‘Unit cell’ type scan strategies for powder bed fusion: The Hilbert fractal

Roshan Sebastian, Sam Catchpole-Smith, Marco Simonelli, Adam Rushworth, Hao Chen, Adam Clare

Research output: Journal PublicationArticlepeer-review

4 Citations (Scopus)


In this study, the melt pool (MP) morphology evolution (solidification) in a Hilbert fractal pattern for the Powder-Bed Fusion Additive Manufacturing (PBF-AM) of Alloy 718 is examined by devising a 'Unit Cell' Methodology (UCM). Since scan strategies are becoming an increasingly important method for managing morphological, microstructural phenomena, and thermally induced stresses, new scan strategies are a requirement. The methodology described here involves defining a 'unit cell' from the larger (higher-order) Hilbert fractal curve and then printing the constitutive lines (vectors) of the 'unit Hilbert cell' and visualising its morphological evolution over a single layer. Process parameters (line length of the 'unit cell,' laser power, and laser speed) variations are performed to analyse its effects on the morphology of the 'unit Hilbert cell' (single layer). The higher-order Hilbert fractal curve is then demonstrated in stages to explain the morphological evolution. The observed coalesced MP propagates over the surface in the larger (higher-order) Hilbert fractal curve, according to the position of the 'unit cells' in the Hilbert fractal curve. The flow of a coalesced MP in PBF-AM using the short vector lengths at a lower linear energy density and three times the width of parallel-line single-track MPs is demonstrated for the first time with the Hilbert fractal. Process parameter variation on the 'unit Hilbert cell' results in MP morphology (dimensions and shape) changes. These variations help to choose the required coalesced MP dimensions in the higher-order Hilbert fractal and ensure good hatching with the adjacent 'unit cell' MPs as it propagates. The proposed methodology could be expanded to allow an understanding of the morphology evolution of other fractal curves in the PBF-AM process.

Original languageEnglish
Article number101588
JournalAdditive Manufacturing
Publication statusPublished - Dec 2020


  • 'Unit Hilbert cell'
  • Fractal scan strategy
  • Hilbert fractal curve
  • MP coalescence and flow
  • Melt Pool (MP)
  • Powder bed fusion

ASJC Scopus subject areas

  • Biomedical Engineering
  • Materials Science (all)
  • Engineering (miscellaneous)
  • Industrial and Manufacturing Engineering


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