# Geometric Benchmarking of Metal Material Extrusion Technology: A Preliminary Study
## 3 Results and Discussion  
First of all, it is important to underline that following the debinding and sintering processes, the features of the GBTAs (Figure 4) underwent dimensional shrinkages equal to about 16% along the X and Y directions and about 20% along the growth direction, as already widely studied and reported in [20]. Subsequently, a comparison of the geometrical characteristics achieved by green parts and white parts was undertaken. Figure 4: GBTAs in the white state resulting at the end of the metal-MEX process: (**a**) thin walls GBTA; (**b**) pillars GBTA; (**c**) hollow cylinders GBTA; (**d**) bridges GBTA. Figure 3: Tolerance surfaces and reference datum surfaces for the different features. A general overview of the geometrical characteristics analysis shows a worsening in perpendicularity and parallelism tolerances assessed through walls, pillars, and bridge features after debinding and sintering treatments, as depicted in Figure 5a, Figure 5b, and Figure 5d, respectively. Notably, a clear trend can be observed for the parallelism of the beams, which exhibits an exponential increase with beam length in the white state. In contrast, Figure 5c shows that coaxiality exhibits an opposite trend, compared to the previous tolerances, with green-part hollow cylinders displaying poorer coaxiality values compared to the final white parts. The acquired results were also leveraged to develop quantitative maps (Figure 6) that offer a comprehensive understanding of how variations in feature dimensions impacted the quality and consistency of the parts manufactured through the metal-MEX process. These maps delineate the reliable operating range of the technology and underline deviations from the nominal geometry of the studied characteristics. Through the systematic analysis of the relationships between feature dimensions and geometric characteristics, these maps offer insights into the optimal dimensional ratio where the metal-MEX process proves most reliable. This type of outline can facilitate the establishment of guidelines to help manufacturers and engineers in the design and fabrication of components within specified ranges, ensuring resulting geometrical characteristics that meet the desired standards. Thus, these maps serve as invaluable tools for process design, enabling practitioners to ascertain the limits and constraints within which the metal-MEX process consistently delivers reliable and high-quality results. The maps also provide minimum achievable feature sizes. Specifically, the results show that the minimum achievable height-to-thickness or length-to-thickness ratios not resulting in collapse are equal to 2.50 (element W12), 1  
Figure 5: Comparison of geometrical characteristics of the green parts and white parts: (**a**) perpendicularity of wall features; (**b**) perpendicularity of pillar features; (**c**) coaxiality of hollow cylinder features; (**d**) parallelism of bridge features. As expected, finer perpendicularity tolerances can be achieved for both wall and pillar elements by increasing the thickness and reducing the height, as depicted in Figures 6a and 6b, respectively. Conversely, excessively increasing the height-to-thickness ratios of the features undermines the stability of the brown parts and leads to structural distortion or collapse, due to the cumulative effects of debinding and sintering, which, in turn, negatively affect the tolerance values. Indeed, Figure 7 depicts how the post-printing treatments resulted in the development of residual stresses within the structures, which ultimately led to the collapse of the thinnest wall and pillar features (W1, W2, W3, W5, P6, and P9) and the torsional deformation of other elements in the white state. On the other hand, it must also be noted that the fabrication of feature P3 failed directly at the printing stage, most likely due to its combination of the highest height and lowest thickness values among pillar features.