QEPAS系统中石英音叉模态仿真计算与研究

对石英音叉增强型光声光谱(QEPAS)系统中常用的石英音叉进行了有限元模态计算，获得石英音叉前6阶振型与模态频率，认知了第4阶对称摆动振型为有效振动，利用单因素法分析了石英音叉的音臂长度l₁、音臂宽度w₁、音臂厚度t、音臂切角θ、音臂圆孔直径d及音臂圆孔高度h对低阶有效共振频率(Fre)的影响，敏感度依次为： l₁> w₁>d>θ>t>h，考虑实际设计情形，筛选出了l₁，w₁，d与h四个石英音叉设计变量，采用Box-Behnken实验设计方案与RSM(response surface methodology)方法，以Fre为函数目标，建立l₁，w₁，d与h的二次回归响应面模型，得到了参数之间的交互作用，利用Design-Expert软件对响应面模型进行设计参数反求，结果表明，在15 000 Hz≤Fre≤25 000 Hz计算区域内误差较小，基本满足QEPAS系统的计算需求，所提出的研究与设计方法具有一定通用性，可为QEPAS系统中石英音叉结构参数设计提供参考。

Modal Simulation Calculation and Research of Tuning Fork Based on QEPAS System

The finite element modes of the quartz tuning fork in the Quartz Enhanced Photoacoustic Spectroscopy (QEPAS) system were calculated and the first 6 modes and modal frequencies of the quartz tuning fork were obtained. The 4th order symmetrically oscillating vibration mode was recognized as an effective vibration. Single factor method was used to analyze the effects of fork’s arm length l₁, fork’s arm width w₁, fork’s arm thickness t, fork’s arm cutting angle θ, fork’s arm diameter d and fork’s arm round hole height h on low effective resonance frequency (Fre). The results of the sensitivity sensitivity were as follows: l₁>w₁>d>θ>t>h. Considering the actual design situation, four design parameters of quartz tuning fork l₁, w₁, d and h were screened. Using Box-Behnken experimental design and RSM (Response Surface Methodology) method, Fre was set as a function target to establish l₁, w₁, d and h quadratic regression response surface model, and get the interaction between the parameters. The Design-Expert software was used to inverse the design parameters of the response surface model. The results showed that the error in the calculation area of 15 000 Hz≤Fre≤25 000 Hz is small, and basically meets the calculation requirements of QEPAS system. The proposed research and design methods have some generality, which can provide references for the design of quartz tuning fork structure in QEPAS system.