Effect of polygon order on additively manufactured lattice structures: a method for defining the threshold resolution for lattice geometry

Additive manufacture (AM) enables the fabrication of highly efficient lattice structures. However, the mathematical efficiency of characterising AM lattice geometry can be poor, potentially restricting the commercial application of AM lattice structures. This research quantifies the effect of the polygon order used to characterise the geometric resolution of lattice strut elements on the associated manufacturability and geometric qualities of the manufactured lattice. The effect of these design parameters on manufactured quality is experimentally determined for aluminium and titanium specimens fabricated by selective laser melting (SLM), although the method can be generally applied to any AM technology. This research finds that geometric thresholds exist, below which additional geometric resolution does not result in increased part quality. These thresholds are a function of material, lattice inclination angle, cross-sectional area and the polynomial order used to represent the cross section. These findings enable significantly reduced computational cost in managing AM lattice structures, and can be directly integrated with algorithmic methods for the optimisation of AM lattice structures.