Fusion metamodeling of the bend deduction in air bending

The results of sheet metal air bending process are still very difficult to predict, despite the high level of automation introduced on the bending press by the computer numerical control. The air bending process results are related to the obtained angle after springback and to the elongation of the component, which can be measured through the so-called bend deduction parameter (BD). While the prediction of the springback phenomenon is largely discussed in the literature and several prediction models are available, the bend deduction is often neglected. Even small errors in the prediction of BD might have a dramatic effect on the tolerances of complex components with several consecutive bends. The aim of this paper is to present a so called "fusion" or "hierarchical" metamodel for the prediction of the bend deduction in air bending. The approach is to first build a kriging interpolator BDkrigover the results of about 400 simulation runs, run with different material parameters, different tools geometry and different punch stroke values. Then, a "fusion" metamodel BDfusis built, which uses the BDkriginterpolator as one of the predictors in a regression model built over a training set of physical experiments. The physical experiments have been conducted with different conditions (tooling, materials, etc.), with 2 or 3 replicates for each condition. The average BDexpvalue of each condition has been measured with two specifically designed measuring rigs, one for acute bend angles (<=90°) and one for angles larger than 90°. The quality of the prediction yielded by the BDfusmetamodel has been successfully verified over a validation experimental set.