基于弹性体拓扑优化的AT切型石英谐振式力传感器研究

Research on AT-Cut Quartz Resonant Force Sensor Based on Elastomer Topology Optimization

摘要: 针对AT切型石英晶体谐振式力传感器小载荷下频率偏移有限、灵敏度受限的问题，提出基于不锈钢弹性体拓扑优化的力信号放大方法。以安装凹槽侧壁平均压应力幅值为目标，优化弹性体中部材料分布，并通过有限元对未挖孔、双圆孔、矩形孔、椭圆孔及拓扑优化结构进行对比。结果表明，0~100 N范围内各结构压应力与载荷近似线性；拓扑优化结构相对未挖孔和双圆孔结构的平均应力放大倍数分别为10.9081和3.1238。将100 N工况下侧壁压应力作为石英晶体等效边界输入，拓扑优化结构对应厚度剪切模态频率较未挖孔结构降低约7 kHz。该方法可改善载荷传递路径，提高局部压应力响应，为传感器灵敏度提升提供参考。

Abstract: To address the limited frequency shift and sensitivity of AT-cut quartz resonant force sensors under small loads, a force-signal amplification method based on topology optimization of a stainless-steel elastic body is proposed. The material distribution in the middle region of the elastic body is optimized by maximizing the average compressive stress magnitude on the sidewalls of the mounting groove. Finite element comparisons are conducted among unperforated, double-circular-hole, rectangular-hole, elliptical-hole, and topology-optimized structures. The results show that the groove-sidewall compressive stress is approximately linear with the applied load in the range of 0~100 N. The topology-optimized structure achieves average stress amplification factors of 10.9081 and 3.1238 relative to the unperforated and double-circular-hole structures, respectively. Using the sidewall compressive stress under 100 N as the equivalent boundary input for the quartz crystal, the corresponding thickness-shear modal frequency is about 7 kHz lower than that of the unperforated structure. The proposed method improves the load transfer path and local compressive stress response, providing a design reference for sensitivity enhancement of quartz resonant force sensors.