Moscow Technical University of Communications and Informatics (Moscow, Russia)

V. N. Shinkin, Dr. Phys.-Math., Prof., Dept. of Physics¹, shinkin-korolev@yandex.ru

In modern practice, two main technological schemes for the production of pipes are used, differing in the stage of bending the edges: the JCOE scheme of the German company SMS Meer (edge bending is performed before forming the main part of the workpiece on presses; the process is step-by-step and symmetrical on both sides, which ensures high accuracy of the edge geometry) and the scheme with three-roll rollers from the Swiss company Haeusler (the edges are bent after rolling the sheet; this is necessary to eliminate non-deformable flat sections of the sheet (slots); the specialized roller edge bending machine is used for this operation). The main parameters that are taken into account in the physic-mechanical process of edge bending are the radius of curvature of the neutral plane, the spring coefficient (which takes into account the elastic partial restoration of the shape of the sheet after removing the load) and the resistance to deformation. The following technological equipment is used for bending edges: edge bending presses and three-roll rollers. Edge bending presses are characterized by the hydraulic drive, the step-by-step principle of operation, symmetrical edge deformation and the ability to adjust the bending radius. In the three-roll rollers, the sheet bends between three rolls. The key technological parameters of bending the edge of the sheet include: the angle of bending the edges (set by the pipe design); the length of the bent edge and the bending force (depends on the thickness of the sheet, Young’s modulus, yield strength and strength of steel). Process features: the edges can be bent in several steps along the entire length of the sheet simultaneously from two sides with the profiled tool; when using presses, the size of the flat sections does not exceed 1.0 – 1.5 sheet metal wall thickness, which ensures high bending quality; the radius of the edge zone is critically important: its incorrect choice can lead to deviations from the theoretical circumference (one of the main geometric defects in pipe production). Optimization of the bending process of the longitudinal edge of the steel sheet makes it possible to increase the tightness of welds, reduce energy consumption and increase the service life of pipes during operation. In this paper, the new mathematical model is constructed for calculating the bending of the edges of a steel sheet on the flanging press with a profile of the contact surface of the matrix: the Archimedes arithmetic spiral.

1. Shinkin V. N. Continuum mechanics for metallurgists. Moscow: MISiS, 2014. 628 p.
2. Shinkin V. N. Bending edges of steel sheet on the press with a second-order die surface (an elliptical cylinder). Chernye metally. 2026. No. 3. рр. 45-49.
3. Zhang Z. Modeling and simulation for cross-sectional ovalization of thin-walled tubes in continuous rotary straightening process. International Journal of Mechanical Sciences. 2019. Vol. 153. No. 2-3. pp. 83-102.
4. Permiakov I. L. Methods of increasing the geometric accuracy of welded seams of largediameter straight-seam pipes. Metallurgist. 2025. Vol. 69. No. 8. pp. 1192-1197.
5. Hwang Y. M., Wang G. Y., Tsui H. S. R. Roller plunge schedule design and finite element analysis on roller flattening of metal sheets. The International Journal of Advanced Manufacturing Technology. 2025. Vol. 141. pp. 2863-2875.
6. Belskiy S. M., Samsonov S. M. On the measure of nonflatness of rolled strips and sheets. Metallurgist. 2025. Vol. 69. No. 2. pp. 212-217.
7. Kuo S. K., Ou Y. L., Wang D. A. An analytical model for stress and curvature prediction of a strip leveling process. Metals. 2022. Vol. 12. Article ID 757.
8. Wang X., Zhu X., Han P. Calculation model of residual stress during quenching and straightening of high-strength plate. Advanced Engineering Sciences. 2021. Vol. 53. No. 3. pp. 166-172.
9. Sun J. L., Li K., Sun M. Q., Lu X. H., Peng Y. Longitudinal profiled plate straightening process based on curvature integral method. Journal of Iron Steel Research International. 2021. Vol. 28. pp. 291-302.
10. Belsky S. M., Usachev M. A., Samsonov S. M. Cubic parabola coefficients for CVC machine roll profiling. Steel in Translation. 2026. Vol. 56. No. 3. pp. 296-300.
11. Shinkin V. N. Analytical dependence of relative elongations on normal stresses at elasticplastic stretching of bimetallic beam with transverse connection of metals. CIS Iron and Steel Review. 2026. Vol. 31. pp. 61-71.
12. Budnikov A. S., Zhigulev G. P., Fadeev V. A., Sidorova T. Y. Calculation of kinematic characteristics of metal forming processes in lagrangian coordinates. CIS Iron and Steel Review. 2026. Vol. 31. pp. 35-39.
13. Polunin D.S., Belskii S.M. Opportunities for the development of high-strength steels in cold rolling mills. Steel in Translation. 2025. Vol. 55. No. 5. pp. 525-529.
14. Feoktistov S. I., Andrianov I. K. Analytical description of the Bauschinger effect using experimental data and the generalized Masing principle. Materials Physics and Mechanics. 2024. Vol. 52. No. 1. pp. 49-59.
15. Gui H., Li Q., Huang Q. The influence of Bauschinger effect in straightening process. Mathematical Problems in Engineering. 2015. Article ID 612840.