Dot-by-dot wire arc additive manufacturing geometry prediction: an analytical model

Abstract Dot-by-dot Wire Arc Additive Manufacturing (DBD-WAAM) is a deposition strategy for manufacturing complex, large-scale metal lattice structures through the successive deposition of individual molten droplets. In this process, precise geometry prediction is essential for high-precision toolpath definition, as even minor errors in dot height and diameter can compromise welding toolpath strategies and the mechanical properties of the printed components, as these inaccuracies propagate and amplify throughout the final structure. Physics-based analytical geometrical models offer significant benefits over experimental ones, providing generalizable solutions across various materials and parameter configurations without requiring extensive experimental characterization. However, while some analytical models have been developed for traditional bead-based WAAM, current DBD-WAAM research lacks such approaches, relying mostly on regressive experimental techniques. This study fills this gap by proposing a physics-based analytical model using heat conduction and mass conservation principles. Validated through 11 case studies involving steel and titanium bars, the model initially yielded absolute percentage errors generally below 20% using constant literature arc efficiency (i.e., a priori accuracy), providing a useful baseline for preliminary process screening. However, experimental validation showed that the highest errors are related to low deposition time and current, which suggests that in such conditions arc efficiency significantly changes. Specifically, with trial-and-error variable arc efficiency values, the model showed accuracy with overall errors below 8% (i.e., calibrated accuracy). These findings demonstrate the model's utility for initial feasibility assessment via a priori estimates, while highlighting the necessity of calibrated efficiency for precise toolpath generation and process repeatability.