# Design of an Energy Harvester Based on a Rubber Bearing Floating Slab Track
## 5 Parameter Optimization Design
### Axial Ratio of Spherical Shell  
When studying the effect of the axial ratio of the spherical shell on the energy harvester, the vertical axis radius of the inner cavity of the spherical shell should be kept consistent, at 11 mm. Because I = r\({}_{1}\)/r\({}_{2}\), the axial ratio can be controlled by changing the radius r\({}_{2}\). In the numerical model, R\({}_{2}\) was defined as a parametric scan with a range of 5-30 mm, and R2 = range (5, 1, 30) was defined in the parameter value list. A simple calculation shows that the corresponding axial ratio range was 0.37-2.20. As the axis ratio increased, the geometry of the spherical shell slowly changed from a flat ellipsoid to a hanging ellipsoid. The stress nephogram of the spherical energy harvester with different axial ratios obtained by the COMSOL simulation is shown in Figure 22.  
Figure 21: Total electricity under different piezoelectric layer radii.  
Figure 22: _Cont._  
Meanwhile, the peak stress, peak vertical displacement, peak voltage, and total electricity of the spherical energy harvester under different axial ratios of the spherical shell were obtained, as shown in Figures 23-26.  
Figure 23: Peak stress under different axial ratios of the spherical shell.  
Figure 24: Peak vertical displacement under different axial ratios of the spherical shell.  
Figure 22: Stress nephogram of the spherical energy harvester with different axial ratios.  
As shown in Figure 23, the peak stress decreased with the increase in the axial ratio of the spherical shell, and the decreasing rate became slower and slower. When the axial ratio of the spherical shell increased from 0.37 to 2.2, the peak stress of the energy harvester decreased from 5.08 MPa to 0.64 MPa, with a decrease of 87.4%. Figure 24 shows the variation of the peak vertical displacement, which decreased with the increase in the axial ratio of the spherical shell, and the decreasing rate also became slower and slower. With the increase in the axial ratio of the spherical shell, the peak vertical displacement decreased from 9.51 \(\times\) 10\({}^{-4}\) mm to 2.02 \(\times\) 10\({}^{-4}\) mm, a decrease by 78.8%.  
As can be seen from Figure 25, the peak voltage of the energy harvester decreased with the increase in the axial ratio, and the decreasing rate slowed down continuously. The overall peak voltage of the energy harvester decreased from 23.7 V to 4.8 V, with the decrease of 79.8%. As shown in Figure 26, the change of total electricity decreased with the increase in the axis ratio, from 6.98 \(\times\) 10\({}^{-6}\) J to 2.35 \(\times\) 10\({}^{-8}\) J, which was two orders of magnitude lower. The variation of the peak voltage with the axial ratio of the spherical shell was analyzed, and it was concluded that the axial ratio of the spherical shell had a great influence on the electrical properties of the spherical energy harvester.  
When the axial ratio of the spherical shell varied from 0.37 to 2.2, the peak stress and vertical displacement of the energy harvester were within the safe range. And the electrical properties such as peak voltage and total electricity changed obviously with the axial ratio, so the electrical properties were given priority to determine the axial ratio of the spherical shell. When the axial ratio of the spherical shell was small, the voltage and electric energy output of the energy harvester became better. That is, when the geometric design of the energy harvester was more inclined to the flat ellipsoid, it had better captive performance. When the axial ratio I was 0.4, the peak voltage was 20.6 V, which met the minimum output  
Figure 26: Total electricity under different axial ratios of the spherical shell.  
Figure 25: Peak voltage under different axial ratios of the spherical shell.  
voltage requirement (0.4-1.5 V). And the total power was 4.40 \(\times\) 10\({}^{-6}\) J, which was at a better level. Therefore, the optimal axial ratio of the spherical shell was 0.4.