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 [1] [2] . Recently, there also has a breakthrough in large power generation by using the technology. According to the report [3] , when a vehicle is driven along the road, the piezoelectric harvester embedded under the pavement is deformed and produces electric charge. Although one piezoelectric harvester can only produce a small amount of electricity, millions of the harvesters generate huge electrical power, which can be transported into the state grid for accumulating or storing it for later use. If the technology is widely applied, the vast road will become a large electricity farm for supplying human being with inexhaustible energy.

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 [4] . Finite element analysis of Cymbal piezoelectric transducers for harvesting energy from asphalt pavement was done in Ref. [5] . Effects of structural parameters and the planted depth of the piezoelectric harvester on electromechanical properties and pavement deformation were studied via the finite element method (FEM), a new kind of piezoelectric harvesting unit was proposed [6] [7] . Based on this structure, this paper proposes the road paving ways and builds piezoelectric harvesting energy model under vehicle loads. Effect of loads on piezoelectric harvesting properties will then be simulated and analyzed. Some conclusions will finally be drawn.

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. [6] [7] is adopted here. That is, a piezoelectric vibrator is made up a cylinder disk of ø30 × 10 mm and copper electrodes welded on up and down surfaces. A 8 × 8 layout of the piezoelectric vibrators in electrically parallel is arranged to constitute a 280 × 280 × 20 mm square of PHU. The space between the vibrators is 4 mm.

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. [7] . During the process of reforming the pavement, the top asphalt layer of 40 mm height is firstly whipped, two trenches of 280 mm width perpendicular to the vehicle’s traveling direction, whose space is 2200 mm, are then excavated. PHU is finally put into the trenches. After the asphalt is replaced, the pavement with PHU is finished. Figure 1 shows the schematic diagram of paving PHU. The PHU width of 280 mm is larger than the standard tire’s width (≤240 mm) for completely harvesting energy from the vehicle load. The spacing distance of 2200 mm is the same as the standard wheelbase. Each PHU is closely layout. All these are to ensure that each PHU is not only able to absorb road vibration energy, but also to avoid a direct impact on PHU from being damaged.

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 [8] :

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., and are the node’s accelerator, speed and displacement vectors.

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

where, are damping co-efficiencies, which are respectively set to be 0.4 and 0.05 based on the empirical value.

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; is the compliance tensor of constant electric field condition; E is the external electric field; D is the charge displacement tensor; d is piezoelectric strain constant tensor; (permittivity) is dielectric constant tensor measure at constant stress condition.

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 d₃₃ mode. According to the above Equations (1), (2), the pavement node displacement is obtained. is then used as the boundary condition of the system to the node of E_i based on Equations (4), (5). Thus, the excited voltage of one vibrator is calculated by Equation (6)

where U₃ 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. is piezoelectric voltage constant, which is deduced from the following equation

where, is vacuum dielectric constant,.

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

where, P₁ 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, P₂ 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 Table 1. Because the contact area between tire and pavement is near a rectangle, tire weight can be treated to evenly act on this area. Table 2 shows the relationship among wheel weight, tire pressure and tire width. The tire contact pressure is also calculated according to Equation (1), as shown in Table 2. PZT -5A material parameters are shown in Table 3. Here, it is supposed that only one tire load is considered and the pressure contact width is the same as the tire’s width. Meanwhile, in order to put more attention on the PHU, only the asphalt layer is considered in FEM and the layers of asphalt surface possess the same properties. In viewing to axial symmetry, the finite element model of the pavement piezoelectric harvesting system is built in Figure 2 via ANSYS 10.0.

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 Figure 2.

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