Packaging device and packaging method of fiber bragg grating strain sensor

Abstract

The invention discloses a packaging device and a packaging method for a fiber bragg grating strain sensor. The device comprises a first optical fiber clamping device, a second optical fiber clamping device, a substrate clamp, a first micro-displacement platform, a second micro-displacement platform, a six-axis optical adjustment platform, a fiber bragg grating demodulator, a high-precision tension meter, a visual observation system, a quantitative glue feeding pump and an adhesive curing device. The first and second optical fiber holders clamp the first and second optical fibers; the substrate clamp installs a strain substrate; the first micro-displacement platform and the second micro-displacement platform control the movable optical fiber holder; the six-axis optical adjustment platform bears the substrate clamp; the fiber bragg grating demodulator monitors the central wavelength and the waveform spectrum of the fiber bragg grating; the high-precision tension meter applies tension to the fiber bragg grating; the visual observation system is used for observing the position postures of the fiber bragg grating and the strain substrate; the quantitative glue feeding pump is used for feeding an adhesive; the adhesive curing device accelerates curing of the adhesive. The packaging quality of the fiber bragg grating strain sensor can be effectively controlled, and the consistency of strain sensitivity is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of fiber grating sensing and strain measurement, and in particular relates to a packaging device and a packaging method for a fiber grating strain sensor. Background Art

[0002] Fiber Bragg grating strain sensor is a type of sensor that measures strain based on the fiber Bragg grating principle. The fiber Bragg grating is packaged together with the strain substrate by gluing. The packaging process directly affects the consistency of the sensor's strain sensitivity. Since the fiber Bragg grating strain sensor cannot be calibrated on site after being installed on the surface of the measured structure, in actual application, the strain calculation is usually performed based on the average sensitivity data of the batch of sensors. If the strain sensitivity of each sensor is inconsistent, it will cause errors in the measurement results. Therefore, improving the sensitivity consistency of the fiber Bragg grating strain sensor is the key to reducing strain measurement errors.

[0003] The current packaging devices and methods for fiber grating strain sensors cannot guarantee the consistency of sensor sensitivity. There is a problem of large differences in sensitivity among sensors in the same batch, resulting in large errors in strain measurement results. As a prior art, CN116817783B discloses a pre-tightening packaging structure and method for optical fiber strain sensors. By setting a translation mechanism, it solves the technical problem of low adjustment accuracy of the pre-tightening amount of the sensing optical fiber, thereby improving the strain measurement accuracy under high temperature. However, this patent does not solve the problem of consistency of strain sensor sensitivity. CN105583484B proposes a packaging device and method for welding packaging of sensors, focusing on improving the packaging efficiency and qualified product rate of fiber grating sensors, but it also fails to improve the consistency of strain sensor sensitivity. Summary of the invention

[0004] The object of the present invention is to provide a packaging device and a packaging method for a fiber grating strain sensor, which can effectively improve the packaging quality of the fiber grating strain sensor and improve the consistency of the strain sensitivity of the sensor.

[0005] In order to achieve the above-mentioned object, one aspect of the present invention provides a packaging device for a fiber Bragg grating strain sensor, comprising a first fiber holder, a second fiber holder, a substrate fixture, a first micro-displacement platform, a second micro-displacement platform, a six-axis optical adjustment platform, a fiber Bragg grating demodulator, a high-precision tensiometer, a visual observation system, a quantitative glue pump and an adhesive curing device;

[0006] The first optical fiber clamp and the second optical fiber clamp are used to clamp the first optical fiber and the second optical fiber at both ends of the optical fiber Bragg grating respectively, and temporarily fix them;

[0007] The base fixture has an installation groove consistent with the shape of the strain base, which is used to install the strain base, limit the strain base, and temporarily fix it;

[0008] The first micro-displacement platform and the second micro-displacement platform are respectively equipped with a first optical fiber clamp and a second optical fiber clamp, and are used to control the movement of the first optical fiber clamp and the second optical fiber clamp to adjust the position and posture of the optical fiber grating;

[0009] The six-axis optical adjustment platform is equipped with a substrate fixture, which is used to control the movement of the substrate fixture to adjust the position and posture of the strain substrate;

[0010] The fiber Bragg grating demodulator is connected to the end of the first optical fiber and is used to monitor the central wavelength and waveform spectrum of the fiber Bragg grating;

[0011] A high-precision tensile force gauge is connected to the end of the second optical fiber and is used to apply tension to the optical fiber Bragg grating;

[0012] The visual observation system is used to observe the position and posture of the fiber grating and the strain substrate;

[0013] The quantitative glue pump is used to quantitatively and controllably dispense adhesive to bond and package the first optical fiber, the optical fiber grating, the second optical fiber and the strain substrate;

[0014] The adhesive curing device is used to accelerate the curing of the adhesive.

[0015] Preferably, the packaging device further comprises a base, which is a breadboard having threaded holes distributed at equal intervals, and is used to carry and install the first micro-displacement platform, the second micro-displacement platform, the six-axis optical adjustment platform, and the fiber grating demodulator.

[0016] Preferably, the first optical fiber clamp and the second optical fiber clamp are respectively provided with V-shaped grooves for non-destructively clamping the first optical fiber and the second optical fiber.

[0017] Preferably, the visual observation system is a multi-axis CCD camera.

[0018] Another aspect of the present invention provides a packaging method for a fiber Bragg grating strain sensor, wherein the packaging device described above is used to package the fiber Bragg grating strain sensor, and the method comprises:

[0019] Step S1: connecting the end of the first optical fiber to a fiber Bragg grating demodulator to record the initial center wavelength and initial waveform spectrum of the fiber Bragg grating;

[0020] Step S2: using a first fiber clamp to non-destructively clamp the first optical fiber, using a second fiber clamp to non-destructively clamp the second optical fiber, using a first micro-displacement platform to adjust the first fiber clamp, using a second micro-displacement platform to adjust the second fiber clamp, to adjust the position of the fiber Bragg grating, using a visual observation system to observe to ensure that the fiber Bragg grating is located at the center of the base fixture, using a high-precision tensile gauge to apply tension to the fiber Bragg grating in the horizontal direction, and adjusting the center wavelength of the fiber Bragg grating to the target center wavelength;

[0021] Step S3: Install the strain substrate in the installation groove of the substrate fixture, limit the strain substrate, use the six-axis optical adjustment platform to adjust the substrate fixture to adjust the position and posture of the strain substrate, use the visual observation system to observe, ensure that the strain substrate and the fiber Bragg grating are accurately aligned in the horizontal direction, and the strain substrate and the fiber Bragg grating are parallel in the horizontal and vertical directions without an angle, so that the fiber Bragg grating is embedded in the grating groove of the strain substrate to reach the target depth;

[0022] Step S4: using a quantitative glue pump to dispense adhesive, bonding and encapsulating the first optical fiber, the fiber grating, the second optical fiber and the strain substrate to form a fiber grating strain sensor, and using an adhesive curing device to accelerate the curing of the adhesive;

[0023] Step S5: Open the first fiber clamp, the second fiber clamp and the substrate fixture, and take out the packaged fiber Bragg grating strain sensor.

[0024] Preferably, in step S2, the tension value F applied to the fiber Bragg grating satisfies:

[0025]

[0026] Among them, λ B is the target center wavelength of the fiber Bragg grating; 0 is the initial center wavelength of the fiber Bragg grating, λ B ≥λ 0 ; A is the circular cross-sectional area of ​​the first and second optical fibers; E is the elastic modulus of the first and second optical fibers; 0.78 is a constant.

[0027] Preferably, in step S3, the fiber Bragg grating is embedded in the grating groove of the strain substrate to a target depth H B satisfy:

[0028]

[0029] Wherein, K is the strain transfer coefficient; L is the bonding length of the adhesive; and C is a constant related to the materials of the first and second optical fibers, the geometric parameters of the first and second optical fibers, and the characteristics of the adhesive.

[0030] Preferably, in step S4, the glue supply quantity Q of the quantitative glue supply pump satisfies:

[0031] Q=(D*L*HA*L) / (1-ρ)

[0032] Wherein, D is the width of the adhesive bonding; L is the length of the adhesive bonding; H is the grating groove depth of the strained substrate; A is the circular cross-sectional area of ​​the first and second optical fibers; and ρ is the curing shrinkage rate of the adhesive.

[0033] The packaging device and packaging method of the fiber Bragg grating strain sensor according to the above aspects of the present invention can effectively improve the packaging quality of the fiber Bragg grating strain sensor and improve the consistency of the strain sensitivity of the sensor. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings used in the description of the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work:

[0035] Figure 1 is a schematic structural diagram of a packaging device for a fiber Bragg grating strain sensor according to an embodiment of the present invention;

[0036] Figure 2 It is a flow chart of a packaging method of a fiber Bragg grating strain sensor according to an embodiment of the present invention.

[0037] Among them, 1. the first optical fiber; 2. the optical fiber Bragg grating; 3. the second optical fiber; 4. the strain substrate; 5. the first optical fiber clamp; 6. the second optical fiber clamp; 7. the substrate fixture; 8. the first micro-displacement platform; 9. the second micro-displacement platform; 10. the six-axis optical adjustment platform; 11. the optical fiber Bragg grating demodulator; 12. the high-precision dynamometer; 13. the visual observation system; 14. the quantitative glue pump; 15. the adhesive curing device; 16. the base. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] The embodiment of the present invention provides a packaging device for a fiber Bragg grating strain sensor. Figure 1 FIG. 1 is a schematic structural diagram of a packaging device for a fiber Bragg grating strain sensor according to an embodiment of the present invention. Figure 1 As shown, the packaging device of the fiber Bragg grating strain sensor according to the embodiment of the present invention includes: a first fiber clamp 5, a second fiber clamp 6, a base clamp 7, a first micro-displacement platform 8, a second micro-displacement platform 9, a six-axis optical adjustment platform 10, a fiber Bragg grating demodulator 11, a high-precision tensile gauge 12, a visual observation system 13, a quantitative glue pump 14, and an adhesive curing device 15.

[0040] The first fiber clamp 5 and the second fiber clamp 6 are respectively provided with a V-groove with a depth of 150 μm, which is used to non-destructively clamp the first optical fiber 1 and the second optical fiber 3, and play a role of temporary fixation. The first optical fiber 1 and the second optical fiber 3 are respectively connected to the two ends of the fiber grating 2, and the first optical fiber 1 and the second optical fiber 3 have the same material and parameters. The substrate fixture 7 has an installation groove consistent with the shape of the strain substrate 4, and the depth of the installation groove is 1 mm, which is used to install the strain substrate 4, limit the strain substrate 4, and temporarily fix it.

[0041] The first micro-displacement platform 8 and the second micro-displacement platform 9 respectively carry and install the first fiber clamp 5 and the second fiber clamp 6, and are used to accurately control the movement of the first fiber clamp 5 and the second fiber clamp 6, with a displacement accuracy of up to 0.5μm. By accurately moving the first optical fiber 1 and the second optical fiber 3, the position and posture of the fiber Bragg grating 2 can be accurately adjusted.

[0042] The six-axis optical adjustment platform 10 carries the installed substrate fixture 7 and is used to precisely control the moving substrate fixture 7 with a displacement accuracy of up to 0.5 μm. The angles of the substrate fixture 7 in the X-axis, Y-axis, and Z-axis can be adjusted to achieve precise adjustment of the position and posture of the strain substrate 4, wherein the horizontal direction of the plane where the packaging device is located is the X-axis, the vertical direction is the Y-axis, and the direction perpendicular to the plane formed by the X and Y axes is the Z-axis.

[0043] The fiber Bragg grating demodulator 11 is connected to the end of the first optical fiber 1 and is used to monitor the central wavelength and waveform spectrum of the fiber Bragg grating 2. The high-precision tensile gauge 12 is connected to the end of the second optical fiber 3 and is used to apply precise tension to the fiber Bragg grating 2 with an accuracy of up to 0.01N. The visual observation system 13 uses a multi-axis CCD camera to observe the position and posture in real time during the adjustment of the fiber Bragg grating 2 and the strain substrate 4.

[0044] The quantitative glue pump 14 is used to quantitatively and controllably dispense adhesive, with a minimum glue output of 0.1 μL, to bond and package the first optical fiber 1, the fiber grating 2, the second optical fiber 3 and the strain substrate 4. The adhesive curing device 15 is used to accelerate the curing of the adhesive. Depending on the type of adhesive used, the curing method can be selected from heating curing or UV curing.

[0045] The packaging device of the embodiment of the present invention may further include a base 16, which is a breadboard having threaded holes distributed at equal intervals of 25.4 mm, and is used to carry and install other components and equipment of the packaging device.

[0046] The embodiment of the present invention further provides a packaging method of a fiber Bragg grating strain sensor, and the fiber Bragg grating strain sensor is packaged using the above packaging device. Figure 2 As shown, the method according to the embodiment of the present invention includes steps S1 to S5.

[0047] In step S1, the end of the first optical fiber 1 is connected to the fiber Bragg grating demodulator 11, and the initial center wavelength value and the initial waveform spectrum of the fiber Bragg grating 2 are recorded.

[0048] In step S2 , the optical fiber is clamped, the position and posture of the fiber grating 2 are adjusted, and tension is applied to the fiber grating 2 .

[0049] Specifically, the first optical fiber holder 5 is used to non-destructively hold the first optical fiber 1 , and the second optical fiber holder 6 is used to non-destructively hold the second optical fiber 3 , and temporarily fix them.

[0050] Use the first micro-displacement platform 8 to adjust the first fiber clamp 5, and use the second micro-displacement platform 9 to adjust the second fiber clamp 6 to adjust the position of the fiber Bragg grating 2; use the visual observation system 13 to observe and ensure that the fiber Bragg grating 2 is located at the center of the base fixture 7 and has no obvious angle with the X-axis and the Z-axis.

[0051] Use a high-precision tensile gauge 12 to apply tension to the fiber Bragg grating 2 in the X-axis direction (horizontal direction), adjust the center wavelength of the fiber Bragg grating 2 to the target center wavelength, and ensure that the center wavelengths of the fiber Bragg gratings in the same batch are the same during packaging. The applied tension value F follows the following formula:

[0052]

[0053] In the formula, λ B is the target center wavelength of the fiber Bragg grating, λ B ≥λ 0 ; 0 is the initial central wavelength of the fiber Bragg grating; A is the circular cross-sectional area of ​​the first and second optical fibers; E is the elastic modulus of the first and second optical fibers; and 0.78 is a constant.

[0054] In one embodiment, the initial center wavelength of the selected fiber Bragg grating 2 is 1549.5 nm, and the target center wavelength is 1550 nm. According to formula (1), the magnitude of the applied tension can be calculated to be 0.36 N.

[0055] In step S3 , the strain substrate 4 is installed and the position and posture of the strain substrate 4 are adjusted.

[0056] Specifically, the strain substrate 4 is installed in the installation groove of the substrate fixture 7, and the strain substrate 4 is limited and temporarily fixed.

[0057] Use the six-axis optical adjustment platform 10 to adjust the substrate fixture 7 to adjust the position and posture of the strain substrate 4; use the visual observation system 13 to observe and ensure that the strain substrate 4 and the fiber grating 2 are accurately aligned in the X-axis direction, and the strain substrate 4 and the fiber grating 2 are parallel and have no angle in the X-axis and Z-axis directions (horizontal and vertical directions). Adjust the relative position of the strain substrate 4 so that the fiber grating 2 is embedded in the grating groove of the strain substrate 4, and ensure that the fiber grating 2 of the same batch is embedded in the groove at the same target depth H B , H B Follow this formula:

[0058]

[0059] Wherein, K is the strain transfer coefficient; L is the bonding length of the adhesive; and C is a constant related to the materials of the first and second optical fibers, the geometric parameters of the first and second optical fibers, and the characteristics of the adhesive.

[0060] In one embodiment, if the strain transfer coefficients of the fiber Bragg grating strain sensors of the same batch all reach 0.95, according to formula (2), it can be calculated that the depth of the fiber Bragg grating embedded in the groove is 10 μm.

[0061] In step S4, the first optical fiber 1, the fiber Bragg grating 2, the second optical fiber 3 and the strain substrate 4 are pasted and packaged to form a fiber Bragg grating strain sensor.

[0062] Specifically, a quantitative glue pump 14 is used to dispense UV adhesive to bond and package the first optical fiber 1, the optical fiber grating 2, the second optical fiber 3 and the strain substrate 4, and an adhesive curing device 15 is used to accelerate the curing of the adhesive. The amount of adhesive Q follows the following formula:

[0063] Q=(D*L*HA*L) / (1-ρ) (3)

[0064] Wherein, D is the width of adhesive bonding; L is the length of adhesive bonding, which is equivalent to the length of the fiber Bragg grating; H is the depth of the strained substrate grating groove; A is the circular cross-sectional area of ​​the first and second optical fibers; and ρ is the adhesive curing shrinkage rate.

[0065] In one embodiment, the bonding width of the selected UV adhesive is 2 mm, the fiber grating length is 7 mm, the grating groove depth is 0.5 mm, and the curing shrinkage rate is 5%. According to formula (3), the glue dosage Q is calculated to be 7.3 μL.

[0066] In step S5, the first fiber clamp 5, the second fiber clamp 6 and the base fixture 7 are opened to take out the packaged fiber Bragg grating strain sensor. The fiber Bragg grating demodulator 11 can be used to record and detect the fiber Bragg grating center wavelength and waveform spectrum after packaging, and the sensor is numbered, and the packaging is completed.

[0067] In one embodiment, strain sensitivity tests were performed on fiber Bragg grating strain sensors of the same batch with a central wavelength of 1550 nm, and the results are shown in Table 1. Table 2 is the calculation result of the dispersion of strain sensitivity of the batch of sensors, and the dispersion of sensitivity to its average value is less than 1%, indicating that the packaging consistency of the sensors is very good.

[0068] Table 1 Strain sensitivity test results of sensors from the same batch

[0069]

[0070] Table 2 Calculation results of strain sensitivity dispersion of sensors in the same batch

[0071]

[0072] In summary, the packaging device and packaging method of the fiber Bragg grating strain sensor according to the embodiment of the present invention have the following beneficial effects:

[0073] 1. It can reduce or avoid the strain sensitivity error caused by the packaging process, improve the packaging consistency of the sensor, and thus achieve accurate strain measurement;

[0074] 2. By setting up a second micro-displacement platform, the central wavelength of the fiber Bragg grating can be adjusted so that the fiber Bragg gratings of the same batch have the same central wavelength when packaged;

[0075] 3. By setting up a six-axis optical adjustment platform and a visual observation system, the position and posture of the strain substrate can be accurately adjusted to ensure that the depth of fiber Bragg gratings embedded in the strain substrate of the same batch is the same;

[0076] 4. By setting a quantitative glue pump, the glue supply amount of each fiber grating strain sensor is the same;

[0077] 5. The dispersion of strain sensitivity to its average value is controlled within 1%, effectively ensuring the consistency of sensor packaging.

[0078] The above description is only by way of illustration of certain exemplary embodiments of the present invention. It is undoubted that those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the above drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A packaging device for a fiber Bragg grating strain sensor, characterized in that: It includes a first optical fiber holder, a second optical fiber holder, a substrate fixture, a first micro-displacement platform, a second micro-displacement platform, a six-axis optical adjustment platform, an optical fiber Bragg grating demodulator, a high-precision tensiometer, a visual observation system, a quantitative glue pump and an adhesive curing device; The first optical fiber clamp and the second optical fiber clamp are used to clamp the first optical fiber and the second optical fiber at both ends of the optical fiber Bragg grating respectively, and temporarily fix them; The base fixture has an installation groove consistent with the shape of the strain base, which is used to install the strain base, limit the strain base, and temporarily fix it; The first micro-displacement platform and the second micro-displacement platform are respectively equipped with a first optical fiber clamp and a second optical fiber clamp, and are used to control the movement of the first optical fiber clamp and the second optical fiber clamp to adjust the position and posture of the optical fiber grating; The six-axis optical adjustment platform is equipped with a substrate fixture, which is used to control the movement of the substrate fixture to adjust the position and posture of the strain substrate; The fiber Bragg grating demodulator is connected to the end of the first optical fiber and is used to monitor the central wavelength and waveform spectrum of the fiber Bragg grating; A high-precision tensile force gauge is connected to the end of the second optical fiber and is used to apply tension to the optical fiber Bragg grating; The visual observation system is used to observe the position and posture of the fiber grating and the strain substrate; The quantitative glue pump is used to quantitatively and controllably dispense adhesive to bond and package the first optical fiber, the optical fiber grating, the second optical fiber and the strain substrate; The adhesive curing device is used to accelerate the curing of the adhesive.

2. The packaging device according to claim 1, characterized in that It also includes a base, which is a breadboard with threaded holes distributed at equal intervals and is used to carry and install the first micro-displacement platform, the second micro-displacement platform, the six-axis optical adjustment platform, and the fiber grating demodulator.

3. The packaging device according to claim 1 or 2, characterized in that: The first optical fiber clamp and the second optical fiber clamp are respectively provided with V-shaped grooves for non-destructively clamping the first optical fiber and the second optical fiber.

4. The packaging device according to claim 1 or 2, characterized in that: The visual observation system is a multi-axis CCD camera.

5. A packaging method for a fiber Bragg grating strain sensor, characterized in that: A fiber Bragg grating strain sensor is packaged using the packaging device according to any one of claims 1 to 4, the method comprising: Step S1: connecting the end of the first optical fiber to a fiber Bragg grating demodulator to record the initial center wavelength and initial waveform spectrum of the fiber Bragg grating; Step S2: using a first fiber clamp to non-destructively clamp the first optical fiber, using a second fiber clamp to non-destructively clamp the second optical fiber, using a first micro-displacement platform to adjust the first fiber clamp, using a second micro-displacement platform to adjust the second fiber clamp, to adjust the position of the fiber Bragg grating, using a visual observation system to observe to ensure that the fiber Bragg grating is located at the center of the base fixture, using a high-precision tensile gauge to apply tension to the fiber Bragg grating in the horizontal direction, and adjusting the center wavelength of the fiber Bragg grating to the target center wavelength; Step S3: Install the strain substrate in the installation groove of the substrate fixture, limit the strain substrate, use the six-axis optical adjustment platform to adjust the substrate fixture to adjust the position and posture of the strain substrate, use the visual observation system to observe, ensure that the strain substrate and the fiber Bragg grating are accurately aligned in the horizontal direction, and the strain substrate and the fiber Bragg grating are parallel in the horizontal and vertical directions without an angle, so that the fiber Bragg grating is embedded in the grating groove of the strain substrate to reach the target depth; Step S4: using a quantitative glue pump to dispense adhesive, bonding and encapsulating the first optical fiber, the fiber grating, the second optical fiber and the strain substrate to form a fiber grating strain sensor, and using an adhesive curing device to accelerate the curing of the adhesive; Step S5: Open the first fiber clamp, the second fiber clamp and the substrate fixture, and take out the packaged fiber Bragg grating strain sensor.

6. The method according to claim 5, characterized in that In step S2, the tension value F applied to the fiber Bragg grating satisfies: Among them, λ B is the target center wavelength of the fiber Bragg grating; λ0 is the initial center wavelength of the fiber Bragg grating, λ B ≥λ0; A is the circular cross-sectional area of ​​the first and second optical fibers; E is the elastic modulus of the first and second optical fibers; 0.78 is a constant.

7. The method according to claim 5 or 6, characterized in that In step S3, the fiber Bragg grating is embedded into the grating groove of the strained substrate to a target depth H B satisfy: Wherein, K is the strain transfer coefficient; L is the bonding length of the adhesive; and C is a constant related to the materials of the first and second optical fibers, the geometric parameters of the first and second optical fibers, and the characteristics of the adhesive.

8. The method according to claim 5 or 6, characterized in that In step S4, the glue quantity Q of the quantitative glue pump satisfies: Q=(D*L*HA*L) / (1-ρ) Wherein, D is the width of the adhesive bonding; L is the length of the adhesive bonding; H is the grating groove depth of the strained substrate; A is the circular cross-sectional area of ​​the first and second optical fibers; and ρ is the curing shrinkage rate of the adhesive.

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