From specified product tolerance to acceptable materialand process scatter: an inverse robust optimization approach

Production efficiency in metal forming processes can be improved by implementing robust optimization. In a robustoptimization method, the material and process scatter are taken into account to predict and to minimize the product variabilityaround the target mean. For this purpose, the scatter of input parameters are propagated to predict the product variability.Consequently, a design setting is selected at which product variation due to input scatter is minimized. If the minimumproduct variation is still higher than the specific tolerance, then the input noise must be adjusted accordingly. For examplethis means that materials with a tighter specification must be ordered, which often results in additional costs. In this article,an inverse robust optimization approach is presented to tailor the variation of material and process noise parameters basedon the specified product tolerance. Both robust optimization and tailoring of material and process scatter are performed onthe metamodel of an automotive part. Although the robust optimization method facilitates finding a design setting at whichthe product to product variation is minimized, the tighter product tolerance is only achievable by requiring less scatter ofnoise parameters. It is shown that the presented inverse approach is able to predict the required adjustment for each noiseparameter to obtain the specified product tolerance. Additionally, the developed method can equally be used to relax materialspecifications and thus obtain the same product tolerance, ultimately resulting in a cheaper process. A strategy for updatingthe metamodel on a wider (noise) base is presented and implemented to obtain a larger noise scatter while maintaining thesame product tolerance