Multi-roll levelling for wave defects of metal sheets based on the beam-membrane method

  • Guodong Yi
  • Yang Wang
  • Xiaojian LiuEmail author
  • Chao Wang


Wave defects are the main flatness defects in rolled metal sheets and typically must be eliminated via multi-roll levelling for further use. Convex work rolls are the key component of the levelling process. The effectiveness of the description of the work roll and its bending characteristics determines the efficiency and accuracy of the levelling numerical analysis, which is also the key problem to be solved in the current research. This paper proposes a finite element expression method for convex work rolls that is based on the beam-membrane method by using a beam element to express the mechanical characteristics of the work rolls and the membrane elements to express the contact characteristics between the work rolls and the metal sheet. An effective multi-roll wave levelling model was established based on the beam-membrane method, and the influence of the bending parameters of the work rolls on the wave levelling performance was analysed. The results demonstrate that work rolls that have a parabolic bending curve can substantially reduce, but not eliminate, residual waves. The residual stress and curvature simulation have been discussed, and the comparison shows that the proposed method is closer to the real experiment result.


Roll levelling Metal sheet Wave defects Beam-membrane method Bending parameters 


Funding information

This work is supported by the National Key R&D Program of China (2018YFB1701601) and the National Natural Science Foundation of China (51875515) and the Natural Science Foundation of Zhejiang Province (LY18E050001).


  1. 1.
    Fischer FD, Rammerstorfer FG, Friedl N, Wieser W (2000) Buckling phenomena related to rolling and levelling of sheet metal. Int J Mech Sci 42(10):1887–1910. CrossRefzbMATHGoogle Scholar
  2. 2.
    Abdelkhalek S, Montmitonnet P, Legrand N, Buessler P (2008) Manifested flatness predictions in thin strip cold rolling. Int J Mater Form 1(1):339–342. CrossRefGoogle Scholar
  3. 3.
    Nakhoul R, Montmitonnet P, Abdelkhalek S (2012) Flatness defect in thin strip cold rolling and the friction impact on it. Trans N Am Manuf Res Inst 40:277–286Google Scholar
  4. 4.
    Nakhoul R, Montmitonnet P, Legrand N (2015) Manifested flatness defect prediction in cold rolling of thin strips. Int J Mater Form 8(2):283–292. CrossRefGoogle Scholar
  5. 5.
    Lopez C, Garcia DF, Usamentiaga R, Gonzalez D, Gonzalez JA (2005) Real time system for flatness inspection of steel strips. Proc Soc Photo-Opt Inst 5679:228–238. CrossRefGoogle Scholar
  6. 6.
    Uppgård T (2008) Estimation of post-rolling effects in cold rolled aluminium strips. Licentiate thesis, Örebro University Studies in Technology Series.Google Scholar
  7. 7.
    Nakhoul R, Montmitonnet P, Potier-Ferry M (2015) Multi-scale method for modeling thin sheet buckling under residual stresses in the context of strip rolling. Int J Solids Struct 66:62–76. CrossRefGoogle Scholar
  8. 8.
    Doege E, Menz R, Huinink S (2002) Analysis of the levelling process based upon an analytic forming model. CIRP Ann-Manuf Technol 51(1):191–194. CrossRefGoogle Scholar
  9. 9.
    Silvestre E, Garcia D, Galdos L, de Argandona ES, Mendiguren J (2016) Roll levelling semi-analytical model for process optimization. J Phys Conf Ser 734(3):32–34. CrossRefGoogle Scholar
  10. 10.
    Chen W-H, Liu J, Cui Z-S, Wang Y-J, Wang Y-R (2015) A 2.5-dimensional analytical model of cold leveling for plates with transverse wave defects. J Iron Steel Res Int 22(8):664–671. CrossRefGoogle Scholar
  11. 11.
    Grüber M, Hirt G (2017) A strategy for the controlled setting of flatness and residual stress distribution in sheet metals via roller levelling. Procedia Eng 207:1332–1337. CrossRefGoogle Scholar
  12. 12.
    Behrens BA, El Nadi T, Krimm R (2011) Development of an analytical 3D-simulation model of the levelling process. J Mater Process Technol 211(6):1060–1068. CrossRefGoogle Scholar
  13. 13.
    Baumgart M, Steinboeck A, Kugi A, Raffin-Peyloz G, Irastorza L, Kiefer T (2012) Optimal active deflection compensation of a hot leveler. IFAC Proc Vol 45(23):30–35. CrossRefGoogle Scholar
  14. 14.
    Liu Z-F, Wang Y-Q, Ou H-G, Yan X-C, Luo Y-X (2014) An analytical leveling model of curvature and residual stress simulation for H-beams. J Constr Steel Res 102:13–23. CrossRefGoogle Scholar
  15. 15.
    Brauneis R, Baumgart M, Steinboeck A, Kugi A, Jochum M (2017) Deflection model of a multi-actuator gap leveler. IFAC Papersonline 50(1):11295–11300. CrossRefGoogle Scholar
  16. 16.
    Brauneis R, Steinboeck A, Jochum M, Kugi A (2018) A robust real-time model for plate leveling. IFAC Papersonline 51(2):61–66. CrossRefGoogle Scholar
  17. 17.
    Yu G, Zhai R, Zhao J, Ma R (2017) Theoretical analysis and numerical simulation on the process mechanism of two-roller straightening. Int J Adv Manuf Technol 94(9-12):4011–4021. CrossRefGoogle Scholar
  18. 18.
    Yan Y, Wang H-B, Li Q, Qian B, Mpofu K (2014) Simulation and experimental verification of flexible roll forming of steel sheets. Int J Adv Manuf Technol 72(1-4):209–220. CrossRefGoogle Scholar
  19. 19.
    Feng X, Montmitonnet P, Yang Q, He A, Wang X (2017) An advanced 3D mathematical model for a 6-high tandem cold rolling process. Procedia Eng 207:1379–1384. CrossRefGoogle Scholar
  20. 20.
    Tsang K-S, Ion W, Blackwell P, English M (2017) Validation of a finite element model of the cold roll forming process on the basis of 3D geometric accuracy. Procedia Eng 207:1278–1283. CrossRefGoogle Scholar
  21. 21.
    Laugwitz M, Seuren S, Jochum M, Hojda S, Lohmar J, Hirt G (2017) Development of levelling strategies for heavy plates via controlled FE models. Procedia Eng 207:1349–1354. CrossRefGoogle Scholar
  22. 22.
    Woo Y-Y, Han S-W, Hwang T-W, Park J-Y, Moon Y-H (2018) Characterization of the longitudinal bow during flexible roll forming of steel sheets. J Mater Process Technol 252:782–794. CrossRefGoogle Scholar
  23. 23.
    Grüber M, Hirt G (2018) Investigation of correlation between material properties, process parameters and residual stresses in roller levelling. Procedia Manuf 15:844–851. CrossRefGoogle Scholar
  24. 24.
    Weiss M, Rolfe B, Hodgson PD, Yang C-H (2012) Effect of residual stress on the bending of aluminium. J Mater Process Technol 212(4):877–883. CrossRefGoogle Scholar
  25. 25.
    Weiss M, Abeyrathna B, Rolfe B, Abee A, Wolfkamp H (2017) Effect of coil set on shape defects in roll forming steel strip. J Manuf Process 25:8–15. CrossRefGoogle Scholar
  26. 26.
    Mathieu N, Potier-Ferry M, Zahrouni H (2017) Reduction of flatness defects in thin metal sheets by a pure tension leveler. Int J Mech Sci 122:267–276. CrossRefGoogle Scholar
  27. 27.
    Traub T, Chen X, Groche P (2017) Experimental and numerical investigation of the bending zone in roll forming. Int J Mech Sci 131:956–970. CrossRefGoogle Scholar
  28. 28.
    Dratz B, Nalewajk V, Bikard J, Chastel Y (2009) Testing and modelling the behaviour of steel sheets for roll levelling applications. Int J Mater Form 2(1):519–522. CrossRefGoogle Scholar
  29. 29.
    Silvestre E, de Argandona ES, Galdos L, Mendiguren J (2014) Testing and modeling of roll levelling process. Key Eng Mater 611-612:1753–1762. CrossRefGoogle Scholar
  30. 30.
    Su C-J, Yang L-Y, Lou S-M, Cao G-H, Yuan F-R, Wang Q (2018) Optimized bending angle distribution function of contour plate roll forming. Int J Adv Manuf Technol 97(5–8):1787–1799. CrossRefGoogle Scholar
  31. 31.
    Lee C-W, Yang D-Y, Kang D-W, Lee T-W (2014) Study on the levelling process of the current collector for the molten carbonate fuel cell based on curvature integration method. Int J Hydrog Energy 39(12):6714–6728. CrossRefGoogle Scholar
  32. 32.
    Weiss M, Abeyrathna B, Pereira M (2018) Roll formability of aluminium foam sandwich panels. Int J Adv Manuf Technol 97(1-4):953–965. CrossRefGoogle Scholar
  33. 33.
    Abdelkhalek S, Montmitonnet P, Legrand N, Buessler P (2011) Coupled approach for flatness prediction in cold rolling of thin strip. Int J Mech Sci 53(9):661–675. CrossRefGoogle Scholar
  34. 34.
    Abdelkhalek S, Montmitonnet P, Potier-Ferry M, Zahrouni H, Legrand N, Buessler P (2010) Strip flatness modelling including buckling phenomena during thin strip cold rolling. Ironmak Steelmak 37(4):290–297. CrossRefGoogle Scholar
  35. 35.
    Kadota K, Maeda R (1993) A model of analysis of curvature in levelling process-numeric study of roller levelling process. J Jpn Soc Technol Plast 34:481–486Google Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Guodong Yi
    • 1
  • Yang Wang
    • 1
  • Xiaojian Liu
    • 1
    • 2
    Email author
  • Chao Wang
    • 1
  1. 1.School of Mechanical EngineeringZhejiang UniversityHangzhouChina
  2. 2.Ningbo Research InstituteZhejiang UniversityNingboChina

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