscow, Metallurgiya Publ., 1986. 480 p.
33. Sadovskiy V.D. Strukturnaya nasledstvennost v stali [Structural heredity in steel]. Moscow, Metallurgiya Publ., 1973. 208 p.
34. Popov A.A. Fazovye prevrashcheniya v metallicheskie elementy [Phase transformations in metal alloys]. Moscow, Metallurgizdat Publ., 1950. 311 p.
35. Rose A., Strassburg W. Darstellung der Austenitbildung untereutektoidischer Stahle in Zeit-Temperatur-Auflosungs-Schaubildern. Stahl und Eisen, 1956, vol. 76, no. 15, pp. 976–983.
36. Bernshteyn M.L., Rakhshtadt A.G. Metallovedenie i termicheskaya obrabotka stali. Tom 2. Osnovy termicheskoy obrabotki [Metal science and heat treatment of steel. Volume 2. Basics of heat treatment]. Moscow, Metallurgiya Publ., 1983. 368 p.
37. Bernshteyn M.L., Zaymovskiy V.A., Kaputkina L.M. Termomekhanicheskaya obrabotka stali [Thermomechanical treatment of steel]. Moscow, Metallurgiya Publ., 1983. 480 p.