# 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

## References

- Wang, Y.; Yang, Z.; Li, P.; Cao, D.; Huang, W.; Inman, D.J. Energy harvesting for jet engine monitoring. Nano Energy
**2020**, 75, 104853. [Google Scholar] [CrossRef] - Fu, H.; Yeatman, E.M. A Miniaturized piezoelectric turbine with self-regulation for increased air speed range. Appl. Phys. Lett.
**2015**, 107, 243905. [Google Scholar] [CrossRef] [Green Version] - Nezami, S.; Jung, H.J.; Lee, S. Design of a disk-swing driven piezoelectric energy harvester for slow rotary system application. Smart Mater. Struct.
**2019**, 28, 074001. [Google Scholar] [CrossRef] - Zhou, G.; Li, Z.; Zhu, Z.; Hao, B.; Tang, C. A new piezoelectric bimorph energy harvester based on the vortex-induced-vibration applied in rotational machinery. IEEE/ASME Trans. Mech.
**2019**, 24, 700–709. [Google Scholar] [CrossRef] - Tang, M.; Guan, Q.; Wu, X.; Zeng, X.; Zhang, Z.; Yuan, Y. A high-efficiency multidirectional wind energy harvester based on impact effect for self-powered wireless sensors in the grid. Smart Mater. Struct.
**2019**, 28, 115022. [Google Scholar] [CrossRef] - Micek, P.; Grzybek, D. Wireless stress sensor based on piezoelectric energy harvesting for a rotating shaft. Sens. Actuators A Phys.
**2020**, 301, 111744. [Google Scholar] [CrossRef] - Zhang, Y.; Luo, A.; Wang, Y.; Dai, X.; Lu, Y.; Wang, F. Rotational electromagnetic energy harvester for human motion application at low frequency. Appl. Phys. Lett.
**2020**, 116, 053902. [Google Scholar] [CrossRef] - Fan, K.; Liu, J.; Cai, M.; Zhang, M.; Qiu, T.; Tang, L. Exploiting ultralow-frequency energy via vibration-to-rotation conversion of a rope-spun rotor. Energy Convers. Manag.
**2020**, 225, 113433. [Google Scholar] [CrossRef] - Luo, A.; Zhang, Y.; Dai, X.; Wang, Y.; Xu, W.; Lu, Y.; Wang, M.; Fan, K.; Wang, F. An inertial rotary energy harvester for vibrations at ultra-low frequency with high energy conversion efficiency. Appl. Energy
**2020**, 279, 115762. [Google Scholar] [CrossRef] - Guo, X.; He, T.; Zhang, Z.; Luo, A.; Wang, F.; Ng, E.J.; Zhu, Y.; Liu, H.; Lee, C. Artificial intelligence-enabled caregiving walking stick powered by ultra-low-frequency human motion. ACS Nano
**2021**, 15, 19054–19069. [Google Scholar] [CrossRef] - Roundy, S.; Tola, J. Energy harvester for rotating environments using offset pendulum and nonlinear dynamics. Smart Mater. Struct.
**2014**, 23, 105004. [Google Scholar] [CrossRef] [Green Version] - Zhang, Y.; Zheng, R.; Nakano, K.; Cartmell, M.P. Stabilising high energy orbit oscillations by the utilisation of centrifugal effects for rotating-tyre-induced energy harvesting. Appl. Phys. Lett.
**2018**, 112, 143901. [Google Scholar] [CrossRef] [Green Version] - Xie, Z.; Xiong, J.; Zhang, D.; Wang, T.; Shao, Y.; Huang, W. Design and experimental investigation of a piezoelectric rotation energy harvester using bistable and frequency up-conversion mechanisms. Appl. Sci.
**2018**, 8, 1418. [Google Scholar] [CrossRef] [Green Version] - Fu, H.; Mei, X.; Yurchenko, D.; Zhou, S.; Theodossiades, S.; Nakano, K.; Yeatman, E.M. Rotational energy harvesting for self-powered sensing. Joule
**2021**, 5, 1074–1118. [Google Scholar] [CrossRef] - Fu, X.; Liao, W.H. Modeling and analysis of piezoelectric energy harvesting with dynamic plucking mechanism. J. Vib. Acoust.
**2019**, 141, 031002. [Google Scholar] [CrossRef] - Janphuang, P.; Lockhart, R.A.; Isarakorn, D.; Henein, S.; Briand, D.; Rooij, N.F. Harvesting energy from a rotating gear using an AFM-like MEMS piezoelectric frequency upconverting energy harvester. J. Microelectromech. Syst.
**2015**, 24, 742–754. [Google Scholar] [CrossRef] - Zou, H.; Zhang, W.; Li, W.; Gao, Q.; Wei, K.; Peng, Z.; Meng, G. Design, modeling and experimental investigation of a magnetically coupled flextensional rotation energy harvester. Smart Mater. Struct.
**2017**, 26, 115023. [Google Scholar] [CrossRef] - He, L.; Wang, Z.; Wu, X.; Zhang, Z.; Zhao, D.; Tian, X. Analysis and experiment of magnetic excitation cantilever-type piezoelectric energy harvesters for rotational motion. Smart Mater. Struct.
**2020**, 29, 055043. [Google Scholar] [CrossRef] - Zhang, Y.; Cao, J.; Zhu, H.; Lei, Y. Design, modeling and experimental verification of circular Halbach electromagnetic energy harvesting from bearing motion. Energy Convers. Manag.
**2019**, 180, 811–821. [Google Scholar] [CrossRef] - Fu, H.; Yeatman, E.M. Rotational energy harvesting using bi-stability and frequency up-conversion for lowpower sensing applications: Theoretical modelling and experimental validation. Mech. Syst. Signal Proc.
**2019**, 125, 229–244. [Google Scholar] [CrossRef] - Rui, X.; Zeng, Z.; Zhang, Y.; Li, Y.; Feng, H.; Huang, X.; Sha, Z. Design and experimental investigation of a self-tuning piezoelectric energy harvesting system for intelligent vehicle wheels. IEEE Trans. Veh. Technol.
**2020**, 68, 1440–1451. [Google Scholar] [CrossRef] - Mei, X.T.; Zhou, R.; Yang, B.; Zhou, S.; Nakano, K. Combining magnet-induced nonlinearity and centrifugal softening effect to realize high-efficiency energy harvesting in ultralow-frequency rotation. J. Sound Vib.
**2021**, 505, 116146. [Google Scholar] [CrossRef] - Hsieh, T.T.; Chen, S.A.; Shu, Y.C. Investigation of various cantilever configurations for piezoelectric energy harvesting under rotational motion. In Proceedings of the SPIE Conference on Active and Passive Smart Structures and Integrated Systems XIII, Denver, CO, USA, 21 March 2019. [Google Scholar] [CrossRef]
- Fang, S.; Wang, S.; Zhou, S.; Yang, Z.; Liao, W.H. Analytical and experimental investigation of the centrifugal softening and stiffening effects in rotational energy harvesting. J. Sound Vib.
**2020**, 488, 115643. [Google Scholar] [CrossRef] - Guan, M.; Liao, W.H. Design and analysis of a piezoelectric energy harvester for rotational motion system. Energy Convers. Manag.
**2016**, 111, 239–244. [Google Scholar] [CrossRef] - Wang, Y.; Yang, Z.; Cao, D. On the offset distance of rotational piezoelectric energy harvesters. Energy
**2021**, 220, 119676. [Google Scholar] [CrossRef] - Liao, W.H.; Wang, K.W. Characteristics of enhanced active constrained layer damping treatments with edge elements, part 2: System analysis. J. Vib. Acoust.
**1998**, 120, 894–900. [Google Scholar] [CrossRef] - Guan, M.; Wang, K.; Xu, D.; Liao, W.H. Design and experimental investigation of a low-voltage thermoelectric energy harvesting system for wireless sensor nodes. Energy Convers. Manag.
**2017**, 138, 30–37. [Google Scholar] [CrossRef]

**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