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 应用科技  2020, Vol. 47 Issue (6): 53-57, 62  DOI: 10.11991/yykj.201911020 0

### 引用本文

MA Kun, YU Tianming, YANG Jiyong, et al. Theoretical model of the fiber-optic flexural disk accelerometer based on multi-turn fiber coils[J]. Applied Science and Technology, 2020, 47(6): 53-57, 62. DOI: 10.11991/yykj.201911020.

### 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 物理与光电工程学院，黑龙江 哈尔滨 150001

Theoretical model of the fiber-optic flexural disk accelerometer based on multi-turn fiber coils
MA Kun1, YU Tianming1, YANG Jiyong1, NIAN Hua1, LI Aiqiu1, YANG Musen2
1. Binxian Seismic Station, Heilongjiang Earthquake Administration, Harbin, 150400, China;
2. College of Physics and Photoelectric Engineering, Harbin Engineering University, Harbin 150001, China
Abstract: For the purpose of improving the sensitivity of the fiber-optic flexural disk accelerometer based on multi-turn fiber coils, the theoretical analysis and finite element simulation of its mechanical properties and strain distribution are carried out. The volume-average method is used to calculate the equivalent parameters of the elastic disk with multi-turn fiber coils, and then the sensitivity and resonance frequency of the fiber-optic flexural disk accelerometer are calculated. The simulation model of vibration pickup structure of the fiber-optic flexural disk accelerometer is built by finite element simulation software, and sources of the difference between theoretical model and simulation model are analyzed. The performance parameters of the actual fabricated fiber-optic flexural disk accelerometer were tested, which is close to the simulation result. Theoretical model and simulation model of the fiber-optic flexural disk accelerometer based on multi-turn fiber coils are built in this paper, which have great significance for designing the high sensitivity fiber-optic flexural disk accelerometer.
Keywords: fiber-optic sensor    fiber-optic flexural disk accelerometer    multi-turn fiber coil    finite element simulation    average volume method    circumferential strain    acceleration sensitivity    resonance frequency

1 系统结构及理论分析

 $\left\{ \begin{array}{l} {E_{{\rm{eq}}}} = \dfrac{{2{E_{{\rm{fc}}}}{V_{{\rm{fc}}}} + 2{E_{\rm{g}}}{V_{\rm{g}}} + {E_{\rm{d}}}{V_{\rm{d}}}}}{{2{V_{{\rm{fc}}}} + 2{V_{\rm{g}}} + {V_{\rm{d}}}}}\\ {\nu _{{\rm{eq}}}} = \dfrac{{2{\nu _{{\rm{fc}}}}{V_{{\rm{fc}}}} + 2{\nu _{\rm{g}}}{V_{\rm{g}}} + {\nu _{\rm{d}}}{V_{\rm{d}}}}}{{2{V_{{\rm{fc}}}} + 2{V_{\rm{g}}} + {V_{\rm{d}}}}}\\ {{t}_{{\rm{eq}}}} = \dfrac{{2\left( {{V_{{\rm{fc}}}} + {V_{\rm{g}}}} \right)}}{{{\rm{{\text{π}} }}\left( {{a^2} - {b^2}} \right)}} + t \end{array} \right.$

 ${D_{{\rm{eq}}}} = \frac{{{E_{{\rm{eq}}}}{t}_{{\rm{eq}}}^3}}{{12\left( {1 - \nu _{{\rm{eq}}}^2} \right)}}$

 $\begin{gathered} \theta (r) = \frac{{wb}}{{4{D_{{\rm{eq}}}}}}\Bigg[\frac{{{a^2}}}{{{a^2} - {b^2}}}\Bigg(r - \frac{{{b^2}}}{r}\Bigg)\Bigg(\frac{{{b^2}}}{{{a^2}}} - 1 + 2\ln \frac{a}{b}\Bigg) - \\ r\Bigg(\frac{{{b^2}}}{{{r^2}}} - 1 + 2\ln \frac{r}{b}\Bigg)(r - b)\Bigg]{\rm{ = }}\frac{{wb}}{{4{D_{{\rm{eq}}}}}}\alpha \left( r \right) \\ \end{gathered}$

 $w = \frac{{MA}}{{2{\rm{{\text{π}} }} b}}$

 ${\varepsilon _\theta }\left( {z,r} \right) = \frac{{z\theta \left( r \right)}}{r}$

 $\Delta l = \int_d^c {\frac{{2{\rm{{\text{π}} }} r}}{\varTheta }{\varepsilon _\theta }\left( {z,r} \right)} {\rm{d}}r{\rm{ = }}\frac{{MAz\beta }}{{{\rm{4}}\varTheta {D_{\rm{eq}}}}}$ (1)

t1为光纤环与弹性盘之间的粘胶厚度。在匝数为n的多匝光纤环中，第1匝和第n匝光纤的高度分别为

 ${z_1} = \frac{t}{2} + {t_1} + \frac{\varTheta }{2}$ (2)
 ${z_n} = \frac{t}{2} + {t_1} + \left( {n - \frac{1}{2}} \right)\varTheta$ (3)

 $\Delta L = \frac{n}{2}\left( {\Delta {l_1} + \Delta {l_n}} \right)$

 $\Delta \varPhi = 0.79k\Delta L$ (4)

 $k = \frac{{2{\rm{{\text{π}} }}{n_0}}}{\lambda }$

 $S = 9.8 \times \frac{{{\rm{4}}\Delta \varPhi }}{A}{\rm{ = }}\frac{{{\rm{3}}{\rm{.871}}kn\beta M}}{{\varTheta {D_{{\rm{eq}}}}}}\left( {t + 2{t_1} + n\varTheta } \right)$ (5)

 ${y_b} = \frac{{w{a^3}}}{{{D_{\rm{eq}}}}}\left( {{L_3} - \frac{{{C_2}{L_6}}}{{{C_5}}}} \right)$

 ${C_5} = \frac{1}{2}\left[ {1 - {{\left( {\frac{b}{a}} \right)}^2}} \right]$
 ${L_3} = \frac{b}{{4a}}\left\{ {\left[ {{{\left( {\frac{b}{a}} \right)}^2} + 1} \right]\ln\frac{a}{b} + {{\left( {\frac{b}{a}} \right)}^2} - 1} \right\}$
 ${C_2} = \frac{1}{4}\left[ {1 - {{\left( {\frac{b}{a}} \right)}^2}\left( {1 + 2\ln\frac{a}{b}} \right)} \right]$
 ${L_6} = \frac{b}{{4a}}\left[ {{{\left( {\frac{b}{a}} \right)}^2} - 1 + 2\ln\frac{a}{b}} \right]$

 ${K_{\rm{eff}}} = \frac{{MA}}{{{y_b}}}$

 ${f_n} = \frac{1}{{2{\rm{{\text{π}} }} }}\sqrt {\frac{{{K_{\rm{eff}}}}}{M}} = \frac{1}{{2{\rm{{\text{π}} }} }}\sqrt {\frac{{2{\rm{{\text{π}} }} b{C_5}{D_{\rm{eq}}}}}{{{a^3}M\left( {{C_5}{L_{\rm{3}}} - {C_{\rm{2}}}{L_{\rm{6}}}} \right)}}}$

2 有限元仿真

3 实验测试