Abstract
Pushed forward by mill complexification and harder product quality requirements, the mathematical treatment has evolved into very complex, multi-coupled models: roll deformation, thermal transfer, lubrication, and oxide scales are a few examples. The diversity of rolled products and rolling mills makes rolling process modelling a vast field indeed. Beyond general, necessarily very costly models, partial descriptions are developed for more targeted goals. Three methods share the market: the Slab Method (SM), the Upper Bound Method (UBM), and the Finite Element Method (FEM). A few modelling strategies based on the above three are described, providing accurate solutions in an industry-compatible computation time: steady-state FEM modelling; faster 2D SM with large roll flattening to build thin sheet or temper rolling force models; low-cost 3D roll stack deformation package for profile/flatness of sheets; FEM results-based UBM models of width variations in the Tandem Cold Mill; post-bite profile and flatness evolution (interstand behavior); FEM description of oxide scale behavior in descaling; SM with modern lubrication modelling. Evolutions of rolling processes are questioned to point to new demands on modelling and how to answer them.
Zusammenfassung
Getrieben durch die steigende Komplexität der Walzwerke und härteren Produktanforderungen haben sich für die mathematische Beschreibung sehr komplexe, multipel-gekoppelte Modelle entwickelt: Walzenverformung, Wärmeübergang, Schmierung und Zunderschichten sind einige Beispiele. Die Vielfalt von Walzprodukten und Walzwerken macht Walzprozessmodellierung in der Tat zu einem breiten Feld. Zusätzlich zu den im Allgemeinen sehr kostspieligen Modellen wurden Teildarstellungen für spezifische Zwecke entwickelt. Drei Methoden teilen sich den Markt: die Slab-Methode (SM), die Upper-Bound-Methode (UBM) und die Finite-Elemente-Methode (FEM). Basierend auf den drei oben beschriebenen Methoden bieten einige Modellierungsstrategien, präzise Lösungen in einer industrietauglichen Rechenzeit: Steady-State-FEM-Modellierung; 2D-SM mit großen Rollenabflachungen, um schneller Modelle für dünnes Blech oder Dressierwalzen zu bauen; Low-Cost-3D-Pakete für Walzgerüste für Profil/Planheit von Bändern; FEM ergebnisorientierte UBM Modelle für Breitenschwankungen in der Tandemstraße; Entwicklung nach dem Walzstich für Profil und Planheit (Verhalten des Zwischengerüstzugs); FEM zur Beschreibung des Verhaltens der Oxidzunderschicht beim Entzundern; SM mit modernen Schmiermodellierungen. Die Entwicklungen von Walzprozessen werden untersucht, um neue Anforderungen an die Modellierung zu zeigen und wie diese zu bewältigen sind.
Similar content being viewed by others
References
von Kármán, T.: Beitrag zur Theorie des Walzvorganges, Z. Angew. Math. Mech., 5 (1925), pp 139–141
Orowan, E.: The calculation of roll pressure in hot and cold flat rolling, Proc. Instn. Mech. Engrg., 150 (1943), pp 140–167
Oh, S. I.; Kobayashi, S.: An approximate method for a three-dimensional analysis of rolling, Int. J. Mech. Sci., 17 (1975), no. 4, pp 293–305
Mori, K.; Osakada, K.: Simulation of 3D deformation in rolling by the FEM, Int. J. Mech. Sci., 26 (1984), no. 9–10, pp 515–525
Huisman, H. J.; Huétink, J.: A combined Eulerian–Lagrangian 3D FEM analysis of edge-rolling, J. Mech. Working Technol., 11 (1985), pp 333–353
Chenot, J.-L.; Montmitonnet, P.; Bern, A.; Bertrand-Corsini, C.: A method for determining free surfaces in steady state finite element computations, Comput. Meth. Appl. Mech. Engrg., 92 (1991), 2, pp 245–260
Kim, T. H.; Lee, W.H.; Hwang, S. M.: An integrated FE process model for the prediction of strip profile in flat rolling, ISIJ Int., 43 (2003), no. 12, pp 1947–1956.
Trull, M.; McDonald, D.; Richardson, A.; Farrugia, D. C. J.: Advanced finite element modelling of plate rolling operations, J. Mat. Proc. Tech., 177 (2006), pp 513–516.
Lee, Y. S.; Dawson, P. R.; Dewhurst, T. B.: Bulge prediction in steady state bar rolling, Proceedings, NUMIFORM 89, Fort Collins, USA, 1989, pp 323–330
Hacquin, A.: 3D thermomechanical modelling of rolling processes: coupling strip and rolls, PhD Dissertation, Ecole des Mines de Paris, 1996 (in French)
Vacance, M.; Massoni, E.; Chenot, J.-L.; Rovelli, C.; Cumino, G.; Lubrano, M.: Multistand pipe mill finite element model, J. Mat. Proc. Tech., 24 (1990), pp 421–430
Ripert, U.; Fourment, L.; Chenot, J.-L.: An upwind Least Squares formulation for free surface calculation of viscoplastic steady state metal forming problems, Adv. Mod. Simul. Engg Sci., 2 (2015), 15
Ngo, Q. T.: Thermo-elasto-plastic uncoupling model of width variation for online application in automotive cold rolling process, PhD Dissertation, University of Paris-Est, 2015 (in French)
Yamada, Y.; Ogawa, S.; Hamauzu, S.; Kikuma, T.: 3D analysis of mandrel rolling using RP-FEM, Proceedings, NUMIFORM 89, Fort Collins, USA, 1992
Forge®NxT 2016 Users’ Meeting programme http://www.transvalor.com/en/actualites/detail/forge-international-user-meeting-2016-newsletter.99.html (July 12th 2016)
Deform Modules brochure, http://www.deform.com/products/deform-forming-modules/ (July 12th 2016)
Jortner, D.; Osterle, J. F.; Zorowski, C. F.: An analysis of cold strip rolling, Int. J. Mech. Sci., 2 (1960), pp 179–194
Grimble, M. J.; Fuller, M. A.; Bryant, G. F.: A non-circular arc force model for cold rolling, Int. J. Numer. Methods Eng., 12 (1978), pp 643–663
Golten, J. W.: Analysis of cold rolling with particular reference to roll deformations, Swansea Doctoral Dissertation, The University of Wales, 1969
Krimpelstätter, K.: Non-circular arc temper rolling model considering radial and circumferential displacements, PhD dissertation, Linz University, Austria, 2005
Meindl, W.: Roll flattening with consideration of shear contact stress, PhD Thesis, Linz University, Linz, Austria, 2001 (in German)
Fleck, N. A.; Johnson, K. L.: Towards a new theory of cold rolling thin foil, Int. J. Mech. Sci., 29 (1987), no. 7, pp 507-524
Shigaki, Y.; Nakhoul, R.; Montmitonnet, P.: Numerical treatment of slipping/no-slip zones in cold rolling of thin sheets with heavy tool deformation, Lubricants, 3 (2015), pp 113–131
Montmitonnet, P.; Wey, E.; Delamare, F.; Chenot, J. L.; Fromholz, C.; de Vathaire, M.: A mechanical model of cold rolling: influence of the friction law on roll flattening calculated by a Finite Element Method, Proceedings, 4th Int. Steel Rolling Conf., Deauville, France, 1987
Matsumoto, H.: Elastic-Plastic theory of cold and temper rolling, Proceedings, 8th Int. Conf. Technology of Plasticity, Kobe, Japan, 2005, paper #359
Yanagimoto , J.; Kiuchi, M.: 3D simulation system for coupled elastic/rigid plastic deformation of rolls and workpieces in strip rolling processes, Proceedings, NUMIFORM 92, Sophia-Antipolis, France, 1992
Hacquin, A.; Montmitonnet, P.; Guillerault, J.-P.: A 3D semi-analytical model of rolling stand deformation with finite element validation, Eur. J. Mech. A (Solids), 17 (1998), no.1, pp 79–106
Berger, B.; Pawelski, O.; Funke, P.: Die elastische Verformung der Walzen von Vier-walzengerüste, Arch. Eisenhüttenwes., 47 (1976), pp 351–356
Montmitonnet, P.: Comparison of profile prediction models for strip rolling, Proceedings, IOM3 Int. Conf. ‘Achieving Profile & Flatness in Flat Products’, Birmingham, UK, 2006)
Legrand, N.; Becker, B.; Roubin, C.: Towards a better width control in cold rolling of flat steel strip, Proceedings, Int. Steel Rolling Conf., Paris – La Défense, France, 2006
Barata Marques, M. J. M.; Martins, P. A. F.: The use of dual stream functions in the analysis of 3D metal forming process, Int. J. Mech. Sci., 33 (1991), pp 313–323
Kim, Y. K.; Kwak, W. J.; Shin, T. J.; Hwang, S. M.: A new model for the prediction of roll force and tension profiles in flat rolling, ISIJ Int., 50 (2010), 11, pp 1644–1652
Zaepffel, D.; Montmitonnet, P.; Salle, R.; Barranx, V.: Post bite creep and thickness heterogeneities in slab hot rolling on a reversing single stand mill, Proceedings, 5th European Rolling Conference, London, UK, 2009
Abdelkhalek, S.; Montmitonnet, P.; Legrand, N.; Buessler, P.: Coupled approach for flatness predictions in thin strip cold rolling, Int. J. Mech. Sci., 53 (2011), pp 651–675
Fischer, F. D.; Friedl, N.; Noe, A.; Rammerstorfer, F. G.: A study on the buckling behaviour of strips and plates with residual stresses. Steel Res. Int., 76 (2005), pp 327–335
Abdelkhalek, S.; Zahrouni, H.; Legrand, N.; Potier-Ferry, M.: Post-buckling modelling for strips under tension and residual stresses using asymptotic numerical method, Int. J. Mech. Sci., 104 (2015), pp 126–137
Counhaye, C.: Modélisation et contrôle industriel de la géométrie des aciers laminés à froid (modelling and industrial control of the geometry of cold rolled steels), PhD thesis, University of Liege, 2000 (in French)
von Plötz, K.: Study of levelling of sheets, PhD dissertation, Leoben University, 1973
Dratz, B.; Nalewajk, V.; Bikard, J.; Chastel, Y.: Testing and modelling the behaviour of steel sheets for roll levelling applications, Int. J. Mater. Form, 2 (2009), Suppl 1, pp 519–522
Park, K. C.; Hwang, S. M.: Development of a FE analysis program of roller levelling and application for removing blanking bow defect of thin steel sheet, ISIJ Int., 42 (2002), no. 9, pp 990–999
Hubert, C.; Dubar, L.; Dubar, M.; Dubois, A.: Finite Element simulation of the edge-trimming/cold rolling sequence, Analysis of edge cracking, J. Mat. Proc. Tech., 212 (2012), pp 1049–1060
Krzyzanowski, M.; Beynon, J. H.; Farrugia, D. C. J.: Oxide Scale Behavior in High Temperature Metal Processing, Wiley, 2010
Picqué, B.; Mouret, S.; Bouchard, P.-O.; Montmitonnet, P.; Picard, M.: Mechanical behaviour of iron oxide scale: experimental and numerical study, Wear, 260 (2006), pp 231–242
Zhang, M. H.; Liu, B.; Boréan, J.-L.; Montmitonnet, P.: Oxide fracture mechanisms in descaling of steel strips on the Hot Strip Mill, Proceedings, 14th ESAFORM Conference, Belfast, Northern Ireland, UK, 2011, AIP Conf. Proc., 1353 (2011), pp 333–338
Nagl, M. M.; Saunders, S. R. J.; Evans, W. T.; Hall, D. J.: The tensile failure of nickel oxide scales at ambient and at growth temperature, Corr. Sci., 35 (1993), no. 5–8, pp 965–969
Tsao, Y. H.; Sargent, L. B.: A mixed lubrication model for the cold rolling of metals, ASLE Transactions, 20 (1977), pp 55–63
Sutcliffe, M. P. F.; Johnson, K. L.: Lubrication in cold strip rolling in the mixed regime, Proc. Instn Mech. Engrs, 204 (1990), pp 249–261
Sheu, S.; Wilson, W. R. D.: Mixed Lubrication of strip rolling, STLE Tribology Trans., 37 (1994), pp 483–493
Qiu, Z. L.; Yuen, W. Y. D.; Tieu, A. K.: Mixed-film lubrication theory and tension effects on metal rolling processes, J. Tribology (Trans. ASME), 121 (1999), pp 908–915
Bergmann, M.; Zeman, K.; Kainz, A.; Krimpelstätter, K.: Enhanced mixed lubrication model for cold rolling based on a modular and hierarchical structure, Proceedings, 4th ICTMP Conference, Nice, France, 2010, pp 789–798
Carretta, Y.; Stéphany, A.; Legrand, N.; Laugier, M.; Ponthot, J. P.: Metalub, a slab method software for the numerical simulation of mixed lubrication regime – application to cold rolling, Proceedings, 4th ICTMP Conference, Nice, France, 2010, pp 799–808
Laugier, M.; Tornicelli, M.; Silvy-Leligois, C.; Bouquegneau, D.; Launet, D.; Alvarez, J. A.: Flexible lubrication concept: the future of cold rolling lubrication, Proceedings, 4th ICTMP Conference, Nice, France, 2010, pp 735–744
Wilson, W. R. D.; Sakaguchi, Y.; Schmid, S. R.: A mixed flow model for lubrication with emulsions, STLE Tribology Trans., 37 (1994), no. 3, pp 543–551
Tieu, A. K.; Kosasih, P. B.; Godbole, A.: A thermal analysis of strip-rolling in mixed-film lubrication with O/W emulsions, Trib. Int., 39 (2006), no. 12, pp 1591–1600
Montmitonnet, P.; Stephany, A.; Cassarini, S.; Ponthot, J. P.; Laugier, M.; Legrand, N.: Modelling of metal forming lubrication by O/W emulsions, Proceedings, 3rd ICTMP Conference, Yokohama, Japan, 2007, pp 85–90
Mizuno, T.; Okamoto, M.: Effects of Lubricant Viscosity at Pressure and Sliding Velocity on Lubricating Conditions in the Compression-Friction Test on Sheet Metals, J. Lub. Tech. (Trans. ASME), 104 (1982), pp 53–59
Bech, J.; Bay, N.; Eriksen, M.: Entrapment and escape of liquid lubricant in metal forming, Wear, 132 (1999), pp 134–139
Laugier, M.; Boman, R.; Legrand, N.; Ponthot, J. P.; Tornicelli, M.; Bech, J. I.; Carretta, Y.: Micro-plasto-hydrodynamic lubrication: a fundamental mechanism in cold rolling, Proceedings, 6th ICTMP Conference, Darmstadt, Germany, 2014, pp 228–241
Montmitonnet, P.: Hot and cold strip rolling processes, Comput. Meth. Appl. Mech. Engg, 195 (2006), pp 6604–6625
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Montmitonnet, P., Fourment, L., Ripert, U. et al. State of the Art in Rolling Process Modelling. Berg Huettenmaenn Monatsh 161, 396–404 (2016). https://doi.org/10.1007/s00501-016-0520-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00501-016-0520-4
Keywords
- Review
- Mathematical modelling
- Coupled problems
- Slab method
- Upper bound method
- Finite element method
- Computational efficiency
- Steady state
- Roll deformation
- Tribology