al 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.

5. Simulation Results and Analysis

5.1. The Excited Voltage of PHU

Effect of the contact pressure on the excited voltage is shown in Figure 3. It can be concluded that the excited voltage is linear with the contact pressure. The relationship can be expressed as following


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.

Table 1. Asphalt and steel material parameters.

Table 2. Tire’s weight and pressure and width [9] .

Table 3. PZT -5A material parameters.

Figure 2. Finite element model.

Figure 3. Excited voltage vary with contact pressure.

The fitted error between the simulation data and the fitted ones is shown in Table 4. The Adj. R-Square is 0.99985, which is almost near to 1. It proves that the fitted result of the excited voltage via contact pressure fits very well with the simulation data.

5.2. The Harvested Electrical Energy of PHU

Figure 4 shows the harvested electrical energy with one piece of the proposed PHU. It can be seen that at least 100 mJ of the electric energy is collected with PHU. The relationship of the harvested electrical energy and the contact pressure is expressed as the following exponential equation


According to the fitted statistics, the error and adj. R-square are listed in Table 5. The fitted exponential curve fits very well with the simulation data.

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.

5.3. The Maximum Deformation of the Pavement

Figure 5 shows relationship of the maximum deformation of pavement with contact pressure. The relationship can be expressed as a liner equation as follows


The error is also calculated, as shown in Table 6. The Adj. R-square is 0.99995. It indicates that the fitted result of the maximum deformation of pavement via contact pressure fits very well with the simulation data.

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.

5.4. The Maximum Stress

Figure 6 shows the stress distribution on the piezoelectric harvesting system from pavement. It can be seen that the maximum stress is located on PZT disk. The maximum stress changes with the contact pressure, as shown in

Table 4. The error of the fitted voltage line.

Table 5. The error of the fitted electrical energy.

Table 6. The error of the fitted deformation line.

Figure 4. Electric energy vary with contact pressure.

Figure 5. Deformation vary with contact pressure.

Figure 6. Stress distribution.

Figure 7. The variation of stress linearly changes with the contact pressure.

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.

5.5. Effect of Contact Pressure Frequency

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 Table 7. According to the transit analysis via FEM, the excited voltage also changes with the speed. The simulation result is shown in Table 7.

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

Figure 8 shows real-time change characteristics of the excited voltage at 80 km/h speed. Obviously, the frequency of excited voltage is the same as the frequency of the vehicle load.

Figure 7. Stress vary with contact pressure.

Figure 8. Real-time vary of the excited voltage.

Table 7. Excited voltages under different speeds.

6. Conclusions

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).

Cite this paper

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


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