doi: 10.18698/2309-3684-2025-4-1948
A numerical scheme and algorithm for calculating the stress-strain state (SSS) of a casting during its solidification in a spherical metal casting mold installed in a spherical die subjected to thermal stress have been developed. The calculation is based on the equations of linear elasticity theory, thermal conductivity, and an approved numerical method. A composite spherical casting structure bounded by orthogonal families of surfaces is considered. An example is the problem of solidification and cooling of a spherical steel casting in a metal mold, which is mounted in a matrix. The calculation results are presented in the form of diagrams of normal stresses, displacements, and temperatures along the cross-section of the spherical structure. The analysis of the obtained calculation results is given
[1] Rudenko V.L., Baranov V.L., Sorokatyj A.V. Svyazannaya termodinamicheskaya model' obzhatiya trubchatogo kreshernogo elementa pri vystrele [Coupled thermodynamic model of compression of a tubular crusher element during firing]. Izvestiya Rossijskoj akademii raketnyh i artillerijskih nauk [News of the Russian Academy of Missile and Artillery Sciences], 2012, no. 3(73), pp. 25–30.
[2] Belopuhova A.K. Lit'e pod davleniem [Casting under pressure].Moscow, Mashinostroyeniye Publ., 1975, 400 p.
[3] Bekker M.B. Lit'e pod davleniem [Casting under pressure].Moscow, Mashinostroyeniye Publ., 1990, 400 p.
[4] Pat. 2841324 C1 Russian Federation, IPC B22C 9/18, B22D 7/06, B22D 15/00. Method for preparing a metal casting mold for pouring metal/ A.I. Evstigneev, V.I. Odinokov, E.A. Dmitriev et al. Applicant: Federal State Budgetary Educational Institution of Higher Education «Komsomolsk-on-Amur State University»; appl. 12.11.2024; publ. 06.06.2025.
[5] Odinokov V.I., Kaplunov B.G., Peskov A.V., Bakov A.V. Matematicheskoe modelirovanie slozhnyh tekhnologicheskih processov [Mathematical modeling of complex technological processes]. Moscow, Nauka Publ., 2008, 178 p.
[6] Boli B., Uejner Dzh. Teoriya temperaturnyh napryazhenij [Theory of thermal stress]. Moscow, Mir Publ., 1964, 512 p.
[7] Karslou G., Eger D. Teploprovodnost' tverdyh tel [Thermal conductivity of solids]. Moscow, Nauka Publ., 1964, 489 p.
[8] Lykov A. V. Teoriya teploprovodnosti [Thermal conduction theory]. Moscow, JSC «Vysshaya Shkola», 1967, 600 p.
[9] Ratnikov P.E. Analiz metodov rascheta termouprugih napryazhenij v termicheski massivnyh stal'nyh zagotovkah pri nagreve (analiticheskij obzor) [Analysis of methods for calculating thermoelastic stresses in thermally massive steel workpieces during heating (analytical review)]. Foundry production and metallurgy, 2005, no. 1, pp. 31–34.
[10] Livshits V.B., Kushnir A.P., Mamedova I.Yu., Zyabneva O.A. An effect of the omnidirectional gas pressure on solidification and properties of steel castings. Foundry. Technology and equipment, 2021, no. 5, pp. 21–23.
[11] Monastyrskiy V.P., Alexandrovich A.I., Monastyrskiy A.V., Soloviev M.B., Tikhomirov M.D. Development of casting technology for large-size gas-turbine engine blades for power installations using the 'POLYGON* and procast systems. Foundry. Technology and equipment, 2007, no. 9, pp. 29-36.
[12] Berezin D.T. Numerical simulation of the heat-stressed state in the "casting - die mold" system for die casting of aluminum alloys. Technology of light alloys, 2023, no. 3, pp. 48-59.
[13] Olkhovik E.O., Desnitskiy V.V., Molchanyuk R.A. Eksperimental'noe issledovanie silovogo vzaimodejstviya mezhdu otlivkoj i formoj v period zatverdevaniya metalla [Experimental study of the force interaction between the casting and the mold during the solidification of the metal]. Foundry production and metallurgy, 2006, no. 4 (40), pp. 101-104.
[14] Duyunova V.A., Molodtsov S.V., Leonov A.A., Trapeznikov A.V. Application of computer modeling methods in the manufacture of complex-contoured shaped casting. Proceedings of VIAM, 2019, no. 11(83), pp. 3-11.
[15] Чучунова С.Ю., Петров Б.И., Макеев К.А., Оборин Л.А. Komp'yuternoe modelirovanie processa formirovaniya litoj zagotovki [Computer modeling of the process of forming a cast billet]. Aktual'nye problemy aviacii i kosmonavtiki [Current problems of aviation and astronautics], 2022, vol.1, pp. 552-555.
[16] Ogorodnikova O.M., Pigina E.V., Martynenko S.V. Computer simulation of hot cracks in cast parts. Foundry. Technology and equipment, 2007, no. 2, pp. 27-30.
[17] Smelov V.G., Vdovin R.A., Agapovichev A.V. spol'zovanie sistem chislennogo modelirovaniya dlya issledovaniya tekhnologicheskogo processa lit'ya lopatok v zagotovitel'nom proizvodstve [Using numerical modeling systems to study the technological process of casting blades in blank production]. Vestnik SGAU [Bulletin of SSAU], 2015, no. 3-2, pp. 391-399.
[18] Ilyukhin V.D., Monastyrskiy A.V. Computer simulation of deformation dispersion in the hot crack control method. Foundry. Technology and equipment, 2021, no. 3, pp. 29-34.
[19] Monastyrskiy A.V., Vlasov Yu.B. POLIGONSOFT for foundry. Foundry production and metallurgy, 2022, no. 3, pp. 40-47.
[20] Kozin R. G., Shevchenko K. N. Stress state of a thick spherical shell enclosing a heat-releasing sphere. Soviet Applied Mechanics, 1971, vol. 7, no. 7, pp. 19–23.
[21] Gamer U. On the elastic-plastic deformation of a sphere subjected to as spherically symmetrical temperature field. Journal of Thermal Stresses, 1988, vol. 11, № 3, pp. 159–173.
[22] Mironov D. N., Goncharenko V. P., CHigareva YU. A., CHigarev V. A. Reshenie stacionarnoj zadachi termouprugosti i termoplastichnosti v priblizhenii effektivnoj modeli dlya tela sfericheskoj formy [Solution of the stationary problem of thermoelasticity and thermoplasticity in the approximation of an effective model for a spherical body]. Teoreticheskaya i prikladnaya mekhanika: mezhdunarodnyj nauchno-tekhnicheskij sborni [Theoretical and applied mechanics: international scientific and technical collection], 2016, no. 31, pp. 185–195.
[23] Artemov M.A., Baranovskiy E.S., Verlin A.A., Semka E.V. Thick-walled spherical shell problem. Advanced Engineering Research (Rostov-on-Don), 2021, vol. 21, no. 1, pp. 22–31.
[24] Nombre S.B., Polyanskiy D.D., Storozhev S.V., Chan B.L.H. Taking into account parametric uncertainty in the model of temperature effects on the inner surface of an elastic hollow ball. Journal of theoretical and applied mechanics, 2023, no. 2(83), pp. 56–66.
[25] Evstigneev A.I., Odinokov V.I., Dmitriev E.A., Chernyshova D.V., Evstigneeva A.A., Ivankova E.P. on the crack resistance of a ceramic shell mold according to the smelted models when a spherical steel casting solidifies in it. Foundry. Technology and equipment, 2022, no. 9, pp. 17-21
[26] Evstigneev A.I., Dmitriev E.A., Chernyshova D.V., Odinokov V.I., et al. Modeling of external force action on a shell mold for pouring steel. Mathematical modeling, 2022, no. 5(34), pp. 61-72.
[27] Odinokov V.I., Dmitriev E.A., Evstigneev A.I., Sviridov A.V. Matematicheskoe modelirovanie processov polucheniya otlivok v keramicheskie obolochkovye formy [Mathematical modeling of processes for obtaining castings in ceramic shell molds]. Moscow, Limited Liability Company «Innovative Mashinostroenie» Publishers, 2020, pp. 256.
[28] Odinokov V. I., Dmitriyev E. A. , Evstigneev A. I. , Potianikhin D. A. , Kvashnin A. E. Mathematical modeling of the metal deformation process on a casting and forging module with a modified drive of the side strikers. Mathematical Modeling and Computational Methods, 2021, no. 3, pp. 3–23.
[29] Odinokov V. I., Evstigneev A. I., Dmitriyev E. A., Koloshenko Y. B., Evstigneeva A. A., Petrov V. V. Modeling the durability of casting shell molds under external force and thermal loads. Mathematical Modeling and Computational Methods, 2024, no. 4, pp. 31–51.
[30] Vvedensky B.A. Great Soviet Encyclopedia. Vol. 28, 2nd edition. Moscow, Great Soviet Encyclopedia, 1954, 624 p.
Евстигнеев А.И., Одиноков В.И., Потянихин Д.А., Колошенко Ю.Б. Численное моделирование влияния внутриформенного высокого газового давления на затвердевание и охлаждение стальной отливки. Математическое моделирование и численные методы, 2025, № 4, с. 19–48.
Исследование выполнено за счет гранта Российского научного фонда №24-29-00214, https://rscf.ru/project/24-29-00214/
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