The quality factor of quartz DETF for resonant sensors: simulation, analysis and verification

Abstract

Due to the excellent material properties of crystal quartz and its simple and effective structure, the quartz double ended tuning fork (DETF) is widely used as a resonance sensing element in resonator sensors, where its quality factor has an important effect on the overall accuracy and stability of such sensors. To optimise the quality factor of quartz DETF, the influence of structural dimensions on structural and air damping is analysed, and the theoretical model used to calculate the quality factor is summarised. Further, under the premise of fabricating resonators with sufficient force–frequency sensitivity, the quality factors of quartz DETFs of different structural dimensions are simulated through finite element simulation. The theoretical model and simulation calculation of the quality factor of quartz DETFs mutually verify its effectiveness. Moreover, an experimental platform was built, and three quartz DETFs with different dimensions were fabricated to test their quality factor. The quality factors of the three DETFs in air and vacuum are 3467.3, 1925.8, 4442.4 and 32 997.6, 11 559.1, 24 795.7, respectively, which means that the environmental factors and their structural dimensions have a great influence on quality factor. With the simulation method and summarised theoretical model in this paper, the quality factor was studied with comprehensive structural damping (thermal damping loss and support loss) and air damping (resistance damping, slide film damping, and squeeze film damping). The influence of the structure size on the quality factor was analysed in detail, including the length of the decoupling region, the distance between the tines, and the length and width of the tines, and the main influencing factors were obtained, providing a basic and comprehensive reference for designing quartz DETF.