CN106940173B - The matrix strain correction method of wide range fiber grating sensor - Google Patents

Abstract

The present invention discloses a kind of matrix strain correction method of wide range fiber grating sensor, it is characterised in that: monitors matrix strain by wide range fiber grating sensor；Structure is: bare optical fibers and bare optical gratings sensor being placed in inside inner layer steel pipe, inner layer steel pipe is placed in inside two sections of outer layer fine steel tubes, guarantees that inside and outside two layers of steel pipe being capable of opposite sliding；Reserving gaps at outer layer pipe transition joint；Selection inner layer steel pipe radius is r_m, outer layer pipe radius is r_i, bare optical fibers and bare optical gratings sensor is placed in inside inner layer steel pipe；Outer layer pipe both ends are more than that inner layer steel pipe length is L₁, i.e., it is L that fiber grating, which pastes length,₁, the distance between glue-line is L₂, i.e. fiber grating gauge length is L₂.The big strain variation of wide range fiber grating sensor real-time perception structure, (FBG) demodulator demodulate reflection wavelength data, obtain structural strain according to matrix strain correction equation, obtain the stress performance parameter of structural elements.

Description

Matrix Strain Correction Method for Large-Range Fiber Bragg Grating Sensors

technical field

The invention relates to a matrix strain correction method of a large-range optical fiber grating sensor, and belongs to the field of the theory of strain transfer of large-range optical fiber gratings.

Background technique

Special engineering structures such as long-span prestressed structures, super high-rise buildings and offshore platforms will undergo large strain changes under the long-term action of environmental erosion and load effects. Once the allowable strain value of the structure is exceeded, brittle failure is likely to occur, resulting in huge losses. It is of great significance to carry out large-strain monitoring for special projects and identify structural damage in time for reducing structural disasters in special projects. Fiber grating sensors are widely used in the field of structural health monitoring due to their high sensitivity, anti-electromagnetic interference and other excellent characteristics. The monitoring range of traditional fiber grating sensors is only 3000με, which cannot meet the requirements of large strain monitoring of special structures. The large strain monitoring method based on fiber grating is a direction worth exploring. Scholars have tried many new methods for large-strain monitoring, including: prestressing measurement method of prestressed steel strands stretched to 5000με and then pasting fiber gratings, and fiber grating desensitization packaging methods for composite structures and variable trapezoidal structures. , but these methods have obvious defects in the whole-process monitoring of strain and the accuracy of strain monitoring. This patent belongs to the field of strain transfer theory of large-range fiber gratings, and relates to a method for correcting large-range fiber grating-substrate strain errors.

SUMMARY OF THE INVENTION

The invention relates to a matrix strain correction method for a large-scale fiber grating sensor. First, a large-scale fiber grating sensor is designed using a double-layer steel tube packaging preparation process, and a strain transmission mechanism of large matrix strain and small fiber grating strain is established. Secondly, the strain correction equation of the long-range fiber grating is given, which realizes the large strain monitoring and correction of the special structure.

The technical scheme adopted in the present invention is:

A substrate strain correction method for a large-range fiber grating sensor, characterized in that: monitoring the substrate strain through the large-range fiber grating sensor;

The structure is as follows: the bare fiber grating sensor is placed inside the inner steel pipe, and the inner steel pipe is placed inside the two outer thin steel pipes to ensure that the inner and outer steel pipes can slide relative to each other; a gap is reserved at the middle joint of the outer steel pipe;

Select the inner layer steel pipe radius as r _m and the outer layer steel pipe radius as r _i , and place the bare fiber grating sensor inside the inner layer steel pipe;

The length of the outer steel pipe over the inner steel pipe is L ₁ , that is, the fiber grating sticking length is L ₁ , and the distance between the glue layers is L ₂ , that is, the fiber grating gauge length is L ₂ .

The large-range fiber grating sensor and the fiber grating demodulator form a strain sensing acquisition system. The demodulator demodulates the reflected wavelength and senses the strain of the bare fiber grating through the wavelength change.

Considering the influence of the holding length of the support, the gauge length of the fiber grating and the intermediate adhesive layer, the matrix strain equation of the wavelength of the fiber grating is obtained:

(1) The strain of bare fiber grating is:

In the formula, ε _bare is the strain of bare fiber grating, K _ε is the strain sensitivity coefficient of bare fiber grating, Δλ _B wavelength change;

(2) Analyze the force of the fiber micro-element model of the cemented section, and establish a mechanical balance equation:

where r _f is the fiber grating radius, τ _f (x, r _f ) is the shear stress on the outer surface of the fiber and the inner surface of the adhesive layer, and σ _f is the normal stress of the fiber section;

(3) Analyze the force of the adhesive layer micro-element model and establish a mechanical balance equation:

2πr _j ·τ _j (x,r _j ) ·dx-2πr _f ·τ _f (x,r _f ) ·dx+π(r _j ² -r _f ² ) ·dσ _j =0

In the formula, r _j is the radius of the microelement of the adhesive layer, τ _j (x, r _j ) is the shear stress of the outer surface of the adhesive layer, and σ _j is the normal stress of the cross-section of the adhesive layer;

(4) Since the change rate of the fiber strain is consistent with the change rate of the adhesive layer strain, and the elastic modulus of the fiber grating and the adhesive layer are quite different, the simplified shear strain variation relationship of the adhesive layer is obtained:

where E _f is the elastic modulus of the fiber, and ε _f is the fiber strain;

(5) Points A and B are the boundary points of the glue layer, points M and N are the boundary points of the fiber in the glued section, and the displacement coordination equation is as follows:

in,

In the formula, u _A is the displacement of point A of the adhesive layer, u _M is the displacement of point M of the fiber in the bonding section, G _j is the shear modulus of the adhesive layer, _{ri is the inner diameter of the outer steel pipe, u i is} the displacement of the matrix at point A, u _f is the deformation of the optical fiber bonding section, L ₁ is the optical fiber bonding length, L ₂ is the optical fiber gauge length, and L _a is the support clamping length;

(6) Derivation to establish the second-order inhomogeneous linear differential equation of the fiber strain and the matrix strain in the cemented section:

where ε _i is the matrix strain;

(7) According to the equivalent section method, the strain of the free fiber is equal to the average strain of the bonded fiber, so the strain of the bare fiber grating is equal to the average strain of the bonded fiber:

where ε _f2 (x) is the strain of bare fiber grating, is the average strain of the fiber in the cemented segment;

(8) The matrix strain correction equation of the long-range fiber grating sensor:

The demodulator demodulates the wavelength data Δλ _B of the long-range fiber grating sensor, and corrects the large strain of the substrate through the matrix strain correction equation of the long-range fiber grating sensor, and solves the problem of accurate measurement of the long-range fiber grating sensor.

The advantage of the present invention is that the strain of the substrate is monitored and corrected based on the large-range fiber grating sensor. The large-range fiber grating sensor senses the large strain changes of the structure in real time, and the demodulator demodulates the reflected wavelength data, obtains the structural strain according to the matrix strain correction equation, and obtains the mechanical performance parameters of the structural components.

Description of drawings

Figure 1 is a schematic diagram of a fiber grating sensor.

FIG. 2 is a partial enlarged view of FIG. 1 .

Figure 3 is the force diagram of the fiber micro-element body in the cemented section.

Figure 4 is the force diagram of the adhesive layer micro-element body.

Detailed ways

In conjunction with the accompanying drawings, the examples of the device are described in detail as follows:

As shown in Figure 1, the bare fiber grating sensor 3 is placed inside the inner steel pipe, the inner steel pipe is placed inside the two sections of outer steel pipe 1, and a 1mm gap is reserved at the middle joint of the outer steel pipe to ensure that the inner and outer layers of steel pipe able to slide relative to each other. The length of the outer steel pipe over the inner steel pipe is L ₁ , that is, the fiber grating sticking length is L ₁ , the distance between the adhesive layers 2 is L ₂ , that is, the fiber grating gauge range is L ₂ , and the support 4 passes through the epoxy glue Bond two outer layers of steel pipes, and the clamping distance between the supports is La.

In Figure 2, Figure 3, and Figure 4, the model assumptions shown in the figure are made, and the influence of parameters such as the holding length of the support, the bonding length of the fiber grating, and the gauge length on the strain transmissibility of the fiber grating is considered, and the matrix large strain- Force transfer mechanism of small strain in fiber gratings. The demodulator demodulates the reflected wavelength data, obtains the structural strain according to the matrix strain correction equation (29), and obtains the strain parameters of the structural member.

Figure 1 is the actual picture of the long-range fiber grating sensor. The packaging scheme of the long-range fiber grating sensor is as follows: adopt the double-layer steel pipe packaging technology, select the inner steel pipe radius as r _m (slightly larger than the bare fiber grating radius), and put the bare fiber grating sensor Placed inside the inner steel pipe. The radius of the outer layer steel pipe is selected as r _i , and the inner layer steel pipe is placed inside the two outer layers of steel pipe to ensure that the inner and outer layers of the steel pipe can slide relative to each other. A gap of 1mm is reserved at the middle joint of the outer steel pipe. The length of the outer steel pipe over the inner steel pipe is L ₁ , that is, the fiber grating sticking length is L ₁ , and the distance between the glue layers is L ₂ , that is, the fiber grating gauge length The length is L ₂ . The inner steel pipe plays the role of fixing the fiber grating, connecting and supporting the two outer steel pipes. The relative displacement of the outer steel pipe is transmitted to the fiber grating through the end glue layer, which plays the role of matrix-fiber grating strain transmission. The supports hold two sections of outer-layer steel pipes respectively, and the clamping distance between the supports is L _a . The bare fiber grating sensor, the double-layer steel tube and the two clamping supports together constitute a large-range fiber grating strain sensor. By adjusting the clamping distance of the support and the length of the fiber grating gauge length, the strain measurability of the multi-range fiber grating sensor is improved. scope.

The large-range fiber grating sensor desensitizes the bare fiber grating sensor, and establishes a force transmission mechanism between the large strain of the matrix and the small strain of the fiber grating. Due to the inconsistency between the matrix strain and the strain of the fiber grating, the strain transfer analysis of the large-range fiber grating needs to be carried out. Continuing to correct the strain measured by the long-range fiber grating sensor, the analysis adopts the following assumptions:

(1) The fiber grating is a linear elastic material.

(2) The axial stress of the fiber grating is transmitted by the shear stress on the contact surface, and the adhesive layer undergoes shear deformation. (3) The support is firmly clamped with the sensor and the substrate, and the optical fiber and the adhesive layer are tightly bonded without relative slippage.

The fiber grating demodulator demodulates the wavelength change, and the bare fiber grating strain is:

In the formula, ε _bare is the strain of the bare fiber grating, K _ε is the strain sensitivity coefficient of the bare fiber grating, and Δλ _B is the wavelength change.

Figure 1 is a schematic diagram of a long-range fiber grating sensor. Points A and B are the boundary points of the glue layer, points M and N are the boundary points of the fiber in the glued section, and point N is the coordinate origin. Figure 3 is the force diagram of the fiber micro-element in the cemented segment. The fiber in the cemented segment is taken as the research object, and its force analysis is:

In the formula, σ _f is the normal stress of the optical fiber section, τ _f (x, r _f ) is the shear stress of the outer surface of the fiber (the inner surface of the adhesive layer), and r _f is the radius of the fiber grating.

Figure 4 is the force diagram of the adhesive layer micro-element body, and its force analysis:

2πr _j ·τ _j (x,r _j ) ·dx-2πr _f ·τ _f (x,r _f ) ·dx+π(r _j ² -r _f ² ) ·dσ _j =0 (4)

In the formula, τ _j (x, r _j ) is the outer surface shear stress of the adhesive layer, r _j is the radius of the micro-element of the adhesive layer, and σ _j is the normal stress of the adhesive layer section.

Substitute equation (3) into (5):

In the formula, E _f is the elastic modulus of the fiber, and E _j is the elastic modulus of the adhesive layer.

The fiber has the same strain rate of change as the bondline:

In the formula, ε _f is the fiber strain, and ε _j is the adhesive layer strain.

The elastic modulus of the fiber grating and the adhesive layer are quite different, so it can be considered that:

Substitute equation (8) (9) into (7)

The adhesive layer undergoes shear deformation, resulting in:

where u is the axial displacement of the adhesive layer, G _j is the shear modulus of the adhesive layer, and γ is the shear strain of the adhesive layer. Integrate equation (11):

In the formula, u _A is the displacement of point A of the adhesive layer, _{u M} is the displacement of point M of the fiber in the bonding section, and ri is the inner diameter of the outer steel pipe.

The coordination equation of the displacement of point A and the displacement of point M is as follows:

In the formula, _ui is the displacement of the corresponding matrix at point A, u _f is the deformation of the fiber bonding section, L ₁ is the fiber bonding length, L ₂ is the fiber gauge length, and L _a is the support clamping length.

in:

where μ is Poisson’s ratio. Taking the derivative of formula (19) with respect to x, the differential equation between the fiber strain in the cemented segment and the matrix strain is obtained:

The general solution of the differential equation is:

In the formula, ε _f (x) is the fiber strain in the cemented section, ε _i is the matrix strain, C ₁ and C ₂ are integral constants, and the boundary point of the cemented fiber is the free end face. Due to the symmetry, the boundary conditions are:

ε _f (L ₁ )=ε _f (-L ₁ )=0 (22)

Determine the integral constant:

The distribution of fiber strain transmissibility in the cemented segment is:

where α(x) is the strain transmissibility of the fiber in the cemented segment. The average strain transmission rate can be expressed as the average value of the strain in the fiber cemented length range, and the average strain transmission rate of the fiber in the cemented section is:

In the formula, is the average strain transmissibility of the fiber in the cemented segment, is the average strain of the fiber in the cemented segment. The uneven strain of the fiber in the cemented section is equivalent to the average strain along the entire length of the fiber in the cemented section. According to the equivalent section method, the strain of the free section of the fiber is equal to the average strain of the fiber in the cemented section, and the strain of the bare fiber grating is equal to the average strain of the fiber in the cemented section. strain:

In the formula, ε _f2 (x) is the strain of the bare fiber grating, and the strain transfer rate of the long-range fiber grating sensor is:

where α is the strain transmissibility of the long-range fiber grating sensor. Obtained from formula (28) and formula (1), the matrix strain correction equation of the long-range fiber grating sensor is:

Formula (29) is the matrix strain correction equation of the large-range fiber grating sensor, which solves the problem of strain measurement and correction of large-strain structures.

Claims (2)

1. A matrix strain correction method of a wide-range fiber grating sensor is characterized by comprising the following steps: monitoring the strain of the matrix through a wide-range fiber grating sensor;

the structure is as follows: placing a bare fiber grating sensor inside an inner-layer steel pipe, and placing the inner-layer steel pipe inside two sections of outer-layer thin steel pipes to ensure that the inner and outer steel pipes can slide relatively; reserving a gap at the middle joint of the outer layer steel pipe;

selecting the radius of the inner layer steel pipe as r_mThe radius of the outer layer steel pipe is r_iThe bare fiber grating sensor is arranged in the inner layer steel tubeA section;

the length of the two ends of the outer layer steel pipe exceeding the inner layer steel pipe is L₁I.e. the fiber grating has a pasting length L₁The distance between the glue layers is L₂I.e. the length of the index space of the fiber grating is L₂；

And (3) considering the influences of the clamping length of the support, the gauge length of the fiber grating and the middle glue layer to obtain a matrix strain equation of the wavelength of the fiber grating:

(1) bare fiber grating strain:

in the formula, epsilon_{Bare chip}For strain of bare fiber grating, K_εIs the strain sensitivity coefficient of bare fiber grating, delta lambda_BA change in wavelength;

(2) analyzing the stress of the cementing section optical fiber micro element model, and establishing a mechanical equilibrium equation:

in the formula, r_fIs the radius of the fiber grating, tau_f(x,r_f) For the external surface shear stress, σ, of the optical fiber_fIs the fiber cross section normal stress;

(3) and (3) analyzing the stress of the glue layer infinitesimal body model, and establishing a mechanical balance equation:

2πr_j·τ_j(x,r_j)·dx-2πr_f·τ_f(x,r_f)·dx+π(r_j ²-r_f ²)·dσ_j＝0

in the formula, r_jIs the radius of the colloidal layer infinitesimal body, tau_j(x,r_j) Shear stress of the outer surface of the adhesive layer, σ_jThe normal stress of the section of the glue layer;

(4) because the change rate of the optical fiber strain is consistent with the change rate of the adhesive layer strain, and the difference between the elastic modulus of the optical fiber grating and the elastic modulus of the cementing layer is large, the simplified adhesive layer shear strain change relation is obtained:

in the formula, E_fIs the modulus of elasticity, ε, of an optical fiber_fIs the fiber strain;

(5) points A and B are boundary points of the glue layer, points M and N are boundary points of the optical fiber of the cementing section, and the displacement coordination equation is as follows:

wherein,

in the formula u_AIs the displacement of the point A of the glue layer, u_MFor cementing sections of fibre with M-point displacement, G_jIs the shear modulus of the glue line, r_iThe inner diameter u of the outer layer steel pipe_iCorresponding to the displacement of the substrate at point A, u_fFor deformation of cemented sections of optical fibres, L₁For sticking lengths of optical fibers, L₂For the length of the optical fibre gauge length, L_aClamping the length for the support;

(6) and (3) derivation is carried out to establish a second-order non-homogeneous linear differential equation of the fiber strain and the matrix strain of the cementing section:

in the formula, epsilon_iStrain of the matrix;

(7) according to the equivalent cross-section method, the strain of the free section of the optical fiber is equal to the average strain of the cemented section of the optical fiber, and therefore, the strain of the bare fiber grating is equal to the average strain of the cemented section of the optical fiber:

in the formula, epsilon_f2(x) In order to strain the bare fiber grating,the average strain of the consolidated length of optical fiber;

(8) matrix strain correction equation of wide-range fiber grating sensor:

demodulator for demodulating wide-range optical fiber grating sensor wavelength data delta lambda_BThe large strain of the matrix is corrected through a matrix strain correction equation of the wide-range fiber grating sensor, and the problem of accurate measurement of the wide-range fiber grating sensor is solved.

2. The method for matrix strain correction of a wide-range fiber grating sensor according to claim 1, wherein: the wide-range fiber grating sensor and the fiber grating demodulator form a strain sensing and collecting system, the demodulator demodulates the reflection wavelength, and the strain of the bare fiber grating is sensed through the change condition of the wavelength.