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A novel taguchi–ocra optimization framework for incremental sheet metal forming of miniature conical cups with multi-response validation and cross-geometry applicability
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  • Published: 23 March 2026

A novel taguchi–ocra optimization framework for incremental sheet metal forming of miniature conical cups with multi-response validation and cross-geometry applicability

  • S. P. Sundar Singh Sivam1,
  • Stalin Kesavan2 &
  • A. Johnson Santhosh3 

Scientific Reports , Article number:  (2026) Cite this article

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We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Engineering
  • Materials science

Abstract

This study aims to optimize the incremental sheet metal forming (ISMF) process for conical miniature cups by simultaneously improving formability, dimensional accuracy, energy efficiency, and sustainability. An L9 Taguchi experimental design was employed to investigate four key process parameters: feed rate, forming depth, step size, and sheet material. Multiple performance responses, including wall angle, thickness reduction, surface roughness, forming time, springback, and power consumption, were evaluated. Operational Competitiveness Rating Analysis (OCRA) was integrated with the Taguchi approach to rank alternatives and identify the optimal parameter combination. The proposed framework was further validated through confirmation experiments, ANOVA, repeatability and reproducibility tests, sensitivity analysis with multiple MCDA methods, dimensional and surface quality assessment, cross-validation using different geometries, and a simplified use-phase life cycle assessment. The optimized condition (90 mm/min feed rate, 0.10 mm depth, 0.25 mm step size, and copper sheet) reduced forming time by 18.75%, power consumption by 56.25%, and per-part energy use and CO₂ emissions by about 64.5% compared with the non-optimized condition. Surface roughness and springback were also reduced, while dimensional accuracy and repeatability remained within acceptable limits. Cross-validation confirmed good transferability to cylindrical geometries, although moderate deviations were observed for prismatic parts. Overall, the study presents a robust Taguchi–OCRA-based decision framework for sustainable ISMF optimization.

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Data availability

All relevant data generated and analyzed during this study are included in the manuscript.

Abbreviations

ISMF:

Incremental Sheet Metal Forming

ISF:

Incremental Sheet Forming

SPIF:

Single Point Incremental Forming

μ-ISF:

Micro Incremental Sheet Forming

OCRA:

Operational Competitiveness Rating Analysis

AHP:

Analytical Hierarchy Process

MCDA:

Multi-Criteria Decision Analysis

MCDM:

Multi-Criteria Decision Making

GRA:

Grey Relational Analysis

TOPSIS:

Technique for Order Preference by Similarity to Ideal Solution

VIKOR:

VlseKriterijumska Optimizacija I Kompromisno Resenje

SAW:

Simple Additive Weighting

CRITIC:

Criteria Importance Through Intercriteria Correlation

COPRAS:

Complex Proportional Assessment 

SWARA:

 Stepwise Weight Assessment Ratio Analysis

ROC:

Rank Order Centroid

PIPRECIA:

Pivot Pairwise Relative Criteria Importance Assessment

ANOVA:

Analysis of Variance

RSM:

Response Surface Methodology

ANN:

Artificial Neural Network

GA:

Genetic Algorithm

PRESS:

Predicted Residual Error Sum of Squares

R²:

Coefficient of Determination

Adj R²:

Adjusted Coefficient of Determination

Pred R²:

Predicted Coefficient of Determination

CI:

Consistency Index

CR:

Consistency Ratio

λmax:

Maximum Eigenvalue

BIC:

Bayesian Information Criterion

AICc:

Corrected Akaike Information Criterion

WA:

Wall Angle

TR:

Thickness Reduction

SR:

Surface Roughness

Ra:

Arithmetic Average Roughness

FT:

Forming Time

SB:

Springback

Pc:

Power Consumption

RTF:

Resultant Tool Force

PC:

Power Consumption

TR (%):

Thickness Reduction Percentage

R&R:

Repeatability and Reproducibility

C. V.:

Coefficient of Variation

Δz:

Incremental Step-Down Depth

H:

Total Forming Height

to:

Initial Thickness

tf:

Final Thickness

CNC:

Computer Numerical Control

HSS:

High-Speed Steel

MS:

Mild Steel

SS304:

Stainless Steel Grade 304

LCA:

Life Cycle Assessment

CO₂:

Carbon Dioxide

kWh:

Kilowatt-Hour

ISO:

International Organization for Standardization

JIS:

Japanese Industrial Standards

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Authors and Affiliations

  1. Department of Mechanical Engineering, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, 603203, Tamil Nadu, India

    S. P. Sundar Singh Sivam

  2. Department of Marine Engineering, Amet University, East Coast Road, 603 112, Kanathur, Chennai, India

    Stalin Kesavan

  3. Faculty of Mechanical Engineering, Jimma Institute of Technology, Jimma University, Jimma, Ethiopia

    A. Johnson Santhosh

Authors
  1. S. P. Sundar Singh Sivam
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  2. Stalin Kesavan
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  3. A. Johnson Santhosh
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Contributions

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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Correspondence to S. P. Sundar Singh Sivam or A. Johnson Santhosh.

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Sivam, S.P.S.S., Kesavan, S. & Santhosh, A.J. A novel taguchi–ocra optimization framework for incremental sheet metal forming of miniature conical cups with multi-response validation and cross-geometry applicability. Sci Rep (2026). https://doi.org/10.1038/s41598-026-44398-4

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  • Received: 26 December 2025

  • Accepted: 11 March 2026

  • Published: 23 March 2026

  • DOI: https://doi.org/10.1038/s41598-026-44398-4

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Keywords

  • Incremental sheet metal forming
  • Taguchi method
  • OCRA
  • Sustainability
  • Miniature cups
  • Process optimization
  • Energy efficiency
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