Optimal-transport-based geometry modeling for material extrusion additive manufacturing

Material extrusion additive manufacturing is increasingly adopted in the automotive, aerospace, and medical industries for its capability to create complex features at low cost. Despite high flexibility, parts fabricated with the material extrusion method continue to suffer from geometric inaccuracies and dimensional instability, particularly when manufacturing structures that require high geometric fidelity, such as those with intricate internal channels. To enhance the precision and stability of the material extrusion process, geometry modeling methods based on manufacturing parameters have been introduced. Researchers have employed physical models and neural networks to predict the geometry of printed parts. However, physical modeling is often characterized by high complexity and significant computational demands, while neural networks require a substantial amount of measurement data, resulting in a high cost in experiments. The high computation load and measurement data demand of existing geometry prediction methods prevent their widespread adoption in industrial settings, as they lead to prohibitively long simulation times and the inability to support real-time process optimization. To close the research gap, we propose an optimal-transport-based geometry modeling (OTB-GM) method for the material extrusion system. The proposed OTB-GM models the ironing effects of the moving nozzle for generating the final extruded profile, by minimizing the energy consumption of the transportation process. The OTB-GM begins by initializing the profile prior to ironing, resembling the shape of a Gaussian distribution. In constructing the model, we take into account the material's viscous resistance, changes in gravitational potential energy, and modifications to the surface geometry during ironing. We derive the formula of OTB-GM in two dimensions (2D) and three dimensions (3D) for modeling steady (like line) and dynamic (like corner) extrusion conditions, respectively. To validate the modeling accuracy of the proposed OTB-GM method, the straight line and corner parts are printed for 2D and 3D verification, respectively. Compared with the conventional ellipse geometry modeling method, the proposed OTB-GM reaches higher accuracy in both 2D and 3D validation cases.