Abstract
This study develops a robust hybrid optimization framework to enhance the tribological performance of directionally rolled copper rods for sustainable, defect-free micro-cup production under uncertain manufacturing conditions, where conflicting responses and imprecise decision environments constrain conventional optimization approaches. A face-centered Central Composite Design (CCD) was employed to investigate the effects of four critical process parameters—applied load (400–800 N), sliding speed (2–6 rpm), sliding distance (20–60 m), and draw ratio (1.69–3.09). Six key tribological responses, namely wear rate, coefficient of friction, material loss, frictional force, wear scar diameter, and temperature rise, were modeled using Response Surface Methodology (RSM). Model adequacy and robustness were rigorously validated through ANOVA, adjusted and predicted R2 statistics, residual diagnostics, Shapiro–Wilk normality tests, k-fold cross-validation, Monte Carlo–based uncertainty analysis, and Pareto front evaluation. To address uncertainty and multi-response trade-offs, a Spherical Fuzzy WASPAS-based multi-criteria decision-making (MCDM) approach was implemented by integrating Weighted Sum and Weighted Product measures. Wear mechanism maps were further developed to associate operating regimes with dominant wear mechanisms. The hybrid framework successfully identified both optimal and critical operating conditions. The optimal parameter combination (800 N load, 6 rpm speed, 20 m sliding distance, and 1.69 draw ratio) delivered superior tribological performance with prediction errors below 5%, exhibiting reduced wear and friction, improved dimensional stability, and controlled thermal response. Conversely, the worst condition (800 N, 2 rpm, 60 m, 3.09 draw ratio) resulted in pronounced wear, higher friction, and elevated temperature rise. Wear mechanism maps revealed a transition from mild oxidative–adhesive wear under optimal conditions to severe adhesive–abrasive wear in adverse regimes. Although limited to copper rods under dry sliding, the proposed framework offers a reliable decision-support tool for precision micro-forming applications and is readily extendable to biodegradable alloys such as magnesium and zinc for emerging biomedical and temporary implant applications.
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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. & Johnson Santhosh, A. A hybrid RSM–spherical fuzzy WASPAS framework for robust tribological optimization of directionally rolled copper rods under manufacturing uncertainty. Sci Rep (2026). https://doi.org/10.1038/s41598-026-42132-8
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DOI: https://doi.org/10.1038/s41598-026-42132-8
