# Vibration Isolation of a Surveillance System Equipped in a Drone with Mode Decoupling
## 4 Results and Suggestions
### Design of a Vibration Isolation System Based on System Identification  
The frequency response function for the original system and the tested commercial vibration isolators (Figure 3) shows that the proposed gimbal significantly amplifies the vibration from the rotors in operational frequencies. This vibration causes deterioration of the images taken by the surveillance system, meaning that a vibration isolation system attached to the gimbal should be properly designed and implemented. The method to reduce vibration transmitted to a camera included two approaches: increasing the mass of the camera and decreasing the stiffness of the isolation element. The payload is limited in drones; therefore, the weight must be as light as possible. Hence, this study proposes a design methodology that lowers stiffness. Commercial mounts having viscoelastic material with the lowest stiffness were used to lower the stiffness and locate the natural frequency below operational frequencies (Figure 5). Specifically, eight dampers were installed between the drone body and the gimbal (a yellow box in Figure 5), and two dampers were installed between the gimbal and the surveillance system (an orange box in Figure 5). The equivalent stiffness of these white jelly dampers was \(6.6~{}\times 10^{3}\) N/m, and that of black DJI dampers in Figure 6 was unavailable. Hereafter, this configuration is defined as an initial design of a vibration isolator. Note that two dampers in a series decrease the equivalent stiffness of a vibration isolator. Hence, this simple design configuration is effective in isolating vibration from the rotors. Figure 5: Configuration of selected mounts for the gimbal system. Figure 6: Comparison of transmissibility before and after applying mount elements: (**a**) fore-after direction, (**b**) side-by-side direction, and (**c**) vertical direction. The frequency response functions for the actual drone system were measured in all directions to verify the vibration isolation performance of the proposed design (Figure 6). The same procedure described in Section 4.1 was performed in this analysis. The natural frequency in the vertical direction was 7 Hz (Figure 6c). Moreover, the overall vibration in the vertical direction was reduced from 1.5899\({}_{\text{RMS}}\) (for a gimbal without vibration isolators) and 1.5082\({}_{\text{RMS}}\) (for a gimbal with DJI vibration isolators) to 0.6080\({}_{\text{RMS}}\) in the 0-100 Hz frequency range, where RMS means the root-mean-square. The vibration was decreased by 61.76% (=1 - 0.6080\({}_{\text{RMS}}\)/1.5899\({}_{\text{RMS}}\)) and 59.69% (1 - 0.6080\({}_{\text{RMS}}\)/1.5082\({}_{\text{RMS}}\)) compared to the vibration of a gimbal without vibration isolators and that with DJI vibration isolators owing to the initial design suggestion. The effectiveness of a vibration isolation system in the operating frequencies was verified by comparing the original system with DJI vibration isolators. However, the natural frequency in the three translational directions was observed at similar locations in this configuration. Specifically, the natural frequencies were adjacent to each other at 7.5 Hz, 7.75 Hz, and 7.0 Hz in the fore-after, side-by-side, and vertical directions, respectively. Therefore, the natural frequencies could affect each other. In other words, the natural frequencies of each direction may be mutually amplified in this configuration because the excitation direction of the internally generated force occurs in the vertical direction and in an undefined random direction. These results also suggest that simply adding vibration isolators cannot be an optimal design. Therefore, it is necessary to simultaneously consider horizontal modes and a vertical mode while designing the vibration isolation system. The response characteristics of the three-DOF system with adjacent natural frequencies for three translational directions were predicted with a coupled multi-DOF model to confirm this hypothesis.