flat work roll surface parallel to the strip middle plane occurs. Enhanced models developed recently. [4, 5] include an elastic compression zone at the roll gap ...
ABAQUS Austria Users’ Conference September 27-28, 2005 Kunsthaus Graz Lendkai 1 A-8020 Graz
“Finite element modelling of temper rolling with particular emphasis on roughness transfer” FE - Modellierungsaspekte zur Rauheitsübertragung beim Dressierwalzen von Kaltband Alexander Kainz1), Dieter Paesold2), Gerald Riha2), Konrad Krimpelstätter3), Klaus Zeman1) 1) Institute for Computer Aided Methods in Mechanical Engineering, Johannes Kepler University of Linz, Altenbergerstr. 69, A - 4040 Linz, Austria. 2) voestalpine Stahl GmbH, VOEST-Alpine Str. 3, A - 4031 Linz, Austria. 3) VOEST-Alpine Industrieanlagenbau GmbH & Co, Turmstr. 44, A-4031 Linz, Austria.
Key words: Cold rolling, Temper rolling, Large deformations, Contact and friction, Rate-dependent elasto-plasticity, Roll flattening, Contained plastic flow, Transfer of surface structure and roughness.
Extended Abstract Skin-pass and temper rolling processes represent the final stage within the production chain of cold rolled flat steel products, in which material and surface properties as well as the flatness of a cold rolled strip can be tailored and customised to satisfy even the most challenging tolerance demands. To attain a comprehensive understanding of the underlying process details, to check and tune semianalytical models, highly sophisticated numerical approaches, based on the method of finite elements, have been performed by utilizing the non-linear capabilities of both Abaqus Standard and Explicit [1]. By systematic parameter studies and regression methods, sets of characteristic curves can be obtained, which serve as an input for online control and process automation systems. Mathematical online and offline models, validated against each other and calibrated with real process data, are essential to determine proper mill setups, to improve the quality of the rolled product, to control the online process of metal forming, and to optimize throughput and yield of a mill. Temper rolling provides a slight reduction in thickness, thereby eliminating the yield point elongation in the stress-strain diagram of the annealed steel, which permits the material to be formed without the appearance of so-called Lüders’ lines. Besides, temper rolling is also used to improve the flatness properties of the strip. Because of the trend to thinner and harder strips and due to the fact that the contact length is very short for small strip elongations (typical temper degrees vary from 0.3 – 3 %), the development of improved offline and online models for temper rolling is essential. Enhanced models developed recently [4, 5] include an elastic compression zone for the strip material at the roll gap entry, an elastic recovery zone at the exit and a plastic zone in between, whereby elastic regions are also allowed to arise between plastic zones. This ensures that a contained plastic flow zone, where the contact surface contour is largely parallel to the horizontal strip mid-plane and therefore no strip reduction occurs, is included automatically in the model and need not be postulated a priori. To obtain a deeper understanding of the occurrence of such contained plastic flow regions, systematic dynamic transient finite element simulations were performed [2, 3, 8, 12]. Due to the very short contact lengths
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for temper rolling conditions, an extremely fine discretization of the work roll sleeve near the contact area is essential. The non-circular arc contour of the work roll is determined simultaneously with the corresponding contact pressure and shear stress distributions. In the skin-pass rolling process [3, 8, 12] the stamping effect of transferring the roll surface structure onto the steel sheet is used to adjust a well defined sheet-surface structure, which is essential for further processing steps. Within the frame of this simulation project study, the transfer behaviour of deterministic roll-surface structures, as generated by the electron beam texturing technique (EBT), was simulated in detail by utilizing the commercial FE-package Abaqus Explicit [1]. The EBT-transfer characteristics for both wet and dry skin-pass rolling of hot-dip galvanized steel strips was investigated and analysed. Special emphasis was put on the accurate and reliable modelling of the liquid enclosed in lubrication pockets (between the work roll surface structure elements and the strip). The results of such FE-simulations clearly point out the basic transfer mechanisms of the 3D elasto-plastic forming processes, namely a combination of penetration processes and reverse extrusion phenomena. Moreover, these simulation data yield valuable insight into the dynamics of the roughness transfer process and its dependence on the material properties and rolling conditions.
Kurzfassung Beim Dressieren handelt es sich um einen Kaltwalzprozeß mit sehr geringen Stichabnahmen (Dressiergrad typischerweise 0.3 – 3%). Die Oberflächenstruktur des Bandes kann dabei maßgeschneidert werden, was für nachfolgende Bearbeitungsschritte, wie z.B. Schweißen, Beschichten, Lackieren und auch für weitere Umformprozesse wie Tiefziehen von essentieller Bedeutung ist. Im Rahmen dieser Simulationsstudie mit Abaqus Explicit wird die Rauheitsübertragung einer deterministischen EBT – Arbeitswalzen-Kraterstruktur auf ein feuerverzinktes Kaltband beim Trocken- und Nassdressieren untersucht. Es handelt sich hierbei um einen kombinierten elastoviskoplastischen Penetrations- und inversen Extrusions - Umformprozess. Infolge der für FESimulationen sehr ungünstigen großen Längenskalenunterschiede, wie eine Zinkschichtdicke von 7 µm bei 0.8 mm Blechdicke, ein Walzendurchmesser von 650 mm im Vergleich zu EBT Kraterdurchmessern von 185 µm und Kratertiefen von ca. 20 µm, bedarf es wohldurchdachter 3DPartitionierungs- und Vernetzungskonzepte. Für eine Minimalanordnung von 7 Kratern (Zentralkrater umgeben von 6 nächsten Nachbarn im Abstand von 350 µm) benötigt man ca. 1.4 Millionen Freiheitsgrade, um genaue Resultate zu erzielen (derzeit noch ohne Berücksichtigung der elastischen Bettung der EBT - Krater). Besonderes Augenmerk wurde auf die Modellierung der in den mesoskopischen Schmierkammern (Zwischenraum zwischen den Walzenkratern und dem Band) eingeschlossenen Flüssigkeit beim Nassdressieren gelegt, wobei der mittlere Füllgrad als Inputparameter vorgegeben wird.
1
Introduction and Survey
Rolling processes can be considered to be key steps within the production of steel. Therefore, the development of highly sophisticated mathematical process models is a vital precondition for manufacturing high quality products satisfying even the narrowest tolerance demands. For annealed strips to be subsequently formed, temper rolling provides a slight reduction in thickness thereby eliminating the yield point elongation in the stress-strain diagram of the steel. This permits the material to be formed without the appearance of so-called Lüders’ lines. Besides, temper rolling is also used to improve the surface quality of the strip and its flatness properties. To optimise these final quality criteria of cold rolled steel strips, the elongation of each strip product must be strictly controlled to a certain value in the temper rolling process. Therefore, an accurate elongation control system, which is based on precise mathematical process models for the prediction of rolling force, torque and forward slip is essential. The key criteria in skin-passing are surface cleanliness and surface structure, which
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are important for subsequent deformation, welding and painting processes. An essential issue is to keep the surface of the work rolls clean to prevent that particles are imprinted into the strip in the roll gap. This task can be accomplished by utilizing either the conventional wet temper system, where a water-agent mixture is sprayed into the entry of the roll bite, or by the dry temper technique (cf. Figure 1), where a combination of rotating and oscillating brushes is pressed slightly against the roll surfaces thereby cleaning all particles sticking to the roll surfaces [5].
Backup-Roll Brushes Backup Roll
Adjustment Cylinders Flatness Measurement Roll
Work Roll
Work-Roll Brushes Bridles
Figure 2: Decomposition of the deformation zones inside the strip into elastic and plastic regions
Figure 1: State of the Art Dry Temper Rolling Equipment (cf. [5])
For temper rolling processes the conditions inside the roll bite are significantly different from those for usual hot or cold rolling processes in reversing or tandem mills. The work rolls are significantly deformed in a way similar to that of Hertzian contact. The strip elongation (or reduction) is of the order of one percent (~0.3–3 %), the deformation is highly localized and a significant elastic springback of the strip can be observed. Therefore, standard circular arc roll gap models (e.g. Bland Ford Ellis combined with an effective Hitchcock curvature [10]) do not apply. A significant improvement was achieved by Jortner et al. [9, 11] describing the work roll deformation in radial direction using influence functions. Fleck and Johnson [6] published a theory appropriate for the rolling of thin strip and foil [14-16]. Their theory omits the use of simplifying presumptions on roll-flattening geometry. Such simplifications can be considered as main reason for failure when applied to thin-gauge rolling. Besides, their model predicts the appearance of an intermediate “contained plastic flow” zone, where a flat work roll surface parallel to the strip middle plane occurs. Enhanced models developed recently [4, 5] include an elastic compression zone at the roll gap entry, an elastic recovery zone at the exit and a plastic zone in between, whereby elastic regions are also allowed to arise between plastic zones, as depicted in Figure 2. This allows for an automatic detection and inclusion of contained plastic flow zones, which need no more be postulated a priori. Transient dynamic Finite Element simulations, which are of course much more calculation time consuming than problem-adequately optimised steady-state 1D solution procedures (nevertheless highly non-linear and ill posed problems), enable a deep insight into the underlying process details and yield valuable feedback to the qualitative and quantitative solution behaviour. The key criterion in skin-passing is the transfer of a well defined topological structure and roughness onto the strip’s surface. These properties are important for subsequent processing steps, such as deepdrawing, welding and painting. The task can be accomplished by utilizing either the conventional wet temper system, where a water-agent mixture is applied to the rolls and strip, or by the dry temper technique [5], where a combination of rotating and oscillating brushes cleans all particles sticking to the roll surface. In the skin-pass rolling process [8, 12] the steel sheet’s surface structure is produced utilizing some kind of “stamping effect” between the work roll surface and the steel sheet. Apart from basic studies using regular work roll surface geometries, the numerical simulation of the transfer process of surface structure seems to be rather unexplored at least for realistic, especially stochastic
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surface structures. Our goal is to develop more insight into this process especially for stochastic surface structures as they are typically produced by modern electro discharge texturing techniques (EDT). Serving as a first benchmark within the frame of this simulation project study and in order to facilitate our access to this problem, the transfer behaviour of deterministic roll-surface structures with regular geometry elements, as they may be generated by the electron beam texturing technique (EBT), was simulated in detail by utilizing the commercial FE-package Abaqus Explicit [1]. The transfer characteristics for both wet and dry skin-pass rolling of hot-dip galvanized steel strips were investigated and analysed in detail. Special emphasis was put on the accurate and reliable modelling of the liquid enclosed in lubrication pockets (between the work roll surface structure elements and the strip), and also on the elastic foundation of the roll surface structure elements. The results of such FEsimulations clearly point out the basic transfer mechanisms of the 3D elasto-viscoplastic forming processes, namely a combination of penetration and reverse extrusion phenomena. Moreover, these simulation data yield valuable insight into the kinematics of the transfer process of surface structure and roughness from the work roll onto the strip and its dependence on the material properties and rolling conditions.
2
Overview of work roll texturing technology
Textured work rolls are used to transfer a special surface structure to the strip. Thereby specifically distributed “craters” should be “stamped” onto the strip surface to generate microscopic lubrication bore relieves (cavities) to hold the lubricant in the subsequent deep drawing process in order to decrease the friction between tool and workpiece. The distribution (regularity) of the “craters” may be realized with stochastic, pseudo-stochastic or deterministic structures to guarantee a polish and goodlooking surface after painting.
Figure 3: Principle of SBT
Figure 4: Principle of LT
Figure 5: Principle of EDT
work roll texturing [13]
work roll texturing [13]
work roll texturing [13]
For the texturing of work rolls several methods are used, which will be outlined in the following (for more information cf. [13]). The texturing methods differ among other things in the regularity of the produced “craters” (stochastic, pseudo-stochastic, deterministic), the peak count (Pc-value), the
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surface roughness of the roll (e.g. Ra-value), the roughness transfer, the reproducibility and the production costs. Shot Blast Texturing (SBT): A blast material (grit) is shot at the work roll via a centrifugal wheel. The impinging grits lead to local plastic deformations on the roll surface and leave the desired craters (cf. Figure 3). Laser Texturing (LT): A laser beam is focused on the surface of the roll. Via a chopper wheel, which interrupts the laser beam temporarily, small material parts of the roll are molten locally. An inert gas blows out the molten material (cf. Figure 4). Electrical Discharge Texturing (EDT): Axially oscillating electrodes are adjusted against the rotating work roll. Via an erode impulse the particles inside the dielectric (between work roll and the electrode) are generating a current flow and a small part of the roll is molten combined with an arising gas bubble. After the erode impulse the gas bubble implodes and the molten material is torn out (cf. Figure 5). Electron Beam Texturing (EBT): An electron beam is used to smelt the roll material locally and leave “craters” with a torus-shaped bulge. Thereby the rotating work roll is shifted axially within a vacuum chamber (cf. Figures 6, 7).
Figure 7 : Work roll surface generated by the EBT
Figure 6: Principle of EBT work roll texturing [13]
method [13]
For the numerical simulation studies, as will be presented in the next section, we will confine to deterministic EBT surface structures. Within the frame of a systematic modelling development, the challenging numerical treatment of pseudo-stochastic EDT structures is scheduled as next step.
3
Numerical Modelling Concepts and Results
The key criterion in skin-passing is the transfer of a well defined topological structure and roughness onto the strip’s surface. These properties are essential for subsequent processing steps, such as deepdrawing, welding and painting. In this section a basic Abaqus Explicit [1] FE-modelling concept for the numerical simulation of the transfer process of a prescribed work roll surface structure onto the sheet surface is presented. We considered either the conventional wet temper system [5], where a water-agent mixture is applied to the rolls and strip, or the novel dry temper technique (cf. Figure 1 in section 1). The numerical simulation of the transfer process especially of praxis-relevant (pseudo-)
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stochastic surface structures, which are typically generated by electro discharge texturing techniques (EDT), seems to be rather unexplored at present. Within the frame of a systematic model development, and in order to facilitate our access to this problem, the transfer behaviour of deterministic roll surface structures with regular idealised geometry elements, as they might be generated by the electron beam texturing technique (EBT), was simulated in detail for both uncoated and hot dip galvanized steel strips.
Figure 8: Meshing concept for the rigid work roll sector
Figure 9: Idealised hexagonal arrangement of deterministic EBT roll surface structure
Figure 10: Mesh refinement concept for the galvanised strip
Figure 11: Strip discretisation in thickness direction (upper half)
As a first benchmark within the frame of this simulation study a hot dip galvanised steel strip of 0.814 mm steel target thickness including a zinc layer of 7 µm thickness was rolled to an elongation of 0.9 % temper degree (i.e. initial half strip thickness of 410.78 µm). For the zinc layer a yield stress of 12 MPa and linear hardening up to 20 MPa for a logarithmic strain value of 0.4 was assumed. Note that the yield strength of the bulk IF-steel (interstitial free steel grade including work hardening and rate dependency) is at least one order of magnitude higher compared to the very soft zinc-layer. For simplicity the work roll with diameter of 650 mm was simulated as a rigid body. It suffices to treat only a 2°-sector, as depicted in Fig. 8, to obtain well pronounced steady state rolling conditions after the embossing of a minimum hexagonal EBT configuration (one crater surrounded by its 6 nearest neighbours at a distance of 350 µm, see Fig. 9). The mesh refinement concepts of the steel sheet are based on sweep mesh control techniques (advancing front algorithm, cf. [1]), as represented in Fig. 10 and Fig. 11. Note that due to the assumption of vertical symmetry only the upper half of the strip has to be simulated. The surface topology of one single crater on the work roll surface is shown in Fig. 12.
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For the outer diameter of this basic EBT surface structure element a value of 185 µm was assumed, whereas for the vertical profile depth a value of 22 µm (centre depression of -14 µm and circular ring elevation of +8 µm) was chosen. For a rigid work roll a triangular surface mesh is appropriate, as depicted in Fig. 13.
Figure 12: Single roll surface crater with a diamater of 185 µm
Figure 13: Triangular roll surface mesh with 2 µm edge length
Figure 14: Topologically continuous master contact surface
Figure 15: Stamping pattern of the hexagonal EBTprofile on the hot dip galvanised strip surface
The resulting topologically continous master surface structure on the work roll, as shown in Fig. 14, leads to a stamping pattern on the strip surface, as depicted in Fig. 15. Concerning the highly nonlinear contact problem between strip and work roll, a master slave concept including kinematic contact, hard pressure overclosure and penalty formulation for the Coulomb friction model with a friction value of μ = 0.15 was applied. The embossed surface roughness structure on the hot dip galvanised strip surface is represented in Fig. 16 and Fig. 21. On account of the short discretization length of merely 3 µm a very fine resolution especially of the circular indentation is obtained, where extremely large element distortions occur. This is due to the very low Mises-stress value of the zinc layer and does not occur in the uncoated case, as depicted in Fig. 17. In this case, however, considerable values for the Mises-stress can be observed at the strip surface, as shown in Fig. 18 and Fig. 20.
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Figure 16: Stamped roughness structure on the zinc coated strip
Figure 17: Stamped surface structure for the strip without zinc layer
Figure 18: Mises stress distribution for the uncoated steel sheet
Figure 19: Additional liquid body to simulate wet temper rolling
Figure 20: Cross-sectional representation of the Misesstress distribution for the uncoated strip.
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Figure 21: Stamped roughness structure (vertical displacement field u3) for the hot dip galvanized strip
Abaqus Austria Users’ Conference 2005, Graz, Austria
For the accurate and reliable simulation of wet skin-pass rolling scenarios, where a certain amount of liquid is enclosed in lubrication pockets between the work roll surface structure elements and the strip, we introduced an additional incompressible “liquid body” (cf. Fig. 19) with a yield stress depending linearly on the plastic strain rate to simulate the Newtonian fluid behaviour of the water-agent mixture. Special attention has to be paid to the contact formalism, as two additional contact surface pairs occur. Note that the effective water filling degree is assumed to be in the range between 25 % and 75 % and serves as an additional adaptation parameter. It should be mentioned, that the realization of such a fluid-structure interaction concept turned out to be rather challenging. Due to severe problems with sharp edges and inappropriate rounding concepts we could not fully accomplish this task. Further modelling extensions comprise the consideration of the elastic foundation of the work roll surface structure elements. This task can be solved by applying highly sophisticated partitioning and mesh refinement techniques near the work roll surface. Such a model enhancement enables the determination of realistic hodographs (relative motion of strip and work roll along the roll gap, cf. [8]) for the embossing (skin-pass rolling) process.
4
Conclusions and Future Prospects
In the present study a typical temper rolling process was simulated by utilizing the finite element package Abaqus [1]. Such investigations yield valuable information about the stress-, velocity- and displacement fields inside the roll gap. Moreover, the non-circular arc contour [2-5] of the work roll is determined simultaneously with the corresponding contact pressure and shear stress distributions, and a “contained plastic flow” zone inside the roll gap can be identified automatically by the model. Due to the very short contact lengths, an extremely fine discretization of the work roll sleeve near the contact region is essential to obtain reliable and praxis-relevant data. In the skin-pass rolling process [3, 8, 12] the transfer of a prescribed deterministic roughness structure of the work roll onto the steel sheet was investigated. This stamping effect is used to adjust a well defined sheet-surface structure, which is essential for further processing steps. A first attempt to study and analyse some EBT-transfer characteristics for both wet and dry skin-pass rolling of hot-dip galvanized steel strips was finished successfully. It could be proven that such 3D FEsimulations are possible and feasible. Therefore, it may be expected that future investigations will yield valuable information about the basic transfer mechanisms of the underlying 3D elastoviscoplastic forming processes, namely a combination of penetration processes and reverse extrusion phenomena.
Acknowledgements: Some part of this work was carried out within the frame of a project with IKMA (Industrial Competence Center for Mechatronics & Automation) according to the K-Ind programme in cooperation with VOEST-ALPINE Industrieanlagenbau GmbH & Co (VAI), voestalpine, VOESTALPINE Mechatronics GmbH, the Johannes Kepler University Linz and was sponsored by the Republic of Austria and the Province of Upper Austria. The FE-results shown above were generated utilizing the "multi-purpose" FEM packages ABAQUS/Standard and ABAQUS/Explicit distributed by HKS (Hibbitt, Karlsson & Sorensen, INC.). The authors wish to express their thank for this support.
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References [1] Abaqus Standard, Explicit, CAE / V6.5, Hibbitt, Karlsson & Sorensen, Inc., 1080 Main Street, Pawtucket, Rhode Island, USA. [2] A. Kainz, K. Krimpelstätter and K. Zeman, FE-Simulation of Thin Strip and Temper Rolling Processes, Abaqus Austria Users' Conference, Vienna, November 25, 2003. [3] A. Kainz, D. Paesold, G. Riha, G. Keintzel, K. Krimpelstätter, K. Zeman, Finite Element Simulation of Skin-Pass and Temper Rolling Processes with Special Emphasis on Roughness Transfer, in: Proceedings of the NAFEMS World Congress 2005 (Nafems Ltd., East Kilbride, Glasgow, G75 0QD, United Kingdom, 52005, ISBN: 1-874376-03-4), St. Julians, Malta, May 17-20, 2005. [4] K. Krimpelstätter, K. Zeman and A. Kainz, Non Circular Arc Temper Rolling Model Considering Radial and Circumferential Work Roll Displacements, in: Proceedings of the Eighth International Conference on Numerical Methods in Industrial Forming Processes, Numiform 2004 , Columbus, Ohio, USA, June 13-17, 2004. [5] K. Krimpelstätter, K. Zeman, G. Finstermann et al, New Advances in Temper and Skin-Pass Rolling Technology, in: Proceedings of the 3rd European Rolling Conference (METEC Conference 03), Düsseldorf, 16-20 June, 2003. [6] N.A. Fleck, K.L. Johnson, Towards a New Theory of Cold Rolling Thin Foil, Int. J. Mech. Sci., Vol. 29, No. 7, pp. 507-524, 1987. [7] S.A. Domanti, W.J. Edwards, P.J. Thomas, A Model for Foil and Thin Strip Rolling, AISE Annual Convention, Cleveland, USA, 1994. [8] F. Rechberger, Dressieren als Kombinierter Präge- und Walzvorgang, Doctoral Thesis at the Johannes Kepler University Linz, Faculty of Mechatronics, 2001. [9] D. Jortner, J.F. Osterle, C.F. Zorowski, An Analysis of Cold Strip Rolling, Int. Journal of Mechanical Sciences, Vol.2, pp. 179-194, 1960. [10] J. Hitchcock, Roll neck bearings, Report of ASME Research Committee, 1935. [11] W. Meindl, Walzenabplattung unter Berücksichtigung der Kontaktschubspannungen, Doctoral Thesis at the Johannes Kepler University Linz, Faculty of Mechatronics, 2001. [12] R. Bünten, K. Steinhoff, W. Rasp, R. Kopp and O. Pawelski, Development of a FEM-Model for the Simulation of the Transfer of Surface Structure in Cold-Rolling Processes, Journal of Material Processing Technology, Vol. 60, pp. 369-376, 1996 [13] J. Staeves, Beurteilung der Topografie von Blechen in Hinblick auf die Reibung bei der Umformung, Dissertation, Universität Darmstadt, 1998. [14] W.Y.D. Yuen, D.N. Nguyen, D.L. Matthews, Mathematical Modelling of the Temper Rolling Processes, 37th Steel Processing Conference, Ontario 1995. [15] W.Y.D. Yuen, A. Dixon, D.N. Nguyen, The Modelling of the Mechanics of Deformation in Flat Rolling, Journal of Materials Processing Technology, Vol. 60, pp. 87-94, 1996. [16] H.R. Le, M.P.F. Sutcliffe, A Robust Model for Rolling of Thin Strip and Foil, Int. Journal of Mechanical Sciences, Vol. 43, pp. 1405-1419, 2001.
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