OpenFOAM® pp 309-323 | Cite as

Lubricated Contact Model for Cold Metal Rolling Processes

  • Vanja ŠkurićEmail author
  • Peter De Jaeger
  • Hrvoje Jasak


A numerical method for calculating lubricated contact pressures and friction in cold metal rolling is presented in this study. In order to have a good representation of the contact phenomena in lubricated metal rolling processes, the interaction between the surface roughness and lubricant flow has to be taken into account. Due to the changes in lubricant thickness during the rolling process, the lubricant flows in four local regimes: hydrodynamic thick film, hydrodynamic thin film, mixed and boundary lubrication regimes. The ability to treat all four lubrication regimes is required. Surface roughness effects, lubrication regimes treatment and lubricant property variations are all implemented within the present model. In order to calculate contact pressures and frictional forces, the Greenwood-Williamson model with the modified Reynolds lubrication equation is used. The Finite Area Method is used to discretize the Reynolds lubrication equation over a curved surface mesh. The implemented model is used as a solid contact boundary condition for a large strain hyperelastoplastic deformation solver developed in the foam-extend framework. The model is tested on wire and sheet rolling cases, and the results are presented here.



Financial support via Ph.D. funding is gratefully acknowledged from Peter De Jaeger and Bekaert.


  1. 1.
    M. Beaudoin and H. Jasak. Development of a generalized grid interface for turbomachinery simulations with OpenFOAM\(^{\textregistered }\). In Open Source CFD International Conference 2008, Berlin, 2008.Google Scholar
  2. 2.
    I. Bijelonja, I. Demirdžić, and S. Muzaferija. A finite volume method for large strain analysis of incompressible hyperelastic materials. International Journal for Numerical Methods in Engineering, 64(12):1594–1609, 2005.CrossRefGoogle Scholar
  3. 3.
    R. Boman and J.P. Ponthot. Finite element simulation of lubricated contact in rolling using the arbitrary lagrangian-eulerian formulation. Comput. Methods Appl. Mech. Engrg., 193:4323–4353, 2004.MathSciNetCrossRefGoogle Scholar
  4. 4.
    P. Cardiff, Ž. Tuković, P. De Jaeger, M. Clancy, and A. Ivanković. A lagrangian cell-centred finite volume method for metal forming simulation. International Journal for Numerical Methods in Engineering, pages n/a–n/a, 2016. nme.5345.Google Scholar
  5. 5.
    W.R. Chang, I.I. Etsion, and D.B. Bogy. An elastic-plastic model for the contact of rough surfaces. Journal of Tribology, 109(2):257–263, 1987.CrossRefGoogle Scholar
  6. 6.
    J. A. Greenwood and J. B. P. Williamson. Contact of nominally flat surfaces. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 295(1442):300–319, 1966.Google Scholar
  7. 7.
    B.J. Hamrock, S.R. Schmid, and B.O. Jacobson. Fundamentals of Fluid Film Lubrication. Marcel Dekker, 2004.Google Scholar
  8. 8.
    A. Ivanković and G.P. Venizelos. Rapid crack propagation in plastic pipe: predicting full-scale critical pressure from s4 test results. Engineering Fracture Mechanics, 59(5):607–622, 1998.CrossRefGoogle Scholar
  9. 9.
    R. L. Jackson and I. Green. On the modeling of elastic contact between rough surfaces. Tribology Transactions, 54(2):300–314, 2011.CrossRefGoogle Scholar
  10. 10.
    Robert L. Jackson and Itzhak Green. A statistical model of elasto-plastic asperity contact between rough surfaces. Tribology International, 39(9):906–914, 2006.CrossRefGoogle Scholar
  11. 11.
    H. Jasak and H. Weller. Finite volume methodology for contact problems of linear elastic solids. In Proceedings of 3rd International Conference of Croatian Society of Mechanics, Dubrovnik, Croatia, 2000.Google Scholar
  12. 12.
    Hrvoje Jasak. OpenFOAM\(^{\textregistered }\): Open source cfd in research and industry. International Journal of Naval Architecture and Ocean Engineering, 1(2):89–94, 2009.Google Scholar
  13. 13.
    M.N. Khan, H. Ruan, L.C. Zhang, X.M. Zhao, and X.M. Zhang. A new approach to the investigation of mixed lubrication in metal strip rolling. In Proc. 7 Australasian Congress on Applied Mechanics, ACAM 7, Adelaide, Australia, 2012.Google Scholar
  14. 14.
    C. Liu, P. Hartley, C.E.N. Sturgess, and G.W. Rowe. Simulation of the cold rolling of strip using an elastic-plastic finite element technique. International Journal of Mechanical Sciences, 27(11):829–839, 1985.CrossRefGoogle Scholar
  15. 15.
    J.I. McCool. Relating profile instrument measurements to the functional performance of rough surfaces. Journal of Tribology, 109(2):264–270, 1987.MathSciNetCrossRefGoogle Scholar
  16. 16.
    N. Patir and H.S. Cheng. An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication. J. of Lubrication Tech., 100(1):12–17, 1978.CrossRefGoogle Scholar
  17. 17.
    N. Patir and H.S. Cheng. Application of average flow model to lubrication between rough sliding surfaces. J. of Lubrication Tech., 102(2):220–229, 1979.CrossRefGoogle Scholar
  18. 18.
    Ž. Tuković, P. Cardiff, A. Karač, H. Jasak, and A. Ivanković. OpenFOAM\(^{\textregistered }\) library for fluid-structure interaction. In 9th OpenFOAM\(^{\textregistered }\)Workshop, Zagreb, 2014.Google Scholar
  19. 19.
    C. Wu, L. Zhang, S. Li, Z. Jiang, and P. Qu. A novel multi-scale statistical characterization of interface pressure and friction in metal strip rolling. International Journal of Mechanical Sciences, 89:391–402, 2014.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Vanja Škurić
    • 1
    Email author
  • Peter De Jaeger
    • 2
  • Hrvoje Jasak
    • 1
  1. 1.Faculty of Mechanical Engineering and Naval ArchitectureZagrebCroatia
  2. 2.NV Bekaert SAZwevegemBelgium

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