Lipetsk State Technical University (Lipetsk, Russia):

S. M. Belsky, Dr. Eng., Prof., Metal Forming Dept., e-mail: Belsky-55@yandex.ru
I. I. Shopin, Cand. Eng., Associate Prof., Metal Forming Dept.

Reducing the specific consumption of raw materials and materials in rolling shops is always an urgent task. Therefore, it is also important to improve the mathematical apparatus, which is a tool for optimizing technology in rolling shops. Most of the time, the metal in the rolling mills is coiled. Moreover, the coil is a complex object. The coil shape is maintained due to non-linear contact stresses distributed over the thickness and width, arising during the winding process. At the same time, the processes taking place in the metal do not stop with its winding into coil. First, stress relaxation occurs and the strip is deformed due to the creep effect. This is most important for cooling hot rolled coils and processing in bell furnaces due to the high temperature. In coils in a cold state, the processes of shaping do not proceed, but the roll may lose stability. This can lead to defects in the shape of the roll such as “birdie” or “settled coil”. Considering the above, modeling the stress-strain state of a coil is an urgent task. This article presents a mathematical model of the stress-strain state of the coil, taking into account the combined effect of non-flatness, roughness and gage thickness variation of the strip. The influence of the nonflatness of the coiled strip on the stress-strain state of the coil is considered in detail. The characteristic distribution of radial and tangential stresses in the roll after removing the roll from the drum is shown for various variants of the initial non-flatness. Taking into account the non-planarity in the mathematical model of the stress-strain state of the coil provides important advantages. First, to improve the accuracy of mathematical models for changing the shape of a strip in a roll. Secondly, to determine the critical values of the non-flatness of the strip, leading to the loss of stability of the coil.

1. Kolikov А. P., Romantsev B. А. Theory of metal forming. Moscow: MISiS, 2015. 451 p.
2. Ginzburg V. B. Metallurgical design of flat rolled steels. New York: Marcel Dekker, 2005. 710 p.
3. Roberts W. L. Cold rolling of steel. New York: Marcel Dekker, 1978. 799 p.
4. Shopin I. I., Belsky S. М. Layered model of the stress-strain state of a coil on a coiler. Proizvodstvo prokata. 2016. No. 8. pp. 13–17.
5. Shopin I. I., Belsky S. М. Influence of strip roughness on the stress-strain state of the coil. Proizvodstvo prokata. 2016. No. 10. pp. 3–7.
6. Shatalov R. L. Management of quality indicators and deformability of strips during rolling. Stal. 2004. No. 9. pp. 31–34.
7. Maksimov Е. А., Shatalov R. L., Boskhamdzhiev N. Sh. Production of flatbed strips by rolling. Moscow: Teplotekhnik, 2008. 336 p.
8. Shinkin V. N. Springback coefficient of round steel beam under elastoplastic torsion. CIS Iron and Steel Review. 2018. Vol. 15. pp. 23–27.
9. Shinkin V. N. Simple analytical dependence of elastic modulus on high temperatures for some steels and alloys. CIS Iron and Steel Review. 2018. Vol. 15. pp. 32–38.
10. Maksimov Е. А., Shatalov R. L., Litvinova N. N. Study of the pulling force of galvanized strips on a straightening machine of a continuous hot-dip galvanizing unit. Metallurg. 2014. No. 5. pp. 78–84.
11. Shatalov R. L., Genkin А. L. Management of a sheet-rolling technological complex, ensuring cost minimization. Metallurg. 2008. No. 9. pp. 31–34.
12. Muhin U., Belskij S., Koynov T. Study of the influence between the strength of antibending of working rolls on the widening during hot rolling of thin sheet metal. Frattura ed Integrita Strutturale. 2016. Vol. 10. No. 37. pp. 318–324.
13. Belsky S. M., Shopin I. I. Parametric model of the stress-strain state of the coil on the coiler. Izvestiya vuzov. Chernaya metallurgiya. 2017. Vol. 60. No. 11. pp. 925–931.
14. Shatalov R. L. Ensuring the stability of the strip rolling process. Proizvodstvo prokata. 2004. No. 9. pp. 27–31.
15. Shatalov R. L., Maksimov Е. А., Lukash А. S. Stability of flat strip taking into account elasticplastic bending by metal thickness in thin sheet rolling. Chernye Metally. 2011. No. 10. pp. 9–13.
16. Shinkin V. N. Preliminary straightening of steel strip. Chernye Metally. 2018. No. 5. pp. 34–40.
17. Shinkin V. N. Direct and inverse non-linear approximation of hardening zone of steel. Chernye Metally. 2019. No. 3. pp. 32–37.
18. Banabic D. Multiscale modeling in sheet metal forming. Romania: Springer, 2016. 405 p.
19. Hu P., Ma N., Liu L.-Z., Zhu Y.-G. Theories, methods and numerical technology of sheet metal cold and hot forming: Analysis, simulation and engineering applications. London: Springer, 2013. 210 p.
20. Shopin I. I. Study of the shape change of a hot-rolled steel strip during coiling to predict the flatness of a strip in a cold state: thesis of inauguration of Dissertation … of Candidate of Engineering Sciences. Moscow: Baikov Institute of Metallurgy and Materials Science, RAS, 2018. 238 p.
21. Belsky S. M., Shchedrin I. N., Shopin I. I. Solving the problem of instability of polymer coated steel strip coils. Proizvodstvo prokata. 2018. No. 7. pp. 5–8.
22. Romantsev B. А., Goncharuk А. V., Vavilkin N. М. et. al. Metal Forming. Moscow: MISiS, 2008. 960 p.
23. Kolikov A. P., Taupek I. M. Simulation of continuous roll forming process for producing welded pipes of small and medium diameters. Metallurgist. 2018. Vol. 61. No. 9–10. pp. 839–843.
24. Zhigulev G. P., Skripalenko M. N., Fadeev V. A., Skripalenko M. M. Modeling of deformation zone during plate stock molding in three-roll plate bending machine. Metallurgist. 2020. Vol. 64. No. 3–4. pp. 348–355.
25. Shinkin V. N. Elastoplastic flexure of round steel beams. 2. Residual stress. Steel in Translation. 2018. Vol. 48. No. 11. pp. 718–723.
26. Shinkin V. N. Elastoplastic flexure of round steel beams. 1. Springback coefficient. Steel in Translation. 2018. Vol. 48. No. 3. pp. 149–153.
27. Ashikhmin G. V., Iroshnikov S. А. Forming the profile of the roll generatrix when winding the strip. Proizvodstvo prokata. 2002. No. 9. pp. 14–17.
28. Ashikhmin G. V., Iroshnikov S. А. The relationship between the distribution of longitudinal stresses along the strip width in the roll and the profile of its generatrix. Proizvodstvo prokata. 2002. No.10. pp. 16–22.
29. Mazur V. L. Production of sheet with a high quality surface. Kiev: Tekhnika, 1982. 166 p.
30. Hu J., Marciniak Z., Duncan J. Mechanics of sheet metal forming. London: Butterworth-Heinemann, 2002. 211 p.