# Withstanding Capacity of Machine Guards: Evaluation and Validation by 3D Scanners
## 3 Results  
Tables 2 and 3 show the results of the ballistic tests, respectively, for 500 \(\times\) 500 mm panels and 300 \(\times\) 300 mm panels in terms of initial velocity, residual velocity, and energy lost during the impact, \(\Delta E\).  
Table 4 reports the best-fit values of the R&I parameters and the total residual error (\(e_{r}\)) for all the tested panels.  
Comparing the results related to the two different panel sizes, one can observe that no substantial variation was evidenced between the two panel formats. In fact, the R&I laws obtained from the experiments on the two panel sizes were practically superimposable and the ballistic limit for both the test conditions was close to 78 m/s [29] (Figure 7).  
\begin{table}
\begin{tabular}{c c c} \hline
**Data** & **500 \(\times\) 500 mm Panels** & **300 \(\times\) 300 mm Panels** \\ \hline \(V_{bl}\) in m/s & 78.8 & 78.4 \\ \(a\) & 0.8 & 0.8 \\ \(p\) & 3.1 & 3.1 \\ \(e_{r}\) & 12.0 & 60.2 \\ \hline \end{tabular}
\end{table}
Table 4: R&I characteristic parameters and sum of squared residual error (\(e_{r}\)) for 500 \(\times\) 500 mm panels and 300 \(\times\) 300 mm panels.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Test No.** & \(V_{i}\) **(m/s)** & \(V_{r}\) **(m/s)** & \(\Delta E\) **(J)** \\ \hline
1 & 91.0 & 50.6 & 284.4 \\
2 & 87.1 & 47.8 & 263.5 \\
3 & 85.4 & 39.8 & 283.4 \\
4 & 83.2 & 35.6 & 281.3 \\
5 & 79.6 & 20.0 & 294.8 \\
6 & 61.5 & N.P. * & 189.1 \\ \hline \end{tabular}  
* No penetration.  
\end{table}
Table 2: Results of the ballistic test on 500 \(\times\) 500 mm panels.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Test No.** & \(V_{i}\) **(m/s)** & \(V_{r}\) **(m/s)** & \(\Delta E\) **(J)** \\ \hline
1 & 89.8 & 53.8 & 258.1 \\
2 & 87.  
Furthermore, the average energy loss after the projectile impact had a slight variation between the two panel sizes, as can be seen from the boxplots in Figure 8.  
Figure 8: Energy loss in the two test conditions.  
Figure 7: Comparison of R&I laws for the two different plate sizes.  
Table 5 reports the values of the threshold diameters found through the deformation analysis by 3D scanners applied to five test panels: three of 300 \(\times\) 300 mm and two of \(500\times 500\) mm.  
The 3D scanning technique, which has never been used before in these types of tests, provided \"the proof\" of the presented empirical findings: the withstanding capacity of polycarbonate machine guards does not depend on the panel dimension in the range of realistic working parameters.  
For bigger free vision panels, the same behavior is expected because the major contribution to \(\Delta E\) is due to plastic deformation of the polycarbonate panel.  
The values of the threshold diameters are all distributed around the mean value of 303.14 mm, with a standard deviation of 9.76 mm, and there is an equivalent distribution of impact plastic deformation after the perforation for the two sets of vision panels.  
Therefore, the experimental results described in this work, compared with the theoretical ones, demonstrate that a maximum deformation range (constant \(\Delta E\)) can be defined, independently of the plate size, given the same material, thickness, and penetrator. This result allows to define new ranges for standardized tests, overcoming the limitation of using specific sample sizes if a minimum free area for the plates is used. The 3D deformation analysis also allowed to define the reduced thickness and the \"permanent deflection\" after the impact (Figure 11).  
Figure 10: Deformation analysis on a panel \(500\times 500\) mm with an open window of \(450\times 450\) mm, and threshold diameter: test 5 of Table 2.  
\begin{table}
\begin{tabular}{c c c} \hline
**Shot Test** & **Dimension (mm)** & **Threshold Diameter (mm)** \\ \hline
6—Table 3 & \(300\times 300\) & 297.23 \\
3—Table 3 & \(300\times 300\) & 298.43 \\
5—Table 3 & \(300\times 300\) & 290.96 \\
5—Table 2 & \(500\times 500\) & 312.26 \\
4—Table 2 & \(500\times 500\) & 316.84 \\ \hline \end{tabular}
\end{table}
Table 5: Threshold diameters.