A Review on Theoretical Analyses of Rolling in Europe.

Montmitonnet, Pierre; Buessler, Pascal

doi:10.2355/isijinternational.31.525

Cited by 42 publications

(25 citation statements)

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“…Further, we assume the friction coefficient to be a prescribed phenomenological constant, with the friction being modelled either by a Coulomb or Tresca law or by a truncated Coulomb law, where the tangential frictional stress is limited by the yield shear stress. Note that the Tresca law is, erroneously, also known as 'sticking friction' in literature, although it does not necessarily imply the absence of sliding, as was pointed out by Montmitonnet and Buessler [1].…”

Section: Governing Equationsmentioning

confidence: 99%

“…If we apply the substantial derivative (13) to the displacement vector, as obtained in our system in (E-L), the following relation between the derivative of the displacement with respect tox 1 and the velocity components is obtained for stationary processes:…”

Section: Formulation In the (E-l) Reference Systemmentioning

confidence: 99%

“…Thereby, N [1] k denotes the kth shape function for v 1 and, since k is fixed, no summation has to be performed over the index k.…”

Section: Implementation Of Boundary Conditionsmentioning

confidence: 99%

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Numerical analysis of a new Eulerian–Lagrangian finite element method applied to steady‐state hot rolling processes

Synka

Kainz

Maringer

et al. 2004

Numerical Meth Engineering

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SUMMARYA finite element code for steady-state hot rolling processes of rigid-visco-plastic materials under planestrain conditions was developed in a mixed Eulerian-Lagrangian framework. This special set up allows for a direct calculation of the local deformations occurring at the free surfaces outside the contact region between the strip and the work roll. It further simplifies the implementation of displacement boundary conditions, such as the impenetrability condition. When applied to different practical hot rolling situations, ranging from thick slab to ultra-thin strip rolling, the velocity-displacement based model (briefly denoted as vu-model) in this mixed Eulerian-Lagrangian reference system proves to be a robust and efficient method.The vu-model is validated against a solely velocity-based model (vv-model) and against elementary methods based on the Kármán-Siebel and Orowan differential equations. The latter methods, when calibrated, are known to be in line with experimental results for homogeneous deformation cases. For a massive deformation it is further validated against the commercial finite-element software package Abaqus/Explicit. It is shown that the results obtained with the vu-model are in excellent agreement with the predictions of the vv-model and that the vu-model is even more robust than its vv-counterpart. Throughout the study we assumed a rigid cylindrical work roll; only for the homogeneous test case, we also investigated the effect of an elastically deformable work roll within the frame of the Jortner Green's function method.The new modelling approach combines the advantages of conventional Eulerian and Lagrangian modelling concepts and can be extended to three dimensions in a straightforward manner.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Formulation In the (E-l) Reference Systemmentioning

confidence: 99%

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Numerical analysis of a new Eulerian–Lagrangian finite element method applied to steady‐state hot rolling processes

Synka

Kainz

Maringer

et al. 2004

Numerical Meth Engineering

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“…The modes of rolling and annealing for the 1 , l 1 -thickness, width and length of the initial/rolled strip, respectively; l d , l de -length of deformation zone (contact between strip and roll) with and without an elastic deformation of rolls; l b , l f -length of backward and forward slip zones; R -roll radius; R e -radius of an elastically deformed roll; Dh = h 0 -h 1 -absolute strip thickness reduction; h m -mean strip thickness, i.e., (h 0 + h 1 )/2; V sx , V rx -horizontal velocities of strip and roll Slika 1: Geometrija podro~ja deformacije z in brez elasti~ne deformacije valjev: h 0 , b 0 , l 0 / h 1 , b 1 , l 1 -debelina, {irina in dol`ina za~etnega oziroma valjanega traku; l d , l de -dol`ina podro~ja deformacije (stik med trakom in valjem) z in brez elasti~ne deformacije valjev; l b , l f -dol`ina podro~ja zaostajanja in prehitevanja; R -premer valja; R e -premer elasti~no deformiranega valja; Dh = h 0 -h 1 -absolutno zmanj{anje debeline traku; h m -povpre~na debelina traku, to je (h 0 + h 1 )/2; V sx , V rx -horizontalna hitrost traku in valja Figure 3. The initial thickness of the 5083-T0 alloy strips is 1.28 ± 0.01 mm.…”

Section: Rolling Processmentioning

confidence: 99%

“…The cold-rolling technology has been constantly developed and improved with the intent to establish reliable quality and high productivity 1,2 . Regardless of the continuous development in all the areas, theoretical models of the process are still the subjects of a comprehensive research 3,4 .…”

Section: Introductionmentioning

confidence: 99%

Deformations and velocities during the cold rolling of aluminium alloys

Misovic¹,

Tadić²,

Jacimovic³

et al. 2016

Mater. Tehnol.

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This paper presents the analysis results of investigations on the deformations and velocities during the cold rolling of strips of aluminium alloys AW2024 and AW5083 obtained with an application of the finite-element method (FEM) and the conventional rolling theory. The results of the simulation obtained using the FEM software DEFORM-2D were analysed for the displacements, effective strain and velocity of rolling. The diagrams of the changes in these values along the deformation zone were presented together with the identified characteristics of the trajectories of the surface and axis as the boundary surfaces for simulating the cold rolling of the strips. The finite effective strains were compared with the degree of reduction of the strip thickness, and equations were derived for the dependence of their ratio on the starting thickness of a strip. The equations for the dependence of the velocity of a strip and the roll ratio on the degree of reduction due to the control of forward and backward slips were also derived. The reliability of the obtained results and derived equations was tested with experimental tests, theoretical relationships for plane strain and the results for the forward slip published in the literature. Keywords: cold rolling, FEM, displacements, effective strain, forward slip lanek predstavlja analizo rezultatov preiskav deformacije in hitrosti pri hladnem valjanju trakov aluminijevih zlitin AW2024 in AW5083, dobljenih z uporabo metode kon~nih elementov (FEM) in konvencionalne teorije valjanja. Analizirani so bili rezultati simulacije, dobljene s FEM programsko opremo DEFORM-2D, za raztezek, efektivno obremenitev in hitrost valjanja. Predstavljeni so diagrami sprememb teh vrednosti vzdol`deformacijske cone, skupaj z identifikacijo zna~ilnosti trajektorij povr{ine in osi, kot mejnih povr{in za simulacijo hladnega valjanja trakov. Kon~ne efektivne obremenitve so bile primerjane s stopnjo redukcije debeline trakov in razvite so bile ena~be za odvisnost njihovega razmerja od za~etne debeline traku. Razvite so tudi ena~be za odvisnost hitrosti traku in razmerja valjev na stopnjo redukcije zaradi kontrole prehitevanja in zaostajanja traku. Zanesljivost dobljenih rezultatov in razvitih ena~b je bila preizku{ena s preizkusom, s teoreti~nimi odvisnostmi za ravninsko napetost in za rezultate prehitevanja, objavljenega v literaturi. Klju~ne besede: hladno valjanje, FEM, raztezek, efektivna obremenitev, prednji zdrs

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Modelling of Stress State, Centre Consolidation and Roll Force in Billet Rolling

Lundberg

Överstam

2007

steel research international

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Roll pressure models have been derived from theoretical studies, FEM simulations and experimental investigations. A model developed from slip line field theory has been shown to fit well to the experimental results. The Finite Element simulations overestimated the pressure function. This is a common problem in hot rolling experiments, since the problem of measuring the correct rolling temperature makes the estimation of the yield strength very difficult. The difference between the FE calculations and the experimental measurements is a measure for the error in the experimental temperature measurements rather than for the accuracy of the Finite Element Method.Traditional modelling has not been an appropriate tool to evaluate the material flow in the centre of the billet. In spite of the fact that the entire stress state can be modelled by slip line field theory, the slip lines which determine the stress state in the centre coincide for actual geometries only in one single point. Thus the strain increments are known only in that single point. Since a material element passes that point instantaneously, it is not possible to find any finite strains in the centre by integrating any incremental function. By FEM, strain modelling is simple and the possibility to consolidate a porous bloom or ingot core can be determined.FE modelling requires an entirely new approach to the modelling problem. It is not reasonable to use FEM to evaluate only the temperature distribution for the use in roll force models from the previous century. Instead, a fully thermomechanically coupled FE model is suggested.However, the calculation time is still far too long to be used for on-line control purposes. For this application hybrid modelling can be a solution, where off-line FE models are combined with empirical modelling, and simplified models can be used for the process control.

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A Review on Theoretical Analyses of Rolling in Europe.

Cited by 42 publications

References 1 publication

Numerical analysis of a new Eulerian–Lagrangian finite element method applied to steady‐state hot rolling processes

Numerical analysis of a new Eulerian–Lagrangian finite element method applied to steady‐state hot rolling processes

Deformations and velocities during the cold rolling of aluminium alloys

Modelling of Stress State, Centre Consolidation and Roll Force in Billet Rolling

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