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To realize the goal of harvesting energy from pavement vibration on a large scale, a new type of piezoelectric harvesting units as the energy transducer has been proposed. The piezoelectric harvesting units are paved 40 mm below the asphalt, which is the same as thickness of the top layer of typical asphalt pavement in China. The spacing distance is 2200 mm, which is the same as the one between two tires of a normal vehicle. A mathematical model of the unit is deduced on Meda empirical formula and Hamilton principle and piezoelectric equations. Effects of the external vehicle load on its harvesting energy properties and pavement deformation and stress are analyzed with the finite element method. The results show that the excited voltage is linearly variation with contact pressure while the harvested electrical energy exponential varies with contact pressure. The more the contact pressure is, the larger the harvested electrical energy and the deformation and stress are. The harvested electrical energy also increases with the load frequency. At least 100 mJ of electrical energy can be collected with the proposed piezoelectric harvesting unit. It shows that the technology application of the piezoelectric harvesting energy from pavement is promising.

Vibration-based piezoelectric harvesting energy technology has received growing attention over the last decade. The main application of the technology is to power small electronic devices by using the vibration energy available in ambient environment, such as MEMS micro-power devices [

The technology of vibration-based piezoelectric energy harvesting from pavement has attracted more and more attention of academia and industry. It will be one important direction of piezoelectric harvesting energy by replacing conventional electricity generation. It also will be a groundbreaking systematic works. However, as a new concept, the state of studying the technology is still in its infancy, a complete theoretical system has not been established. Few researches have dealt with it until now. Patent on the piezoelectric method and system for harvesting vibration from road was invented [

To efficiently harvest vibration energy from pavement on large scale and do not affect the vehicle’s safety and comfort, the piezoelectric harvesting unit (PHU) proposed in Ref. [

Taking the typical pavement structure in China into consideration, the surface of asphalt pavement always includes 2 - 3 layers. The thickness of the top layer is 40 mm. For the better comprehensive result, the PHU is embedded 40 mm under the bottom of the top asphalt layer. About the optimal design for layouting the PHUs is discussed in detail in Ref. [

Assuming that vertical load uniformly acts on the pavement when a vehicle passes, the pressure between the tire and the pavement can be deduced from the Meda’s empirical formula [

where F is the contact pressure in MPa, F' is wheel weight in kN, F_{i} is tire inner pressure in MPa.

Based on Hamilton principle, the pavement’s dynamic finite element equation is

where [M], [C], [K] are pavement quality matrix, damping and stiffness matrices, respectively.

The damping matrix of [C] is usually calculated according to the Raleigh damping assumption in the following equation

where

When a piezoelectric vibrator is embedded under the pavement, it will generate strain under the vehicle load. The piezoelectric equations are described as the following equations

where, i, j = 1, 2, 3, ∙∙∙, 6; m, k = 1, 2, 3; S is the strain tensor; T is the stress tensor;

The system, which is constituted by vehicle, pavement and PHU, is a complex multi-bodies dynamics one. To meet the requirement of large stress, low frequency and random vibration and to improve the usage life, the designed PHU adopts the d_{33} mode. According to the above Equations (1), (2), the pavement node displacement _{i} based on Equations (4), (5). Thus, the excited voltage of one vibrator is calculated by Equation (6)

where U_{3} is the electric potential (voltage) at the direction 3 caused by polarization changing, which can be obtained via the finite element analysis (FEA); t is the thickness of PZT disk.

where,

The electric energy stored in one piece of piezoelectric vibrator can be calculated by

where, P_{1} is the stored electric energy of a vibrator; A is the surface area of PZT disk.

As described above, a PHU, which is the 8 × 8 array of the vibrator, can then harvest the total electric energy

where, P_{2} is electric energy harvested by one piece of PHU.

According to the above proposed PHU size and laying way, about 14, 280 pieces of PHU are embedded under one mile of two-side pavement. Thus, one piece of PHU may be harvested minimal energy, but the total electric energy is still considerable if the PHU is paved on large scale. Therefore, study on the technology of piezoelectric harvesting energy from pavement vibration will cause a major contribution to social and environment, especially to some countries which mainly rely on coal power generation. The resulting low carbon effect is immeasurable.

It can be drawn from the Formula (1)-(9) that the harvested electric energy of a PHU is relevant to the properties of piezoelectric material and the wheel weight and tire pressure. Here, the effect of wheel weight and tire pressure on the harvested electric energy is discussed.

The typical semi-rigid pavement structure is adopted to be the pavement model. The material’s parameters of pavement layer and steel are shown in

During simulation, Plane13 is chosen to mesh PZT disk and Plane42 is used to mesh pavement and steel. The electrical potential of the top layer of PZT disk is set to zero, the same potential is set for the bottom of PZT disk. The displacement of the bottom of the model is set to zero. These boundary conditions are shown in

Effect of the contact pressure on the excited voltage is shown in

From the equation, it can be known that intercept and slope are 0.523 and 1123.255, respectively. It shows that the fitted line is almost through the origin and the contact pressure takes great influence on the excited voltage.

Material | Elastic modulus/MPa | Poisson ratio | Density/kg∙m^{−3} |
---|---|---|---|

Asphalt | 1800 | 0.32 | 2400 |

Metal | 200,000 | 0.3 | 7800 |

No. | Tires’ weight F'/kN | Tire pressure F_{i}/MPa | Tire width/mm | Contact pressure F/MPa |
---|---|---|---|---|

1 | 20 | 0.6 | 220 | 0.4 |

2 | 40 | 0.7 | 220 | 0.52 |

3 | 50 | 0.75 | 220 | 0.573 |

4 | 60 | 0.8 | 220 | 0.63 |

5 | 80 | 0.9 | 240 | 0.74 |

6 | 100 | 1.0 | 240 | 0.855 |

Parameters | Value |
---|---|

Density (kg/m^{3}) | 7500 |

Poisson’s ratio | 0.32 |

Relative permittivity ^{−}^{9} F/m) | |

Piezoelectric voltage constant matrix [d] (pC/N)^{ } | |

Flexible piezoelectric constant matrix [s] (GPa) |

The fitted error between the simulation data and the fitted ones is shown in

According to the fitted statistics, the error and adj. R-square are listed in

Expanding the project to a length of one kilometer along two lanes, about 450 KWh electrical energy can be harvested with these PHU modules, provided that approximately 600 heavy trucks travel along through the interval per hour on average.

The error is also calculated, as shown in

Taken these comprehensive factors into consideration, when the contact pressure increases, the harvested electrical energy increases. Meanwhile, the pavement displacement also increases. The maximum deformation of pavement is located on the model of x = 0, the point of the contact center of the tire and the pavement.

Intercept | Slope | Statistics | ||
---|---|---|---|---|

Value | Error | Value | Error | Adj. R-Square |

0.523 | 3.92849 | 1123.255 | 6.16763 | 0.99985 |

y_{0} | A_{1} | t_{1} | Statistics | |||
---|---|---|---|---|---|---|

Value | Error | Value | Error | Value | Error | Adj. R-Square |

0.00114 | 0.00136 | 0.69773 | 0.00213 | 0.58519 | 0.03272 | 0.99978 |

Intercept | Slope | Statistics | ||
---|---|---|---|---|

Value | Error | Value | Error | Adj. R-Square |

0.00114 | 0.00136 | 0.69773 | 0.00213 | 0.99995 |

The maximum stress on a PZT disk is 8.8 MPa when the maximum contact pressure acts on the pavement. Contrast to the allowable limit stress of 100 MPa, 8.8 MPa is so small that the PHU can normally work.

When a vehicle is driven at different speed, the frequency of the vehicle load varies. Taken a vehicle with 2 axes and the axial distance of 4.5 m, two tire weight of 80 kN for example, the various speeds cause different frequencies of the vehicle load, as shown in

The excited voltage increases with the increase of the vehicle load frequency. However, its effect is significantly smaller than contact pressure.

Speed (km/h) | Frequency (Hz) | Excited voltage (V) |
---|---|---|

60 | 3.71 | 847.6 |

70 | 4.32 | 850 |

80 | 4.94 | 852.6 |

90 | 5.56 | 855 |

100 | 6.18 | 857.5 |

110 | 6.79 | 860 |

120 | 7.41 | 862.4 |

The layout of piezoelectric harvesting energy units is discussed. Effect of vehicle loads on piezoelectric energy properties is discussed via the finite element analysis. The harvested energy variation with contact pressure is concluded.

The results show that the maximum stress happens on the PZT disk and lies within the allowable limit stress. Effect of vehicle speed on the excited voltage and the harvested electrical energy is significantly smaller than contact pressure. One piece of PHU can harvest at least 100 mJ electrical power.

All proves that the technology of piezoelectric harvesting energy from pavement vibration has a promising prospect. The future work will focus on the consistency of PHUs and pavement along with the pavement test.

This research was supported by the National Natural Science Foundation of China (No. 51175359) and the 4th “333 Engineering” Research Funding Project of Jiangsu Province (BRA2014086).

ChunhuaSun,HongbingWang,JieLiu,GuangqingShang, (2015) Finite Element Analysis of Vehicle Load Effect on Harvesting Energy Properties of a Piezoelectric Unit. Energy and Power Engineering,07,500-508. doi: 10.4236/epe.2015.710047