Skip to main content

On Adequacy of Parameters of Strip Cross-Section Profile. Part 2. Local Thickenings and Thinnings


At present, the cross-section profile of the rolled strip is characterized by geometrical parameters such as wedging, convexity, difference of thickness, displacement of convexity, and edge wedging. Some of these parameters are redundant. The values of these parameters are calculated by known and generally accepted methods. However, some of the features of the cross-section profile of rolled strips, such as local thickenings/thinnings are calculated by unconventional methods. Practically every scientific school of rolling mill operators or rolling production specialists uses their own techniques, which often provide different results for the same cross-section profiles. The identification and calculation of the local thickenings/thinnings parameters of the cross-section profile of rolled strips consists in defining a so-called zero level, the excess/understatement of which is a sign of local thickening/thinning. The paper continues analyzing for the calculation of the parameters of the cross-section profile of rolled strips regarding local thickenings/thinnings for accuracy and adequacy. A new method based on statistical methods is proposed. The target function, the thickness distribution across the width of the rolled strip, is a symmetrical quadratic parabola. However, the actual distribution is always different from the target one for several reasons, such as ring wear of work rolls. In the first step of the proposed technique, strip thickness values dramatically different from the target distribution are eliminated as emissions by the Walter-Shewhart procedure (control charts). However, this procedure cannot be applied without excluding the nonlinear (parabolic) component of the measured cross-section profile and, therefore, applies to the first derivative of the function of the cross-section profile thickness distribution. To determine zero level, all of the thicknesses associated with these emissions are eliminated after calculating the upper and lower limits of the allowed values of the first derivative. The result of the repetitive process is zero level according to which the local thickening/thinning parameters are calculated.

This is a preview of subscription content, access via your institution.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.


  1. Ginzburg, V.B., Flat-Rolled Steel Processes: Advanced Technologies, Boca Raton, Fl.: CRC Press, 2009.

    Book  Google Scholar 

  2. Ginzburg, V.B., Metallurgical, Design of Flat Rolled Steels, Boca Raton, Fl., Marcel Dekker, 2005.

    Book  Google Scholar 

  3. Roberts, W.L., Cold Rolling of Steel, Marcel Dekker, 1978.

    Google Scholar 

  4. Bel’skii, S.M., Kotsar’ S.L., Polyakov, B.A., Calculation of rolling force distribution along the strip width and residual stresses in a strip by variational method, Izv. Vuzov. Chernaya Metallurg., 1990, no. 10, pp. 32–34.

  5. Bel’skii, S.M. and Shopin, I.I., Predictive mathematical model of strip breakage during cold rolling, Chern. Met., 2020, no. 3, pp. 18–23.

  6. Muhin, U., Belskij, S., Makarov, E., and Koynov, T., Simulation of accelerated strip cooling on the hot rolling mill run-out roller table, Frattura Integrita Strutturale, 2016, vol. 10, no. 37, pp. 305–311.

    Article  Google Scholar 

  7. Shinkin, V.N., The mathematical model of the thick steel sheet flattening on the twelve-roller sheet-straightening machine. Message 1. Curvature of sheet, CIS Iron Steel Rev., 2016, vol. 12, pp. 37–40.

    Article  Google Scholar 

  8. Hingole, R.S., Advances in Metal Forming: Expert System for Metal Forming, Springer Series in Materials Science, vol. 206, Berlin: Springer, 2015.

  9. Lim, Y., Venugopal, R., and Ulsoy, A.G., Process Control for Sheet-Metal Stamping: Process Modeling, Controller Design and Stop-Floor Implementation, Advances in Industrial Control, London: Springer, 2014.

  10. Advanced Methods in Materials Processing Defects, Predeleanu, M. and Gilormini, P., Eds., Studies in Applied Mechanics, vol. 45, Amsterdam: Elsevier, 1997.

  11. Wilko, C.E., Formability: A Review of Parameters and Processes that Control, Limit or Enhance the Formability of Sheet Metal, SpringerBriefs in Applied Sciences and Technology, Heidelberg: Springer, 2011.

  12. Shinkin, V.N., Simplified calculation of the bending torques of steel sheet and the roller reaction in a straightening machine, Steel Transl., 2017, vol. 47, pp. 639–644.

    Article  Google Scholar 

  13. Banabic, D., Multiscale Modeling in Sheet Metal Forming, ESAFORM Bookseries on Material Forming, Cham: Springer, 2016.

  14. Spokoiny, V. and Dickhaus, T., Basics of Modern Mathematical Statistics, Springer Texts in Statistics, Berlin: Springer, 2015.

  15. Hu, P., Ma, N., Liu, L.-Z., and Zhu, Y.-G., Theories, Methods and Numerical Technology of Sheet Metal Cold and Hot Forming: Analysis, Simulation and Engineering Applications. Springer Series in Advanced Manufacturing, London: Springer, 2013.

  16. Lenard, J.G., Metal Forming Science and Practice: A State-of-the-Art Volume in Honour of Professor J.A. Schey’s 80th Birthday, Elsevier, 2002, p. 378.

    Book  Google Scholar 

  17. Shinkin, V.N., Geometry of steel sheet in a seven-roller straightening machine, Steel Transl., 2016, vol. 46, pp. 776–780.

    Article  Google Scholar 

  18. Shinkin, V.N., Preliminary straightening of thick steel sheet in a seven-roller machine, Steel Transl., 2016, vol. 46, pp. 836–840.

    Article  Google Scholar 

  19. Shatalov, R., Maksimov, E., Koinov, T., and Babkin, A., Research of flatness defects forming at 20-hi steel strips rolling mill, J. Chem. Technol. Metall., 2017, vol. 52, no. 2, pp. 199–204.

    Google Scholar 

  20. Shatalov, R. and Aldunin, A., The development of mathematical models to improve the technology and the quality of copper alloys sheets, J. Chem. Technol. Metall., 2016, vol. 51, no. 2, pp. 242–244.

    CAS  Google Scholar 

  21. Shatalov, R. and Genkin, A., Sheet mill control in steel strip hot rolling, J. Chem. Technol. Metall., 2015, vol. 50, no. 6, pp. 624–628.

    CAS  Google Scholar 

  22. Vollersten, F., Micro Metal Forming, Lecture Notes in Production Engineering, Berlin: Springer, 2013.

  23. Shinkin, V.N., Arithmetical method of calculation of power parameters of 2N-rollwer straightening machine under flattening of steel sheet, CIS Iron Steel Rev., 2017, vol. 14, pp. 22–27.

    Article  Google Scholar 

  24. Khlopotin, M.V., Investigation of the thermal regime of rolls of wide-strip hot-rolling mills and its effect on the transverse profile of hot-rolled strips, Cand. Sci. (Eng.) Dissertation, Cherepovets: Cherepovets State Univ., 2010.

  25. Kuznetsova E.V., Shkarin A.N. Use of approximation methods for modeling the surface of hot rolled transverse profile, Sovremennye naucho-prakticheskie resheniya XXI veka (Modern Scientific and Practical Solutions of the 21st century), Voronezh, 2016, pp. 243–248.

  26. Pimenov, V.A., Bel’skii, S.M., and Shkarin, A.N., Increasing the approximation accuracy of cross-section profile shape of hot semi-finished rolled stock, Vestn. Lipetsk. Gos. Tekh. Univ., 2019, no. 1, pp. 70–73.

  27. Pimenov, V.A., Kuznetsova, E.V., and Shkarin, A.N., Structural identification of the model of hot rolled transverse profile, Aktual’nye napravleniya nauchnykh issledovanii XXI veka. Teoriya i praktika (Topical Directions of Scientific Studies of the 21st: Theory and Practice), 2016, vol. 4, no. 6, pp. 88–92.

  28. Levykina, A.G., Shkatov, V.V., and Mazur, I.P., Hot rolling strips at the casting and rolling unit during coil-to-coil and endless rolling modes, Procedia Manuf., 2019, vol. 37, pp. 472–477.

    Article  Google Scholar 

  29. GOST R (State Standard) ISO 7870-1–2011: Statistical methods. Control charts. Part 1. General guidelines, 2011.

  30. Rouaud, M., Probability, Statistics and Estimation: Propagation of Uncertainties in Experimental Measurement.

  31. GOST (State Standard) 50 779.42–99 Statistical methods. Shewhart control charts, 1999.

  32. Hastie, T., Tibshirani, R., Friedman, J., and Tibshirani, R., The Elements of Statistical Learning: Data Mining, Inference and Prediction, Springer Series in Statistics, New York: Springer, 2009.

Download references


The work was supported by the Russian Foundation for Basic Research, project no. 19-38-90 257.

Author information

Authors and Affiliations


Corresponding author

Correspondence to S. M. Bel’skii.

Additional information

Translated by S. Kuznetsov

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bel’skii, S.M., Shopin, I.I. & Shkarin, A.N. On Adequacy of Parameters of Strip Cross-Section Profile. Part 2. Local Thickenings and Thinnings. Steel Transl. 52, 76–80 (2022).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • thin sheet rolling
  • strip’s cross-section profile
  • local thickening
  • Walter–Shewhart procedure
  • predictive interval