# A Bio-Inspired Flapping Wing Rotor of Variant Frequency Driven by Ultrasonic Motor

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## Abstract

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## 1. Introduction

## 2. Structure Design and Numerical Method

#### 2.1. Flapping Wing Rotor Model

**A**and ${A}^{\prime}$) are present for the flapping motion as per Figure 2 and Figure 3. As shown in Figure 3, the front spar, chord-wise beam and two reinforced oblique beams of each wing are plotted in black lines. The span-wise and chord-wise length of the wing membrane skin are 205 mm, and 150 mm, respectively.

#### 2.2. Kinematics of the Flapping Wing Rotor

#### 2.3. CFD Model and Validation

#### 2.4. Assembly of Experimental Devices

## 3. Experiment Results and Discussion

#### 3.1. Parametric Study for the Effect of Flapping Frequency Variation

#### 3.2. Experimental Results of the VFF Effect on Inertial Force

#### 3.3. Experimental and CFD Simulation Comparison

#### 3.4. Flow Field Simulation and Analysis by CFD Method

#### 3.5. The Effect of Different Installation Angles on the Lift Generation and Rotational Speed Generation

_{0}= 30°. In order to evaluate the effect of the installation angle on the lift, the FWR model, with alternative installation angles, including θ

_{0}= 15°, 45° and 60° and have also been tested with the results presented in Figure 18.

_{0}increases due to the increased drag force. In general, the larger the flapping frequency and power input, the larger the rotational speed. Furthermore, the rotational speed for CFF case 1 remains almost constant when θ

_{0}< 30° before decrease afterwards, while the rotational speed for the other cases of smaller power input is decreased in the whole range of θ

_{0}, and even close to zero when θ

_{0}reaches 45°. The maximum average lift force, generated by the FWR, is shown in Figure 18b. It is also observed that the lift force increases with the installation angle until it reaches the maximum at θ

_{0}= 30° and then decreases when θ

_{0}> 30° for all the cases. The results indicate that there is an optimal installation angle to achieve the largest lift for different power, flapping frequency, and rotational speed. In terms of lift-to-power ratio, the higher value is generally associated with higher flapping frequency or input power, as shown in Figure 18c. However the lift-to-power ratio of the FWR at 3Hz reduces dramatically when θ

_{0}> 30° and becomes smaller than the VFF case (3 Hz & 1 Hz) when θ

_{0}= 43°–53°, and the 1.3 Hz case, which has much smaller input power.

_{0}≥ 45° in all cases of different flapping frequencies, it is found that the resulting 0.1 > S

_{t}> 0.6 is far beyond the high propulsion efficiency around S

_{t}= 0.3 of flying animals and the associated lift efficiency ${P}_{f}<0.02$ is very low. For the cases with installation angles 15°–30°, the ${S}_{t}$ values fall in the range of 0.25–0.6 with most of the associated ${P}_{f}>0.05$ as shown in Figure 19. In particular the ${P}_{f}$ reaches a value 0.28 associated with S

_{t}= 0.36 for the CFF case 1 (3 Hz), which is similar to an optimal result in previous study [19]. Comparing all the CFF cases, the ${S}_{t}$ number for all the VFF cases of equivalent power output falls in the range of 0.3–0.36 with slightly higher ${P}_{f}$ values. For example, the VFF case 4 (3 & 1 Hz) results in S

_{t}= 0.31 and ${P}_{f}$ = 0.11 while the CFF case of equivalent frequency (1.3 Hz) and power (1.09 W) results in S

_{t}= 0.53 and significant smaller ${P}_{f}=0.02$. It is clear that the VFF cases with an installation angle θ

_{0}= 30° result in higher ${P}_{f}$ and optimal S

_{t}number comparing with the other cases and installation angles.

## 4. Conclusions

_{0}of the wings is a key factor that influences the FWR performance and lift. From the parametric study for a range of installation angles θ

_{0}= 15°–60°, it is found that the larger the installation angle, the greater the lift force at a rotational speed. In practice however, a large installation angle results in a large drag and reduced rotational speed. When θ

_{0}≥ 45°, the rotational speed is decreased to nearly zero. Without rotary motion, the FWR works like a conventional flapping wing with the lift reduced dramatically as shown in Figure 18. For this FWR model, an optimal θ

_{0}is found around 30° for both CFF and VFF cases while the VFF normally results in a higher power efficiency and propulsion efficiency. With the optimal installation angle θ

_{0}= 30°, the Strouhal number for the VFF cases is in the range of high propulsion efficiency 0.3–0.36 and higher ${P}_{f}$ values than the CFF cases of the same power and equivalent flapping frequency. The ultrasonic motor provides a feasible solution for the FWR to obtain VFF and generate higher lift under a specified input power.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 9.**Comparison in lift coefficients and rotational moment coefficients between CFD calculation by fluent software and computational results by Wang et al.

**Figure 13.**Lift force comparison between the experiment and CFD in (

**a**) 3 Hz case; (

**b**) 1 Hz case; (

**c**) 3&1 Hz case.

**Figure 14.**Comparison between lift curves of the flapping wing rotor measured in (

**a**) 2 Hz case; (

**b**) 3&2 Hz case.

**Figure 17.**(

**a**) Mechanical output curves of motor; (

**b**) the relationship between lift and output power.

**Figure 18.**The (

**a**) rotational speeds; (

**b**) lift forces; (

**c**) the ratio between lift and power produced by the FWR in different installation angles.

Variables | r | l | $\mathit{O}\mathit{A}\left({\mathit{O}\mathit{A}}^{\prime}\right)$ | $\mathit{A}\mathit{B}\left({\mathit{A}}^{\prime}{\mathit{B}}^{\prime}\right)$ |
---|---|---|---|---|

Dimensions (mm) | 6 | 35 | 9 | 8 |

Case No. | Flapping Mode | ${\mathit{f}}_{\mathit{d}}$ (Hz) | ${\mathit{f}}_{\mathit{u}}$ (Hz) | $\dot{\mathit{\psi}}$ (Hz) |
---|---|---|---|---|

1 | CFF | 3 | 3 | 2 |

2 | CFF | 2 | 2 | 1 |

3 | CFF | 1 | 1 | 0.41 |

4 | VFF | 3 | 1 | 1 |

5 | VFF | 3 | 2 | 1.67 |

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**MDPI and ACS Style**

Chen, S.; Wang, L.; Guo, S.; Zhao, C.; Tong, M.
A Bio-Inspired Flapping Wing Rotor of Variant Frequency Driven by Ultrasonic Motor. *Appl. Sci.* **2020**, *10*, 412.
https://doi.org/10.3390/app10010412

**AMA Style**

Chen S, Wang L, Guo S, Zhao C, Tong M.
A Bio-Inspired Flapping Wing Rotor of Variant Frequency Driven by Ultrasonic Motor. *Applied Sciences*. 2020; 10(1):412.
https://doi.org/10.3390/app10010412

**Chicago/Turabian Style**

Chen, Si, Le Wang, Shijun Guo, Chunsheng Zhao, and Mingbo Tong.
2020. "A Bio-Inspired Flapping Wing Rotor of Variant Frequency Driven by Ultrasonic Motor" *Applied Sciences* 10, no. 1: 412.
https://doi.org/10.3390/app10010412