North Caucasus Mining and Metallurgical Institute (State Technological University) (Vladikavkaz, Russia):

A. M. Belenkiy, Dr. Eng., Prof., Dept. of Metallurgy of Non-ferrous Metals and Automation of Metallurgical Processes, e-mail: belenky.bam@yandex.ru

National University of Science and Technology “MISiS” (Moscow, Russia):
M. Zh. Bogatova, Graduate student, Dept. of Energy Efficient and Resource-Saving Industrial Technologies, e-mail: ma95bers@gmail.com
S. I. Chibizova, Cand. Eng., Associate Prof., Dept. of Energy Efficient and Resource-Saving Industrial Technologies, e-mail: s_kalimulina@mail.ru

The article proposes a method for improving the thermal performance of walking beam reheating furnaces using a statistical mathematical model of metal heating. The main part of the study refers to the creation of a metal heating model based on a comprehensive analysis of 15 industrial experiments carried out on the Russian continuous furnaces. The first stage of statistical model creation consists of factors’ selection, construction of regression model, correlation analysis and assessment of the variables’ significance, adjustment of factors and obtaining regression equations. As a result, a quasi-dynamic statistical mathematical model of a five-zone walking beam reheating furnace has been created and adapted, that actually makes it possible to trace the heating process in dynamics. The adaptation of the statistical model and error calculation has been carried out using the results of industrial experiments on the investigated furnaces of mills 2000 and 5000. The article contains graphs comparing real temperatures and temperatures calculated on the basis of mathematical and statistical models for one of the experiments. The second stage of quasidynamic statistical model creation has shown that temperature of the combustion products of neighboring zones is a significant factor, that enhances calculation accuracy by 1-3%. The main conclusions are formulated based on the results of the research done. For the first time in metallurgical practice, a quasi-dynamic statistical model has been developed and adapted which describes the process of metal heating in a walking beam reheating furnaces. Since the regression function is defined, interpreted and justified, and the assessment of the accuracy of the regression analysis meets the requirements, it can be assumed that the model and predicted values have sufficient reliability.

1. Belenkiy А. М., Bursin А. N., Mordovkin D. S., Ulanovskiy А. А., Chibizova S. I. Tasks of improvement of thermal work and design of heating furnaces of hot rolling mills. Works of the XI Rollers Congress: collection of works. Vol. 1. Magnitogorsk, 2017. pp. 29–35.
2. Orelkina D. I., Petelin А. L., Polulyakh L. А., Podgorodetskiy G. S. Model for calculating the concentration of secondary metallurgical emissions in the atmosphere. Izvestiya Vysshikh Uchebnykh Zavedeniy. Chernaya Metallurgiya. 2016. Vol. 59. No. 5. pp. 300–305.
3. Loshkarev N. B., Noskov V. А., Druzhinin G. М. Mathematical model of metal heating in a methodical walking beam furnace. Heat engineering and informatics in education, science and production: proceedings of the VII All-Russian scientific-practical conference of students, graduate students and young scientists. (TIM’2018) 17–18 May 2018, Ekaterinburg. pp. 223–228.
4. Antipkina М. Е., Krupennikov S. А., Levitskiy I. А. Determination of the optimal thickness of the heating furnace lining. Novye Ogneupory. 2019. No. 10. pp. 42–47.
5. Arutyunov V. А., Levitskiy I. А., Ibadullaev Т. B. Development of methods for mathematical modeling of thermophysical processes in industrial fuel furnaces. Metallurg. 2011. No. 1–2. pp. 33–37.
6. Chen Y. W., Chai T. Y. Modelling and prediction for steel billet temperature of heating furnace. International Journal of Advanced Mechatronic Systems. 2010. Vol. 2. No. 5–6. pp. 342–349.
7. Ginkul S. I., Biryukov A. B., Gnitiev P. A. Predictive Mathematical Model of the Process of Metal Heating in Walking-Beam Furnaces. Metallurgist. 2018. No. 62. pp. 15–21.
8. Tang G., Wu B., Bai D. Modeling of the slab heating process in a walking beam reheating furnace for process optimization. International Journal of Heat and Mass Transfer. 2017. No. 113 (10). pp. 1142–1151.
9. Logunova О. S., Agapitov Е. B., Barankova I. I., Andreev S. М., Chusavitina G. N. Mathematical models to study the bodies thermal state and control thermal processes. Elektrotekhnicheskie sistemy i kompleksy. 2019. No. 2 (43). pp. 25–34.
10. Han S. H., Chang D., Kim C. Y. A numerical analysis of slab heating characteristics in a walking beam type reheating furnace. International Journal of Heat and Mass Transfer. 2010. No. 53. pp. 3855–3861.
11. Wild D., Meurer T., Kugi A. Modelling and experimental model validation for a pusher-type reheating furnace. Mathematical and Computer Modelling of Dynamical Systems. 2009. Vol. 15. pp. 209–232.
12. Dozhdikov V. I., Ganul А. О., Mordovkin D. S. Optimization of operation of the energytechnological complex of heating metal before rolling. Stal. 2018. No. 2. pp. 69–71.
13. Belenkiy А. М., Dubinskiy М. Yu., Kalimulina S. I. The industrial experiment is the basis for conducting energy-saving policy in metallurgical heat engineering. Metallurg. 2010. No. 5. pp. 26–29.
14. Ulanovskiy А. А., Тааке М., Belenkiy А. М., Bursin А. N., Chibizova S. I. Using Phoenix TM autonomous automated system for monitoring temperature field of metal to be heated in metallurgical furnaces. Chernye Metally. 2019. No. 9. pp. 59–64.
15. Radchenko Yu. S. Fundamentals of statistical modeling: textbook for universities. Voronezh: IPTs VGU, 2010. 30 p.