Catherine Knopf-Lenoir

Optimization of drawbead restraining forces and drawbead design in sheet metal forming process

Abstract This paper presents an optimization procedure of drawbead restraining forces in order to improve the sheet metal formability in deep drawing process. A simplified finite element method called inverse approach (IA) has been developed for sheet forming analysis with the consideration of the drawbead restraining forces. This IA is combined with a mathematical programming algorithm to optimize the restraining forces and then to design the drawbeads. The obtained optimization procedure is very efficient due to the simplified assumptions of the IA and the analytical sensitivity analysis. The Square cup of Numisheet’93 and the Renault Twingo dashpot cup are presented to demonstrate the usefulness of the proposed optimization procedure for industrial applications. Verifications of the obtained results have been carried out using a precise incremental commercial code OPTRISTM based on explicit dynamic approach to show the effectiveness of our approach.

Optimal design and optimal control of structures undergoing finite rotations and elastic deformations

In this work, we deal with the optimal design and optimal control of structures undergoing large rotations and large elastic deformations. In other words, we show how to find the corresponding initial configuration through optimal design or the corresponding set of multiple load parameters through optimal control, in order to recover a desired deformed configuration or some desirable features of the deformed configuration as specified more precisely by the objective or cost function. The model problem chosen to illustrate the proposed optimal design and optimal control methodologies is the one of geometrically exact beam. First, we present a non-standard formulation of the optimal design and optimal control problems, relying on the method of Lagrange multipliers in order to make the mechanics state variables independent from either design or control variables and thus provide the most general basis for developing the best possible solution procedure. Two different solution procedures are then explored, one based on the diffuse approximation of response function and gradient method and the other one based on genetic algorithm. A number of numerical examples are given in order to illustrate both the advantages and potential drawbacks of each of the presented procedures.

Response Surface Methodology for the Design of Sheet Metal Forming Parameters to Control Springback Effects using the Inverse Approach

This paper deals with the optimization of tools geometry in sheet metal forming in order to reduce the springback effects after forming. A Response Surface Method (RSM) based on Diffuse Approximation (DA) is used. A new modified version of the Inverse Approach (IA) used to analyze the stamping operation is presented. The bending/unbending moments and the final shape are used to calculate springback using an incremental approach based on the Updated Lagragian Formulation (ULF). The U‐bending benchmark of Numisheet’93 is used and good results of springback elimination have been obtained.

Optimization of the blankholder force distribution with application to the stamping of a car front door panel (Numisheet’99)

New materials such as dual phase steel or aluminium and complex geometries of industrial parts increase the difficulties to obtain a defect free part by stamping. One way of solution is a better regulation of the blankholder pressures. Our work is based on an original idea of Siegert, Haussermann and Haller. The goal is to control the movement of the blank under the blankholder. Thanks to a deformable flexible blankholder, it is possible to create some independent zones. In each zone, a blankholder force can be applied on the sheet, so that a strong force can hold the blank in a zone, and a smaller one can let it move in another zone. The methodology is presented as well as some results dealing with the optimization of the blankholder force considering the drawing of a front door panel (Numisheet’99 benchmark test). The numerical simulations are performed using ABAQUS Explicit. The parameters of the finite element model (mesh density, speed of punch) are set to achieve a good prediction with a minimum sim...

Optimization Of The Blankholder Force With Application To The Numisheet’02 Deep Drawing Benchmark Test B1

The increasing use of new materials such as dual phase steel or aluminium alloys leads to some difficulties to overcome regarding their formability. One way to obtain good parts in deep drawing operations is to modify the process parameters to achieve a better control of the strains in the sheet. Our work is based on an original idea of Siegert, Haussermann and Haller. The goal is to control the movement of the blank under the blankholder by varying locally the blankholder force. This is achieved by a deformable blankholder and by different pressures in the pins (in time and space). In this paper, we present the methodology and some results dealing with the optimization in time of the blankholder force considering the drawing of a cylindrical cup (Numisheet’02 benchmark test). The numerical simulations are performed using Abaqus Explicit. The parameters of the finite element model (mesh dimension, speed, contact algorithms) are set to achieve a good prediction. The objective function is to minimize the wo...

Optimisation des forces de retenue pour le contrôle de la qualité des tôles minces embouties

ABSTRACT In the deep drawing process, drawbead restraining forces can control the material flow and thus the part quality in the sheet forming process. The Inverse Approach (I.A.) developed at UTC can be used for sheet forming simulation more efficiently than incremental methods. This I.A. is combined with a Sequential Quadratic Programming (SQP) algorithm to optimize the restraining forces in order to avoid necking and wrinkling. This optimization procedure seems to be very efficient due to the simplified assumptions of the I.A. and the analytical sensitivity analysis.

Approche inverse améliorée pour la minimisation du retour élastique de pièces embouties

Dans ce travail on s’intéresse à la minimisation de la deformation élastique des pièces embouties suite au retrait des outils en fin d’emboutissage. Nous utilisons une méthode de surface de réponse (MSR) basée sur l’approximation diffuse (AD) et un algorithme spécifique pour la recherche du minimum. Pour la simulation d’emboutissage, nous adoptions l’approche inverse avec une amélioration des contraintes pour prendre en compte les effets de cambrage et de décambrage dans la zone de brin libre. Les efforts internes et la forme finale de la pièce emboutie sont utilisés pour le calcul du retour élastique en adoptant une formulation lagrangienne actualisée. Deux tests d’emboutissage sont utilisés pour la validation de la procédure d’optimisation proposée en référence aux codes commerciaux Abaqus® et Stampack®.

Contrôle des défauts d’emboutissage par optimisation des efforts serre-flan

Ce travail concerne l’optimisation des efforts serre-flan en emboutissage, le serreflan étant constitué de zones indépendantes. Les forces optimales appliquées sur ces zones sont calculées pour éviter les défauts d’emboutissage (striction et plissement de la tôle). Dans le cadre de ces travaux, un critère de striction a été formulé. La procédure d’optimisation utilise une surface de réponse basée sur une approximation par moindres carrés pondérés. La méthode est appliquée à un panneau de porte, cas-test de la conférence Numisheet’99.

Optimisation des efforts serre-flan pour l’emboutissage d’une boîte carrée: Contrôle de la striction et du plissement sous serre-flan

L’objectif de la simulation numérique en emboutissage est principalement l’amélioration de la qualité de la pièce finale obtenue par le contrôle et l’optimisation de paramètres du procédé. Pour éviter la rupture, un critère de striction localisée a été formulé et validé sur un godet cylindrique et un test de Nakazima, sur lesquels des ruptures ont été observées expérimentalement. La deuxième partie de ce travail est consacrée à l’optimisation des efforts serre-flan d’une boîte carrée afin d’améliorer sa formabilité.

Conception optimale des pièces mécaniques modélisées par des coques minces

ABSTRACT This paper is concerned with a numerical method to solve some thin shell optimization problems. The functions to minimize or to limit are the mass and the Von Mises stress. Sensitivity analysis is developed in the discrete case. Numerical results are presented for an aeronautic piece (gear case) of complex shape.