双端固支石英振梁力频系数与热弹性品质因数分析

双端固支石英振梁作为微型谐振式石英传感器的核心敏感元件，其力频系数和品质因数对传感器的灵敏度和分辨率具有重要的影响。石英振梁的力频系数越高，同等条件下传感器的灵敏度也越高；振梁品质因数越高，传感器的分辨力亦越高。对于工作于一阶振动模态的石英振梁而言，力频系数与热弹性品质因数仅与其自身的结构尺寸参数有关。通过分析发现，石英振梁的力频系数与热弹性品质因数之间存在一定的矛盾。详细分析了石英振梁力频系数与热弹性品质因数的特点及两者之间的定量影响，给出了两者的理论模型与仿真方法，建立了力频系数-热弹性品质因数的目标优化函数。分析结果表明，在音叉尺寸范围内，目标优化函数值从0.064增加为0.64，且变化趋势与品质因数相类似。最后，分析了在设计用于微型谐振式石英传感器的双端固支石英振梁时该如何获得最佳的传感器性能。

Analysis on the Force-frequency Coefficient and Thermal Elastic Quality Factor for Quartz Double Ended Tuning Fork

As the sensitive component of quartz resonant micro sensors, the force-frequency coefficient and quality factor of quartz double ended tuning fork have an important influence on sensor sensitivity and resolution. The sensor sensitivity and resolution increase with the force-frequency coefficient and quality factor. For the quartz vibrating beam working in the first-order vibration mode, the force-frequency coefficient and the thermal elastic quality factor are only related to its own structural parameters. Through the analysis, it is found that there is a certain contradiction between the force-frequency coefficient and thermal elastic quality factor of the quartz vibrating beam. In this paper, the characteristics of the force-frequency coefficient and thermal elastic quality factor of the quartz vibrating beam and their quantitative influence are analyzed in detail. Their theoretical model and simulation method are given. A target optimization function of the force-frequency coefficient and thermal elastic quality factor is established. The analysis results show that the target optimization function value increases from 0.064 to 0.64 in the range of tuning fork size, and its variation trend is similar to the quality factor. Finally, the possible way to obtain best sensor performance is analyzed when designing a sensor with double ended tuning fork as sensing element.