# Finite Element Analysis of the Distribution Parameters of a Metal Dot Array in a SAW Gyroscope
## 3 Modeling and Simulation
### Simulation Results and Discussion
#### 3.2.2 Influence of Rotation Speed on the Distribution Parameters of the Metal Dot Array  
Next, it is analyzed whether the change of the rotation speed of the substrate will affect the optimum size of the metal dot array. Increasing the value of \(a\) from \(1\times 10^{-3}\) to \(1\times 10^{-2}\) to analyze the relationship between the factor \(g\) and the 'width' of the metal dot on the three substrates at high rotation speed. As shown in Figure 7, the optimum sizes of the metal dot on the 128\({}^{\circ}\)YX-LiNbO\({}_{3}\) substrate and X112\({}^{\circ}\)Y-LiTaO\({}_{3}\) substrate do not change with the increase in the rotation speed, and their strongest SAW gyroscopic effect appears when the metal dot size is 5/16\(\lambda\) and 1/16\(\lambda\), respectively. In contrast, the optimum metal dot size of ST-X quartz has changed from 3/16\(\lambda\) to 11/16\(\lambda\). Combined with the simulation results in Figures 6 and 7, it can be seen that the optimum metal dot sizes of the 128\({}^{\circ}\)YX-LiNbO\({}_{3}\) substrate and X112\({}^{\circ}\)Y-LiTaO\({}_{3}\) substrate are not affected by the rotation speed, while that of ST-X quartz substrates are closely related to the rotation speed of the substrate.  
2.3 The Relationship between the Metal Dot Array Distribution Parameters and Rotation Speed in a ST-X Quartz Substrate  
In order to clarify the relationship between the distribution parameters of the metal dot array and the rotation speed when ST-X quartz is used as the substrate, the growth rates of the SAW gyroscopic effect with the rotation speed when the metal dot size is 3/16\(\lambda\) and 11/16\(\lambda\), respectively, are calculated based on the SAW gyroscopic effect when \(a=1\times 10^{-3}\). The results are shown in Figure 8. With the increase in the rotation speed, the growth rate of the SAW gyroscopic effect at 3/16\(\lambda\) and 11/16\(\lambda\) is obviously different, and the growth rate at 11/16\(\lambda\) is much higher than that at 3/16\(\lambda\). As shown in Figure 9, when the rotation speed increases to a certain extent, for example, when the value increases from \(6\times 10^{-3}\) to \(7\times 10^{-3}\), the optimum size of the metal dot for the ST-X quartz substrate will change from 3/16\(\lambda\) to 11/16\(\lambda\), which is also consistent with the conclusion mentioned above that the  
Figure 6: SAW gyroscopic effects of three piezoelectric substrates when \(a=1\times 10^{-3}\).  
Figure 7: SAW gyroscopic effects of three piezoelectric substrates when \(a=1\times 10^{-2}\).  
optimum metal dot size of the ST-X quartz substrate will change with the increase in the rotation speed.  
Table 2 lists the strongest SAW gyroscopic effect obtained for three piezoelectric substrates with different characteristics under the condition of matching the optimum metal dot array (i.e., the data obtained from the simulation in Figure 6). Among them are 128\({}^{\circ}\)YX-LiNbO\({}_{3}\) with a large electromechanical coupling coefficient and ST-X quartz with a temperature coefficient close to zero; both of which show a very strong SAW gyroscopic effect. However, the specific reasons for the superior performance of 128\({}^{\circ}\)YX-LiNbO\({}_{3}\) and ST-X quartz piezoelectric substrates in angular velocity detection are not clear and require more in-depth study.