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The Influence of External Heat Exposure on the Stress State of Shell Molds by Smelting Models

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Mathematical Models and Computer Simulations Aims and scope

Abstract

The problem of determining the force effect of the support filler on the resistance of the shell mold (SM) during the crystallization of liquid metal (steel) in it is formulated and solved. The tensile normal stress that occurs in the outer layers of the mold in the initial time moments when liquid metal is poured into it is taken as the leading physical quantity that affects the crack resistance of the SM. The force factor affecting the stress-strain state (SSS) of the SM is the friction between the SM and the supporting filler (SuFi), which appears during the elastic expansion of the outer layer in the SM as a result of the temperature exposure from the crystallizing liquid metal. The problem of mathematical programming (minmax function) is formulated to determine the coefficient of friction between the SM and SuFi to obtain the smallest value of the normal tensile stress in the SM over the area under consideration in the presence of a system of constraints. An axisymmetric body of rotation is considered, which has four regions: liquid metal, solid metal, SM, and SuFi, which is considered to be a solid body that creates friction at the contact point with the outer layer of the SM. To solve the problem, equations of the linear theory of elasticity, the equation of thermal conductivity and a proven numerical method are used, according to which the area under study is divided into elements by a system of orthogonal surfaces. For each element, the formulated system of equations is written in a difference form. An algorithm for solving the problem is developed and the results of the solution are presented, stress diagrams in the SuFi are constructed using the found value of the friction coefficient. The analysis of the received results is given.

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REFERENCES

  1. A. I. Evstigneev, V. I. Odinokov, E. A. Dmitriev, A. V. Sviridov, and E. P. Ivankova, “Influence of external heat exposure on the stress state of shell forms by smelting models,” Math. Models Comput. Simul. 13 (5), 780–789 (2021). https://doi.org/10.1134/S2070048221050112

    Article  MathSciNet  MATH  Google Scholar 

  2. A. I. Evstigneev, V. I. Odinokov, E. A. Dmitriev, E. P. Ivankova, A. V. Sviridov, and G. I. Usanov, “Influence of the heating temperature of the support filler on the stress state of shell molds when pouring steel,” Liteinoe Proizvod., No. 3, 20–24 (2021).

  3. V. I. Odinokov, E. A. Dmitriev, A. I. Evstigneev et al., “Modeling and optimizing the property choices of materials and structures of shell molds for investment casting,” Steel Transl. 50 (10), 684–695 (2020). https://doi.org/10.3103/S0967091220100071

    Article  Google Scholar 

  4. Yu. V. Golenkov, V. A. Rybkin, and R. F. Yusipov, “Force interaction of the support material with the shell mold during investment casting,” Liteinoe Proizvod., No. 2, 14–15 (1988).

  5. V. I. Odinokov, A. I. Evstigneev, E. A. Dmitriev. D. V. Chernyshova, and A. A. Evstigneeva, “The influence of internal factor on crack resistance of shell mold for investment models,” Steel Transl. 52 (2), 159–164 (2022). https://doi.org/10.3103/S0967091222020152

    Article  Google Scholar 

  6. S. I. Repyakh, Technological Basics of Casting by Investment Models (Lira, Dnepropetrovsk, 2006) [in Russian].

    Google Scholar 

  7. G. M. Sevastianov, A. M. Sevastianov, and V. I. Odinokov, “On the initial-boundary heat conduction problem for a system with phase transfer,” Mat. Model. 25 (3), 119–133 (2013).

    Google Scholar 

  8. V. I. Odinokov, B. G. Kaplunov, A. V. Peskov, and A. V. Bakov, Mathematical Modeling of Complex Technological Processes (Nauka, Moscow, 2008) [in Russian].

    Google Scholar 

  9. V. I. Odinokov, A. N. Prokudin, A. M. Sergeeva, aand G. M. Sevastianov, “Odissey,” RF Certificate of State Registration of Computer Program No. 2012661389 (2012) [in Russian].

  10. V. I. Odinmokov, E. A. Dmitriev, A. I. Evstigneev, and E. P. Ivankova, “Mathematical simulation program for optimizing the choice of the temperature of the support filler, the physical properties of the material and the structure of the shell mold using investment models to increase its crack resistance when the casting is cooled in it,” RF Certificate of State Registration of Computer Program No. 2021616121 (2021) [in Russian].

  11. V. I. Odinokov, E. A. Dmitriev, A. I. Evstigneev, and V. I. Sviridov, Mathematical Modeling of Castings Obtaining in Ceramic Shell Molds (Mashinostroenie, Moscow, 2020) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Komsomolsk-na-Amure State University, 681013, Komsomolsk-on-Amur, Russia

    A. I. Evstigneev, E. A. Dmitriev, D. V. Chernyshova, V. I. Odinokov, A. A. Evstigneeva & E. P. Ivankova

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  1. A. I. Evstigneev
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  2. E. A. Dmitriev
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  3. D. V. Chernyshova
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  4. V. I. Odinokov
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  5. A. A. Evstigneeva
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  6. E. P. Ivankova
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Correspondence to A. I. Evstigneev or D. V. Chernyshova.

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Evstigneev, A.I., Dmitriev, E.A., Chernyshova, D.V. et al. The Influence of External Heat Exposure on the Stress State of Shell Molds by Smelting Models. Math Models Comput Simul 14, 995–1001 (2022). https://doi.org/10.1134/S2070048222060059

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  • DOI: https://doi.org/10.1134/S2070048222060059

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