Title of the article DEFORMATION-OXIDATION ACTIVATION OF THE SURFACE LAYER OF CARBON STEEL TO ACCELERATE GAS NITROCARBURIZING
Authors

KONSTANTINOV Valerij M., D. Sc. in Eng., Prof., Head of the Department “Materials Science in Mechanical Engineering”, Belarusian National Technical University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.

LESHOK Vladislav A., Assistant Lecturer of the Department “Materials Science in Mechanical Engineering”, Belarusian National Technical University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.

In the section MATERIALS SCIENCE IN MECHANICAL ENGINEERING
Year 2026
Issue 2(75)
Pages 87–96
Type of article RAR
Index UDK 621.785.533
DOI https://doi.org/10.46864/1995-0470-2026-2-75-87-96
Abstract The effect of deformation-oxidation activation of the surface layer on the kinetics of gas nitrocarburizing was investigated. It was found that preliminary plastic deformation of steel and surface oxidation lead to the acceleration of the gas nitrocarburizing. The dependences of the intensification degree on deformation level and oxidation temperature were studied. The optimal ranges of the deformation and oxidation temperature were determined. The predominant effect of intensification techniques at the stage of the chemical- thermal treatment was assessed. Reasons for the acceleration of gas nitrocarburizing are discussed.
Keywords plastic deformation, oxidation, activation, steel, nitrocarburizing, acceleration, chemicalthermal treatment, intensification
  You can access full text version of the article.
Bibliography
  1. Minkevich A.N. Khimiko-termicheskaya obrabotka metallov i splavov [Thermochemical treatment of metals and alloys]. Moscow, Mashinostroenie Publ., 1965. 493 p. (in Russ.). 
  2. Voroshnin L.G., Mendeleeva O.L., Smetkin V.A. Teoriya i tekhnologiya khimiko-termicheskoy obrabotki [Theory and technology of thermochemical treatment]. Moscow, Novoe znanie Publ.; Minsk, Novoe znanie Publ., 2010. 304 p. (in Russ.). 
  3. Borisenok G.V., et al. Khimiko-termicheskaya obrabotka metallov i splavov [Thermochemical treatment of metals and alloys]. Moscow, Metallurgiya Publ., 1981. 424 p. (in Russ.). 
  4. Arzamasov B.N., et al. Materialovedenie [Materials science]. Moscow, Moskovskiy gosudarstvennyy tekhnicheskiy universitet imeni N. E. Baumana Publ., 2003. 648 p. (in Russ.). 
  5. Kidin I.N., Andryushechkin V.M., Volkov V.V., Kholin A.S. Elektrokhimiko-termicheskaya obrabotka metallov i splavov [Electrochemical and thermal treatment of metals and alloys]. Moscow, Metallurgiya Publ., 1978. 320 p. (in Russ.). 
  6. Panteleenko F.I., Lyakhovich L.S., Kukharev B.S. O klassifikatsii sposobov intensifikatsii protsessov khimiko-termicheskoy obrabotki metallov i splavov [On classification of methods for intensification of thermochemical treatment processes of metals and alloys]. Metallurgiya, 1980, iss. 14, pp. 5–6 (in Russ.). 
  7. Petrova L.G., Aleksandrov V.A., Demin P.E., Sergeeva A.S. Intensifikatsiya protsessov khimiko-termicheskoy obrabotki staley [Intensification of thermochemical treatment processes of steels]. Moscow, Moskovskiy avtomobilno-dorozhnyy gosudarstvennyy tekhnicheskiy universitet Publ., 2019. 160 p. (in Russ.).
  8. Konstantinov V.M., Kukareko V.A. Puti energosberezheniya pri termicheskoy i khimiko-termicheskoy obrabotke stalei za schet uskoreniya diffuzionnykh protsessov [Ways of energy saving during thermal and chemicalthermal treatment of steel due to acceleration of diffusion processes]. Foundry production and metallurgy, 2023, no. 4, pp. 72–80. DOI: https://doi. org/10.21122/1683-6065-2023-4-72-80 (in Russ.). 
  9. Kukareko V.A., Gacuro V.M., Grigorchik A.N., Chichin A.N. Matematicheskoe modelirovanie i mekhanizm ukrupneniya austenitnogo zerna pri vysokotemperaturnom nagreve legirovannykh konstruktsionnykh staley [Mathematical modeling and mechanism of coarsening of austenitic grain at high-temperature heating of alloyed structural steels]. Mechanics of machines, mechanisms and materials, 2019, no. 3(48), pp. 58–68 (in Russ.). 
  10. Kukareko V.A., Chichin A.N., Valko A.L., Rudenko S.P., Tarasevich I.Yu. Vliyanie rezhima nagreva staley 20KhN3A i 20KhGNMB na razmer austenitnogo zerna, formiruyushchegosya pri vysokotemperaturnoy termicheskoy obrabotke [Influence of heating mode of steels 20ХН3А (20KhN3A) and 20ХГНМБ (20KhGNMB) on the size of austenitic grain formed during high-temperature heat treatment]. Aktualnye voprosy mashinovedeniya, 2020, iss. 9, pp. 273–275 (in Russ.). 
  11. Kukareko V.A. Zakonomernosti rosta austenitnogo zerna v stali 18KhNVA [Regularities of growth of austenitic grain in 18KhNVA steel]. Metallovedenie i termicheskaya obrabotka, 1981, no. 9, pp. 15–17 (in Russ.). 
  12. Voroshnin L.G., Konstantinov V.V. Aktualnye problemy khimiko- termicheskoy obrabotki [Topical problems of thermochemical treatment]. Vestnik BNTU, 2002, no. 4, pp. 22–26 (in Russ.). 
  13. Voroshnin L.G., Voroshnin A.L. Novye podkhody k sozdaniyu i ispolzovaniyu poroshkovykh nasyshchayushchikh sred dlya khimiko-termicheskoy obrabotki [New approaches to the development and use of powder saturating media for thermochemical treatment]. Proceedings of the Academy of Sciences of Belarus. Physical-technical series, 1997, no. 3, pp. 13–17 (in Russ.). 
  14. Konstantinov V.M. Diffuzionno-legirovannye splavy dlya zashchitnykh pokrytiy. Diss. dokt. tekhn. nauk [Diffusion-alloyed alloys for protective coatings. D. Sc. Thesis]. Minsk, 2008. 474 p. (in Russ.). 
  15. Protasevich G.F., Voroshnin L.G. Izobretatelskaya rabota v oblasti khimiko-termicheskoy obrabotki metallov [Inventive activity in the field of thermochemical treatment of metals]. Metallovedenie i termicheskaya obrabotka metallov, 1988, no. 5, pp. 26–30 (in Russ.). 
  16. Konstantinov V.M., Leshok V.A. Aktivatsiya termodiffuzionnogo nasyshcheniya nizkouglerodistoy stali metodom okisleniya poverkhnosti [Activation of thermodiffusion saturation of low-carbon steel by surface oxidation]. Nauchye trudy 8 mezhdunarodnoy nauchnoy konferentsii “Fundamentalnye issledovaniya i innovatsionnye tekhnologii v mashinostroenii” [Proc. 8th international scientific conference “Fundamental research and innovative technologies in mechanical engineering”]. Moscow, 2024, pp. 117–118 (in Russ.). 
  17. Konstantinov V.M., Leshok V.A., Shtempel O.P. Analiz vliyaniya predvaritelnoy i tsiklicheskoy plasticheskoy deformatsii na khimiko-termicheskuyu obrabotku konstruktsionnykh staley [Analysis of the effect of preliminary and cyclic plastic deformation on the chemical-thermal treatment of structural steels]. Mechanics of machines, mechanisms and materials, 2024, no. 1(66), pp. 37–42. DOI: https://doi.org/10.46864/1995- 0470-2024-1-66-37-42 (in Russ.). 
  18. Ilinskiy V.A., Zhukov A.A., Kostyleva L.V., Loktyushkin V.A. Sverkhbystroe pereraspredelenie ugleroda v tsementovannykh sloyakh stalnykh izdeliy [Ultrafast redistribution of carbon in carburized layers of steel products]. Metally, 1998, no. 3, pp. 46–50 (in Russ.). 
  19. Farber V.M. Vklad diffuzionnykh protsessov v strukturoobrazovanie pri intensivnoy kholodnoy plasticheskoy deformatsii metallov [Contribution of diffusion processes to structure formation during intense cold plastic deformation of metals]. Metallovedenie i termicheskaya obrabotka metallov, 2002, no. 8, pp. 3–9 (in Russ.). 
  20. Shtremel M.A. V kakuyu storonu idet diffuziya [To which direction diffusion proceeds]. Metallovedenie i termicheskaya obrabotka metallov, 2004, no. 4, pp. 12–13 (in Russ.). 
  21. Bokshtein S.Z. Diffuziya i struktura metallov [Diffusion and structure of metals]. Moscow, Metallurgiya Publ., 1973. 208 p. (in Russ.). 
  22. Honeycombe R.W.K. The plastic deformation of metals. Cambridge, Edward Arnold (Publishers) Ltd, 1988. 
  23. Kolbasnikov N.G. Teoriya obrabotki metallov davleniem. Fizicheskie osnovy prochnosti i plastichnosti metallov [Theory of metal forming. Physical fundamentals of strength and plasticity of metals]. Saint Petersburg, 2004. Available at: http://elib.spb stu.ru/dl/local/637.pdf (accessed February 1, 2026) (in Russ.). 
  24. Sidor J.J., et al. Assessment of dislocation density by various techniques in cold rolled 1050 aluminum alloy. Metals, 2021, vol. 11, iss. 10. DOI: https://doi.org/10.3390/met11101571. 
  25. Odnobokova M., Belyakov A., Kaibyshev R. Development of nanocrystalline 304L stainless steel by large strain cold working. Metals, 2015, vol. 5, iss. 2, pp. 656–668. DOI: https://doi. org/10.3390/met5020656. 
  26. Tanaka Y., Takaki S., Tsuchiyama T., Uemori R. Effect of grain size on the yield stress of cold worked iron. ISIJ international, 2018, vol. 58, iss. 10, pp. 1927–1933. DOI: https://doi. org/10.2355/isijinternational.ISIJINT-2018-371.

Title of the article METHOD FOR CALCULATING STATIC TECHNOLOGICAL PARAMETERS OF AN ELECTROMAGNETIC DRIVE WITH A FERROMAGNETIC AUSTENITIC SHAPE-MEMORY CRYSTAL ACTUATOR WITH A SINGLE MARTENSITIC INTERLAYER
Authors

OSTRIKOV Vladislav O., M. Sc. in Eng., Ph. D. Student of the Department “Mechanical Engineering Technology, Automation and Robotics”, Sukhoi State Technical University of Gomel, Gomel, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.

OSTRIKOV Oleg M., D. Sc. in Eng., Ph. D. in Phys. and Math., Assoc., Prof. Head of the Department “Graphics”, Belarusian State University of Transport, Gomel, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.

In the section MATERIALS SCIENCE IN MECHANICAL ENGINEERING
Year 2026
Issue 2(75)
Pages 80–86
Type of article RAR
Index UDK 539.4
DOI https://doi.org/10.46864/1995-0470-2026-2-75-80-86
Abstract The behavior of a ferromagnetic crystal acting as an actuating element with a shape memory effect in an electromagnetic drive is considered. The design of an electromagnetic measuring transducer with the shape-memory ferromagnetic crystal actuating element is described. A design feature is shown, which consists in combining magnetic and non-magnetic components for better passage of the magnetic field through the working element. The effect of a magnetic field on the occurrence of shear forces at the austenite/ martensite interfaces has been studied, which lead to deformation of a ferromagnetic crystal with a shape memory effect in a rigid enclosure. The purpose of solving the static problem was to find the force created by the sample as a result of the action of the magnetic field and driving the rod by changing the linear dimensions of the actuator. In the course of solving the static problem, systems of equilibrium of forces and moments for the martensitic layer, the first and second austenitic volumes are compiled. It is established that the problem is statically indefinable due to the discrepancy between the number of unknown quantities and the number of equations. To solve this problem, an assumption was made that represents the equality and parallelism of forces arising at the austenite/martensite interfaces as a result of the action of the magnetic field. Using the known parameters of the crystal lattice, it was possible to calculate the angle of rotation of the martensitic interlayer relative to the crystal surface, as well as the angle of rotation of the austenite/martensite interfaces and the height of the martensitic interlayer. Taking the known values of the forces occurring at the austenite/martensite interfaces and parallel to the applied magnetic field, it was determined that these forces are equal to the compensating forces providing static equilibrium and the magnitude of the force occurring at the end of the sample having a direct connection to the rod. A relationship has been found between the forces resulting from the action of the magnetic field at the austenite/martensite interfaces and shear forces directed parallel to the austenite/martensite interfaces.
Keywords electromagnetic drive, ferromagnetic crystal with shape memory, martensitic interlayer, interface
  You can access full text version of the article.
Bibliography
  1. Ullakko K. Magnetically controlled shape memory alloys: a new class of actuator materials. Journal of materials engineering and performance, 1996, vol. 5, iss. 3, pp. 405–409. DOI: https://doi.org/10.1007/BF02649344. 
  2. Gabdullin N., Khan S.H. Review of properties of magnetic shape memory (MSM) alloys and MSM actuator designs. Journal of physics: conference series, 2015, vol. 588. DOI: http:// dx.doi.org/10.1088/1742-6596/588/1/012052. 
  3. Holz B., Riccardi L., Janocha H., Naso D. MSM actuators: design rules and control strategies. Advanced engineering materials, 2012, vol. 14, iss. 8, pp. 668–681. DOI: https://doi. org/10.1002/adem.201200045. 
  4. Laitinen V., Saren A., Sozinov A., Ullakko K. Giant 5.8% magnetic- field-induced strain in additive manufactured Ni-Mn-Ga magnetic shape memory alloy. Scripta materialia, 2022, vol. 208. DOI: https://doi.org/10.1016/j.scriptamat.2021.114324. 
  5. Ullakko K., et al. Large magnetic-field-induced strains in Ni2MnGa single crystals. Applied physics letters, 1996, vol. 69, iss. 13, pp. 1966–1968. DOI: https://doi.org/10.1063/1.117637. 
  6. Ullakko K., Huang J.K., Kokorin V.V., O’Handley R.C. Magnetically controlled shape memory effect in Ni2MnGa intermetallics. Scripta materialia, 1997, vol. 36, iss. 10, pp. 1133–1138. DOI: https://doi.org/10.1016/S1359-6462(96)00483-6. 
  7. Ostrikov V.O., Ostrikov O.M. Statika i dinamika granitsy razdela austenit/martensit v nagruzhennom prizmaticheskom monokristalle s effektom pamyati formy, nakhodyashchemsya v zhestkoy zadelke [Statics and dynamics of the austenite/martensite interface in a loaded prismatic single crystal with a shape memory effect located in a rigid seal]. Mashinostroenie, 2021, iss. 33, pp. 139–147 (in Russ.).  
  8. Ostrikov V.O., Ostrikov O.M. Staticheskaya i dinamicheskaya zadacha dlya edinichnoy martensitnoy prosloyki v ferromagnitnom monokristalle s effektom pamyati formy, nakhodyashchemsya v magnitnom pole v zhestkoy zadelke [A static and dynamic problem for a single martensitic layer in a ferromagnetic single crystal with a shape memory effect in a magnetic field in a rigid embodiment]. Problems of physics, mathematics and technics, 2023, no. 1(54), pp. 43–46. DOI: https://doi.org/1 0.54341/20778708_2023_1_54_43 (in Russ.). 
  9. Vasilevich Yu.V., Ostrikov V.O., Ostrikov O.M. Statika i dinamika granits razdela austenit / martensit martensitnoy prosloyki v nagruzhennom prizmaticheskom ferromagnitnom monokristalle s effektom pamyati formy, nakhodyashchemsya v zhestkoy zadelke [Statics and dynamics of the austenite / martensite interface of a martensitic interlayer in a loaded prismatic ferromagnetic single crystal with a shape memory effect located in a rigid seal]. Mashinostroenie, 2023, iss. 34, pp. 139–146 (in Russ.). 
  10. Ostrikov V.O., Ostrikov O.M. Raschet sil, deystvuyushchikh na neparallelnykh granitsakh razdela austenite/martensit v ferromagnitnom monokristalle s pamyatyu formy, nakhodyashchemsya v zhestkoy zadelke [Calculation of forces acting at non-parallel austenite/martensite interfaces in a ferromagnetic single crystal with shape memory located in a rigid embedding]. Proceedings of Francisk Skorina Gomel State University. Humanities, 2024, no. 3(144), pp. 116–121 (in Russ.). 
  11. Saren A., Ullakko K. Dynamic twinning stress and viscous-like damping of twin boundary motion in magnetic shape memory alloy Ni-Mn-Ga. Scripta materialia, 2017, vol. 139, pp. 126– 129. DOI: https://doi.org/10.1016/j.scriptamat.2017.06.010. 
  12. Malla A. Effect of composition on the magnetic and elastic properties of shape memory Ni-Mn-Ga. Master’s Thesis. Ohio, 2003. 191 p.

Title of the article BENDING OF AN ELASTOPLASTIC FIVE-LAYER CIRCULAR PLATE SYMMETRIC IN THICKNESS
Authors

STAROVOITOV Eduard I., D. Sc. in Phys. and Math., Prof., Professor of the Department “Structural Mechanics, Geotechnical and Structural Engineering”, Belarusian State University of Transport, Gomel, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.

SALICKI Vladislav S., PhD Student, Belarusian State University of Transport, Gomel, Republic of Belarus,  This email address is being protected from spambots. You need JavaScript enabled to view it.

In the section MECHANICS OF DEFORMED SOLIDS
Year 2026
Issue 2(75)
Pages 62–70
Type of article RAR
Index UDK 539.3
DOI https://doi.org/10.46864/1995-0470-2026-2-75-62-70
Abstract The problem of bending of a five-layer circular plate symmetric in thickness by axisymmetric distributed load is considered. The central and outer layers are assumed to be load-bearing, thin, and of increased rigidity. They perceive the main part of the force load and can exhibit elastoplastic properties. Their deformation follows the Kirchhoff hypotheses. Two relatively thick nonlinearly elastic fillers are used to connect the load-bearing layers. They provide redistribution of forces between the layers and are used to protect against unwanted external influences such as temperature and radiation. The deformation of the fillers is described by Timoshenko hypotheses, which take into account the relative shift, the additional rotation of the normal to the middle surface of the layer. The system of differential equations of equilibrium for the considered plate is obtained using the variational method of Lagrange. It includes a system of two nonlinear differential equations. The sought-for functions are the deflection of the plate, the radial displacement of the midplane of the central supporting layer, and two relative shear displacements in the fillers. The Ilyushin method of elastic solutions is used to solve the corresponding boundary value problem. The general solution is obtained in a recursive form. Formulas are provided for calculating the sought-for displacements and relative shear displacements under the boundary conditions of rigid clamping of the plate contour. The convergence of the method and the dependence of the solution on the physical nonlinearity of the layer materials are numerically investigated.
Keywords five-layer circular plate, physical nonlinearity, bending, analytical solution, numerical results
  You can access full text version of the article.
Bibliography
  1. Carrera E., Fazzolari F.A., Cinefra M. Thermal stress analysis of composite beams, plates and shells: computational modelling and applications. Academic Press, 2016. 440 p. 
  2. Aghalovyan L.A. Asimptoticheskaya teoriya anizotropnykh plastin i obolochek [Asymptotic theory of anisotropic plates and shells]. Moscow, Nauka Publ., Fizmatlib Publ., 1997. 414 p. (in Russ.). 
  3. Zhuravkov M., Lyu Y., Starovoitov E. Mechanics of solid deformable body. Singapore, Springer Singapore, 2023. 308 p. DOI: https://doi.org/10.1007/978-981-19-8410-5. 
  4. Abdusattarov A., Starovoitov E.I., Ruzieva N.B. Deformirovanie i povrezhdaemost uprugoplasticheskikh elementov konstruktsiy pri tsiklicheskikh nagruzheniyakh [Deformation and damage of elastic-plastic structural elements under cyclic loads]. Tashkent, IDEAL PRESS, 2023. 381 p. (in Russ.). 
  5. Starovoitov E.I., Nesterovich A.V., Shafieva Yu.V., Kozel A.G. Deformirovanie trekhsloynykh plastin pri termosilovykh nagruzkakh [Deformation of three-layer plates under thermal force loads]. Gomel, Belorusskiy gosudarstvennyy universitet transporta Publ., 2024. 395 p. (in Russ.). 
  6. Starovoitov E., Zhuravkov M., Leonenko D., Lyu Y. Deformation of three-layer structural elements in thermal radiation fields. Singapore, Springer Singapore, 2024. 384 p. DOI: https://doi.org/10.1007/978-981-97-7217-9. 
  7. Mikhasev G.I., Tovstik P.E. Localized dynamics of thin-walled shells. New York, Chapman and Hall/CRC, 2020. 366 p. DOI: https://doi.org/10.1201/9781315115467. 
  8. Mikhasev G.I., Altenbach H. Free vibrations of elastic laminated beams, plates and cylindrical shells. Thin-walled laminated structures. Buckling, vibrations and their suppression, 2019, pp. 157–198. DOI: https://doi.org/10.1007/978-3-030-12761-9_4. 
  9. Lachugina E.A. Poperechnye kolebaniya pyatisloynoy uprugoy krugovoy plastiny s zhestkim zapolnitelem [Transverse vibrations of the five-layer elastic circular plate with rigid fillers]. Mechanics. Researches and innovations, 2022, iss. 15, pp. 116– 122 (in Russ.). 
  10. Lachugina E.A. Svobodnye kolebaniya pyatisloynoy krugovoy plastiny s legkimi zapolnitelyami [Free vibrations of a five-layer circular plate with lightweight fillers]. Mechanics. Researches and innovations, 2023, iss. 16, pp. 111–116 (in Russ.). 
  11. Budnikova D.A. Analiz sobstvennykh kolebaniy pyatisloynogo sterzhnya [Analysis of a five-layer rod natural oscillations]. Mechanics. Researches and innovations, 2024, iss. 17, pp. 33–39 (in Russ.). 
  12. Budnikova D.A. Sobstvennye chastoty kolebaniy pyatisloynogo sterzhnya [Natural frequencies of vibration of a five-layer rod]. Problems of physics, mathematics and technics, 2025, no. 2(63), pp. 11–15 (in Russ.). 
  13. Gorshkov A.G., Starovoitov E.I., Leonenko D.V. Kolebaniya trekhsloynykh sterzhney pod deystviem lokalnykh nagruzok razlichnykh form [Vibrations of three-layered beams under the action of local loads of various shapes]. Ecological bulletin of research centers of the Black Sea economic cooperation, 2004, no. 1, pp. 45–52 (in Russ.). 
  14. Starovoitov E.I., Leonenko D.V., Yarovaya A.V. Osobennosti kolebaniya trekhsloynogo sterzhnya pri lokalnykh i impulsnykh vozdeystviyakh [Vibrations of a sandwich rod under local and impulsive forces]. Prikladnaya mekhanika, 2005, vol. 41, no. 7, pp. 122–129 (in Russ.). 
  15. Fedotenkov G.V., Tarlakovsky D.V., Vahterova Y.А. Identification of non-stationary load upon Timoshenko beam. Lobachevskii journal of mathematics, 2019, vol. 40, iss. 4, pp. 439– 447. DOI: https://doi.org/10.1134/S1995080219040061. 
  16. Pradhan M., Dash P.R., Pradhan P.K. Static and dynamic stability analysis of an asymmetric sandwich beam resting on a variable Pasternak foundation subjected to thermal gradient. Meccanica, 2016, vol. 51, iss. 3, pp. 725–739. DOI: https://doi. org/10.1007/s11012-015-0229-6. 
  17. Bakulin V.N., Boitsova D.A., Nedbai A.Ya. Parametric resonance of a three-layered cylindrical composite rib-stiffened shell. Mechanics of composite materials, 2021, vol. 57, iss. 5, pp. 623–634. DOI: https://doi.org/10.1007/s11029-021-09984-9.
  18.  18. Tarlakovskii D.V., Fedotenkov G.V. Two-dimensional non-stationary contact of elastic cylindrical or spherical shells. Journal of machinery manufacture and reliability, 2014, vol. 43, iss. 2, pp. 145–152. DOI: https://doi.org/10.3103/ S1052618814010178. 
  19. Mogilevich L.I., Popov V.S., Kondratov D.V., Rabinskiy L.N. Bending oscillations of a cylinder, surrounded by an elastic medium and containing a viscous liquid and an oscillator. Journal of vibroengineering, 2017, vol. 19, iss. 8, pp. 5758–5766. DOI: https://doi.org/10.21595/jve.2017.18179. 
  20. Paimushin V.N., Gazizullin R.K. Static and monoharmonic acoustic impact on a laminated plate. Mechanics of composite materials, 2017, vol. 53, iss. 3, pp. 283–304. DOI: https://doi. org/10.1007/s11029-017-9662-z. 
  21. Leonenko D.V., Markova M.V. Kolebaniya krugovoy trekhsloynoy stupenchatoy plastiny pri udarnom periodicheskom vozdeystvii [Vibrations of a three-layer circular step plate under periodic impact]. Mechanics of machines, mechanisms and materials, 2022, no. 3(60), pp. 68–76. DOI: https://doi. org/10.46864/1995-0470-2022-3-60-68-76 (in Russ.). 
  22. Leonenko D.V., Markova M.V. Kolebaniya krugovoy trekhsloynoy plastiny pod deystviem vneshney nagruzki [Oscillations of a circular three-layer plate under external linear in time load]. Journal of the Belarusian State University. Mathematics and informatics, 2023, vol. 1, pp. 49–63 (in Russ.). 
  23. Ageev R.V., Mogilevich L.I., Popov V.S. Kolebaniya stenok shchelevogo kanala s vyazkoy zhidkostyu, obrazovannogo trekhsloynym i tverdym diskami [Vibrations of the walls of a slot channel with a viscous fluid formed by three-layer and solid disks]. Problemy mashinostroeniya i nadezhnosti mashin, 2014, no. 1, pp. 3–11 (in Russ.). 
  24. Grover N., Singh B.N., Maiti D.K. An inverse trigonometric shear deformation theory for supersonic flutter characteristics of multilayered composite plates. Aerospace science and technology, 2016, vol. 52, pp. 41–51. DOI: https://doi.org/10.1016/j. ast.2016.02.017. 
  25. Starovoitov E.I., Dorovskaya E.P. Izgib pryamougolnoy trekhsloynoy plastiny na uprugom osnovanii [Bending of rectangular sandwich plate on elastic foundation]. Problemy mashinostroeniya i avtomatizatsii, 2006, no. 3, pp. 45–50 (in Russ.). 
  26. Starovoitov E.I., Kozel A.G. Izgib uprugoy krugovoy trekhsloynoy plastiny na osnovanii Pasternaka [The bending of an elastic circular sandwich plate on the Pasternak foundation]. Mekhanika kompozitsionnykh materialov i konstruktsii, 2018, vol. 24, no. 3, pp. 392–406 (in Russ.). 
  27. Starovoitov E.I., Leonenko D.V., Suleyman M. Termouprugiy izgib koltsevoy trekhsloynoy plastiny na uprugom osnovanii [Thermoelastic bending of a ring sandwich plate on the elastic foundation]. Ecological bulletin of research centers of the Black Sea economic cooperation, 2006, vol. 3, no. 4, pp. 55–62 (in Russ.). 
  28. Starovoitov E.I., Leonenko D.V., Suleyman M. Deformirovanie lokalnymi nagruzkami kompozitnoy plastiny na uprugom osnovanii [Deformation of a composite plate on an elastic foundation by local loads]. Mekhanika kompozitnykh materialov, 2007, vol. 43, no. 1, pp. 109–120 (in Russ.). 
  29. Kozel A.G. Sravnenie resheniy zadach izgiba trekhsloynykh plastin na osnovaniyakh Vinklera i Pasternaka [Comparison of solutions to the bending problems of three-layer plates on the Winkler and Pasternak foundations]. Mechanics of machines, mechanisms and materials, 2021, no. 1(54), pp. 30–37. DOI: https://doi.org/10.46864/1995-0470-2021-1-54-30-37 (in Russ.). 
  30. Gorshkov A.G., Starovoitov E.I., Yarovaya A.V. Tsiklicheskie nagruzheniya uprugoplasticheskikh tel v neytronnom potoke [Cyclic loading of elastic-plastic bodies in neutron flux]. Izvestiya Akademii nauk. Mekhanika tverdogo tela, 2001, no. 1, pp. 79–85 (in Russ.). 
  31. Starovoitov E.I. Uprugo-plasticheskoe deformirovanie trekhsloynykh sterzhney v temperaturnom pole [Elastoplastic deformation of three-layer beam in a temperature field]. Problemy mashinostroeniya i avtomatizatsii, 2012, no. 3, pp. 91–98 (in Russ.). 
  32. Babaytsev A.V., Kalyagin M.Yu., Rabinskiy L.N. Defect development in multilayer composites under static loads. Russian engineering research, 2024, vol. 44, iss. 1, pp. 112–115. DOI: https://doi.org/10.3103/S1068798X24010064. 
  33. Zakharchuk Yu.V. Deformirovanie krugovoy trekhsloynoy plastiny so szhimaemym zapolnitelem [Deformation of the circular three-layer plate with a compressible filler]. Problems of physics, mathematics and technics, 2017, no. 4(33), pp. 53–57 (in Russ.).
  34. Salicky V.S. Izgib zaschemlennoy po konturu krugovoy pyatisloynoy plastiny [Bending of a circular five-layer plate clamped on the contour]. Mechanics. Researches and innovations, 2022, iss. 15, pp. 209–213 (in Russ.).
  35. Salicki V.S. Izgib lokalnoy nagruzkoy krugloy pyatisloynoy plastiny [Bending a circular five-layer plate by local load]. Problems of physics, mathematics and technics, 2024, no. 3(60), pp. 27–31. DOI: https://doi.org/10.54341/20778708_2024_3_6 0_27 (in Russ.). 
  36. Salicki V.S. Local loading of circular five-layer plate. AIP conference proceedings, 2025, vol. 3265, iss. 1. DOI: https://doi. org/10.1063/5.0265375.

Title of the article ANALYSIS OF THE FEATURES OF THE STRESS-STRAIN STATE OF THE THIN SILICON WAFER DURING BLADE CUTTING PROCCES
Authors

MARMYSH Denis E., 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.

BASINIUK Vladimir L., D. Sc. in Eng., Prof., Chief of the R&D Center “Mechanical Engineering Technologies and Processing Equipment” – Head of the Laboratory of Gearing Systems and Processing Equipment, 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.

TYCHINSKAYA Irina D., Researcher of the Laboratory of Gearing Systems and Processing Equipment of the R&D Center “Mechanical Engineering Technologies and Processing Equipment”, 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.

In the section MECHANICS OF DEFORMED SOLIDS
Year 2026
Issue 2(75)
Pages 71–79
Type of article RAR
Index UDK 539.3
DOI https://doi.org/10.46864/1995-0470-2026-2-75-71-79
Abstract The article presents the modeling of the stress-strain state (SSS) of a thin silicon wafer during high-speed blade cubic boron nitride cutting process. The mathematical model of the system SSS is formulated, as well as a model of contact interaction between the wafer and the cutter. The mechanical and mathematical model is solved using the finite element method in ANSYS Workbench software package. The distribution of stress fields in the area of contact interaction is analyzed for various values of the cut-off wafer allowance. Patterns have been established that relate the amount of allowance to the normal stresses that occur during processing. Their analysis showed that with a decrease in the cut-off allowance from 20 to 1.5 μm, normal stresses also decrease. This may be due to the fact that at relatively small cutting depths, the angle of inclination of the contact segment between the plate and the cutter to the x axis decreases and the influence of stresses σxx on the stress state also decreases, while at the same time the influence of stresses σyy increases. Data on the experimental processing of three silicon wafer samples with preset cutting modes are presented. The numerical variation of the values of the average roughness Ra for all samples varies in the range of 0.25–0.55 μm, the sample with the largest amount of allowance has the highest numerical value for all the characteristics presented. A logarithmic scale with superposition of average values according to the characteristics Ra, Rq, Rsk, Rku, mathematical reconstruction of the 3D relief according to the parameters Rsk, Rku and the ratio of nominal to total area are shown.
Keywords silicon wafer, cubic boron nitride, stress-strain state, SSS, blade processing, numerical simulation
  You can access full text version of the article.
Bibliography
  1. Trofimov A.A. Rezhimy shlifovaniya i polirovaniya plastin iz sapfira i karbida kremniya, soderzhashchikh SVCh monolitnye integralnye skhemy [Modes of lapping and polishing plates made of sapphire and silicon carbide containing microwave monolithic integrated сircuits]. Applied physics, 2017, no. 3, pp. 89–95 (in Russ.). 
  2. Ha M.-T., Jeong S.-M. A review of the simulation studies on the bulk growth of silicon carbide single crystals. Journal of the Korean Ceramic Society, 2022, vol. 59, iss. 2, pp. 153–179. DOI: https://doi.org/10.1007/s43207-022-00188-y. 
  3. Torbilo V.M. Almaznoe vyglazhivanie [Diamond smoothing]. Moscow, Mashinostroenie Publ., 1972. 105 p. (in Russ.). 
  4. Borodavko I.V., et al. Obrabotka i uprochnenie poverkhnostey pri izgotovlenii i vosstanovlenii detaley [Processing and strengthening of surfaces in the manufacture and restoration of parts]. Minsk, Belorusskaya nauka Publ., 2013. 462 p. (in Russ.). 
  5. Sirotkin O.S. Osnovy innovatsionnogo materialovedeniya [Fundamentals of innovative materials science]. Moscow, INFRA-M Publ., 2016. 156 p. (in Russ.). 
  6. Radchenko M.V. Elektrotekhnicheskoe materialovedenie [Electrical engineering materials science]. Saint Petersburg, Lan Publ., 2023. 116 p. (in Russ.). 
  7. Bai L., et al. Friction between silicon and diamond at the nanoscale. Journal of physics D: applied physics, 2015, vol. 48, no. 25. DOI: https://doi.org/10.1088/0022-3727/48/25/255303. 
  8. Popov V.L. Contact mechanics and friction: physical principles and applications. Berlin, Springer, 2010. 362 p. 
  9. Aleksandrov V.M., Chebakov M.I. Vvedenie v mekhaniku kontaktnykh vzaimodeystviy [Introduction to the mechanics of contact interactions]. Rostov-on-Don, OOO “TsVVR” Publ., 2007. 114 p. (in Russ.). 
  10. Shpeizman V.V., et al. Prochnost plastin monokristallicheskogo kremniya dlya solnechnykh elementov [Strength of silicon single-crystal wafers for solar cells]. Zhurnal tekhnicheskoy fiziki, 2020, vol. 90, iss. 1, pp. 79–84. DOI: https://doi. org/10.21883/JTF.2020.01.48665.148-19 (in Russ.). 
  11. Sekhar H., et al. Mechanical strength problem of thin silicon wafers (120 and 140 μm) cut with thinner diamond wires (Si kerf 120 → 100 μm) for photovoltaic use. Materials science in semiconductor processing, 2020, vol. 119. DOI: https://doi. org/10.1016/j.mssp.2020.105209. 
  12. Carton L. Mechanical properties of thin silicon wafers for photovoltaic applications: Influence of material quality and sawing process. Ph. D. Thesis. Lyon, 2020. 240 p. 
  13. Kremniy [Silicon]. Available at: https://www.tydexoptics.coм/ Silicon_ru.pdf (accessed May 15, 2025) (in Russ.). 
  14. Moghadasi K., et al. Experimental and numerical study on thin silicon wafer CO2 laser cutting and damage investigation. The international journal of advanced manufacturing technology, 2024, vol. 132, iss. 9–10, pp. 4857–4884. DOI: https://doi. org/10.1007/s00170-024-13675-9. 
  15. Ogorodnikov A.I. Parametricheskoe kompyuternoe modelirovanie mekhanicheskoy obrabotki khrupkikh materialov dlya integratsii v avtomatizirovannuyu sistemu tekhnologicheskoy podgotovki proizvodstva. Avtoref. diss. kand. tekhn. nauk [Parametric computer modeling of mechanical processing of brittle materials for integration into an automated system of technological preparation of production. Extended Abstract of Ph. D. Thesis]. Yekaterinburg, 2021. 24 p. (in Russ.).

Title of the article DETERMINING THE STATIONARY MOTIONS OF A STATICALLY UNBALANCED ROTOR WITH A BALL SELF-BALANCING DEVICE BY A SMALL PARAMETER METHOD
Authors

SIDIKOV Mansur N., Ph. D. in Eng., Associate Professor of the Department “General Technical Disciplines”, Almalyk branch of NUST “MISIS”, Almalyk, Republic of Uzbekistan, This email address is being protected from spambots. You need JavaScript enabled to view it.

In the section MECHANICAL ENGINEERING COMPONENTS
Year 2026
Issue 2(75)
Pages 52–61
Type of article RAR
Index UDK 531.01
DOI https://doi.org/10.46864/1995-0470-2026-2-75-52-61
Abstract The small parameter method was used to analyze the necessary conditions for stationary motions of a rotor mounted on a flexible shaft with a ball self-balancing device, when running tracks of the balancing balls are installed not only by eccentricity, but also have a horizontal axis of rotation. In this case, the parameter inversely proportional to the square of the angular velocity of the rotor is taken as the small parameter. In a particular case, an asymptotic solution is obtained taking into account the second power of the small parameter, as well as an exact solution to one of the cases of unbalanced rotor motion.
Keywords self-balancing device, eccentricity, running track, generalized coordinates
You can access full text version of the article.
Bibliography
  1. Genta G. Dynamics of rotating systems. New York, Springer, 2005. 658 p. 
  2. Yamamoto T., Ishida Y. Linear and nonlinear rotordynamics: a modern treatment with applications. New York, Wiley, 2001. 325 р. 
  3. Nikiforov A.N. Sostoyanie problemy uravnoveshivaniya rotorov [State of rotors balancing problem]. Bulletin of science and technical development, 2013, no. 4(68), pp. 20–28 (in Russ.). 
  4. Bykov V.G., Kovachev A.S. Dinamika rotora s ekstsentricheskim sharovym avtobalansirovochnym ustroystvom [Dynamic of a statically unbalanced rotor with eccentric ball autobalancer]. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2014, vol. 1, no. 4, pp. 579–588 (in Russ.). 
  5. Bykov V.G., Kovachev A.S. Prokhozhdenie cherez rezonans staticheski neuravnoveshchannogo rotora s “neidealnym” avtobalansirovochnym mekhanizmom [Passage through the resonance of a statically unbalanced rotor with “imperfect” autobalancing device]. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2017, vol. 4, no. 4, pp. 671–680 (in Russ.). 
  6. Bykov V.G., Kovachev A.S. Dinamika staticheski neuravnoveshennogo rotora s ellipticheskim sharovym avtobalansirovochnym ustroystvom [Dynamics of a statically unbalanced rotor with an elliptic automatic ball balancer]. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6, no. 3, pp. 452– 461 (in Russ.). 
  7. Bykov V.G. Nestatsionarnye rezhimy dvizheniya staticheski neuravnoveshennogo rotora s avtobalansirovochnym mekhanizmom [Nonstationary behavior of statically unbalanced rotor with the automatic balancеr]. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2010, no. 3, pp. 89–96 (in Russ.). 
  8. Bykov V.G., Melnikov A.E. Matematicheskaya model gibkogo rotora na osnove obobshchennykh lagranzhevykh koordinat [A mathematical model of a flexible rotor using the generalized Lagrangian coordinates]. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2010, no. 4, pp. 110– 118 (in Russ.). 
  9. Pasynkova I.A. Sovmestnye nelineynye kolebaniya neuravnoveshennogo rotora i korpusa [Non-linear vibration of the rotor-housing system]. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2014, vol. 1, no. 1, pp. 152–161 (in Russ.).
  10. Gorbenko A.N. Nekotorye netrivialnye svoystva mekhanicheskoy sistemy “rotor – sharikovyy avtobalansir” [Some non– trivial properties of the “rotor – ball auto-balancer” mechanical system]. Vibratsii v tekhnike i tekhnologiyakh, 2002, no. 3(24), pp. 33–36 (in Russ.). 
  11. Kydyrbekuly A.B., Ibrayev G.E. Ob avtokolebaniyakh v vertikalnykh rotornykh sistemakh, ustanovlennykh na uprugikh oporakh [The self-oscillation in the vertical rotor system mounted on elastic supports]. Journal of mathematics, machanics, computer science, 2020, no. 1(105), pp. 160–173. DOI: https://doi. org/10.26577/JMMCS.2020.V105.I1.14 (in Russ.).
  12. Ollson K.-O. Limits for the use of auto-balancing. International journal of rotating machinery, 2004, vol. 10, iss. 3, pp. 221– 226. DOI: https://doi.org/10.1155/S1023621X04000235. 
  13. Zaytsev N.N., Zaytsev D.N., Makarov A.A. Inzhenernyy analiz ustanovivshikhsya rezhimov odnodiskovogo rotora s mnogoryadnym sharovym avtobalansiruyushchim ustroystvom [Engineering analysis of steady-state regimes of the single-disk rotor with multi-row ball self-balancing device]. PNRPU aerospace engineering bulletin, 2017, no. 48, pp. 43–59. DOI: https://doi. org/10.15593/2224-9982/2017.48.05 (in Russ.). 
  14. Dimentberg F.M., Shatalov K.T., Gusarov A.A. Kolebaniya mashin [Machine fluctuations]. Moscow, Mashinostroenie Publ., 1964. 308 p. (in Russ.). 
  15. Kelzon A.S., Malinin L.M. Upravlenie kolebaniyami rotorov [Rotor oscillation control]. Saint Petersburg, Politekhnika Publ., 1992. 118 p. (in Russ.). 
  16. Kelzon A.S., Tsimanskiy Yu.P., Yakovlev V.I. Dinamika rotorov v uprugikh oporakh [Dynamics of rotors in elastic supports]. Moscow, Nauka Publ., 1982. 280 p. (in Russ.). 
  17. Nayfeh A.H. Perturbation methods. Wiley-VCH, 1973. 448 p.