# Design of an Energy Harvester Based on a Rubber Bearing Floating Slab Track
## 5 Parameter Optimization Design
### Piezoelectric Layer Thickness  
The parametric numerical model of the spherical energy harvester was established according to the initial size, and the parametric scanning was defined. Thickness H scanning range was 0.5-8 mm, defined H = range (0.5, 0.5, 8). The peak stress, peak vertical displacement, peak voltage, and total electricity of the spherical energy harvester with different piezoelectric layer thicknesses were obtained.  
The peak stress under different piezoelectric layer thicknesses is shown in Figure 14. The peak stress increased with the thickness of the piezoelectric layer, and the overall curve showed an increasing trend, although there were small fluctuations at some thickness values. With the increase in piezoelectric layer thickness H from 0.5 mm to 8 mm, the peak  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Unit** & **Description** \\ \hline H & 2 & mm & Piezoelectric layer thickness \\ R & 16 & mm & Piezoelectric layer radius \\ r\({}_{1}\) & 11 & mm & Vertical axis radius of the inner cavity of the spherical shell \\ r\({}_{2}\) & 11 & mm & Horizontal axis radius of the inner cavity of the spherical shell \\ I & 1 & 1 & Axis ratio \\ T & 5 & mm & Spherical shell thickness \\ \hline \hline \end{tabular}
\end{table}
Table 4: Initial size parameters.  
Figure 13: Geometric model of the spherical energy harvester.  
stress of the energy harvester increased from 1.3 MPa to 1.56 MPa, and the whole increase was 20%. Figure 15 shows the peak vertical displacement under different piezoelectric layer thicknesses. The peak vertical displacement decreased with the increase in piezoelectric layer thickness, and the decreasing trend was basically linear. When the thickness of the piezoelectric layer increased, the peak value of vertical displacement decreased from 2.47 \(\times\) 10\({}^{-4}\) mm to 2.29 \(\times\) 10\({}^{-4}\) mm, with a decrease of 7.3%.  
As can be seen from Figure 16, the peak voltage increased with the increase in piezoelectric layer thickness, being almost linear as a whole. The peak voltage of the energy harvester increased from 1.6 V to 20.8 V, with a total rise of 13 times. Figure 17 shows the change of total electricity with the increase in piezoelectric layer thickness. It can be seen that the total electricity increased with the increase in piezoelectric layer thickness, and it increased from 2.66 \(\times\) 10\({}^{-8}\) J to 3.10 \(\times\) 10\({}^{-7}\) J, with an increase of 11.7 times.  
Figure 14: Peak stress under different piezoelectric layer thicknesses.  
Figure 15: Peak vertical displacement under different piezoelectric layer thicknesses.  
Considering that the thickness of the piezoelectric layer exceeded 7 mm, the processing cost increased sharply and the material stability became poor. As can be obtained from Equation (1), with the increase in thickness, the capacitance \(C_{0}\) decreased, which was not conducive to matching with the load capacitance \(C_{1}\), resulting in low output efficiency when containing an external circuit. Therefore, the thickness of the piezoelectric layer should not be too thick, and if it is too thin, the total electric output will be too small. The minimum total electrical energy output was taken as a 1 \(\times\) 10\({}^{-7}\) J order of magnitude, and the minimum thickness of the piezoelectric layer under the electric energy output of this order of magnitude was 2 mm, so the optimal thickness of the piezoelectric layer was selected as 2 mm comprehensively.