# Numerical and Experimental Investigation of a Compressive-Mode Hull Piezoelectric Energy Harvester under Impact Force

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Analysis

## 3. Materials and Methods

#### 3.1. Fabrication

#### 3.2. Experimental Setup

^{®}Piezotronics 086D20 impact hammer (PCB Piezotronics, Depew, NY, USA) with a sensitivity of 0.23 mV/N was used to induce the impact force on the PEHs. The PEH prototypes were fixed under a metal bar. The PZT wires were connected through National Instrument Data Acquisition (NI DAQ) devices (National Instruments, Austin, TX, USA), i.e., NI cDAQ-9174 and NI-9232 to a personal computer (PC), while the impact hammer was connected to a DAQ NI-9234.

## 4. Experimental Results

#### 4.1. Open-Circuit Voltage Test

#### 4.2. Power Output Test

#### 4.3. FE Model Validation with Experimental Result and Further Simulation Analysis

^{3}under 1 kN of impact force, which is higher than the reported 1.817 kW/m

^{3}in [29] under the harmonic force of same magnitude. This is due to the difference in optimum resistance (50 kΩ for impact force and 5.99 MΩ for harmonic force), and a higher voltage is obtained under the impact force.

#### 4.4. Efficiency

## 5. Conclusions

^{3}based on the maximum power output and a higher loading capacity than the Cymbal PEH. It has a greater capability to work in a higher-force environment since the PZT’s compressive yield strength is 10 times higher than its tensile yield strength. It is also proven that the tensile-type benchmark structure will reach the saturated stress at a lower force with limited power output if compared with the Hull PEH. Moreover, an energy conversion efficiency of 84.38% is proven for the Hull PEH under 1 kN of impact force, which is higher than that of a harmonic force. This is due to the fact that impact forces induce sudden, high strain rates in PZT, potentially generating higher instantaneous voltages than the slower, spread-out deformations caused by harmonic forces, which might lead to a lower voltage and power output. In short, the harvesting performance of the Hull PEH is experimentally validated under the impact force, marking it a pivotal development in the journey toward a greener, sustainable future. It is concluded to have a better overall performance than the benchmark Cymbal PEH based on the voltage output, power output, loading capacity, and efficiency.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Ghenai, C.; Albawab, M.; Bettayeb, M. Sustainability indicators for renewable energy systems using multi-criteria decision-making model and extended SWARA/ARAS hybrid method. Renew. Energy
**2020**, 146, 580–597. [Google Scholar] [CrossRef] - Evans, A.; Strezov, V.; Evans, T.J. Assessment of sustainability indicators for renewable energy technologies. Renew. Sustain. Energy Rev.
**2009**, 13, 1082–1088. [Google Scholar] [CrossRef] - Østergaard, P.A.; Duic, N.; Noorollahi, Y.; Kalogirou, S. Renewable energy for sustainable development. Renew. Energy
**2022**, 199, 1145–1152. [Google Scholar] [CrossRef] - Viet, N.V.; Xie, X.D.; Liew, K.M.; Banthia, N.; Wang, Q. Energy harvesting from ocean waves by a floating energy harvester. Energy
**2016**, 112, 1219–1226. [Google Scholar] [CrossRef] - Kaur, N.; Mahesh, D.; Singamsetty, S. An experimental study on piezoelectric energy harvesting from wind and ambient structural vibrations for wireless structural health monitoring. Adv. Struct. Eng.
**2020**, 23, 1010–1023. [Google Scholar] [CrossRef] - Li, C.; Liu, S.; Zhao, H.; Tian, Y. Performance Assessment and Comparison of Two Piezoelectric Energy Harvesters Developed for Pavement Application: Case Study. Sustainability
**2022**, 14, 863. [Google Scholar] [CrossRef] - Wang, L.; Fei, Z.; Qi, Y.; Zhang, C.; Zhao, L.; Jiang, Z.; Maeda, R. Overview of Human Kinetic Energy Harvesting and Application. ACS Appl. Energy Mater.
**2022**, 5, 7091–7114. [Google Scholar] [CrossRef] - Turkmen, A.C.; Celik, C. Energy harvesting with the piezoelectric material integrated shoe. Energy
**2018**, 150, 556–564. [Google Scholar] [CrossRef] - Yingyong, P.; Thainiramit, P.; Jayasvasti, S.; Thanach-Issarasak, N.; Isarakorn, D. Evaluation of harvesting energy from pedestrians using piezoelectric floor tile energy harvester. Sens. Actuators A Phys.
**2021**, 331, 113035. [Google Scholar] [CrossRef] - Sharma, S.; Kiran, R.; Azad, P.; Vaish, R. A review of piezoelectric energy harvesting tiles: Available designs and future perspective. Energy Convers. Manag.
**2022**, 254, 115272. [Google Scholar] [CrossRef] - Cao, Y.; Sha, A.; Liu, Z.; Li, J.; Jiang, W. Energy output of piezoelectric transducers and pavements under simulated traffic load. J. Clean. Prod.
**2021**, 279, 123508. [Google Scholar] [CrossRef] - Mota, B.C.; Neto, B.A.; Barroso, S.H.A.; Aragão, F.T.S.; Ferreira, A.J.L.; Soares, J.B.; Brito, L.A.T. Characterization of Piezoelectric Energy Production from Asphalt Pavements Using a Numerical-Experimental Framework. Sustainability
**2022**, 14, 9584. [Google Scholar] [CrossRef] - Sheng, W.; Xiang, H.; Zhang, Z.; Yuan, X. High-efficiency piezoelectric energy harvester for vehicle-induced bridge vibrations: Theory and experiment. Compos. Struct.
**2022**, 299, 116040. [Google Scholar] [CrossRef] - Yang, C.C.; Bin Noor Hanafi, N.F.R.; Bt Mohamad Hanif, N.H.H.; Ismail, A.F.; Chang, H.-H. A Novel Non-Intrusive Vibration Energy Harvesting Method for Air Conditioning Compressor Unit. Sustainability
**2021**, 13, 10300. [Google Scholar] [CrossRef] - Zhang, L.; Zhang, F.; Qin, Z.; Han, Q.; Wang, T.; Chu, F. Piezoelectric energy harvester for rolling bearings with capability of self-powered condition monitoring. Energy
**2022**, 238, 121770. [Google Scholar] [CrossRef] - Zhang, L.; Qin, L.; Qin, Z.; Chu, F. Energy harvesting from gravity-induced deformation of rotating shaft for long-term monitoring of rotating machinery. Smart Mater. Struct.
**2022**, 31, 125008. [Google Scholar] [CrossRef] - Shan, X.; Tian, H.; Chen, D.; Xie, T. A curved panel energy harvester for aeroelastic vibration. Appl. Energy
**2019**, 249, 58–66. [Google Scholar] [CrossRef] - Molino-Minero-Re, E.; Carbonell-Ventura, M.; Fisac-Fuentes, C.; Mànuel-Làzaro, A.; Toma, D.M. Piezoelectric energy harvesting from induced vortex in water flow. In Proceedings of the 2012 IEEE International Instrumentation and Measurement Technology Conference Proceedings, Graz, Austria, 13–16 May 2012; pp. 624–627. [Google Scholar]
- Huet, F.; Boitier, V.; Seguier, L. Tunable Piezoelectric Vibration Energy Harvester With Supercapacitors for WSN in an Industrial Environment. IEEE Sens. J.
**2022**, 22, 15373–15384. [Google Scholar] [CrossRef] - Jettanasen, C.; Songsukthawan, P.; Ngaopitakkul, A. Development of Micro-Mobility Based on Piezoelectric Energy Harvesting for Smart City Applications. Sustainability
**2020**, 12, 2933. [Google Scholar] [CrossRef] - Castillo-Mingorance, J.M.; Sol-Sánchez, M.; Moreno-Navarro, F.; Rubio-Gámez, M.C. A Critical Review of Sensors for the Continuous Monitoring of Smart and Sustainable Railway Infrastructures. Sustainability
**2020**, 12, 9428. [Google Scholar] [CrossRef] - Long, S.X.; Khoo, S.Y.; Ong, Z.C.; Soong, M.F.; Huang, Y.-H.; Prasath, N.; Noroozi, S. A comprehensive review on mechanical amplifier structures in piezoelectric energy harvesters. Mech. Adv. Mater. Struct.
**2023**, 1–30. [Google Scholar] [CrossRef] - Zhao, H.; Yu, J.; Ling, J. Finite element analysis of Cymbal piezoelectric transducers for harvesting energy from asphalt pavement. J. Ceram. Soc. Jpn.
**2010**, 118, 909–915. [Google Scholar] [CrossRef] - Bejarano, F.; Feeney, A.; Lucas, M. A cymbal transducer for power ultrasonics applications. Sens. Actuators A Phys.
**2014**, 210, 182–189. [Google Scholar] [CrossRef] - Wu, Z.; Xu, Q. Design and testing of a novel bidirectional energy harvester with single piezoelectric stack. Mech. Syst. Signal Process.
**2019**, 122, 139–151. [Google Scholar] [CrossRef] - Wen, S.; Xu, Q.; Zi, B. Design of a New Piezoelectric Energy Harvester Based on Compound Two-Stage Force Amplification Frame. IEEE Sens. J.
**2018**, 18, 3989–4000. [Google Scholar] [CrossRef] - Feenstra, J.; Granstrom, J.; Sodano, H. Energy harvesting through a backpack employing a mechanically amplified piezoelectric stack. Mech. Syst. Signal Process.
**2008**, 22, 721–734. [Google Scholar] [CrossRef] - Kuang, Y.; Chew, Z.J.; Zhu, M. Strongly coupled piezoelectric energy harvesters: Finite element modelling and experimental validation. Energy Convers. Manag.
**2020**, 213, 112855. [Google Scholar] [CrossRef] - Long, S.X.; Khoo, S.Y.; Ong, Z.C.; Soong, M.F. Design, modeling and testing of a new compressive amplifier structure for piezoelectric harvester. Smart Mater. Struct.
**2021**, 30, 125010. [Google Scholar] [CrossRef] - Wen, S.; Xu, Q. Design of a two-stage force amplification frame for piezoelectric energy harvesting. In Proceedings of the 2017 IEEE International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE Conference on Robotics, Automation and Mechatronics (RAM), Ningbo, China, 19–21 November 2017; pp. 490–495. [Google Scholar]
- Wang, Y.; Chen, W.; Guzman, P. Piezoelectric stack energy harvesting with a force amplification frame: Modeling and experiment. J. Intell. Mater. Syst. Struct.
**2016**, 27, 2324–2332. [Google Scholar] [CrossRef] - Kuang, Y.; Daniels, A.; Zhu, M. A sandwiched piezoelectric transducer with flex end-caps for energy harvesting in large force environments. J. Phys. D Appl. Phys.
**2017**, 50, 345501. [Google Scholar] [CrossRef] - Kuang, Y.; Chew, Z.J.; Dunville, J.; Sibson, J.; Zhu, M. Strongly coupled piezoelectric energy harvesters: Optimised design with over 100 mW power, high durability and robustness for self-powered condition monitoring. Energy Convers. Manag.
**2021**, 237, 114129. [Google Scholar] [CrossRef] - Avvari, P.V.; Yang, Y.; Soh, C.K. Long-term fatigue behavior of a cantilever piezoelectric energy harvester. J. Intell. Mater. Syst. Struct.
**2016**, 28, 1188–1210. [Google Scholar] [CrossRef] - Long, S.X.; Khoo, S.Y.; Ong, Z.C.; Soong, M.F. Stress enhancement of a trapezoidal bridge piezoelectric transducer in high force environment. Ferroelectrics
**2021**, 573, 23–41. [Google Scholar] [CrossRef]

**Figure 1.**Various types of mechanical amplifier structures in the piezoelectric energy harvester (reproduced from [22]).

**Figure 2.**Artist’s impression of the Hull PEH as a sustainable power supply for the WSN of a traffic monitoring system.

**Figure 4.**Stress distribution of (

**a**) the overall Hull PEH and (

**b**) its PZT as well as (

**c**) the overall benchmark Cymbal PEH and (

**d**) its PZT under 1 kN impact force.

**Figure 10.**Experimental comparison of voltage output from the Hull PEH, the Cymbal PEH, and the standalone PZT plate under impact force.

**Figure 11.**Maximum power output of Hull PEH across several load resistances (10 kΩ to 200 kΩ) under various impact forces.

**Figure 13.**Power output and the average PZT nodal stress of the Rectangular Cymbal PEH under different loading forces (reproduced from [35]).

**Figure 14.**Raw data for Hull PEH’s energy conversion efficiency calculation, i.e., (

**a**) force, (

**b**) voltage, (

**c**) acceleration, and (

**d**) displacement under 1 kN impact force.

**Figure 15.**(

**a**) Force, (

**b**) displacement, (

**c**) input, and (

**d**) output energy curves per cycle extracted from the raw data, and (

**e**) the efficiency calculation for Hull PEH under 1 kN impact force.

Parameters | Symbol | Hull PEH [29] | Cymbal PEH [32] |
---|---|---|---|

PZT length (mm) | l_{PZT} | 52 | 52 |

PZT thickness (mm) | t_{PZT} | 4 | 4 |

Width (mm) | w | 30 | 30 |

Frame length (mm) | l | 186 | 52 |

Frame thickness (mm) | t | 2 | 2 |

Cavity height (mm) | h | 4.9 | 3.5 |

Horizontal linkage length (mm) | l_{h} | 46.5 | 18 |

Joint length (mm) | l_{j} | 7 | 6 |

Inclined angle (°) | θ | 6 | 15 |

Apex length (mm) | l_{a} | - | 14 |

Substrate thickness (mm) | t_{s} | - | 0.6 |

Parameters | Symbols | Values | |
---|---|---|---|

Density (kg/m^{3}) | ρ | 7900 | |

Elastic Coefficient | Stiffness constant (×10 ^{10} N/m^{2}) | C_{11} | 16.9 |

C_{12} | 11.8 | ||

C_{13} | 10.9 | ||

C_{33} | 12.3 | ||

C_{44} | 2.7 | ||

C_{55} | 2.7 | ||

C_{66} | 2.5 | ||

Elastic constant (×10 ^{−12} m^{2}/N) | S_{11} | 15.1 | |

S_{12} | −4.5 | ||

S_{13} | −9.4 | ||

S_{33} | 24.8 | ||

S_{44} | 37.1 | ||

S_{55} | 37.1 | ||

S_{66} | 39.2 | ||

Piezoelectric stress constant(C/m^{2}) | e31 | −12 | |

e33 | 18.2 | ||

e15 | 21.9 | ||

Piezoelectric strain constant(×10^{−12} C/N) | d31 | −300 | |

d33 | 680 | ||

d15 | 810 | ||

Dielectric permittivity | Clamp dielectric constant, ε^{S} (At constant strain) | ε11 | 1550 |

ε33 | 1390 | ||

Free dielectric constant, ε^{T} (At constant stress) | ε11 | 3550 | |

ε33 | 3850 |

Force (N) | 10 | 50 | 100 | 200 | 400 | 1000 |
---|---|---|---|---|---|---|

FEA simulation V_{oc, peak} (V) | 9.64 | 48.80 | 98.14 | 197.81 | 400.76 | 1031.12 |

Experimental V_{oc, peak} (V) | 9.78 | 48.88 | 97.75 | 195.50 | 391.00 | 977.50 |

Percentage error (%) | 1.40 | 0.15 | 0.39 | 1.17 | 2.44 | 5.20 |

Force (kN) | 1.0 | 2.0 | 2.5 |
---|---|---|---|

V_{peak} (V) | 619.96 | 1163.94 | 1624.14 |

P_{max} (W) | 7.69 | 27.10 | 52.76 |

PZT maximum stress (MPa) | 62.37 | 124.17 | 163.63 |

Frame maximum stress (MPa) | 254.53 | 610.85 | 609.29 |

PZT average nodal stress (MPa) | 33.10 | 56.20 | 88.30 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Long, S.X.; Khoo, S.Y.; Ong, Z.C.; Soong, M.F.; Huang, Y.-H.
Numerical and Experimental Investigation of a Compressive-Mode Hull Piezoelectric Energy Harvester under Impact Force. *Sustainability* **2023**, *15*, 15899.
https://doi.org/10.3390/su152215899

**AMA Style**

Long SX, Khoo SY, Ong ZC, Soong MF, Huang Y-H.
Numerical and Experimental Investigation of a Compressive-Mode Hull Piezoelectric Energy Harvester under Impact Force. *Sustainability*. 2023; 15(22):15899.
https://doi.org/10.3390/su152215899

**Chicago/Turabian Style**

Long, Su Xian, Shin Yee Khoo, Zhi Chao Ong, Ming Foong Soong, and Yu-Hsi Huang.
2023. "Numerical and Experimental Investigation of a Compressive-Mode Hull Piezoelectric Energy Harvester under Impact Force" *Sustainability* 15, no. 22: 15899.
https://doi.org/10.3390/su152215899