Abstract
Precision micro-cups for electronic and medical applications require stringent control of resultant tool force (RTF) and spring-back (SB) to prevent defects, excessive tool loading, and material waste. However, conventional micro deep-drawing processes remain reliant on costly trial-and-error experimentation and exhibit limited predictive reliability under severe plastic deformation and rolling-induced anisotropy. To address this challenge, a robust and computationally reproducible optimization framework is developed for sustainable, high-volume manufacturing. Multistage deep drawing of unidirectionally rolled copper strips subjected to 200% thickness reduction (true strain − 2.78) is investigated using validated finite element modeling (FEM), with clearance (C), punch nose radius (PNR), and coefficient of friction (µ) systematically varied through a Central Composite Design. The resulting FEM-generated dataset is used to train predictive models based on Response Surface Methodology (RSM), Levenberg–Marquardt artificial neural networks (LM-ANN), and Bayesian Regularized artificial neural networks (BR-ANN). Experimental trials are conducted independently for model validation and performance assessment, ensuring that the ANN models are FEM-trained and experimentally validated rather than experimentally trained. These predictive models are integrated with a Genetic Algorithm (GA) for global optimization of RTF and SB. Model performance is evaluated using R², RMSE, MAPE, MSRE, and Nash–Sutcliffe Efficiency (NSE) for both seen (simulation-based) and unseen (experimental) datasets. The BR-ANN–GA framework demonstrates superior predictive accuracy and robustness, identifying optimal parameters of C = 0.57, PNR = 2, and µ = 0.10, minimizing RTF and SB. Prediction errors are limited to 0.35% (RTF) and 0.41% (SB) for FEM-trained data, while experimental validation trials maintain low errors of 1.7% and 2.68%, respectively, outperforming FEM, RSM, and LM-ANN approaches. Although the study is constrained to axisymmetric geometries and unidirectionally rolled copper, the proposed FEM-trained and experimentally validated BR-ANN–GA framework significantly enhances predictive reliability while reducing energy consumption, material waste, and experimental cost, offering a scalable optimization methodology for precision micro deep drawing.
Data availability
All relevant data generated and analyzed during this study are included in the manuscript.
Abbreviations
- PNR or R:
-
Punch nose radius
- COF or µ:
-
Coefficient of friction
- LDR:
-
Limiting drawing ratio
- ID:
-
Inner diameter
- OD:
-
Outer diameter
- FEA:
-
Finite element analysis
- FEM:
-
Finite element method
- ANN:
-
Artificial neural network
- GA:
-
Genetic Algorithm
- RSM:
-
Response surface methodology
- CCD:
-
Central composite design
- BR-ANN:
-
Bayesian Regularized Artificial Neural Network
- LM-ANN:
-
Levenberg–Marquardt Artificial Neural Network
- CAE:
-
Computer-aided engineering
- ANOVA:
-
Analysis of variance
- R2 :
-
Coefficient of determination
- RMSE:
-
Root mean square error
- MAPE:
-
Mean absolute percentage error
- MSRE:
-
Mean squared relative error
- NSE:
-
Nash–Sutcliffe efficiency
- MSE:
-
Mean squared error
- ETP:
-
Electrolytic Tough Pitch (Copper)
- UDR:
-
Unidirectionally rolled
- UTS:
-
Ultimate tensile strength
- EBSD:
-
Electron backscatter diffraction
- KAM:
-
Kernel average misorientation
- SEM:
-
Scanning electron microscopy
- DSC:
-
Differential scanning calorimetry
- RD:
-
Rolling direction
- ND:
-
Normal direction
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**S. P. Sundar Singh Sivam: ** Conceptualisation, Methodology, Resources, Software, Supervision, and Writing ‐ original draft.**Stalin Kesavan: ** Data curation, Formal analysis, Investigation, Visualisation, and Writing – review & editing.**Johnson Santhosh: ** Project administration, Validation, and Writing – review & editing.
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Sivam, S.P.S.S., Kesavan, S. & Santhosh, A.J. A sustainable hybrid FEA–AI optimization framework for multistage deep drawing of unidirectionally rolled copper micro-cups. Sci Rep (2026). https://doi.org/10.1038/s41598-026-45011-4
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DOI: https://doi.org/10.1038/s41598-026-45011-4