石英摆片两侧金镀膜的应力及其对称性直接影响石英挠性加速度计的零位和精度, 应力分布的建模仿真与原位测量表征显得尤为重要。该文建立了石英摆片的有限元模型, 计算了石英摆片的基本模态, 分析了石英摆片两侧应力差值对摆片变形及电容的影响规律, 建立了摆片的应力-应变-位移-电容的变化关系。提出了一种基于电容法的非接触式应变测量方法, 搭建了基于AD7747芯片的飞法级多通道测量装置, 实现了20 nm级微小变形测量。该研究为石英摆片微小变形及其复杂环境条件下的原位检测提供了高精度有效测量方法。

Objective: The quartz pendulum is a critical sensitive component in quartz flexible accelerometers, and the stress distribution of the gold coating on both sides directly affects the deformation, zero position, and measurement accuracy of the pendulum. Enhancing the precision of the accelerometer requires an understanding of the influence of stress distribution on both sides of the pendulum on its zero position. This paper proposes a non-contact strain measurement method based on capacitance, introducing a high-precision, in-situ strain measurement technique. This method provides effective technical support for detecting small deformations of the quartz pendulum in complex environments. Methods: This study begins by calculating the fundamental modes of the quartz pendulum using a finite element simulation model, which serves as the basis for constructing and calibrating the measurement device. Thermal loads are then applied to both sides of the quartz pendulum's coating in the simulation to induce stress, allowing the resulting deformation of the pendulum to be calculated. The relationship between the stress difference on both sides of the pendulum and its deformation, as well as the corresponding capacitance change, is subsequently derived. This process establishes the stress-strain-displacement-capacitance variation relationship, providing theoretical guidance for the development of the quartz pendulum stress-strain measurement device. Afterward, a non-contact strain measurement method based on capacitance is proposed, and a multi-channel quartz pendulum stress-strain measurement system is developed utilizing the AD7747 chip. Through the adjustment of the displacement platform to modify the pendulum position, a series of corresponding capacitance values are recorded. A linear relationship is then fitted to calibrate the device. Finally, the system is validated, and its ability to accurately measure micro-deformations as small as 20 nm is demonstrated. Results: Using finite element simulation, this study successfully establishes the relationship between the stress difference on both sides of the quartz pendulum and the resulting deformation and capacitance changes, providing a crucial theoretical foundation for quartz pendulum strain measurements. Traditionally, measuring the deformation of a quartz pendulum requires disassembly and the use of a white light interferometer—a cumbersome process that cannot reliably capture the pendulum's true deformation. In this paper, we present an innovative in-situ, online, non-contact strain measurement method based on capacitance, enabling continuous monitoring of the quartz pendulum's deformation state. Furthermore, a stress-strain measurement system for the quartz pendulum is developed and calibrated. The system can operate accurately under various environmental conditions. Conclusions: This paper presents a high-precision, non-contact, in-situ measurement method for detecting small deformations of the quartz pendulum. Through finite element model simulation and analysis, the relationship between the stress difference on both sides of the pendulum and the resulting capacitance changes is clarified, and the relationship between stress, strain, displacement, and capacitance is established. An in-situ measurement system based on capacitance is also designed and constructed. Following calibration and verification, the system demonstrates the capability to measure micro-deformations as small as 20 nm. This work provides an effective and precise method for detecting small deformations of the quartz pendulum and for conducting in-situ measurements in complex environmental conditions.