Uncertainty estimation using Gaussian error propagation in metal forming process simulation

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Abstract The ease of estimating the uncertainties of numerical simulations in metal forming is of particular interest. This uncertainty arises from, for example, material parameter identification, geometric dimensions, external loads, and contact conditions. In this paper, we aim to address this issue with the extension to geometric influences, and boundary as well as friction conditions. The uncertainty quantification from material parameter identification – here, in terms of sensitivities of the resulting simulations based on the confidence interval of the parameters – is transferred from the literature and the individual proportions are quantified and compared, respectively. For material parameter identification, experiments on steel and glass fiber reinforced plastic are used and the confidence intervals are determined. Particularly in the case of sequential determination of the parameters, the uncertainties are estimated with the aid of Gaussian error propagation. This concept can also be transferred to geometric dimensions or loads. The application of numerical differentiation for the sensitivities within the Gaussian error propagation leads to a concept where the finite element program can be treated as a black‐box. Here, all uncertainties of the simulation results are obtained, leading to the result that geometric influences in the deep drawing process used as well as the friction coefficient have the largest effect. This provides a very simple procedure for the uncertainty quantification of all individual influencing variables in any finite element simulation.

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