The Arbitrary Lagrangian Eulerian (ALE) formalism is a breakthrough technique in the numerical simulation of the continuous-type roll-forming process. In contrast to the classical Lagrangian approach, the ALE formalism can compute the hopefully stationary state for the entire mill length with definitely effortless set-up tasks thanks to a nearly-stationary mesh. In this paper, advantages of ALE and Lagrangian formalisms are extensively discussed for simulating such continuous-type processes. Through a highly complex industrial application, the ease of use of ALE modelling is illustrated with the in-house code METAFOR. ALE and Lagrangian results are in good agreement with each other.

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In industry, cold roll forming is more and more used as a manufacturing process mainly for its high productivity and its close geometric tolerances. However, most of the finite element simulations are restricted to the sheet to sheet process - the sheet length being smaller than the whole roll forming line - because the numerical models rely on a Lagrangian kinematics that is not very well suited for the forming of long sheets in a reasonable computational time. The Arbitrary Lagrangian Eulerian (ALE) formalism, which consists in decoupling the motion of the material and the mesh, has the capability to simulate the continuous process for the whole roll forming line at reduced CPU cost by optimization of the mesh. In the particular case of roll forming, the mesh nodes are fixed in the rolling direction but are free to move in transverse directions. Taking advantage from this approach, the mesh is only refined in the neighbourhoods of the forming tools for accurate modeling of contact and bending.

Finite element simulation of the roll forming process is regarded as an essential tool for the early design and optimization stages of a roll forming mill. However, such simulations are generally incredibly time-consuming, limited to some simple cases and to the pre-cut forming method. In contrast to the classical Lagrangian approach, the Arbitrary Lagrangian Eulerian (ALE) formalism, which consists in decoupling the motion of the material and the mesh, can simulate the continuous process for the entire roll forming line at reasonable CPU cost by using a nearly-stationary mesh. In this work, the numerical results are compared to some experimental data on a U-channel in order to validate both Lagrangian and ALE models using our in-house code METAFOR. Furthermore, advantages of the ALE formalism are highlighted with the simulation of a tubular rocker panel on a 16-stand forming mill, which is a real industrial mill.

L’application du formalisme Arbitraire Lagrangien Eulérien (ALE) à la simulation numérique du procédé de profilage permet de calculer l’état espéré stationnaire du procédé de type continu en modélisant de manière efficace l’intégralité de la ligne grâce à un maillage quasi-Eulérien. Ce type de simulation sera comparé à l’approche classique en formalisme Lagrangien dans le cadre d’une application industrielle de profilage. Les performances de la parallélisation de l’algorithme ALE seront analysées dans l’état actuel des développements du code de calcul METAFOR.

Cold roll forming is a rather old process for which there is a renewed interest due to its capacity to form ultra high-strength steels. For the first time ever in the literature, the manufacturing chain involving both the continuous cold roll-forming process, the in-line welding operation for closed sections and the post-cut operation is numerically modelled. The first phase of this process sequence consists in computing the hopefully steady state configuration of the strip for the total length of the roll-forming mill, including the in-line welding phase. For addressing this problem, the Arbitrary Lagrangian Eulerian (ALE) formalism is used. Once the ALE steady state is reached, the computation is pursued with a second Lagrangian phase which is aimed at simulating the post-cut operation that releases the formed section from the rolling tools of the mill, enabling to determine the final geometry of the product. In this paper, the computational modelling framework employed within the in-house finite element code METAFOR is described. In particular, the proposed techniques — which are definitely original within an ALE formalism — for modelling the in-line welding operation and the post-cut operation are extensively detailed. The welding is considered with three different methods: (1) symmetry boundary conditions coupled with a well-suited node relocation procedure, (2) a closed mesh of the closed section coupled with a well-suited node relocation procedure, and (3) sticking elements based on a spring constitutive formulation. A set of simple numerical examples demonstrates the confidence in all the proposed modelling methods. Finally, these methods are successfully applied in the cases of two complex roll-forming mills of closed tubular sections.