Strain Transfer and Its Influencing Factors of Matrix Encapsulated Fiber Bragg Grating Sensor

Dingyi Dan; Keqin Ding; Anqing Shu

doi:10.3788/LOP202259.0506006

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 5 >Page 0506006 > Article

Laser & Optoelectronics Progress
Vol. 59, Issue 5, 0506006 (2022)

Strain Transfer and Its Influencing Factors of Matrix Encapsulated Fiber Bragg Grating Sensor

Dingyi Dan^1、2, Keqin Ding^2、*, and Anqing Shu¹

Author Affiliations

¹School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan , Hubei 430205, China

²China Special Equipment Inspection and Research Institute, Beijing 100029, China

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DOI: 10.3788/LOP202259.0506006 Cite this Article Set citation alerts

Dingyi Dan, Keqin Ding, Anqing Shu. Strain Transfer and Its Influencing Factors of Matrix Encapsulated Fiber Bragg Grating Sensor[J]. Laser & Optoelectronics Progress, 2022, 59(5): 0506006 Copy Citation Text

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Abstract

The strain transfer of fiber Bragg grating (FBG) strain sensor determines its accuracy when monitoring the structural strain. To study the influencing factors of strain transfer of FBG strain sensor, the mechanical model of the sensor strain transfer is developed in this paper. The theoretical derivation of the strain transfer is conducted, and the formula of strain transfer rate of the sensor is obtained. Meanwhile, to ensure proper computation the finite element simulation and calculation are performed for its special structure. Furthermore, the influencing factors and effects of the strain transfer of the sensor are analyzed, and different influencing factors are simulated using the finite element simulation, which verifies the accuracy of the theoretical derivation.

Keywords

fiber optics finite element simulation influencing factors strain transfer

π {r_{f}}^{2} (σ_{f} + d σ_{f}) + 2 π r_{f} τ_{1} d x = π {r_{f}}^{2} σ_{f}

，（1）

τ_{1} = - \frac{r_{f} d σ_{f}}{2 d x}

，（2）

τ_{1} = - \frac{r_{f} E_{f} d ε_{f}}{2 d x}

。（3）

(D_{1} h_{1} - π {r_{f}}^{2}) (σ_{a} + d σ_{a}) + (2 h_{1} + D_{1}) τ_{2} d x - (D_{1} h_{1} - π {r_{f}}^{2}) d σ_{a} - 2 π r_{f} τ_{1} d x = 0

，（4）

τ_{2} = - \frac{π {r_{f}}^{2} E_{f} d ε_{f}}{(2 h_{1} + D_{1}) d x} - \frac{(D_{1} h_{1} - π {r_{f}}^{2}) E_{a} d ε_{a}}{(2 h_{1} + D_{1}) d x}

。（5）

\frac{d ε_{f}}{d x} \approx \frac{d ε_{a}}{d x}

，（6）

τ_{2} = \frac{(- π {r_{f}}^{2} E_{f} - D h_{1} E_{a} + π {r_{f}}^{2} E_{a}) d ε_{f}}{(2 h_{1} + D_{1}) d x}

。（7）

τ (x, y) = G \cdot γ (x, y) = G (\frac{\partial u}{\partial y} + \frac{\partial w}{\partial x}) \approx G (\frac{d u}{d y})

，（8）

\begin{array}{l} u_{m} - u_{f} = \int_{y_{1}}^{y_{2}} \frac{τ_{2}}{G_{a}} d y + \int_{- \frac{D_{1}}{2}}^{- r_{f}} \frac{τ_{2}}{G_{a}} d z + \int_{r_{f}}^{\frac{D_{1}}{2}} \frac{τ_{2}}{G_{a}} d z = \\ - \frac{(π {r_{f}}^{2} E_{f} + D_{1} h_{1} E_{a} - π {r_{f}}^{2} E_{a}) (h_{2} + D_{1} - 2 r_{f})}{(2 h_{1} + D_{1}) G_{a}} \cdot \frac{d ε_{f}}{d x} \end{array}

。（9）

u_{m a} - u_{a f} = - \frac{1}{k^{2}} \cdot \frac{d ε_{f}}{d x}

，（10）

k = \sqrt[]{\frac{(2 h_{1} + D_{1}) G_{a}}{(π {r_{f}}^{2} E_{f} + D_{1} h_{1} E_{a} - π {r_{f}}^{2} E_{a}) (h_{2} + D_{1} - 2 r_{f})}}

，（11）

G = \frac{E}{2 (1 + λ)}

，（12）

k = \sqrt[]{\frac{(2 h_{1} + D_{1}) E_{a}}{2 (π {r_{f}}^{2} E_{f} + D_{1} h_{1} E_{a} - π {r_{f}}^{2} E_{a}) (h_{2} + D_{1} - 2 r_{f}) (1 + λ_{a})}}

。（13）

\frac{d^{2} ε_{f} (x)}{d x^{2}} - k^{2} ε_{f} (x) = - k^{2} ε_{m}

，（14）

ε_{f} (x) = C_{1} e x p (k x) + C_{2} e x p (- k x) + ε_{m}

。（15）

\{\begin{matrix} ε_{f} (0) = 0 \\ ε_{f} (L) = ε_{1} \end{matrix}

，（16）

\{\begin{array}{l} C_{1} = \frac{ε_{1} - ε_{m} [1 - e x p (- k L)]}{2 s i n h (k L)} \\ C_{2} = \frac{- ε_{1} + ε_{m} [1 - e x p (- k L)]}{2 s i n h (k L)} \end{array}

，（17）

ε_{f} (x) = \frac{ε_{1} - ε_{m} [1 - e x p (- k L)]}{2 s i n h (k L)} e x p (k x) + \frac{- ε_{1} + ε_{m} [1 - e x p (k L)]}{2 s i n h (k L)} e x p (- k x) + ε_{m}

。（18）

ε_{1} = Δ L_{f} / L_{f}

。（19）

ε_{m} (L_{f} + 2 L) = Δ L_{f} + 2 Δ L

，（20）

\begin{matrix} Δ L = \int_{0}^{L} ε_{f} (x) d x = \int_{0}^{L} \{\frac{ε_{1} - ε_{m} [1 - e x p (- k L)]}{2 s i n h (k L)} e x p (k x) + \frac{- ε_{1} + ε_{m} [1 - e x p (k L)]}{2 s i n h (k L)} e x p (- k x) + ε_{m}\} d x = \\ \frac{ε_{1} c o s h (k L) - ε_{1} + 2 ε_{m} - 2 c o s h (k L) ε_{m}}{k s i n h (k L)} + ε_{m} L \end{matrix}

。（21）

\bar{ϕ} = \frac{ε_{1}}{ε_{m}} = 1 - \frac{2 s i n h (k L)}{k L_{f} s i n h (k L) + 2 k L c o s h (k L)}

，（22）

\bar{ϕ^{'}} = \bar{ϕ} \times k^{'}

。（23）

\bar{ϕ^{'}} = \bar{ϕ} \times k' = 1.068 \times 0.9196 = 0.98213

。（24）

Dingyi Dan, Keqin Ding, Anqing Shu. Strain Transfer and Its Influencing Factors of Matrix Encapsulated Fiber Bragg Grating Sensor[J]. Laser & Optoelectronics Progress, 2022, 59(5): 0506006

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