Sensitivity Analysis of the Square Cup Forming Process Using PAWN and Sobol Indices
<p>Square cup forming process: (<b>a</b>) dimensions of the tools in mm; (<b>b</b>) numerical model. adapted with permission from [<a href="#B18-metals-14-00432" class="html-bibr">18</a>]; (<b>c</b>) mesh sensitivity.</p> "> Figure 2
<p>Plots of mean and standard deviation for (<b>a</b>) EPS, (<b>b</b>) TR, (<b>c</b>) GC, (<b>d</b>) SB.</p> "> Figure 3
<p>Evolution of the mean (<b>a</b>) and standard deviation (<b>b</b>) of the force applied by the punch.</p> "> Figure 4
<p>Distribution of maximum model response for (<b>a</b>) PF; (<b>b</b>) EPS; (<b>c</b>) TR; (<b>d</b>) GC; and (<b>e</b>) SB.</p> "> Figure 5
<p>Stabilization analysis for (<b>a</b>) PF; (<b>b</b>) EPS; (<b>c</b>) TR; (<b>d</b>) GC; and (<b>e</b>) SB.</p> "> Figure 6
<p>Sobol and PAWN indices for (<b>a</b>) PF; (<b>b</b>) EPS; (<b>c</b>) TR; (<b>d</b>) GC; and (<b>e</b>) SB.</p> "> Figure 7
<p>Pareto analysis for PAWN indices for the responses (<b>a</b>) PF; (<b>b</b>) EPS; (<b>c</b>) TR; (<b>d</b>) GC; and (<b>e</b>) SB.</p> "> Figure 8
<p>Pareto analysis for Sobol indices for the responses (<b>a</b>) PF; (<b>b</b>) EPS; (<b>c</b>) TR; (<b>d</b>) GC; and (<b>e</b>) SB.</p> "> Figure 9
<p>Distribution of PAWN (<b>left</b>) and Sobol (<b>right</b>) indices for equivalent plastic strain: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>n</mi> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>90</mn> </mrow> </msub> </mrow> </semantics></math>.</p> "> Figure 10
<p>Distribution of PAWN (<b>left</b>) and Sobol (<b>right</b>) indices for thickness reduction: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>n</mi> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>90</mn> </mrow> </msub> </mrow> </semantics></math>.</p> "> Figure 11
<p>Distribution of PAWN (<b>left</b>) and Sobol (<b>right</b>) indices for the geometry changes: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>n</mi> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>90</mn> </mrow> </msub> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math>.</p> "> Figure 12
<p>Distribution of PAWN (<b>left</b>) and Sobol (<b>right</b>) indices for springback: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>H</mi> <mi>F</mi> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>C</mi> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>90</mn> </mrow> </msub> </mrow> </semantics></math>.</p> "> Figure 13
<p>Parameters corresponding to the maximum PAWN index (<b>left</b>) and Sobol index (<b>right</b>) in each zone of for (<b>a</b>) EPS; (<b>b</b>) GC; (<b>c</b>) TR; and (<b>d</b>) SB.</p> "> Figure 14
<p>Indices of punch force as a function of displacement for (<b>a</b>) PAWN indices and (<b>b</b>) Sobol indices.</p> ">
Abstract
:1. Introduction
2. Numerical Model
3. Sensitivity Analysis
3.1. Stabilization Analysis
3.2. Pareto Analysis
3.3. Sensitivity Indices per Region of the Square Cup
3.4. Maximum Sensitivity Indices per Region of the Square Cup
3.5. Evolution of Sensitivity Indices for the Punch Force
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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[GPa] | [MPa] | [MPa] | [mm] | [N] | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|
206.00 | 0.300 | 1.790 | 1.510 | 2.270 | 157.12 | 0.259 | 565.32 | 0.780 | 0.1440 | 9800.0 | |
3.85 | 0.015 | 0.051 | 0.037 | 0.121 | 7.16 | 0.018 | 26.85 | 0.013 | 0.0288 | 490 |
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Parreira, T.G.; Rodrigues, D.C.; Oliveira, M.C.; Sakharova, N.A.; Prates, P.A.; Pereira, A.F.G. Sensitivity Analysis of the Square Cup Forming Process Using PAWN and Sobol Indices. Metals 2024, 14, 432. https://doi.org/10.3390/met14040432
Parreira TG, Rodrigues DC, Oliveira MC, Sakharova NA, Prates PA, Pereira AFG. Sensitivity Analysis of the Square Cup Forming Process Using PAWN and Sobol Indices. Metals. 2024; 14(4):432. https://doi.org/10.3390/met14040432
Chicago/Turabian StyleParreira, Tomás G., Diogo C. Rodrigues, Marta C. Oliveira, Nataliya A. Sakharova, Pedro A. Prates, and André F. G. Pereira. 2024. "Sensitivity Analysis of the Square Cup Forming Process Using PAWN and Sobol Indices" Metals 14, no. 4: 432. https://doi.org/10.3390/met14040432