盘式光纤加速度计的灵敏度增强方法研究
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 应用科技  2018, Vol. 45 Issue (3): 61-65  DOI: 10.11991/yykj.201706020 0

### 引用本文

MA Kun, WU Haijun, YANG Jiyong, et al. Research on the sensitivity enhancing method for fiber-optic disc accelerometer[J]. Applied Science and Technology, 2018, 45(3), 61-65. DOI: 10.11991/yykj.201706020.

### 文章历史

1. 黑龙江省地震局 宾县地震台，黑龙江 哈尔滨 150400;
2. 哈尔滨工程大学 理学院，黑龙江 哈尔滨 150001

Research on the sensitivity enhancing method for fiber-optic disc accelerometer
MA Kun1, WU Haijun1, YANG Jiyong1, TIAN Shuaifei2
1. Seismic Station of Binxian County, Heilongjiang Earthquake Administration, Harbin 150400, China;
2. College of Sciences, Harbin Engineering University, Harbin 150001, China
Abstract: A sensitivity enhancement method based on multilayer fiber sensing coils is proposed to achieve high sensitivity sensing of fiber optic disc accelerometer. Through analyzing the stress-strain state of the single-layer fiber sensing disc, the influence of fiber sensing coil's paste area, elastic disc size and sensing fiber type on the acceleration sensitivity are discussed, an effective sensitivity enhancing method with the multilayer fiber sensing coils is proposed with its simulation model of finite element software. A fiber optic flexural disc accelerometer based on multilayer fiber sensing coils has been produced with a high sensitivity of 6243.4rad/g, and the results show that the sensitivity has been effectively enhanced.
Key words: fiber sensing    acceleration    sensitivity    fiber optic disc accelerometer    fiber sensing coils    finite element simulation    fiber interferometer    stress and strain

1 系统结构及工作原理

 $\frac{\rm d}{{{\rm d}r}}\left[ {\frac{1}{r}\frac{\rm d}{{{\rm d}r}}\left( {r\frac{{{\rm d}\omega }}{{{\rm d}r}}} \right)} \right] = \frac{{{Q_r}}}{{D'}}$ (1)

 $\omega \left| {_{r = a} = 0} \right.,\frac{{{\rm d}\omega }}{{{\rm d}r}}\left| {_{r = a} = 0} \right.,{M_r}\left| {_{r = b} = 0} \right.$ (2)

 $\omega = \frac{{P{r^2}}}{{8\pi D^{^\prime}}} \left( {\ln \frac{r}{a}- 1} \right) + \frac{{P{r^2}}}{{16\pi D^{^\prime}}}{Q_1} + \frac{{P{a^2}{b^2}}}{{4\pi D^{^\prime}}}\ln \frac{r}{a}{Q_2} + \frac{{P{a^2}}}{{16\pi D^{^\prime}}}{Q_3}$

 ${Q_1} = \frac{{(1 - \mu )({a^2} - {b^2}) - 2{b^2}(1 + \mu )\ln ({b \mathord{\left/ {\vphantom {b a}} \right.} a})}}{{{b^2}(1 + \mu ) + {a^2}(1 - \mu )}}$
 ${Q_2} = \frac{{1 + (1 + \mu )\ln ({b \mathord{\left/ {\vphantom {b a}} \right. } a})}}{{{b^2}(1 + \mu ) + {a^2}(1 - \mu )}}$
 ${Q_3} = \frac{{(1 - \mu ){a^2} + (3 + \mu ){b^2} + 2{b^2}(1 + \mu )\ln ({b \mathord{\left/ {\vphantom {b a}} \right. } a})}}{{{b^2}(1 + \mu ) + {a^2}(1 - \mu )}}$

 $\begin{split}{\varepsilon _r}(r) = & - \frac{t}{2}\frac{{{{\rm d}^2}\omega }}{{{\rm d}{r^2}}} = \\& - \frac{t}{2}\left[ {\frac{P}{{8\pi D^{^\prime}}}\left( {2\ln \frac{r}{a} \!+\! 1} \right) \!+\! \frac{P}{{8\pi D^{^\prime}}}{Q_1} \!-\! \frac{{P{a^2}{b^2}}}{{4\pi D^{^\prime}{r^2}}}{Q_2}} \right]\end{split}$ (3)
 $\begin{split}{\varepsilon _\theta }(r) & = - \frac{t}{{2r}}\frac{{d\omega }}{{dr}} = \\& \!-\! \frac{t}{2}\left[ \!{\frac{P}{{8\pi D^{^\prime}}}\left( {2\ln \frac{r}{a} \!-\! 1} \right) \!+\! \frac{P}{{8\pi D^{^\prime}}}{Q_1} \!+\! \frac{{P{a^2}{b^2}}}{{4\pi D^{^\prime}{r^2}}}{Q_2}} \!\right]\end{split}$ (4)

 $\Delta \phi = 0.79 \times 4\beta \times \Delta L$ (5)

 $S = \frac{{\Delta \phi }}{{A/9.8}} = 2 \times 9.8 \times 0.79\frac{{12(1 - {{\mu '}^2})\pi {{m}}n}}{{\lambda DE{t^2}}}{Q_4}$ (6)

 ${f_{n{\kern 1pt} }} = \frac{{{\varLambda ^2} \cdot t}}{{2\pi \cdot {a^2}}}\sqrt {\frac{E}{{12(1 - {\mu ^2})\rho }}}$ (7)

2 灵敏度增强方法分析 2.1 单层光纤敏感盘增敏分析

 ${r_0} = \exp \left[ {\frac{{2{b^2}(1 + \mu )\ln \displaystyle\frac{b}{a} - (1 - \mu )({a^2} - {b^2})}}{{2{b^2}(1 + \mu ) + 2{a^2}(1 - \mu )}} + \ln a} \right]$

2.2 多层光纤敏感盘增敏分析

3 实验结果分析