# Vibration Isolation of a Surveillance System Equipped in a Drone with Mode Decoupling

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## Abstract

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## 1. Introduction

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- The entire process of vibration isolation with mode decoupling is presented as a countermeasure to minimize the vibration effects on the surveillance system.
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- System identification with a coupled multi-DOF model is presented to identify a problem of mode coupling on a vibration isolator and predict vibration isolation performance for optimized configuration of vibration isolators.
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- Design optimization of a vibration isolator is executed with the coupled multi-DOF model to separate vertical and horizontal natural frequencies by 1 Hz or more.
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- The effectiveness of the presented method is validated through experiments based on vibration isolation performance (VIP).

## 2. Theories for System Identification

#### 2.1. Mathematical Model of a Multi-DOF System

#### 2.2. Levenberg-Marquardt Algorithm

**;**${\mu}_{k}$ is the non-negative damping factor to be adjusted at each iteration. The damping factor, ${\mu}_{k}$, is updated until the error function $E\left(\mathbf{\beta}\right)$ converges to a predefined threshold, and the updating process is as follows:

## 3. Experimental Vibration Characterization

#### 3.1. Frequency Response Function

#### 3.2. Modal Testing

## 4. Results and Suggestions

#### 4.1. Vibration Characteristics of the Original System

#### 4.2. Design of a Vibration Isolation System Based on System Identification

_{RMS}(for a gimbal without vibration isolators) and 1.5082

_{RMS}(for a gimbal with DJI vibration isolators) to 0.6080

_{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

_{RMS}/1.5899

_{RMS}) and 59.69% (1 − 0.6080

_{RMS}/1.5082

_{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.

^{3}N/m, as mentioned in the specification sheet. The initial damping value was assumed to be 0.1, which is the general known damping ratio of a rubber [23], and the mass was measured using a precision balance. The frequency range below 100 Hz was used. Therefore, we filtered the frequency range that lies above the target range using the ideal low pass filter in the frequency domain when applying the least squares cost function. The results (blue dotted lines in Figure 6) show that estimated parameters correspond well to the experimental results because the correlation coefficients (R) for the fore-after, side-by-side, and vertical directions were 0.91, 0.91, and 0.95, respectively. Parameters estimated from measurement results are described in Table 2. The stiffness elements used for the coupled effects in each direction were assumed to be bounded between 1% and 25% of the stiffness in the main direction. This can be explained by the fact that the coupled-stiffness term observed from the experiment of the rotating machine was 1% to 25% [24,25,26].

#### 4.3. Design Enhancement of Vibration Isolator for a Camera System Deployed in a Drone

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Measured transmissibility with modal testing: (

**a**) fore-after direction, (

**b**) side-by-side direction, and (

**c**) vertical direction.

**Figure 4.**Vibration pathway of a surveillance system in a drone: (

**a**) original pathway and (

**b**) proposed pathway.

**Figure 6.**Comparison of transmissibility before and after applying mount elements: (

**a**) fore-after direction, (

**b**) side-by-side direction, and (

**c**) vertical direction.

**Figure 7.**Simulation results of the coupled three‒DOF mathematical model in (

**a**) the time domain and (

**b**) in the frequency domain.

**Figure 9.**Comparison of transmissibility before and after the mount design modification in (

**a**) fore-after, (

**b**) side-by-side, and (

**c**) vertical directions.

**Figure 10.**Mode shape of rigid body modes for (

**a**) initial and (

**b**) optimal designs from measurement and prediction.

**Figure 11.**Simulation results of the coupled three‒DOF mathematical model between initial and optimal designs in (

**a**) the time domain and (

**b**) the frequency domain.

**Table 1.**Natural frequency (${\mathit{f}}_{\mathit{N}})$ and its amplitude $\left({\mathit{M}}_{{\mathit{f}}_{\mathit{N}}}\right)$ in transmissibility.

Axis | X | Y | Z | ||||
---|---|---|---|---|---|---|---|

${\mathit{N}}^{\mathit{t}\mathit{h}}\mathbf{Frequency}$ | ${\mathit{f}}_{\mathit{N}}$ (Hz) | ${\mathit{M}}_{{\mathit{f}}_{\mathit{N}}}$ | ${\mathit{f}}_{\mathit{N}}$ (Hz) | ${\mathit{M}}_{{\mathit{f}}_{\mathit{N}}}$ | ${\mathit{f}}_{\mathit{N}}$ (Hz) | ${\mathit{M}}_{{\mathit{f}}_{\mathit{N}}}$ | |

1^{st} | 2.5 | 1.846 | 2.75 | 1.609 | 1.0 | 1.02 | |

2^{nd} | 6.5 | 2.265 | 9.25 | 5.499 | 8 | 2.356 | |

3^{rd} | 56.25 | 4.029 | 30 | 5.939 | 22.25 | 3.842 | |

4^{th} | 70.25 | 5.874 | 35.75 | 3.716 | 25.5 | 8.094 | |

5^{th} | 85.25 | 4.243 | 60.25 | 2.407 | 37.5 | 1.294 |

Item | Value | Item | Value | Item | Value | Item | Value |
---|---|---|---|---|---|---|---|

m | 3.4 kg | ||||||

${k}_{x}$ | 7.55 × 10^{3} N/m | ${c}_{x}$ | 15.94 Ns/m | ${k}_{xy}$ | 0.78 × 10^{3} N/m | ${c}_{xy}$ | 1.08 Ns/m |

${k}_{y}$ | 8.06 × 10^{3} N/m | ${c}_{y}$ | 5.71 Ns/m | ${k}_{yz}$ | 0.75 × 10^{3} N/m | ${c}_{yz}$ | 2.15 Ns/m |

${k}_{z}$ | 6.96 × 10^{3} N/m | ${c}_{z}$ | 37.25 Ns/m | ${k}_{xz}$ | 0.73 × 10^{3} N/m | ${c}_{xz}$ | 2.66 Ns/m |

System Type | Fore-After Direction | Side-by-Side Direction | Vertical Direction | |||||||
---|---|---|---|---|---|---|---|---|---|---|

${\mathit{f}}_{\mathit{N}}$ (Hz) | No | Initial | Optimal | No | Initial | Optimal | No | Initial | Optimal | |

1st | 2.5 | 2.5 | 2.5 | 2.75 | 2.75 | 2.75 | 1.0 | 1.0 | 1.0 | |

2nd (rigid body mode) | 6.25 | 7.5 | 10 | 9.25 | 7.75 | 7.5 | 8.0 | 7.0 | 8.5 | |

3rd | 56.25 | - | - | 30.0 | - | - | 22.5 | - | - | |

4th | 70.25 | 35.75 | 25.5 |

**Table 4.**Comparison of the root-mean-square (RMS), the ratio between a payload and base, and vibration isolation performance (VIP) in the frequency range of 30–85 Hz.

Original System | Initial Design | Suggested Design | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

X | Y | Z | X | Y | Z | X | Y | Z | ||

RMS $\left(\frac{M}{{S}^{2}}\right)$ | Base | 0.072 | 0.078 | 0.207 | 0.089 | 0.091 | 0.187 | 0.069 | 0.074 | 0.215 |

Payload | 0.230 | 0.119 | 0.061 | 0.008 | 0.008 | 0.008 | 0.004 | 0.007 | 0.004 | |

Ratio $\left(\frac{Payload}{Base}\right)$ | 3.190 | 1.517 | 0.292 | 0.085 | 0.090 | 0.043 | 0.055 | 0.091 | 0.016 | |

VIP | - | - | - | 97.4% | 94.1% | 86% | 98.3% | 94.0% | 94.6% |

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**MDPI and ACS Style**

Shin, Y.-H.; Kim, D.; Son, S.; Ham, J.-W.; Oh, K.-Y.
Vibration Isolation of a Surveillance System Equipped in a Drone with Mode Decoupling. *Appl. Sci.* **2021**, *11*, 1961.
https://doi.org/10.3390/app11041961

**AMA Style**

Shin Y-H, Kim D, Son S, Ham J-W, Oh K-Y.
Vibration Isolation of a Surveillance System Equipped in a Drone with Mode Decoupling. *Applied Sciences*. 2021; 11(4):1961.
https://doi.org/10.3390/app11041961

**Chicago/Turabian Style**

Shin, Yun-Ho, Donggeun Kim, Seho Son, Ji-Wan Ham, and Ki-Yong Oh.
2021. "Vibration Isolation of a Surveillance System Equipped in a Drone with Mode Decoupling" *Applied Sciences* 11, no. 4: 1961.
https://doi.org/10.3390/app11041961