# Geometric Benchmarking of Metal Material Extrusion Technology: A Preliminary Study
## 3 Results and Discussion
The graphs in Figure 6 show that no positive results were achieved for features with thicknesses closely related to the 0.6 mm nozzle diameter used in this study. However, it is important to note that the results should be adapted for smaller nozzle diameters. A further elaboration of these graphs can be performed to clarify the relationship between the smallest feasible size of the basic features and the aspect ratio between the feature's thickness and the nozzle's diameter. Introducing the ratio between the feature's thickness and the nozzle's diameter in the previous maps, as illustrated in Figure 8, enables the generalization of the results. This inclusion allows for a comprehensive examination of how the nozzle might impact the quality of replicated features. Notably, Figure 8a allows for the assumption that when the wall thickness matches the diameter of the nozzle, structural failure consistently occurs, regardless of the selected height. However, increasing the feature-nozzle ratio to a minimum value of 3.33 might prevent collapse, particularly if the feature's height  
Figure 7: Details of collapsed and distorted features of white parts. does not exceed 20 mm. Further increasing the ratio could possibly diminish the adverse impact of height restrictions, thus enabling the production of taller, slender walls. It is also observed that achieving heightened precision in terms of perpendicularity might necessitate that wall thickness be ten times greater than the nozzle diameter. A similar pattern is observed for cuboidal pillars, as depicted in Figure 8b. In this case, a thickness exceeding 8.33 times the nozzle diameter might be imperative to prevent structural failure throughout all stages, from printing to sintering. Additionally, it might prove beneficial to limit pillar height while simultaneously augmenting the feature-nozzle ratio up to 16.66 to enhance the perpendicularity values of the features. Hollow cylindrical features can be manufactured without experiencing collapse within a feature-nozzle ratio range of 1.66 to 8.33, as depicted in Figure 8c. Even for such geometries, increasing the ratio of feature thickness to nozzle diameter might enhance the fabrication of more accurate reproductions of coaxially aligned features. A similar elaboration of the map devised for bridge structures could not be provided, as the length of the beams was the only dimension to be varied in this study. The number of strands deposited for each layer would indeed remain the same for differently sized nozzles. However, it is still possible to assume that an accurate reproduction of bridge features with a thickness ten times higher than the nozzle's diameter might be achieved only when limiting the length of the beam below 18 mm, even if support structures are also kept in place during debinding and sintering. The generalization of the results suggests the assumption that an effective approach to prevent structural collapse and to enhance geometrical precision is to produce geometric features with a thickness largely exceeding the diameter of the extrusion nozzle. However, the validation of such an assumption requires further experiments to be performed. Increasing this ratio leads to the deposition of a greater number of material strands per layer, thereby enhancing interlayer adhesion. Ensuring strong material adhesion during printing is crucial for preserving structural integrity during later stages of the metal-MEX process, particularly in the brown state, where metal particles have not yet undergone sintering and bonding. Figure 8: Maps for white-state geometric tolerances considering the ratio between the feature’s thickness and the nozzle’s diameter: (**a**) wall features; (**b**) pillar features; (**c**) hollow cylinder features.