# Robust Design of Deep Drawing Process through In-Line Feedback Control of the Draw-In
## 3 Results
### Influence of Noise Parameters on the Quality of the Drawn Component  
The influence of the noise parameter fluctuations on the quality of the drawn component was evaluated in terms of the thinning, surface deflections, and draw-in at points A, B, and C. The variability ranges of the noise parameters are shown in Table 3 along with their nominal values. For the friction coefficient, its nominal value was set equal to the experimentally calibrated one, i.e., 0.11, and a variability between 0.05 and 0.15 was imposed. Sixty-three numerical simulations were performed by means of Latin Hypercube sampling. Data collected from FE simulations were processed by means of MATLAB DACE toolbox (2.0, Technical University of Denmark DK-2800 Kgs, Lyngby, Denmark) to derive metamodels with the kriging technique [43]. Metamodels highlighted in Figure 12 show the correlation between the thinning percentage and noise parameters such as \(\mu\) and \(\sigma_{0}\) (Figure 12a) and \(\mu\) and \(r_{m}\) (Figure 12b). The other noise parameters are set to their nominal values (\(\sigma_{R}\) and \(r_{m}\) for the metamodel in Figure 12a, while \(\sigma_{0}\) and \(\sigma_{R}\) for the metamodel in Figure 12b). The results shown in Figure 12a highlight that \(\sigma_{0}\) has little to no influence on thinning percentage, unlike \(\mu\), whose increasing values cause an increase in the thinning percentage. This thinning trend as a function of the friction coefficient is in agreement with the literature [10,44]. Figure 12b shows an increase in thinning percentage with a decrease in the mean anisotropy coefficient \(r_{m}\). This behavior agrees with the literature [45]. Metamodels related to the curvature results are shown in Figure 13. Specifically, Figure 13a shows the curvature as a function of \(\mu\) and \(\sigma_{0}\) (\(\sigma_{R}\) and \(r_{m}\) set to the nominal values), while Figure 13b shows the curvature as a function of \(\mu\) and \(r_{m}\) (\(\sigma_{0}\) and \(\sigma_{R}\) set to nominal values). From the metamodel in Figure 13a, it is possible to observe a great  
Figure 11: Graphical scheme of the combination of BHF and p parameters which assure/do not assure the threshold values for (**a**) thinning and (**b**) curvature. Figure 12: Metamodel of thinning percentage for a fluctuation in (**a**) \(\mu\) and \(\sigma_{0}\) and (**b**) \(\mu\) and \(r_{m}\). influence of \(\sigma_{0}\) on the curvature, which becomes even greater with increasing values of \(\mu\). The metamodel in Figure 13b shows that lower values of the friction coefficient result in a greater value of the curvature. This is due to the greater material flow with the reduction in the friction coefficient. Moreover, if the mean value of anisotropy has high values too, the curvature reaches its most critical levels. From the metamodels shown in Figures 12 and 13, it emerges that the most significant noise parameter for both quality indices is the friction coefficient. This result is confirmed by the variable dominating scatter analysis in AutoForm, which is an analysis that defines the most significant noise variable for the quality indexes and the regions where the noise variables exert the greatest influence. Figure 14 shows the obtained results. Metamodels of the draw-in as a function of the noise parameters are illustrated in Figures 15-17, respectively, for sensors A, B, and C. From these figures, it is evident that for all three sensors, lower values of the friction coefficient increase the draw-in. While for the friction coefficient the relationship with the draw-in is quite linear and is the same for all three points considered, for the other two noise parameters this is not true. Specifically, the \(r_{m}\) coefficient has a low influence on the draw-in at sensors A and C (Figures 15b and 17b), whereas at sensor B higher values of it increase the draw-in (Figure 16b).