Gradient, non-gradient and hybrid algorithms for optimizing 3D forging sequences with uncertainties

Reprinted with permission from AIP Conf. Proc May 17, 2007 Volume 908, pp. 475-480 MATERIALS PROCESSING AND DESIGN; Modeling, Simulation and Applications; NUMIFORM '07; Proceedings of the 9th International Conference on Numerical Methods in Industrial Forming Processes; doi:10.1063/1.2740856. Copyright 2007 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of PhysicsInternational audienceIn the frame of computationally expensive 3D metal forming simulations, optimization algorithms are studied in order to find satisfactory solutions within less than 50 simulations and to handle complex optimizations problems with several extrema. Two types of algorithms are selected, which both utilize a meta-model to approximate the objective function and so reduce computational cost. This model either supports standard Evolutionary Algorithms, such as Genetic Algorithms, or is sequentially improved until finding a satisfactory and well approximated solution. The Meshless Finite Difference Method is the utilized meta-model, without (standard algorithm) or with (hybrid algorithm) the gradient information. This meta-model approach allows taking into account uncertainties on optimization parameters in an inexpensive way. The optimization procedure is modified accordingly. The proposed algorithms are first evaluated and compared on standard analytic functions, and then applied to a 3D forging benchmark, the shape optimization of preform tool in order to minimize the potential of fold formation

3D numerical simulation of the three stages of Friction Stir Welding based on friction parameters calibration

International audienceAn Arbitrary Lagrangian Eulerian (ALE) formulation was developed to simulate the different stages of the Friction Stir Welding (FSW) process with the FORGE3® F.E. software. A splitting method was utilized: a) the material velocity/pressure and temperature fields are calculated, b) the mesh velocity is derived from the domain boundary evolution and an adaptive refinement criterion provided by error estimation, c) P1 and P0 variables are remapped. The proposed ALE formulation is applied to FSW simulation. Steady state welding, but also transient phases are simulated, showing good robustness and accuracy of the developed formulation. Friction parameters are identified for an Eulerian steady state simulation by comparison with experimental results. Simulations of the transient plunge and welding phases help to better understand the deposition process that occurs at the trailing edge of the probe, and in particular possible void formation. Flexibility and robustness of the model allows investigating the influence of threads and tooling designs

Error estimation and accurate mapping based ALE formulation for 3D simulation of friction stir welding

Reprinted with permission from AIP Conf. Proc. May 17, 2007 -- Volume 908, pp. 185-190 MATERIALS PROCESSING AND DESIGN; Modeling, Simulation and Applications; NUMIFORM '07; Proceedings of the 9th International Conference on Numerical Methods in Industrial Forming Processes; doi:10.1063/1.2740809 Copyright 2007 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of PhysicsInternational audienceAn Arbitrary Lagrangian Eulerian (ALE) formulation is developed to simulate the different stages of the Friction Stir Welding (FSW) process with the FORGE3® F.E. software. A splitting method is utilized: a) the material velocity/pressure and temperature fields are calculated, b) the mesh velocity is derived from the domain boundary evolution and an adaptive refinement criterion provided by error estimation, c) P1 and P0 variables are remapped. Different velocity computation and remap techniques have been investigated, providing significant improvement with respect to more standard approaches. The proposed ALE formulation is applied to FSW simulation. Steady state welding, but also transient phases are simulated, showing good robustness and accuracy of the developed formulation. Friction parameters are identified for an Eulerian steady state simulation by comparison with experimental results. Void formation can be simulated. Simulations of the transient plunge and welding phases help to better understand the deposition process that occurs at the trailing edge of the probe. Flexibility and robustness of the model finally allows investigating the influence of new tooling designs on the deposition process

Metamodel Assisted Evolutionary Algorithm for Multi-objective Optimization of Non-steady Metal Forming Problems

International audienceMultiobjective optimization problems are considered in the field of nonsteady metal forming processes, such as forging or wire drawing. The Pareto optimal front of the problem solution set is calculated by a Genetic Algorithm. In order to reduce the inherent computational cost of such algorithms, a surrogate model is developed and replaces the exact the function simulations. It is based on the Meshless Finite Difference Method and is coupled to the NSGAII Evolutionary Multiobjective Optimization Algorithm, in a way that uses the merit function. This function offers the best way to select new evaluation points: it combines the exploitation of obtained results with the exploration of parameter space. The algorithm is evaluated on a wide range of analytical multiobjective optimization problems, showing the importance to update the metamodel along with the algorithm convergence. The application to metal forming multiobjective optimization problems show both the efficiency of the metamodel based algorithms and the type of practical information that can be derived from a multiobjective approach

Accurate 3D friction stir welding simulation tool based on friction model calibration

International audienceFriction Stir Welding (FSW) is one of the most effective solid states joining process and has numerous potential applications in many industries. A FSW numerical tool, based on Forge® F.E software, has been developed. Its main features are an Arbitrary Lagrangian Eulerian (ALE) formulation and an adaptive remeshing procedure based on error estimation. A 3D FSW simulation based on friction models calibration has been presented using Eulerian and ALE formulation. Two friction models have been studied to model friction in the tool-plate interface in aluminium alloy 6061-T6: Norton's and Coulomb's. Comparisons with experimental results considering various travel speed has been performed

Simulation 3D du soudage par frottement malaxage (FSW) à l'aide d'une formulation Arbitrairement Lagrangienne ou Eulérienne (ALE)

National audienceLe procédé FSW est un procédé de soudage par frottement et malaxage dont la complexité résulte d'un très fort couplage thermomécanique. Nous présentons une nouvelle formulation Arbitrairement Lagrangienne ou Eulérienne (ALE) en vue de le modéliser avec précision. Son utilisation montre qu'elle est parfaitement adaptée à la simulation du FSW en 3D. Elle permet notamment de simuler des soudures de qualité ou la formation de défauts tels que les bavures ou les trous tunnels qui peuvent apparaître en arrière du pion. Des améliorations ont été apportées au logiciel afin d'augmenter la précision de la simulation. Un filetage numérique a ainsi été modélisé sur l'outil pour augmenter le malaxage du matériau. Le transport des champs continus a été perfectionné pour gérer des instabilités de surface

Quasi-symmetrical formulations for contact and friction between deformable bodies: application to 3D forging

http://congress.cimne.com/complas05/admin/Files/FilePaper/p16.pdfTo properly handle the contact conditions without introducing spurious numerical constraints, the master / slave approach is inescapable but it results into a non-symmetric formulation for non-coinciding meshes [1]. From a theoretical standpoint, this unsatisfactory treatment of the contact area results into a decrease of the convergence rate of the finite element method [2]. From a more practical standpoint, severe problems arise when the discretization of the master surface is much finer than the slave surface. In metal forming, the workpiece is always the slave while the tools are the masters. So aiming at accurate tool stress calculations require masters meshes that are locally much finer than the corresponding mesh on the slave-workpiece. With a standard formulation, parts of the tool contact surface may result to be numerically unloaded, so providing very inaccurate finite element solution where high accuracy is required. A symmetric formulation has been proposed in [3], but it introduces spurious constraints. In [1], an accurate calculation of the contact conditions between the contacting bodies in proposed, while in [2], a L2 enhanced projection of the displacement field on the contact surface is developed. Both algorithms are written in 2D for an integrated formulation. Their extension in 3D seems quite uneasy. We then proposed a quasi-symmetric formulation [4]. It can be compared to [3] but the contact Lagrange multipliers are not duplicated on both contact surfaces. It so allows avoiding introducing spurious constraints, while keeping a simple and almost symmetric formulation. The implementation is not too complex. It is carried out into the FORGE3® finite element software, where a nodal (node to facet) contact formulation is utilized and the contact conditions are handled by a penalty method. A series of patch tests that have been proposed in [1] and [2], allows evaluating the convergence rate of this formulation and its robustness

Optimisation multi-objectifs à base de méta-modèle pour les problèmes de mise en forme

http://giens2009.lmt.ens-cachan.fr/actes2.phpNational audiencePour appliquer des méthodes d'optimisation multi-objectifs à des problèmes de mise en forme des matériaux très coûteux en temps de calcul, nous étudions le couplage de l'algorithme NSGA-II proposé par K. Deb avec des méta-modèles inspirés de la méthode des Différences Finies sans Maillages de Liszka et Orkisz. Nous observons l'importance d'améliorer itérativement le méta-modèle au cours des itérations d'optimisation, et la possibilité de déterminer avec précision les fronts de Pareto du problème en moins d'une centaine de calculs

Meta-model assisted multi-objective optimization for non-steady 3D metal forming processes

International audienceThis paper studies efficient techniques to find the optimal set of solutions (Pareto front) for multiobjective optimization problems in the context of time expensive evaluation of functions. These techniques make use of a meta-model based on the Meshless Finite Difference Method (MFDM) coupled with evolutionary Multi-Objective algorithm (here: NSGA-II) in order to minimize the time consuming evaluations and to achieve a faster convergence to the Pareto front. The different studied methods differ in the choice of master points, the evolution of the meta-model, and the updating of elitism. They are studied and compared on several analytical functions, with only 100 exact evaluations of the objective function. The obtained results show the efficiency of these techniques

A 3D study of the influence of friction on the Adiabatic Shear Band formation during High Speed Machining

International audienceAdiabatic Shear Band (ASB) may form at very high speeds with materials having poor thermal conductivity. It results from the competition between plastic hardening and strain softening and initiates when the latter becomes predominant. Because of high speeds, the heat created does not have sufficient time to propagate, leading to the formation of high strain localized zones. Starting from a previous description of the ASB formation process where the friction phenomenon has been considered as negligible, the aim of this paper is to describe the influence of the latter on the ASB formation process. Consequently, using a very general 3D finite element code where mesh adaptation is triggered by an error estimator within an Arbitrary Lagrangian Eulerian formulation, the formation of several ASB has been simulated in 3D High Speed Machining taking friction into account. The results obtained allow proposing a description of its influence on both the ASB build up process and the final chip geometry