Cherepovets State University (Cherepovets, Russia)

D. L. Shalaevsky, Cand. Eng., Associate Prof., Dept. of Metallurgy, Mechanical Engineering and Technological Equipment, shal-dmitrij@yandex.ru

Uneven elastic deformations of the work roll barrel surfaces in a quarto rolling mill stand are one of the main factors determining the transverse profile of the finished rolled steel strip and its flatness characteristics. Known factors that determine the cross-section of the rolled product include work roll deflection due to rolling forces and forces of additional bending systems, uneven thermal expansion, and work roll barrel surface wear. The most significant factor contributing most to the formation of the rolled product’s transverse profile is the elastic deformation of the roll system. The most common methods for calculating roll deflection, which are used in roll barrel contouring, are based on the Castigliano theorem; this theorem defines the required parameter as a partial derivative of the potential deformation energy due to this deformation presented by contact pressure in the deformation area, counterbending forces, or additional bending forces. It should be also noted that most known methods do not take into account the uneven distribution of contact stresses in the deformation area, caused, among other things, by transverse thickness deviation in the rolled product. To account for the latter noted parameter, this study proposes an approach to calculating the elastic deformations of the working rolls of a quarto rolling mill using the initial parameter method, taking into account all applicable loads. The results presented in the study demonstrate that the transverse profile of rolled semiproduct has very little effect on the cross-section profile of the finished rolled product. It is concluded that there is no need to consider the cross-section profile of the rolled steel at the rolling stand entrance when evaluating the cross-section profile of the rolled steel strip. The paper also presents the results of calculating the cross-section convexity of the rolled steel strip and compares the obtained characteristics with their calculated values. The subject of this study is the cross-section convexity of the rolled steel strip. The proposed method allows the reliable calculation of the cross-section profile of the finished rolled steel strip. Its accuracy is no lower than that of known approaches, but the calculation complexity is significantly lower. The objective of this study is to develop a reliable and least labor-intensive method for calculating the cross-section convexity of flat rolled steel. The results can be used in the development of roll contouring for sheet rolling mills.

1. Korolev A. A. mechanical equipment of rolling shops in ferrous and nonferrous metallurgy. M. : Metallurgiya. 1976. 544 p.
2. Budakva A. A., Konovalov K. N., Tkalich K. N. et al. Roll contouring at sheet rolling mills. Kiev : Tekhnika. 1986. 190 p.
3. Murgul V., Popovic Z. (eds.). Advances in Intelligent Systems and Computing. International Scientific Conference “Energy Management of Municipal Transportation Facilities and Transport” EMMFT 2017. 2017. 692. DOI: 10.1007/978-3-319-70 987-1_115.
4. Pimenov V. A., Belsky S. M., Kuznetsova E. V., Shkarin A. N. Mathematical model for cross-section profile identification of hot-rolled strips and distribution of elongations along width of cold-rolled strips. Message 1. Proizvodstvo prokata. 2018. No. 1. pp. 11–15.
5. Shalaevsky D. L. Prediction of steel strip flatness on the base of elongation coefficients along its width in rolling. Chernaya metallurgiya. Bulleten nauchno-tekhnicheskoy i ekonomichesloy informatsii. 2024. Vol. 80. No. 10. pp. 20–27.
6. Rumyantsev M. I., Kolybanov A. N. Setting the problem of simplification of deformation calculations for rolling rolls and strip profile during rolling in a quarto stand. Kalibrovochnoe byuro. 2018. No. 12. pp. 18–21.
7. Garber E. A., Khlopotin M. V., Trayno A. I., Popov E. S., Savinykh A. F. Simulation of thermal conditions for wide hot strip mill rolls to determine efficient procedures of their cooling. Metally. 2009. No. 3. pp. 34–37.
8. Belsky S. M., Mazur I. P., Astakhov A. A. Simplified technique for calculation of thermal contouring of working rolls in a hot rolling mill. Proizvodstvo prokata. 2018. No. 2. pp. 3–6.
9. Antonyuk V. V., Fedin A. G., Mustafin V. A., Dema R. R., Platov S. I., Amirov R. N., Koldin A. V., Kharchenko M. V. Experience of adjusting and managing a thermal state of working rolls in the wide hot strip rolling mill 2000 at Magnitogorsk Iron and Steel Works. Proceedings of the XI International Congress of Rollermen. 2017. Vol. 2. pp. 84–87.
10. Garber E. A., Mishnev P. A., Shalaevsky D. L., Paligin R. B., Mikheeva I. A., Bolobanova N. L. New methods of simulation and decrease of unflatness of steel strips in hot rolling at wide strip mills. Materials of the International scientific seminar “Scientific and technical progress in metallurgy 2013”. 2014. pp. 70–82.
11. Hamraoui M. Thermal behaviour of rollers during the rolling process. Applied Thermal Engineering. 2009. Vol. 29. No. 11–12. pp. 2386–2390.
12. Shalaevsky D. L. Study of a thermal procedure for working rolls at hot rolling mill in order to increase calculation accuracy for surface temperatures of their barrels. Izvestiya vuzov. Chernaya metallurgiya. 2023. No. 3. pp. 283–289.
13. Garber E. A., Shalaevsky D. L., Mishnev P. A. et al. Study, simulation and decrease of unflatness in hot rolling of wide steel strips. M. : Teplotekhnik. 2016. 112 p.
14. 14. Pimenov V. A., Kovalev D. A., Dagman M. A., Mazur I. P. Development of mathematical models for formation of the cross profile of strips during hot rolling, taking into account the wear of rolls. Chernye metally. 2021. No. 10. pp. 13–19.
15. Shatalov R. L., Kharakterov N. V., Karpov S. A. Regression model for wear of rolls in tot rolling of strips made of complex alloyed copper alloys. Proizvodstvo prokata. 2006. No. 2. pp. 42–46.
16. Kukhta Yu. B., Logunova O. S., Egorova L. G., Torchinsky V. E., Belyavsky A. B., Romanov P. Yu. Modelling the barrel body wear of the backup roll: mathematical model and software implementation. The Int. J. of Advanced Manufacturing Technology. 2018. Vol. 97. pp. 1363–1370. DOI: 10.1007/s00170-018-2058-y
17. Bátorfi J. G., Chakravarty P., Sidor J. Investigation of the wear of rolls in asymmetric rolling. Engineering and IT Solutions. 2021. No. 2. pp. 14-20. DOI: 10.37775/EIS.2021.2.2.
18. Labiapari W. da S., de Alcântara C. M., Costa H. L., De Mello J. D. B. Wear debris generation during cold rolling of stainless steels. J. of Mater. Proc. Technol. 2015. Vol. 223. pp. 164–170.
19. Pesin A., Pustovoytov D., Shveyova T., Sverdlik M. Finite Element Modeling of Roll Wear during Cold Asymmetric Sheet Rolling of Aluminum Alloy 5083. MATEC Web of Conf. 2015. Vol. 26. DOI: 10.1051/matecconf/20152601010
20. Chekmarev A. P., Mashkovtsev R. A. Wear of rolling rolls. M. : Metallurgizdat. 1955. 148 p.
21. Borisov V. I., Golubyev V. V. Study of wear of sheet rolling rolls in quarto rolling systems at hot strip mills. Vestnik MGTU im N. E. Baumana. Seriya “Mashinostroenie”. 2005. No. 4. pp. 49–62.
22. Volegov V. P., Freidenzon M. E., Zhdanov A. A. Contouring of rolling rolls in quarto stands at continuous hot rolling mills. Stal. 1966. No. 6. pp. 523–525.
23. Chelyustkin A. B. et al. Determination of relationship between wear of rolls and rolling conditions. Izvestiya vuzov. Metallurgiya. 1970. No. 3. pp. 92–95.
24. Shalaevsky D. L. Determination of wear of barrels’ surfaces of rolling rolls in continuous finishing group of stands at wide hot strip rolling mill. Chernaya metallurgiya. Bulleten nauchno-tekhnicheskoy i ekonomichesloy informatsii. 2022. Vol. 78. No. 12. pp. 1054–1059.
25. Garber E. A. Cold rolling mills (theory, equipment, technology). M. : Chermetinformatsiya. 2004. 416 p.
26. Shalaevsky D. L. Evaluation of the type and amplitude of the flatness defect of a hot-rolled steel strip produced on a continuous mill. Metallurgist. 2024. Vol. 67. pp. 1604–1613.
27. Shalaevsky D. L. Study of the effect of cross-section profile on flatness of steel rolled product. Stal. 2025. No. 11. pp. 22–25.