The optimal design seeks the best possible solution(s) for a mechanical structure, device, or system, satisfying a series of requirements and leading to the best performance. In this work, optimized nozzle shapes have been designed for a wide range of polymer melts to be used in extrusion-based additive manufacturing, which aims to minimize pressure drop and allow greater flow control at large extrusion velocities. This is achieved with a twofold approach, combining a global optimization algorithm with computational fluid dynamics for optimizing a contraction geometry for viscoelastic fluids and validating these geometries experimentally. In the optimization process, variable coordinates for the nozzle's contraction section are defined, the objective function is selected, and the optimization algorithm is guided within manufacturing constraints. Comparisons of flow-type and streamline plots reveal that the nozzle shape significantly influences flow patterns. Depending on the rheological properties, the optimized solution either promotes shear or extensional flow, enhancing the material flow rate. Finally, experimental validation of the nozzle performance assessed the actual printing flow, the extrusion force and the overall print control. It is shown that optimizing the nozzle can significantly reduce backflow-related pressure drop, positively impacting total pressure drop (up to 41 %) and reducing backflow effects. This work has real-world implications for the additive manufacturing industry, offering opportunities for increased printing speeds, enhanced productivity.

Fused Filament Fabrication is an additive manufacturing technique in which molten thermoplastic polymers are extruded through a nozzle. Therefore, the interplay between the viscoelastic nature of the polymer melt, temperature, printing conditions and nozzle shape may lead to inconsistent extrusion. To improve the extrusion control and optimize the print-head performance, a better understanding of the flow process of the polymer melt both in the nozzle and the liquefier is needed. However, several challenges need to be overcome due to the complexity of gathering experimental data on the melt pressure in the nozzle and the lack of numerical models able to capture the full rheology of the molten polymer. This research introduces an innovative approach for monitoring the pressure within a material extrusion 3D printer's nozzle. This method involves utilizing a pin in direct contact with the molten material, which then transmits the applied force from the material to an externally mounted load cell. The setup provides reliable, repeatable pressure data in steady-state conditions for two nozzle geometries and at different extrusion flows and temperatures. Moreover, the Giesekus model enabled capturing the viscoelastic rheometric features of the melt, and the numerical predictions have been compared with the experimental data. Results show that the numerical model accurately describes the flow conditions in the nozzle and allows the estimation of the behavior of the melt in the liquefier zone, the area of the print-head where the filament is molten. It could be concluded that the backflow, which is the backward flow of the molten polymer in the gap between the filament and the liquefier towards the cold end, caused significant non-linearities in the total pressure drop measured in the feeders, which were related to normal forces induced by shear in that region.

Polymer rheology profoundly influences the intricate dynamics of material extrusion in fused filament fabrication (FFF). This numerical study, which uses the Giesekus model fed with a full rheometric experimental dataset, meticulously examines the molten flow patterns inside the printing nozzle in FFF. Our findings reveal new insight into the interplay between elastic stresses and complex flow patterns, highlighting their substantial role in forming upstream vortices. The parametric map α-λ from the Giesekus model allowed us to sort the materials and connect the polymer rheology with the FFF nozzle flow dynamics. The identification of elastic instabilities, the characterization of flow types, and the correlation between fluid rheology and pressure drop variations mark significant advancements in understanding FFF processes. These insights pave the way for tailored nozzle designs, promising enhanced efficiency and reliability in FFF-based additive manufacturing.

Material extrusion is an additive manufacturing process in which material is selectively dispensed through a nozzle. In this work, we are focused on fused filament fabrication (FFF) and we intend to analyze the melt flow patterns generated by a commercial version of polycarbonate, modeled by means of a viscoelastic model (Giesekus) based on rheological properties experimentally determined under viscometric flows. The axisymmetric flow through the same longitudinal section nozzle geometry used in the work of Mendes et al. (2019) has been numerically simulated in steady state at a constant temperature using OpenFOAM® (O. Ltd, 2019) and rheoTool (Pimenta and Alves, 2016). The results show that although the extensional flow type is predominant in the fluid domain, the shear-induced normal stress differences are relevant, and even dominating, not only at the exit of the die but also in the tapered region of the nozzle. Shear-induced normal stress differences are responsible for the excess pressure drop, and also for the equilibrium height (H^∗) in the backflow region, where the polymer melt flows upwards, between the solid filament that enters into the print-core and the liquefier wall.