Volgograd State Technical University, Volgograd, Russia:

O. B. Kryuchkov, Cand. Eng., Associate Prof., Dept. of Technology of Materials, Deputy Dean of the Faculty of Technology of Structural Materials, e-mail: bardb@mail.ru

Tula State University, Tula, Russia:
P. I. Malenko, Cand. Eng., Associate Prof., Dept. of Mechanical Engineering and Materials Science, e-mail: malenko@tsu.tula.ru
L. G. Saranin, Postgraduate Student
A. E. Boldyrev, Master Student

The initial temperature of the furnace, at which the cold ingot is loaded, has a decisive effect on the occurrence of temperature stresses in the heated workpiece in the elastic region. Heating of the ingot after its transition from the elastic region to the plastic state should be carried out at the maximum power of the furnace to the final surface temperature, because under these conditions, the risk of cracks is eliminated. Control of the temperature field in the workpiece after the metal is languished by plastic deformation, namely, the temperature difference between the surface and the center of the ingot, which should be no more than 50 °C, helps to eliminate the banding of the structure in the deformed metal, reduce the likelihood of various kinds of distortion of the shape of the workpiece, as well as reduce the heterogeneity of its mechanical properties. In order to develop a rational heating mode for a cold ingot weighing 10 tons of steel 35 in a chamber fuel furnace, the MathConnex mathematical package (part of MathCad Pro) was used in the work, in which an Excel tool was added to solve the differential equation of thermal conductivity in partial derivatives by the finite difference method using an implicit difference scheme, on the basis of which a flowchart was created for the calculation. Varying the temperature of the furnace and the heating time of the ingot at various stages of heating, namely the initial, in the middle of heating and metal exposure, a rational heating mode was chosen, including the ingot landing in the furnace at a temperature of 880 °C, heating at average furnace temperatures: 1090, 1350, 1425 and 1450 °C and metal exposure to equalize the cross-section temperature to 50 °C at a temperature of 1330 °C, respectively, for a time, h: 1,86; 0,83; 0,54; 0,43; 0,004 and 4,82. The use of the proposed heating mode contributes to obtaining maximum furnace performance and minimum values of heating time, fuel consumption and thickness of the decarbonized metal layer, which is confirmed by the generalized desirability function equal to 0,676.

1. Panferov V. I. On economical control of metal heating in industrial furnaces. Vestnik YuUrGU. Seriya "Kompyuternye tekhnologii, upravlenie, radioelektronika". 2018. Vol. 18. No. 2. pp. 71–80.
2. Parsunkin B. N., Andreev S. M., Zhadinskiy D. Yu., Akhmetova A. U. Optimum fuel-saving modes of heating continuously cast billets in continuous furnaces. Vestnik Magnitogorskogo gosudarstvennogo tekhnicheskogo universiteta imeni G. I. Nosova. 2015. No. 3. pp. 89–96.
3. Panferov V. I., Panferov S. V. To the solution of the problem of controllability of metal heating in industrial furnaces. Vestnik YuUrGU. Seriya "Metallurgiya". 2019. Vol. 19. No. 2. pp. 79–85.
4. Andreev S. М. Prediction of the heating time of billets in the conditions of non-stationary mode of operation of continuous furnaces. Elektrotekhnicheskie sistemy i kompleksy. 2017. No. 3 (36). pp. 35–40.
5. Smirnova D. А., Obushenko S. V. Modes of cooling, temperature control of heating slabs on the line "continuous casting machine – thermostat – heating furnace". Vestnik nauki i obrazovaniya. 2019. No. 3–1 (57). pp. 15–18.
6. Lee D. E., Kim M. Y. Optimum residence time for steel productivily and energy saving in a hot rolled reheating furnace. Journal of Mechanical Science and Technology. 2013. Vol. 27. No. 9. pp. 2869–2877.
7. Panferov V. I., Trenin N. A., Panferov S. V. Estimation of the massive body temperature based on the measured values of the heat transfer process. Vestnik YuUrGU. Seriya "Kompyuternye tekhnologii, upravlenie, radioelektronika". 2018. Vol. 18. No. 1. pp. 133–139.
8. Lukin S. V., Levashev К. Yu., Zbrodov А. А. Mathematical modeling of the thermal state of a square-section billet in a billet caster and in a thermos. Vestnik Cherepovetskogo gosudarstvennogo universiteta. 2018. No. 3 (84). pp. 37–45.
9. Yang Z., Luo X. Optimal set values of zone modeling in the simulation of a walking beam type reheating furnace on the steady-state operating regime. Applied Thermal Engineering. 2016. Vol. 101. pp. 191–201.
10. Steinboeck A., Wild D., Kugi A. Nonlinear model predictive control of a continuous slab reheating furnace. Control Engineering Practice. 2013. Vol. 21. No. 4. pp. 495–508.
11. Steinboeck A., Graichen K., Wild D., Kiefer T., Kugi A. Model-based trajectory planning, optimization, and open loop control of a continuous slab reheating furnace. Journal of Process Control. 2011. Vol. 21. No. 2. pp. 279–292.
12. Xu J. Y., Bu J. R. Research of furnace temperature optimization control method in hot rolling process. Advanced Materials Research. 2011. Vol. 230–232. pp. 7–11.
13. Lian P., Junjie S. The research of fuzzy nerve network control system on steel rolling heating furnace, implementation of steel rolling heating furnace adopting fuzzy nerve network control system. International Conference on Electrical and Control Engineering. 2010. pp. 2407–2410.
14. German М. L., Korneev S. L., Fayn I. V. Determination of thermal stresses during heating of steel billets using the finite element method. Metallurgy: republican interdepartmental collection of scientific papers. Minsk : Vysheyshaya shkola, 2005. Iss. 29. pp. 59–67.
15. Miranda S., Ubertini F. On the consistency of finite element. Computer Methods in Applied Mechanics and Engineering. 2001. Vol. 190. No. 18–19. pp. 2411–2427.
16. Cannarozzi А., Ubertini F. A mixed variational method for linear coupled thermoelastic analysis. International Journal of Solids and Structures. 2001. Vol. 38. No. 4. pp. 717–739.
17. Bathe K.-J. The inf-sup condition and its evaluation for mixed finite element methods. Computers & Structures. 2001. Vol. 79. No. 2. pp. 243–252.
18. Arnold D. N. Mixed finite element methods for elliptic problems. Computer Methods in Applied Mechanics and Engineering. 1990. Vol. 82. No. 1–3. pp. 281–300.
19. Kryuchkov О. B., Gabelchenko N. I., Malenko P. I., Saranin L. G. Usage of MathConnex mathematical package for thermotechnical calculation of heating furnaces. Chernye Metally. 2019. No. 12. pp. 52–60.
20. Kryuchkov О. B., Volchkov V. М., Krokhalev А. V. Modeling and thermotechnical calculations of processes in heating and thermal furnaces: tutorial. Part 2: The use of computer technology to calculate the heating time of metal articles. Volgograd : VolgGTU, 2017. 184 p.
21. Kryuchkov О. B., Krokhalev А. V., Belov А. А., Malenko P. I. Influence of the location of billets in chamber furnaces on time of their heating and the temperature drop over the section at cold and hot charging. Chernye Metally. 2021. No. 6. pp. 20–26.
22. Spivak E. I. Methods for accelerated calculation of heating furnaces. Moscow : Metallurgiya, 1988. 141 p.
23. Gubinskiy V. I., Minaev А. N., Goncharov Yu. V. Reduction of scale formation in the production of rolled products. Kiev : Tekhnika, 1981. 135 p.
24. Spivak E. I. Prediction of waste and decarburization during heating before rolling. Metallurg. 1984. No. 2. pp. 28, 29.
25. Oxidation and decarburization of steel. Edited by А. I. Vashchenko. Moscow : Metallurgiya, 1972. 336 p.
26. Krivandin V. А., Markov B. L. Metallurgical furnaces. Moscow : Metallurgiya, 1977. 464 p.
27. Mastryukov B. S. Theory, design and calculations of metallurgical furnaces. In 2 volumes. Vol. 2. Calculations of metallurgical furnaces. Moscow : Metallurgiya, 1986. 376 p.
28. Metallurgical heat engineering: textbook for students of metallurgical universities. Vol. 1: Theoretical basis. Edited by V. А. Krivandin. Moscow : Metallurgiya, 1986. 422 p.
29. Metallurgical heat engineering: textbook for students of metallurgical universities. Vol. 2: Design and operation of furnaces. Edited by V. А. Krivandin. Moscow : Metallurgiya, 1986. 590 p.
30. Kryuchkov О. B., Pegisheva S. А. Modeling and heat engineering calculations of processes in heating and thermal furnaces: textbook. Part 1: Calculation of the heating time of metal articles and internal dimensions of the furnace. Volgograd : VolgGTU, 2017. 240 p.
31. Krokhalev А. V., Kosova Е. А. Statistical methods and organization of experiment in metallurgy: textbook. Volgograd : VolgGTU, 2019. 80 p.