# Design and Experimental Investigation of a Rotational Piezoelectric Energy Harvester with an Offset Distance from the Rotation Center

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Design and Theoretical Analysis

_{0}, the centrifugal force F

_{cent}of the rotating object is given by

_{cent}= m

_{0}ω

_{0}

^{2}r

_{0},

_{0}is the mass of the rotating object, and r

_{0}is the radius of the rotation. The centrifugal force is oriented away from the axis of the rotation.

_{0}will be greatly decreased. Therefore, the centrifugal force of the rotational mass will be greatly decreased too.

_{b}, w

_{b}and t

_{b}are the length, width and thickness of the substrate beam; l

_{p}, w

_{p}and t

_{p}are the length, width and thickness of the piezoelectric element; r

_{m}

_{1}and r

_{m}

_{2}are the outer radius and inner radius of the ring mass; the width of the ring mass is w

_{m}. In order to avoid that the beam and mass are stuck at some place due to an overlarge centrifugal force, the centrifugal force F

_{cent}of the rotating parts should be smaller than the gravity of the rotating parts. Therefore, we have a constraint on the radius of the rotation r

_{0}that r

_{0}< g/ω

_{0}

^{2}. Using a rotating frequency of 15 Hz as an example, the radius of the rotation should be smaller than 1.103 mm. In our design, the gap, i.e., the radius of the rotation r

_{0}is designed at 1 mm considering the application. The rotational mass is not related to the radius of the rotation r

_{0}, but it will influence the vibration acceleration of the cantilever beam. A larger rotational mass will increase the vibration acceleration of the beams and therefore increase the voltage outputs of the piezoelectric elements. In our design, a large rotational mass is used. In the design, to guarantee the reliability of the structure, the mechanical strains of the piezoelectric elements and other structures should be kept within material specifications.

## 3. Experimental Validations

_{0}between the piezoelectric elements and the respective fixed supports. Dimensions of the beam structure and piezoelectric elements are given in Table 1, where m

_{ring}is the mass of the ring mass; r

_{g}is the external radius of the groove in the wheel hub; h

_{l}is the height of the limiter. In Table 1, the inner radius of the ring mass r

_{m}

_{2}is 170 mm, the external radius of the groove in the wheel hub r

_{g}is 159 mm, and the height of the limiter h

_{l}is 10 mm. Therefore, the gap distance r

_{0}is 1 mm.

_{opt}under a particular frequency f

_{n}is R

_{opt}= 1/(2πf

_{n}C

_{p}), where C

_{p}is the capacitance of the piezoelectric element. The output voltages with respective external resistors at several rotating frequencies are shown in Figure 10. The external resistors used are 839.7, 372.9, 175.3 and 100.2 kΩ for the rotating frequencies 1.67, 3.76, 8 and 14 Hz, respectively. From Figure 10, it can be found that the waves of the output voltages with external resistors became steeper than the open-circuit voltage curves shown in Figure 9. The waves at the high frequencies of 8 and 14 Hz are similar to a sawtooth wave.

^{3}.

## 4. Conclusions and Discussion

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Schematic of a conventional cantilever beam structure with compact mass in a rotational energy harvester.

**Figure 3.**Structure of wheel and the rotational energy harvester: (

**a**) three-dimensional view; (

**b**) front view; (

**c**) close view.

Parameter | Value |
---|---|

l_{b}, w_{b}, t_{b} | 60, 50, 1.2 mm |

r_{m1}, r_{m2}, w_{m} | 200, 170, 30 mm |

l_{p}, w_{p}, t_{p} | 28.5, 50, 0.267 mm |

r_{g} | 159 mm |

h_{l} | 10 mm |

m_{ring} | 2680 g |

C_{p} | 113.5 nF |

x_{0} | 1.5 mm |

r_{0} | 1 mm |

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**MDPI and ACS Style**

Chen, J.; Liu, X.; Wang, H.; Wang, S.; Guan, M.
Design and Experimental Investigation of a Rotational Piezoelectric Energy Harvester with an Offset Distance from the Rotation Center. *Micromachines* **2022**, *13*, 388.
https://doi.org/10.3390/mi13030388

**AMA Style**

Chen J, Liu X, Wang H, Wang S, Guan M.
Design and Experimental Investigation of a Rotational Piezoelectric Energy Harvester with an Offset Distance from the Rotation Center. *Micromachines*. 2022; 13(3):388.
https://doi.org/10.3390/mi13030388

**Chicago/Turabian Style**

Chen, Jun, Xiangfu Liu, Hengyang Wang, Sheng Wang, and Mingjie Guan.
2022. "Design and Experimental Investigation of a Rotational Piezoelectric Energy Harvester with an Offset Distance from the Rotation Center" *Micromachines* 13, no. 3: 388.
https://doi.org/10.3390/mi13030388