# Design and Experiment of a Passive Vibration Isolator for Small Unmanned Aerial Vehicles
## 2 Design of the Vibration Isolator and Test of Rubber Stiffness
### Comparative Verification of Vibration Isolator Stiffiness through Experiment and FEM Analysis  
To prevent damage to the vibration isolator during operation, AL6061 was chosen because of its high corrosion resistance and yield strength, low weight, design flexibility, machinability, and excellent characteristics in dispersing vibration and shock energy. The vibration isolator is primarily fabricated using rubber. Considering that the mechanical properties of rubber largely depend on temperature, a rubber composite suitable for the operating temperature conditions was selected [13]. Figure 4 presents a graph depicting the non-linearity of rubber stiffness due to temperature and prepressure [14]. In this study, rubber stiffness experiments were conducted in specific areas (temperature: 20 \({}^{\circ}\)C), where linearity is maintained under the influence of temperature and prepressure. [PERSON] et al. [15] classified rubber into three types by using the Shore A measurement method: soft (Shore A 5\(\rightarrow\)45), semi-rigid (Shore A 50\(\rightarrow\)70), rigid (Shore A 80\(\rightarrow\)95), and plastic (Shore A 100). In this study, to understand the trend of vibration characteristics corresponding to hardness, rubbers with hardness levels of 30, 50, and 70, from the range used in the vibration isolators (30\(\rightarrow\)70), were selected as representative hardness levels for conducting the stiffness measurement experiments. To measure the stiffness of rubber, the weight of the test mass was set as a variable, which varied from 1 to 4 kg in incremental steps of 1 kg, to measure the displacement of the vibration isolator for each weight increment. Figure 5b depicts the experimental setup, including the test mass, vibration isolator, and laser displacement sensor. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component No.** & **Designation** & **Material** & **Weight** \\ \hline \⃝1 & Upper plate & AL6061 & 0.062 kg \\ \⃝2 & Vibration isolator Bracket & AL6061 & 0.022 \(\times\) 2 kg \\ \⃝3 & Damping unit & CR-Rubber & 0.0013 \(\times\) 12 kg \\ \⃝4 & Equipment plate & AL6061 & 0.073 kg \\ \⃝5 & Lower plate & AL6061 & 0.1 kg \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Vibration isolator component detailed description. Figure 4: Curves demonstrating change in stiffness: (**a**) stiffness variation under different temperature and prepressure; (**b**) stiffness variation under different temperatures and compression amplitudes [14]. Table 2 is the result of the stiffness measurement experiment according to the hardness. The stiffness values were calculated using a linear function based on the data of the mass's weight and the displacement of the rubber. The stiffness data derived from the experiment on measuring the stiffness of rubber were validated by comparing it with the stiffness analysis results obtained using Ansys workbench 2019 R3. Figure 6 illustrates the boundary conditions for the static structural analysis. Figure 6 shows the boundary conditions of the static structural analysis to realize the experimental conditions shown in Figure 5b. The fixed support was applied as shown in Figure 6 [unit C], and a point mass was applied to the inner surface of the top plate where the jig of the weight was contacted, as shown in Figure 6 [unit E]. Additionally, static structural analysis was consistently performed for cases ranging from 0.5 to 2 kg. The top and bottom plates were connected with 12 points of the spring contact as depicted in Figure 6 [unit D]. Before utilizing the rubber stiffness measurement experimental data, a simulation was conducted to verify the reliability of the stiffness measurement data. Static structural