Robust design and optimization of forming processes

Abstract

A current trend in the metal forming industry is the coupling of Finite Element (FE) simulations with an optimization procedure. Using a so-called simulation-based optimization approach, forming processes can be designed for which optimal use is made of the material and process capabilities. However, in practice metal forming processes are subject to input uncertainty or variation, e.g. variation of material properties or fluctuating process settings. In cases where these uncertainties are neglected in simulation-based optimization, very often an optimal deterministic process design is found which is at the limits of the material and process capabilities. The presence of input variation might lead to violation of the limits in practice, resulting in product rejects. To avoid this undesirable situation, uncertainty has to be taken into account explicitly in the optimization of forming processes. A robust optimization strategy has been developed for modeling and efficiently solving simulation-based robust optimization problems of forming processes. The strategy consists of the following main stages: modeling, variable screening, robust optimization, validation and sequential improvement. In the modelling step, input variation is quantified and accounted for explicitly in the optimization strategy. For solving, use is made of a metamodel-based approach combined with Monte Carlo analyses to obtain the statistical measures of the objective function and constraints. The strategy enables finding the optimal process design which meets the constraints, even in the presence of uncertainty. This type of optimal design is referred to as a robust design in this thesis. The strategy has been applied to robust optimization problems of various industrial metal forming processes, i.e. a roll forming process, a V-bending process, a stretching process and a stretch-drawing process. Several research topics have been treated in more detail and evaluated by application to the industrial forming processes, i.e. sequential robust optimization, numerical noise, and quantification and modeling of material scatter. The application studies demonstrated that it is necessary to include uncertainty in the optimization strategy, that it can be done efficiently and that it leads to a considerably improved robustness of the resulting forming process.