# Research on the Design Method of Cushioning Packaging for Products with Unbalanced Mass
## 4 Experimental Design and Analysis  
Static compression tests were conducted on EPE with different densities according to Chinese National Standard GB/T 8168-2008 [33], which is a static compression test method for packaging cushioning materials, as shown in Figure 5. The size and number of test samples are taken as a regular 100 mm \(\times\) 100 mm histograms. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Product** & **Eccentric** & \begin{tabular}{c} **Damping Factor** \\ **at the Distal** \\ **Center of Mass** \\ **(N-s/m)** \\ \end{tabular} & \begin{tabular}{c} **Damping Factor** \\ **Near the Center** \\ **of Mass End** \\ **(N-s/m)** \\ \end{tabular} & \
\begin{tabular}{c} **Maximum** \\ **Acceleration** \\ **(m/s\({}^{2}\))** \\ \end{tabular} &
\begin{tabular}{c} **Difference** \\ **Ratio** \\ **(\%)** \\ \end{tabular} \\ \hline \multirow{4}{*}{9} & 19.79 & 0 & 0 & 5.91 & - \\  & 19.79 & 2.5 & 2.5 & 5.73 & \(-\)3.0\% \\  & 19.79 & 2.5 & 2.6 & 5.51 & \(-\)6.7\% \\  & 19.79 & 2.4 & 2.5 & 5.68 & \(-\)3.9\% \\  & 19.79 & 2.5 & 2.4 & 5.88 & \(-\)0.5\% \\  & 35.88 & 2.7 & 2.7 & 9.98 & \(-\)17.2\% \\  & 35.88 & 2.7 & 2.8 & 9.05 & \(-\)24.9\% \\
11 & 35.88 & 2.6 & 2.7 & 10.59 & \(-\)12.1\% \\  & 35.88 & 2.8 & 2.7 & 11.33 & \(-\)6.0\% \\  & 35.88 & 0 & 0 & 12.05 & - \\  & 83.69 & 0 & 0 & 20.68 & - \\  & 83.69 & 3.1 & 3.1 & 15.79 & \(-\)23.6\% \\
15 & 83.69 & 3.1 & 3.2 & 11.26 & \(-\)45.6\% \\  & 83.69 & 3.0 & 3.1 & 14.32 & \(-\)30.7\% \\  & 83.69 & 3.2 & 3.1 & 17.65 & \(-\)14.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Response results of packaging systems for mass-unbalanced products with different damping packaging materials. Figure 6 shows that below a certain strain value, the stress-strain relationship is linear, and the stress is less than the yield limit, i.e., the material is in the elastic deformation stage. For the same strain value, the stress corresponding to the EPE of higher density is higher, the energy absorbed by the material is also higher. The effect of different densities on the vibration response of the cushioning packaging system for mass non-equilibrium products is experimentally studied. The damping material was cut with a hand knife and standard ruler into different areas and different thicknesses as shown in Figure 7 for a sine sweep experiment. The experimental apparatus shown in Figure 8 consisted of an aluminum alloy block (20 cm \(\times\) 20 cm \(\times\) 20 cm) with a mass of 9 kg, a cushioning vibration-isolation material, a counterweight block, and a sensor. The block was smoothly connected to a Suzhou DY300-3 vibration test rig [34] via the vibration-isolation material and a transducer was attached to the block using an instantaneous dry glue. To ensure the reliability of the experimental results, the experiment was repeated three times, and the average values were calculated. This approach helps to reduce the influence of random factors and increases the statistical significance of the obtained data. A sinusoidal sweeping experiment [35] is conducted by applying an excitation of 1 m/s\({}^{2}\) to the block along the \(y\)-direction and longitudinal acceleration curves of the buffered packaging system are obtained for mass-balanced and mass-unbalanced products with different vibration-isolation material installation methods. Figure 5: Static compression test. Figure 6: Stress-strain curves. Figure 9 shows the vibration-response results of a mass-unbalanced-product packaging system under different buffered-packaging-material densities. The thickness of the damping material is set to a constant 50 cm, and the length x width, i.e., contact area, is varied.