Application of the Arbitrary Lagrangian Eulerian Formalism to Stationary Roll Forming Simulations

Due to the length of the mill, accurate modelling of stationary solution of continuous cold
roll forming by the finite element method using the classical Lagrangian formulation usually requires a very large mesh leading to huge CPU times. In order to model industrial forming lines including many tools in a reasonable time, the sheet has to be shortened or the element size has to be increased leading to inaccurate results. On top of this, applying loads and boundary conditions on this smaller sheet is usually more difficult than in the continuous case. Moreover, transient dynamic vibrations, which are unnecessarily computed, may appear when the sheet hits each tool, decreasing the convergence rate of the numerical simulation. Beside this classical Lagrangian approach, an alternative method is given by the Arbitrary Lagrangian Eulerian (ALE) formalism which consists in decoupling the motion of the material and the mesh. Starting from an initial guess of the sheet geometry between the rolls, the numerical simulation is performed until the stationary state is reached with a mesh, the nodes of which are fixed in the rolling direction but are free to move on perpendicular plane, following the geometrical boundary of the sheet. The whole forming line can then be modelled using a limited number of brick and contact elements because the mesh is only refined near the tools where bending and contact occur. In this paper, ALE results are compared to previous Lagrangian simulations and experimental measurement on a U-channel, including springback.