Asymmetric hydrodynamic roll gap model and its experimental validation

  • Martin MüllerEmail author
  • Andreas Steinboeck
  • Katharina Prinz
  • Andreas Ettl
  • Andreas Kugi
  • Kurt Etzelsdorfer
  • Stefan Fuchshumer
  • Hannes Seyrkammer
Open Access


In tandem hot strip rolling mills, different friction between the rolls and the strip material on the upper and lower strip surface can occur due to asymmetric surface temperatures or different conditions of oil lubrication. To capture these effects, this paper presents a hydrodynamic roll gap model with asymmetric friction. Based on similarities between the rolled material and viscous fluids, fluid mechanics theory is used to derive this model. Due to the nature of this model, the influence of the rolling speed is inherently taken into account, which allows an accurate prediction of the rolling force and the forward slip. As an analytic solution for the hydrodynamic roll gap model is available, it is well suited for online applications in rolling plants. For validation of the proposed model, an experiment with asymmetric work roll roughness was performed. A specimen of steel strip with copper pins inserted was repeatedly rolled to visualize the material flow inside the roll gap for multiple passes. The resulting deformed copper pins were cut out of the strip and show good agreement with the deformation profiles calculated by the developed model.


Hot rolling Hydrodynamic roll gap model Asymmetric friction Deformation profile Oil lubrication 



Open access funding provided by TU Wien. The authors kindly express their gratitude to voestalpine Stahl GmbH for the realization of the industrial experiments.

Funding information

This work was supported by the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development, and voestalpine Stahl GmbH.


  1. 1.
    Prinz K, Steinboeck A, Müller M, Ettl A, Kugi A (2017) Automatic gauge control under laterally asymmetric rolling conditions combined with feedforward. IEEE Trans Ind Appl 53(3):2560–2568. CrossRefGoogle Scholar
  2. 2.
    Prinz K, Steinboeck A, Kugi A (2018) Optimization-based feedforward control of the strip thickness profile in hot strip rolling. J Process Control 64:100–111. CrossRefGoogle Scholar
  3. 3.
    Montmitonnet P, Fourment L, Ripert U, Ngo QT, Ehrlacher A (2016) State of the art in rolling process modelling. BHM Berg- und Hüttenmännische Monatshefte 161(9):396–404. CrossRefGoogle Scholar
  4. 4.
    Lenard JG, Pietrzyk M (1992) Rolling process modelling. In: Numerical modelling of material deformation processes. Springer, London, pp 274–302.
  5. 5.
    Lenard JG (2007) Primer on flat rolling, 1st edn. Elsevier, New York. Google Scholar
  6. 6.
    von Kármán T (1925) Beitrag zur Theorie des Walzvorganges. Z Angew Math Mech 5:139–141zbMATHGoogle Scholar
  7. 7.
    Siebel E (1925) Kräfte und Materialfluss bei der bildsamen Formänderung. Stahl Eisen 45:1563–1566Google Scholar
  8. 8.
    Orowan E (1943) The calculation of roll pressure in hot and cold flat rolling. Proc Inst Mech Eng 150 (1):140–167. CrossRefGoogle Scholar
  9. 9.
    Sims RB (1954) The calculation of roll force and torque in hot rolling mills. Proc Inst Mech Eng 168(1):191–200. CrossRefGoogle Scholar
  10. 10.
    Alexander J (1972) On the theory of rolling. Proc R Soc Lond A 326 (1567):535–563. CrossRefzbMATHGoogle Scholar
  11. 11.
    Freshwater IJ (1996) Simplified theories of flat rolling—I. The calculation of roll pressure, roll force and roll torque. Int J Mech Sci 38(6):633–648. zbMATHGoogle Scholar
  12. 12.
    Chen S, Li W, Liu X (2014) Calculation of rolling pressure distribution and force based on improved Karman equation for hot strip mill. Int J Mech Sci 89:256–263. CrossRefGoogle Scholar
  13. 13.
    Li WG, Liu C, Liu B, Yan BK, Liu XH (2017) Modeling friction coefficient for roll force calculation during hot strip rolling. Int J Adv Manuf Technol 92(1):597–604. CrossRefGoogle Scholar
  14. 14.
    Hwang YM, Tzou GY (1993) An analytical approach to asymmetrical cold strip rolling using the slab method. J Mater Eng Perform 2(4):597–606. CrossRefGoogle Scholar
  15. 15.
    Hensel A, Spittel T (1978) Kraft- und Arbeitsbedarf bildsamer Formgebungsverfahren. VEB Deutscher Verlag für Grundstoffindustrie, LeipzigGoogle Scholar
  16. 16.
    Oh S, Kobayashi S (1975) An approximate method for a three-dimensional analysis of rolling. Int J Mech Sci 17(4):293–305. CrossRefzbMATHGoogle Scholar
  17. 17.
    Martins PAF, Barata Marques MJM (1999) Upper bound analysis of plane strain rolling using a flow function and the weighted residuals method. Int J Numer Methods Eng 44(11):1671–1683.<1671::AID-NME559>3.0.CO;2-2 CrossRefzbMATHGoogle Scholar
  18. 18.
    Komori K (2002) An upper bound method for analysis of three-dimensional deformation in the flat rolling of bars. Int J Mech Sci 44(1):37–55. CrossRefzbMATHGoogle Scholar
  19. 19.
    Kiefer T, Kugi A (2008) An analytical approach for modelling asymmetrical hot rolling of heavy plates. Math Comput Modell Dyn Syst 14(3):249–267. CrossRefzbMATHGoogle Scholar
  20. 20.
    Liu YM, Ma GS, Zhao DW, Zhang DH (2015) Analysis of hot strip rolling using exponent velocity field and MY criterion. Int J Mech Sci 98:126–131. CrossRefGoogle Scholar
  21. 21.
    Zhang DH, Liu YM, Sun J, Zhao DW (2016) A novel analytical approach to predict rolling force in hot strip finish rolling based on cosine velocity field and equal area criterion. Int J Adv Manuf Technol 84(5-8):843–850. Google Scholar
  22. 22.
    Peng W, Zhang D, Zhao D (2017) Application of parabolic velocity field for the deformation analysis in hot tandem rolling. Int J Adv Manuf Technol 91(5):2233–2243. CrossRefGoogle Scholar
  23. 23.
    Kobayashi S, Oh S, Altan T (1989) Metal forming and the finite-element method. Oxford series on advanced manufacturing. Oxford University Press, New YorkGoogle Scholar
  24. 24.
    Park JJ, Oh SI (1990) Application of three dimensional finite element analysis to shape rolling processes. J Eng Ind 112(1):36–46. CrossRefGoogle Scholar
  25. 25.
    Zhang SH, Zhang GL, Liu JS, Li CS, Mei RB (2010) A fast rigid-plastic finite element method for online application in strip rolling. Finite Elem Anal Des 46(12):1146–1154. CrossRefGoogle Scholar
  26. 26.
    Alexander JM (1955) A slip line field for the hot rolling process. Proc Inst Mech Eng 169(1):1021–1030. CrossRefGoogle Scholar
  27. 27.
    Dewhurst P, Collins IF (1973) A matrix technique for constructing slip-line field solutions to a class of plane strain plasticity problems. Int J Numer Methods Eng 7(3):357–378. CrossRefzbMATHGoogle Scholar
  28. 28.
    Kneschke A (1954) Hydrodynamische Theorie des Walzvorganges. Z Bergakad 6(1):1–11Google Scholar
  29. 29.
    Li S, Wang Z, Liu C, Ruan J, Xu Z (2017) A simplified method to calculate the rolling force in hot rolling. Int J Adv Manuf Technol 88(5):2053–2059. CrossRefGoogle Scholar
  30. 30.
    Li S, Wang Z, Ruan J, Liu C, Xu Z (2017) Hydrodynamics method and its application in hot strip rolling. Steel Res Int 88(4):1600220. CrossRefGoogle Scholar
  31. 31.
    Weber KH (1963) Erfassung der walztechnischen Kenngrößen nach Gesichtspunkten der hydrodynamischen Walztheorie beim Walzen von Flachquerschnitten. Freiberg. Forschungsh B 91:1–80Google Scholar
  32. 32.
    Kneschke A, Bandemer H (1964) Eindimensionale Theorie des Walzvorganges. Freiberg. Forschungsh B 94:9–75Google Scholar
  33. 33.
    Kiefer T, Heeg R, Kugi A (2005) Feedforward control strategies for hot rolling in a reversing plate mill. PAMM 5(1):165–166. CrossRefzbMATHGoogle Scholar
  34. 34.
    Heeg R, Kiefer T, Kugi A, Fichet O, Irastorza L (2007) Feedforward control of plate thickness in reversing plate mills. IEEE Trans Ind Appl 43(2):386–394. CrossRefGoogle Scholar
  35. 35.
    Cristescu N (2007) Fast material working: Wire drawing. In: Advanced methods in material forming. Springer, Berlin, pp 199–214.
  36. 36.
    Hitchcock J (1935) Roll neck bearings. ASME Res Publ, pp 33–41Google Scholar
  37. 37.
    Kneschke A (1958) Zur hydrodynamischen Theorie des Warmwalzens. Arch Eisenhüttenwes 29(1):11–22. CrossRefGoogle Scholar
  38. 38.
    Roberts WL (1978) Cold rolling of steel. Manufacturing engineering and materials processing. Taylor & Francis, New YorkGoogle Scholar
  39. 39.
    Geleji A (1960) Bildsame Formung der Metalle in Rechnung und Versuch. Akademie-Verlag, BerlinGoogle Scholar
  40. 40.
    Weber KH (1966) Stand der hydrodynamischen Walztheorie. Arch Eisenhüttenwes 37(10):783–794. CrossRefGoogle Scholar
  41. 41.
    Müller M, Steinboeck A, Prinz K, Kugi A (2018) Optimal parameter identification for a hydrodynamic roll gap model in hot strip rolling. In: Proceedings of the 5th IFAC Workshop on Mining, Mineral and Metal Processing (MMM). ShanghaiGoogle Scholar
  42. 42.
    Colas R (1995) Modelling heat transfer during hot rolling of steel strip. Model Simul Mater Sci Eng 3(4):437. CrossRefGoogle Scholar
  43. 43.
    Koohbor B, Moaven K (2017) Finite-element modeling of thermal aspects in high speed cold strip rolling. Proc Inst Mech Eng B: J Eng Manuf 231(8):1350–1362. CrossRefGoogle Scholar
  44. 44.
    Speicher K, Steinboeck A, Kugi A, Wild D, Kiefer T (2014) Analysis and design of an extended kalman filter for the plate temperature in heavy plate rolling. J Process Control 24(9):1371–1381. CrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Martin Müller
    • 1
    Email author
  • Andreas Steinboeck
    • 2
  • Katharina Prinz
    • 1
  • Andreas Ettl
    • 1
  • Andreas Kugi
    • 1
  • Kurt Etzelsdorfer
    • 3
  • Stefan Fuchshumer
    • 3
  • Hannes Seyrkammer
    • 3
  1. 1.Christian Doppler Laboratory for Model-Based Control in the Steel Industry, Automation and Control Institute (ACIN)TU WienViennaAustria
  2. 2.Automation and Control Institute (ACIN)TU WienViennaAustria
  3. 3.voestalpine Stahl GmbHLinzAustria

Personalised recommendations