## 4 Energy Measurement Results
### Transferred Energy Results
#### 4.2.2 Energy Measurement Results of the Aluminum Honeycomb Type of Device  
We used the splitting method shown on the left of Figure 16 to divide the hexagonal aluminum honeycomb and calculated the cross-sectional area of the aluminum honeycomb by counting the number of Y-shaped units. In the no. one test, an aluminum honeycomb with a regular hexagonal structure with seven complete hexagonal units on the longest side (\(M=7\)) was selected. After the test, the aluminum honeycomb was completely flattened and reached the densification stage, which did not meet the requirements. An aluminum honeycomb with \(M=11\) was selected in the next test. The result is that the compression length was only 2.22 mm, so the deformation was too small to meet the requirements. Finally, it is determined that \(M=9\) is the best choice. A total of 17 tests were carried out, and the obtained compression lengths of the aluminum honeycombs is shown in Table 4.  
Among the 17 tests, the measurement results are invalid in no. one and no. two. In no. nine, an O-ring was missing on the pin-rod, which resulted in serious air leakage during the test. In tests no. 11 and no. 12, the pin puller vent holes were blocked, so the gas pressure was low, and thus the test data were invalid. After the firing test of no. 15, it was found that the pin puller was not fixed tightly, which may cause poor coaxiality during the test, and the force transferred by the pin-rod may be absorbed by the cylinder. It is found that in the no. 17 test, the compression length was 27.89 mm, which is a large deviation from other test values in Table 4. This value may be an abnormal value. Furthermore, using the \"Grubbs test method\" to make judgments means the result can be obtained as there are no outliers, and the value should not be discarded. After excluding the above invalid test data, the sample statistical data of transferred energy measured by the aluminum honeycomb device can be obtained, as shown in Table 5. \begin{table}
\begin{tabular}{c c c c c c} \hline
**No.** & **Compression Length (mm)** & **No.** & **Compression Length (mm)** & **No.** & **Compression Length (mm)** \\ \hline
**1** & **40.53** & 7 & 31.17 & 13 & 34.98 \\
**2** & **2.22** & 8 & 39.65 & 14 & 37.14 \\
3 & 34.48 & **9** & **4.46** & **15** & **0.64** \\
4 & 36.62 & 10 & 39.85 & 16 & 39.65 \\
5 & 39.86 & **11** & **2.40** & 17 & 27.89 \\
6 & 38.78 & **12** & **3.11** & & \\ \hline \end{tabular}
\end{table} 
Table 4: Compression lengths of the aluminum honeycombs. Figure 16: Y-shaped unit division of the hexagonal aluminum honeycomb structure. The impact velocity of the aluminum honeycomb in the drop-weight test and the firing test has a different changing process. In the drop-weight test, the compression velocity of the aluminum honeycomb gradually decreased from the maximum value to zero, while in the firing test, the velocity gradually increased from zero to the maximum value and then decreased to zero. Therefore, in this approach, the maximum compression speed during the deformation process of the aluminum honeycomb in the firing test is used to approximate the initial impact speed in the drop-weight test, and the corresponding mean plastic crushing stress at this maximum speed is calculated according to the authors' previous work [17]. \[\sigma_{m}^{d}=4.081\sigma_{0}\left(\frac{t}{l}\right)^{\frac{3}{2}}\left[1+ \left(\frac{\pi\omega_{0}}{16 CI}\right)^{\frac{1}{2}}\right] \tag{9}\]  
where, \(\sigma_{m}^{d}\) is the dynamic mean compressive stress, \(\sigma_{0}\) is the yield stress, \(t\) is the wall thickness, \(l\) is the side length, \(v_{0}\) represents the initial speed of impact, while \(C\) and \(p\) are both strain rate sensitivity factors of aluminum honeycomb, which are determined by the experiment. The working process of the pin puller was recorded with a high-speed camera, whose frame rate is 5000 fps, that is, each frame corresponds to 0.2 ms. As shown in Figure 17, the distance between the two lines is 20 mm.