Due to technological advances in science, the complexity of processes under investigation increased continuously in recent years. For example, in mechanical engineering, there are often highly nonlinear input-output relationships combined with a large number of constraints. Sheet metal spinning is one example of such a production process. Many flexible and powerful methods to global optimization have been developed. In this paper, a sequential approach originally developed for computer experiments will be adopted and applied to optimize the spinning process based on physical experiments. This approach sequentially refines the model by adding new design points based on the expected improvement criterion. This criterion balances the need to observe at the predicted optimum with the need to investigate the design space in areas of high uncertainty. However to guarantee an efficient optimization of the spinning process, this approach has to be embedded in a more substantial procedure. One reason for this is the liability of workpiece failure for most of the operable design space. Since the shape of the failure region is unknown, many missing observations have to be expected when exploring the design space. The other reason is the need to incorporate available process knowledge of sheet metal spinning to improve the efficiency in optimization. The main problem in implementing this information is a changing process behavior for different geometries and materials used. Hence, if a component with a new geometry has to be optimized, it is difficult to include available process knowledge. In this paper, an adaptive sequential optimization procedure (ASOP) is presented to cope with these problems in order to guarantee an efficient optimization of such complex processes. The approach is exemplified by optimizing the spinning process for a fixed geometry.
An efficient sequential optimization approach for complex computer models was presented by Jones et al. (1998). After fitting a stochastic process model based on an initial space filling design, this model is sequentially refined by the expected improvement criterion. This criterion balances the need to search in areas in the design space where the prediction is optimal with the need to search where the model uncertainty is high. This approach can easily be extended to physical processes. Since in practice the overall quality of products of production processes is assessed by more than one response, a multivariate version of the expected improvement criterion is proposed based on desirability functions. This criterion is then used to optimize a metal spinning process.
Due to the high complexity and the large number of possible geometries to be formed, a systematic design of the sheet metal spinning process is, up to now, difficult and time consuming. Sustainable models of the spinning process do not exist so far. Due to this, a new approach for the systematic design and optimization of the spinning process has been developed. In a first step of the planning sequence, a prediction of initial parameter settings is given by a case-based-reasoning approach. A first adaptation of the pre-selected parameters is then realized on a fuzzy-based model. In the next step, a model based optimization using statistical design of experiments is performed. For this, a new statistical approach has been developed being optimized regarding the requirements of the spinning process. In this paper, the methods used and the implementation of the approach in a process planning software are described. The approach is verified by the example of setting up a
process to manufacture a cylindrical model workpiece.
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