# Finite Element Analysis of the Distribution Parameters of a Metal Dot Array in a SAW Gyroscope
## 1 Introduction  
In recent years, the surface acoustic wave (SAW) gyroscope has been widely studied by scholars because of its significant advantages, such as its simple structure, small size, long service life, superior inherent shock robustness, and so on, and it has the prospect of broad applications in attitude monitoring and motion control [1; 2; 3; 4; 5]. The SAW gyroscopes mainly include the traveling wave mode and standing wave mode. The standing wave mode SAW gyroscope cannot be put into use due to its output signal being difficult to detect, and it cannot achieve temperature compensation [6]. The traveling wave mode SAW gyroscope, which uses a differential scheme for temperature compensation and the output signal is easy to detect, has been studied deeply [7]. However, a weak Coriolis force leads to a low detection sensitivity, which limits its practicality. Therefore, recently, many teams have devoted themselves to solving the bottleneck problem of the low detection sensitivity of the SAW gyroscope, and they proposed various methods to improve the sensor performance in terms of selection and optimal design of the interdigital transducer and the piezoelectric substrate [8; 9; 10; 11; 12]. In addition, our team proposed a traveling wave mode SAW gyroscope structure combined with a metal dot array in the previous research work, and verified the effectiveness of this structure in improving the detection sensitivity performance of the SAW gyroscope, both theoretically and experimentally [13; 14]. The principle of the SAW gyroscope is based on the SAW gyroscopic effect, which is specifically explained as follows: a Rayleigh wave (a wave pattern of SAW) propagates on the surface of the substrate, and the particles in the medium (elements of infinitesimalsize) vibrate along an elliptical trajectory in the plane composed of the direction of the acoustic wave propagation and the normal direction of the substrate. When the Coriolis force induced by external rotation acts on the particles, a secondary SAW will be induced and coupled with the initial SAW; thus, the particle vibration trajectory changes, resulting in the change of the velocity and the frequency of the SAW. In this way, the magnitude of the rotation vector can be characterized by detecting the change in frequency [13]. The schematic diagram is shown in Figure 1. The Rayleigh wave propagates along the \(x\)-axis direction, and the amplitude decays exponentially along the \(z\)-axis direction. The particle in the medium (hereinafter referred to as the vibrating particle) moves along an elliptical trajectory in the plane formed by the \(x\)-axis and the \(z\)-axis. Commonly used piezoelectric substrates in SAW devices include quartz, AlN, ZnO, LiNbO\({}_{3}\), LiTaO\({}_{3}\), etc. The performance parameters of the substrate, such as the electromechanical coupling coefficient (\(\kappa^{2}\)), dielectric constant (\(\epsilon_{ij}\)), elastic constant (\(C_{ij}\)), piezoelectric constant (\(e_{ij}\)) and temperature coefficient (TCF), will directly affect the performance of the SAW gyroscope devices [15; 16]. In this paper, three piezoelectric substrates that can excite Rayleigh wave are selected as research objects; among them, 128\({}^{\circ}\)YX-LiNbO\({}_{3}\) has a strong electromechanical coupling coefficient, ST-X Quartz has an excellent temperature characteristic close to 0 and X112\({}^{\circ}\)Y-LiTaO\({}_{3}\), with a moderate temperature coefficient and electromechanical coupling coefficient, is taken as a contrast [17; 18; 19; 20; 21; 22] We established 3D models of these three piezoelectric substrates, distributing copper dot arrays of different sizes, and calculated the influence of angular velocity on the phase velocity and frequency of the SAW using the finite element method [23].