*2.3. Precision, Accuracy and Surface Roughness of the Printed Parts*

A study on the accuracy of the two printers was carried out after the printing parameters had been selected. The reference geometry in Figure 3 was printed five times with FFF and five times with VPAM and measured to evaluate accuracy and repeatability. Figure 4 shows the deviation in *x, y* and *z* directions from the nominal dimensions. The largest deviations can be detected in *x* and *y* directions on the parts printed with VPAM, showing how the photopolymer is more sensitive to shrinkage in comparison to PLA.

**Figure 3.** Reference geometry used to determine printer accuracy with dimensions L × H × W: 5 mm × 20 mm × 20 mm. The printing direction is in *z*.

**Figure 4.** Deviation in *x*, *y* and *z* directions of reference geometries printed with FFF and VPAM.

The standard deviation bars in Figure 4 depict the accuracy of the two printers relative to dimensions given in Figure 3. Overall, the VPAM printer showed better accuracies in comparison to FFF Accuracies of 0.03 mm and 0.02 mm were detected, respectively, for the x and y directions with the VPAM printer, while FFF showed accuracies of 0.02 mm in *x* and 0.06 mm in *y*. A particularly good accuracy was detected in the z direction for the VPAM with a value of 0.01 mm.

The surface roughness of the printed tools was investigated by using an Olympus LEXT confocal microscope. The linear mean height *Ra* of the tools was evaluated parallel and perpendicular to the printing direction. The *Ra* is comparable for both FFF and VPAM when looking at the surface parallel to the printing direction, with a value of 0.78 ± 0.45 µm and 0.81 ± 0.25 µm, respectively. The investigation of the roughness on the surface perpendicular to the printing direction showed instead higher *Ra* for FFF compared to VPAM, having *Ra* values of 2.96 ± 0.27 µm and 1.43 ± 0.21 µm, respectively. Even though VPAM was found to be more accurate than FFF, this additive manufacturing technology needs post-processing after the printing, increasing time and cost for the production of the tool. Therefore, FFF was selected as the preferred method of RP for further investigation.

#### *2.4. Measurement Procedures and Strategy*

The objective of this work is to study the geometrical accuracy of parts formed by RP polymer tools. The final shape of formed components and RP tools is compared to the nominal shape by use of a ZEISS DuraMax coordinate measuring machine. All measurements that are reported are averaged along the entire width of the respective component.

The nominal geometry of the component created by V-bending is shown in Figure 1a. The measurement strategy used to determine the geometrical accuracy of the formed component is outlined in Figure 5a. Five measurements of angles (M1–M5) are performed along the arms of the bent components at equal intervals of 6 mm. The radius (R) where the arms meet is also measured.

The geometrical accuracy of the part formed by groove pressing, shown in Figure 1b, is determined by the strategy outlined in Figure 5b. The angularity of the four flat parts (P1–P4) is measured with respect to the outer tangential plane touching the planes P2 and P3. The height of the three main grooves (H1, H2, H3) were measured with respect to the outer tangential plane touching the planes P1 and P2, P2 and P3, P3 and P4, respectively. The overall angularity of the workpiece is measured between P1 and P4.

**Figure 5.** Measurement strategies for sheets formed by (**a**) V-bending and (**b**) groove pressing.

For evaluating the geometrical accuracy of the printed punch, as shown in Figure 6, the strategy consists of five angle measurements (M1–M5) located at an equal distance from each other of 5 mm on the tilted surfaces and in five radius measurements (R1–R5) on the punch nose located at an equal distance of 8 mm from each other across the width.

**Figure 6.** V-bending punch measurement locations and surface inspection locations (red marks) on both punch and die.

## **3. Accuracy and Wear in V-Bending**

*3.1. Change in Tool Geometry and Surface vs. Number of Strokes*

A visual inspection at selected points of the tool surfaces was performed using a LEXT OLS4000 confocal microscope (Olympus, Tokyo, Japan). The locations, indicated by the red marks in Figure 6, were selected as the highest tribological load would be found there. The resulting pictures are shown in Table 3, as a function of the number of bending strokes. The picture taken for stroke #0 is not necessarily in the same location as others, as there were no existing marks which could be used as a reference point. It does, however, show that the surface is not perfect even before forming, with defects possibly having been caused by improper handling. Pictures taken for strokes #3–30 are taken in the same location to showcase how the wear progresses. The figures show that the punch does not experience significant changes to the surface, while the die does. The surface of the die changes more gradually after the fifth stroke, which may indicate some form of steady state. There is considerably less sliding occurring in the interface between the punch and the workpiece than in the interface between the die and the workpiece, which is likely the reason for the difference in wear between the two tools.


**Table 3.** Images of tool surfaces for different numbers of strokes that have been performed. Each figure shows an area that is 600 µm by 600 µm.

#### *3.2. Springback, Geometrical Accuracy and Comparison to Tool Accuracy*

The results of the geometrical accuracy study of the workpiece and punch, obtained by employing the measurement strategy described in Section 2.4, are shown in Figures 7 and 8.

Figure 7 shows the geometrical accuracy of the 3D-printed punches after they have been used to form five parts. The mean angle that is measured is 90.2 ± 0.1 ◦ . The figure also shows the averaged angle over measurements of parts formed in five consecutive strokes. The angle is smaller than nominal and grows with distance from the punch nose. The deviation from nominal is largest at the punch nose. This behavior is most obvious for the tool with a 1 mm radius, where the mean angle grows from 86.1 ◦ to 89.8 ◦ as the measurements are taken further away from the punch nose.

Figure 8 shows the average angle measured in location M3 of the workpieces, over five strokes, for the three different punch nose radii. The largest difference from nominal is found when using the 3 mm radius tool after three strokes, where the measured value is 88.2 ± 0.8 ◦ . The smallest deviation from nominal is found when using the 1 mm radius tool at the second stroke, where the measured value is 88.7 ± 0.27 ◦ . The workpieces formed by the 2 mm radius tool have small deviations among them and a steady response over the five strokes, characterized by a standard deviation of 0.08 ◦ . This behavior is not observed for the workpieces formed by the 1 mm and 3 mm radii tools.

**Figure 7.** Measured angles as function of measurement location for tools with different nose radii.

**Figure 8.** Measured angle at location *M*3 as function of no. strokes performed for tools with different nose radii.

#### *3.3. Bend Radius*

Another aspect of the accuracy is the bend radius that is achievable by 3D-printed tools. Three different radii are tested in V-bending, with results shown in Figures 9 and 10. The bend radii of the workpieces as function of the number of strokes in the same tool is shown in Figure 9. Figure 10 shows a comparison between the radius of the printed tools and the radius measured on the formed components. The nose radii of the R1 and R2 tools are not nominal, but the formed component adopts the measured nose radius closely. The scatter of measurements is also low, indicating that the repeatability is good. This implies that the deviation from nominal in the formed components is due to the accuracy of the printed tools, which could be compensated for. The R3 tool is different, in that the radius of the tool is close to nominal, but the radius of the formed component is not. The scatter in the measured radius is also larger than for components formed using the R1 and R2 tools. The shell thickness that is used when printing the tools is 2.1 mm for all punches regardless of the punch nose radius. As larger punch nose radius implies a larger contact area towards the workpiece, the constant shell thickness results in less stiff behavior from the punch nose when the radius is increased. The corresponding larger elastic deflection of the R3 tool would explain the increased radius and scatter measured on the bent workpieces.

**Figure 9.** Measured radius of workpiece as function of no. strokes and of punches normalized with respect to nominal dimensions.

**Figure 10.** Average radius of workpiece over five strokes and of punches with different nose radii.

#### **4. Groove Pressing**

The geometrical accuracy obtained by groove pressing (Figure 1b) is evaluated by the measurement strategy shown in Figure 5b. The geometrical accuracy of the tools, shown in Figure 2b, is also evaluated so that the analysis can be corrected for tool dimensions deviating from nominal. Two key features were selected for evaluating the workpiece accuracy: the angularity of the four flat parts and the height of the three grooves.

Figure 11 shows that the tools are printed with slight increasing height from H1 to H3. This is probably due to a slight tilting of the building plate during printing. The measured heights of the workpiece groove heights were relatively close to the heights imposed by the tools. The workpiece groove heights are very repeatable, with standard deviations between 0.6–1.1% across the three groves.

**Figure 11.** Average groove height in workpiece and tools compared to the nominal height 3.4 mm.

Figure 12 shows the angularity measured between the features that nominally sit on the same plane. The nominal angularity is therefore 180 ◦ . The figure shows that the tools are close to nominal. The average angularity measured on the workpiece is far from the nominal value of 180 ◦ due to spring-back and varies between the features. The largest deviation was observed on P4, which has an average value of 178.3 ± 0.12 ◦ . P3 has the closest value to nominal by 179.2 ± 0.11 ◦ . Spring-back after the nominally symmetric groove pressing is expected to increase angularity deviation from nominal with distance from the center. This explains why the deviation is larger in P4 than in P3. However, Figure 12 also shows that this cannot explain P1 and P2, because there is no symmetry in the resulting angularities. Since the tools are symmetrical in terms of angularity with respect to each other, the asymmetric angularity in the workpiece is due to the asymmetric groove heights in the tools, as shown in Figure 11.

**Figure 12.** Average angularity of workpiece and tools for the four key planes.

The performance of the tools was also investigated over a small number of strokes. In this case, as mentioned in Section 2.4, the overall workpiece angularity is described by the angle between P1 and P4 and the reported height is an average value of H1, H2 and H3. Figure 13 shows the measured dimensions normalized with respect to the nominal values. The stability and repeatability of the measured values are good.

Regarding the height measurements, it is noticed that the standard deviations of both tools and workpieces are around 4%. The angularity is more stable and has standard deviations of 0.2%. The normalization shows that the angularity of the entire part is much closer to the nominal value than the height of the grooves. This is clearly linked to the deviation in the die, which could be compensated for. The angularity of the tools could also be altered by a small curvature to result in angularity of the workpieces after spring-back even closer to nominal.

**Figure 13.** Normalized measurements of workpiece and tool feature dimensions.
