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<p>Additive manufacturing demands precise control of track formation and process parameters. Here we show a unified mathematical framework that links key variables to track geometry: we derive analytical expressions for solid and liquid contact angles, introduce dimensionless wetting shape factors to compute segment area and volume, and develop quadratic models relating powder layer thickness to track width and height. We further present a normalized enthalpy formulation that correlates laser energy input with melt pool depth and absorption, enabling prediction of the transition from single-track behavior to steady-state and the derivation of optimal hatch spacing. Validation on IN625, IN738LC, AA1000, and Al10SiMg powders reveals excellent agreement between predicted and measured track morphologies in conduction and keyhole modes. Although tailored for laser powder bed fusion, this framework is broadly applicable across additive manufacturing processes, offering a robust tool for process optimization, in situ monitoring, and quality control.</p>

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Mathematical approaches for track analysis and process optimization in additive manufacturing

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年7月8日

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  • Mahdi Alishavandi,
  • Rahmi Ünal,
  • Metin Uymaz Salamci

摘要

Additive manufacturing demands precise control of track formation and process parameters. Here we show a unified mathematical framework that links key variables to track geometry: we derive analytical expressions for solid and liquid contact angles, introduce dimensionless wetting shape factors to compute segment area and volume, and develop quadratic models relating powder layer thickness to track width and height. We further present a normalized enthalpy formulation that correlates laser energy input with melt pool depth and absorption, enabling prediction of the transition from single-track behavior to steady-state and the derivation of optimal hatch spacing. Validation on IN625, IN738LC, AA1000, and Al10SiMg powders reveals excellent agreement between predicted and measured track morphologies in conduction and keyhole modes. Although tailored for laser powder bed fusion, this framework is broadly applicable across additive manufacturing processes, offering a robust tool for process optimization, in situ monitoring, and quality control.