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<p>Incremental forming offers a flexible, die-less alternative to conventional forming methods, enabling the efficient production of complex geometries without the need for high-cost tooling. Among its various applications, Incremental Tube Forming (ITF) has emerged as a promising technique for forming tubular components. However, the transformation of circular thin-walled tubes into square cross-sections, particularly for non-axisymmetric geometries, remains insufficiently explored. This study presents a comprehensive experimental investigation to optimize ITF for copper tubes, systematically evaluating the effects of axial feed, radial feed, and velocity on surface roughness, maximum thinning, springback, and geometric uniformity. A full factorial design was employed, and the responses were modeled using response surface methodology (RSM), demonstrating reasonably good model fit (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\text{R}}^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mtext>R</mtext> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> &gt; 0.86), given the inherent variability of the ITF process. Multi-objective optimization was performed using both desirability functions and the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The results indicate that axial feed is the dominant parameter affecting surface roughness and thinning, while radial feed primarily influences springback and geometric uniformity. Significant interaction effects between axial and radial feed highlight the necessity of jointly tuning these parameters to achieve balanced quality outcomes. Both RSM and NSGA-II identified similar optimal process settings, including a velocity of 350&#xa0;mm/min, an axial feed of 0.2&#xa0;mm, and a radial feed of 0.25&#xa0;mm. This integrated optimization framework enhances process understanding and provides a robust basis for improving quality control and process efficiency in ITF.</p> Graphical Abstract <p></p>

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Experimental investigation and multi-objective optimization of incremental tube forming for squaring thin-walled tubes via RSM and NSGA-II

  • 期刊论文

  • 发表日期：

    2026年6月1日

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  • Moataz Abd El Kafy,
  • Mostafa Shazly,
  • Gamal Abd El Nasser,
  • Noha Naeim

摘要

Incremental forming offers a flexible, die-less alternative to conventional forming methods, enabling the efficient production of complex geometries without the need for high-cost tooling. Among its various applications, Incremental Tube Forming (ITF) has emerged as a promising technique for forming tubular components. However, the transformation of circular thin-walled tubes into square cross-sections, particularly for non-axisymmetric geometries, remains insufficiently explored. This study presents a comprehensive experimental investigation to optimize ITF for copper tubes, systematically evaluating the effects of axial feed, radial feed, and velocity on surface roughness, maximum thinning, springback, and geometric uniformity. A full factorial design was employed, and the responses were modeled using response surface methodology (RSM), demonstrating reasonably good model fit ( \({\text{R}}^{2}\) R 2  > 0.86), given the inherent variability of the ITF process. Multi-objective optimization was performed using both desirability functions and the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The results indicate that axial feed is the dominant parameter affecting surface roughness and thinning, while radial feed primarily influences springback and geometric uniformity. Significant interaction effects between axial and radial feed highlight the necessity of jointly tuning these parameters to achieve balanced quality outcomes. Both RSM and NSGA-II identified similar optimal process settings, including a velocity of 350 mm/min, an axial feed of 0.2 mm, and a radial feed of 0.25 mm. This integrated optimization framework enhances process understanding and provides a robust basis for improving quality control and process efficiency in ITF.

Graphical Abstract