Research on Theoretical Model of High Sensitivity Fiber Bragg Grating Accelerometer
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摘要: 针对两点封装，建立光纤光栅加速度检波器通用模型，理论推导加速度检波器灵敏度和谐振频率的解析表达式，深入研究加速度灵敏度和谐振频率的影响因素，讨论封装光纤刚度系数与检波器结构刚度系数之比对检波器响应特性的影响，并分析刚度比分别在0～1、0～100范围随着等效质量的增大（0～100 g），加速度灵敏度和谐振频率的制约关系，及在0～500 Hz（中低频）和0～1 200 Hz（中高频）范围内灵敏度的变化规律。此外，分别以封装光纤长度为10 mm和60 mm举例分析长度对上述二者的影响，各项仿真中灵敏度均会高达～1 000 pm/G，并引入品质因数的概念。所提理论研究对FBG加速度检波器的设计和综合性能的评价具有重要的指导意义，为器件参数优化提供理论依据。Abstract: A general model of fiber Bragg grating (FBG) acceleration detector has been established for the two-point package model. The sensitivity and the resonance frequency's analytical expressions of the acceleration detector have been deduced theoretically, and the influence factors which affecting the sensitivity and resonance frequency have been researched deeply, the acceleration detector’s response characteristics have been discussed, which would be affected by the ratio, that the package fiber stiffness to the structure stiffness. Based on this basis, the restrictive relation between the sensitivity and the resonance frequency have been analyzed, among the equivalent mass and the ratio have been in the range of 0~100 g, 0~1 and 0~100, respectively. And the resonance frequency’s change rule within the scope of 0~500 Hz (low-medium frequency) and 0~1200 Hz (medium-high frequency) also has been studied. Furthermore, the package fibers have been chosen 10 mm and 60 mm as examples to analyze the influence to the above two mentioned, the sensitivity of each simulation would reach up to ~1 000 pm/G, and the quality factor has been introduced. This study has played a significant role in the design and comprehensive performance evaluation of the acceleration detector, and provided a theoretical reference for the optimization of structural parameters to it.
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Key words:
- fiber Bragg grating /
- accelerometer /
- sensitivity /
- resonant frequency /
- figure of merit
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图 2 谐振频率和灵敏度之间一般关系曲线
Fig. 2 The general relationship curve between resonant frequency and sensitivity
图 3 (a) η不同时谐振频率和灵敏度曲线；(b) η不同时随着质量的增加品质因数Q曲线
Fig. 3 (a) The curve of fn and S with different η; (b) The curve of Q with different η as the M
图 4 (a)不同质量下谐振频率和灵敏度曲线；(b)不同质量下品质因数Q曲线(η∈[0, 100]) (c)不同质量下谐振频率和灵敏度曲线；(d)不同质量下品质因数Q曲线(η∈[0, 1])
Fig. 4 (a) The relationship between fn and S with different M; (b) The curve of Q with different M (η∈[0, 100]) (c) The relationship between fn and S with different M; (d) The curve of Q with different M (η∈[0, 1])
图 5 (a) η值不同时系统谐振频率和灵敏度曲线；(b) η值不同时品质因数Q曲线
Fig. 5 (a) relationship between fn and S with different η; (b) The curve of Q with different η
表 1 检波器结构参数
Table 1 The parameter of the acceleration detector
参数/单位 数值 $ {E_f}/{P_a}$ $ 7.2 \times {10^{10}}$ $ {d_f}$ /μm125 $ {\lambda _B}$ /nm1 550.151 $ M$ /gram$ M = 20, \; M = 30$ $ L$ /mm$ L = 10, \; L = 15$ $ \eta $ $ \eta \in \left[ {1,100} \right]$ $ {P_e}$ 0.22 
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表 2 加速度检波器结构参数取值
Table 2 The parameter variation of the acceleration detector
参数/单位 数值 $M$ /gram$M \in [0,100]$ $L$ /mm10 $\eta $ $\eta = 1, \; \eta = 10$
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表 3 加速度检波器结构参数取值
Table 3 The parameter variation of the acceleration detector
参数/单位 数值 $M$ /gram$M = 20, \; M = 100$ $L$ /mm10 $\eta $ $\eta \in \left[ {0,100} \right]$ 、$\eta \in \left[ {0,1} \right]$
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表 4 加速度检波器结构参数取值
Table 4 The parameter variation of the acceleration detector
参数/单位 数值 $M$ /gram$M \in \left[ {0,100} \right]$ $L$ /mm$L = 10$ 、$L = 60$ $\eta $ $\eta = 10$
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