Push-pull fiber optic accelerometer with FBG based self-compensation of cross-talk

Abstract

The application discloses a push-pull type optical fiber accelerometer based on FBG crosstalk self-compensation, and relates to the technical field of fiber grating sensors.The accelerometer comprises an optical fiber, both ends of the optical fiber pass through a shell and are fixedly connected with the shell, an elastic diaphragm is fixedly arranged in the shell, a first mass block is fixedly arranged on the upper side of the elastic diaphragm, a second mass block is fixedly arranged on the lower side of the elastic diaphragm, a first spring is coaxially arranged outside the optical fiber on the upper side of the first mass block, a second spring is coaxially arranged outside the optical fiber on the lower side of the second mass block, the optical fiber passes through the first mass block, the elastic diaphragm and the second mass block in sequence from top to bottom, a first fiber Bragg grating is formed on the optical fiber on the upper side of the first mass block, and a second fiber Bragg grating is formed on the optical fiber on the lower side of the second mass block.The accelerometer has the advantages of simple structure, good stability, low cost and high precision.

Description

Technical Field

[0001] This invention relates to the field of fiber optic sensor technology, and in particular to a push-pull fiber optic accelerometer with crosstalk self-compensation based on FBG. Background Technology

[0002] Vibration is a common physical phenomenon, representing the reciprocating motion of an object around its equilibrium position. Moderate vibration is fundamental to the normal operation of many mechanical devices, but abnormal, excessive, or uncontrolled vibration is almost always harmful, with far-reaching and extensive effects. Implementing vibration monitoring is an inevitable requirement for modern industry and society to move towards intelligence, safety, and efficiency.

[0003] Fiber optic sensing technology utilizes the changes in light transmission characteristics within optical fibers due to external environmental influences. By detecting changes in the wavelength, phase, and intensity of the optical signal, environmental parameters can be detected and measured. The inherent properties of optical fibers endow fiber optic sensors with advantages such as resistance to electromagnetic interference, intrinsic safety, corrosion resistance, and long lifespan, while also enabling high sensitivity and high precision detection of the measured quantity. To adapt to extreme environments and meet the demands of modern high-standard monitoring, fiber optic accelerometers based on fiber optic sensing technology have seen rapid development. Under vibration, the inertial force generated by the mass block in the fiber optic accelerometer causes deformation of the optical fiber, resulting in changes in the wavelength, phase, and other properties of the output optical signal. By detecting and analyzing this optical signal, vibration signals can be monitored.

[0004] As a mature fiber optic sensing technology, a fiber Bragg grating (FBG) is a structure with a periodic refractive index distribution artificially created using technologies such as lasers. When light propagates in the fiber, the FBG reflects a specific wavelength, exhibiting advantages such as stable performance, good spectral characteristics, and strong anti-interference capabilities, leading to its widespread application in fiber optic accelerometers. As one of the main types of fiber optic accelerometers, wavelength-type accelerometers use FBGs as sensing elements, converting changes in acceleration into changes in the fiber's refractive index and the grating's period, which are then expressed as changes in the grating's center wavelength. This allows for the monitoring of vibration signals by quantifying the wavelength shift.

[0005] Because many applications require high sensitivity, FBG accelerometers are designed to optimize low-frequency performance, resulting in their operating frequency band primarily concentrated below several hundred hertz. However, high-frequency vibration signals also carry extremely rich information, and measuring high-frequency vibration signals is of equal or even greater importance in industrial fields. Furthermore, most fiber optic accelerometers have fixed resonant frequencies and sensitivities that cannot be adjusted. Therefore, the design and development of fiber optic accelerometers with higher resonant frequencies and the ability to adjust resonant frequencies and sensitivity is of great significance and has broad application prospects. Summary of the Invention

[0006] The technical problem to be solved by the present invention is how to provide a push-pull fiber optic accelerometer based on FBG with crosstalk self-compensation that has a simple structure, good stability, low cost and high accuracy.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a push-pull fiber optic accelerometer with crosstalk self-compensation based on FBG, comprising an optical fiber, both ends of which pass through a housing and are fixedly connected to the housing. An elastic diaphragm is fixed inside the housing. A first mass block is fixed to the upper side of the elastic diaphragm, and a second mass block is fixed to the lower side of the elastic diaphragm. A first spring is coaxially arranged on the outer side of the optical fiber on the upper side of the first mass block, and a second spring is coaxially arranged on the outer side of the optical fiber on the lower side of the second mass block. The optical fiber passes through the first mass block, the elastic diaphragm, and the second mass block sequentially from top to bottom, and the middle region of the optical fiber is fixedly connected to the first mass block, the elastic diaphragm, and the second mass block. A first fiber Bragg grating is formed on the optical fiber on the upper side of the first mass block, and a second fiber Bragg grating is formed on the optical fiber on the lower side of the second mass block.

[0008] A further technical solution is that both ends of the optical fiber are fixed to the outer shell by a fastener.

[0009] A further technical solution is that the outer shell includes an upper shell and a lower shell, which are made of metal or high-strength engineering plastic. The upper and lower shells clamp the edge of the elastic diaphragm, and the interior accommodates a mass block and a spring, providing overall mechanical support.

[0010] A further technical solution is that the elastic diaphragm is a thin-film elastic structure with an optical fiber insertion hole in its center. Its edges are fixed between the upper and lower shells of the outer shell, and its center is fixedly connected to the upper and lower mass blocks to provide flexible support for them, allowing the upper and lower mass blocks to move under vibration, while introducing part of the system stiffness.

[0011] A further technical solution is that the first spring and the second spring are replaceable helical springs or disc springs, placed between the first mass block and the upper cover of the outer shell and the second mass block and the lower bottom of the outer shell, arranged symmetrically in the upper and lower parts, to provide adjustable system stiffness. By replacing springs with different stiffnesses, the resonant frequency can be adjusted, thus expanding the operating frequency band.

[0012] A further technical solution is that the first and second mass blocks are made of high-density metal materials, and optical fiber insertion holes are opened in their centers for optical fibers to pass through. Under vibration, inertial force is generated, driving the optical fibers to produce periodic strain.

[0013] A further technical solution is that the first fiber Bragg grating and the second fiber Bragg grating are inscribed on the optical fiber, and are composed of two fiber gratings with different center wavelengths, and are demodulated using wavelength division multiplexing technology.

[0014] A further technical solution is that the diameter of the optical fiber insertion hole at the center of the first mass block, the second mass block, and the elastic diaphragm is slightly larger than the diameter of the optical fiber, which is used for the insertion and exit of the optical fiber, and fixes the optical fiber region between the two fiber Bragg gratings in the insertion hole.

[0015] The beneficial effects of adopting the above technical solution are as follows: The accelerometer uses an FBG as the sensing unit and is implemented by constructing a push-pull structure. Under the action of acceleration excitation, the periodic oscillation of the mass block causes the optical fibers on both sides of the push-pull structure to deform in opposite directions. When one side is in a stretched state, the other side is in a compressed state. The sensor's response to the acceleration signal is obtained by subtracting the wavelength offset of the two gratings. Compared with the structure of a single FBG, the push-pull structure can achieve a twofold increase in sensitivity.

[0016] The fiber grating array consists of two FBGs with different center wavelengths, and demodulation is performed using wavelength division multiplexing (WDM). It can simultaneously and independently track the wavelength shifts of the two FBGs, avoiding signal crosstalk issues when the grating spacing is small, and supporting the construction of multi-point sensor networks. This structure allows for switching of the fiber optic accelerometer's resonant frequency by changing the stiffness level provided by springs with different parameters. Increasing the spring stiffness leads to an increase in the resonant frequency, thus expanding the frequency detection range of the fiber optic accelerometer. However, increasing the stiffness level also reduces the deformation capability of the fiber optic accelerometer, thereby reducing its sensitivity and increasing the upper limit of acceleration amplitude measurement.

[0017] This invention eliminates the need for soldering or coupling any discrete optical components inside the sensor; all optical functions are achieved by an FBG array inscribed on an optical fiber. This offers the following advantages: simplified structure and reduced manufacturing difficulty; improved long-term stability and reliability; and facilitates sensor miniaturization and weight reduction. Attached Figure Description

[0018] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0019] Figure 1 This is a three-dimensional structural diagram of the accelerometer described in an embodiment of the present invention; Figure 2 This is a perspective structural diagram of the accelerometer described in an embodiment of the present invention; Figure 3 This is a perspective structural diagram of the accelerometer described in an embodiment of the present invention; Figure 4 This is a schematic diagram of the structure of a portion of the optical fiber in the accelerometer described in an embodiment of the present invention; Wherein: 11, optical fiber; 12, fastener; 13, outer shell; 21, elastic diaphragm; 22, first mass block; 23, second mass block; 24, first spring; 25, second spring; 31, first fiber Bragg grating; 32, second fiber Bragg grating. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0021] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0022] like Figures 1-3 As shown, this embodiment of the invention discloses a push-pull fiber optic accelerometer with crosstalk self-compensation based on FBG, including an optical fiber 11. Both ends of the optical fiber 11 pass through a housing 13 and are fixedly connected to the housing 13. An elastic diaphragm 21 is fixed inside the housing 13. A first mass block 22 is fixed to the upper side of the elastic diaphragm 21, and a second mass block 23 is fixed to the lower side of the elastic diaphragm 21. A first spring 24 is coaxially arranged outside the optical fiber 11 on the upper side of the first mass block 22, and a second spring 25 is coaxially arranged outside the optical fiber 11 on the lower side of the second mass block 23. The optical fiber 11 passes through the first mass block 22, the elastic diaphragm 21, and the second mass block 23 sequentially from top to bottom, and the middle region of the optical fiber is fixedly connected to the first mass block 22, the elastic diaphragm 21, and the second mass block 23. A first fiber Bragg grating 31 is formed on the optical fiber 11 located on the upper side of the first mass block 22, and a second fiber Bragg grating 32 is formed on the optical fiber 11 located on the lower side of the second mass block 23.

[0023] This application utilizes FBG (Fiber Bragg Grating) as the sensing unit, implemented through a push-pull structure. Under acceleration excitation, the periodic oscillation of the mass block causes opposite deformations in the optical fibers on both sides of the push-pull structure; when one side is stretched, the other is compressed. The sensor's response to the acceleration signal is obtained by subtracting the wavelength offsets of the two FBGs. Compared to a single FBG structure, the push-pull structure achieves twice the sensitivity. Furthermore, for temperature-induced wavelength offsets, both FBGs exhibit similar trends and degrees of wavelength offset, significantly suppressing temperature-induced crosstalk during the final response calculation. The stiffness of the designed fiber optic accelerometer consists of three parts: the stiffness of the elastic diaphragm, the additional stiffness introduced by the optical fiber, and the stiffness introduced by the spring. This structure can change the stiffness level provided by springs with different parameters, thereby switching the resonant frequency and adjusting the sensitivity of the fiber optic accelerometer. Increasing the spring stiffness is accompanied by an increase in the resonant frequency, thus expanding the frequency detection range of the fiber optic accelerometer; increasing the stiffness is accompanied by a decrease in sensitivity, thereby raising the upper limit of acceleration measurement. This application utilizes FBG as a sensing unit. As a mature technology, FBG has advantages such as good spectral performance, good long-term stability, long lifespan, and small size and light weight.

[0024] The optical fiber 11 described in this application can be a single-mode optical fiber, which serves as the optical signal transmission medium, runs through the entire interior of the sensor, and is fixed to the exterior of the housing 13 at both ends by a fastener 12.

[0025] The fixing member 12 can adopt a mechanical clamping or threaded pressing structure, located outside the housing 13, mechanically connected to the housing 13, clamping both ends of the optical fiber 11, ensuring the stability of the boundary conditions at both ends of the optical fiber, avoiding the influence of external disturbances on the measurement results, and supporting disassembly to replace the spring 22.

[0026] The outer shell 13 consists of an upper shell and a lower shell, made of metal or high-strength engineering plastic. The upper and lower shells clamp the edge of the elastic diaphragm 21, and the interior contains a mass block and a spring, providing overall mechanical support, encapsulating the internal sensitive structure, and protecting the optical components from external environmental interference.

[0027] The elastic diaphragm 21 is a thin sheet elastic structure with an optical fiber insertion hole in the center. Its edges are fixed between the upper and lower shells of the outer shell 13, and its center is fixedly connected to the mass block 23, providing flexible support and allowing the mass block 23 to move under vibration, while also introducing some system stiffness.

[0028] The first spring 24 and the second spring 25 are replaceable helical springs or disc springs, which are placed between the first mass block 22 and the upper cover of the outer shell 13 and the second mass block 23 and the lower bottom of the outer shell 13, arranged symmetrically to provide adjustable system stiffness. By replacing springs with different stiffnesses, the resonant frequency can be adjusted and the operating frequency band can be extended.

[0029] The mass block consists of two parts, a first mass block 22 and a second mass block 23, made of high-density metal material. The two parts are fixed to the upper and lower sides of the elastic diaphragm 21 respectively. An optical fiber insertion hole is opened in the center. Under the action of vibration, it generates inertial force, which drives the optical fiber 11 to generate periodic strain. It is the core mass element for vibration sensing.

[0030] like Figure 4 As shown, a first fiber Bragg grating 31 and a second fiber Bragg grating 32 are inscribed on the optical fiber 11. They are composed of two fiber gratings with different center wavelengths, such as 1545 nm and 1555 nm, and are demodulated using wavelength division multiplexing (WDM). The wavelength shift of the two FBGs can be tracked independently and simultaneously, avoiding signal crosstalk problems when the grating spacing is small. Furthermore, it supports the construction of multi-point sensor networks, ensuring accurate identification and tracking of the two fiber gratings.

[0031] The diameter of the optical fiber insertion hole at the center of the first mass block 22, the second mass block 23, and the elastic diaphragm 21 is slightly larger than the diameter of the optical fiber. This hole is used for the insertion and exit of the optical fiber 11 and to fix the middle area of ​​the two fiber gratings to the insertion hole.

[0032] By releasing the clamping force of the fixing member 12, the fixed state of the optical fiber 11 can be released, and the spring can be replaced by disassembling the outer shell, thereby achieving the effect of adjusting the stiffness level of the optical fiber accelerometer.

[0033] This invention employs a push-pull layout, dividing the mass block into upper and lower parts, fixed on both sides of an elastic diaphragm 21. An optical fiber 11 passes through the center of the mass block, and two fiber optic groups (FBGs) are located on the upper and lower sides of the mass block, respectively. Under vibration excitation, the mass block undergoes periodic displacement; when the mass block moves upward, the upper fiber is compressed and the lower fiber is stretched; when the mass block moves downward, the upper fiber is stretched and the lower fiber is compressed. This layout ensures that the two FBGs are always in opposite strain states, providing a basis for subsequent differential calculations.

[0034] The structural mechanical behavior of this fiber optic accelerometer can be analyzed using a "mass-spring-damping" model. Under a simple harmonic external force with amplitude F=ma, the force analysis of the mass block yields the following results: (1) In the formula, m represents the sum of the masses of the two masses, c represents the damping coefficient, k represents the spring stiffness, x represents the displacement of the mass relative to the lower shell, and ω represents the angular frequency of the excitation source. An increase in the sensor stiffness level reduces the accelerometer's ability to deform under vibration, thereby reducing the sensor's sensitivity.

[0035] A fiber Bragg grating is a narrowband reflector with a specific wavelength formed by the change in the refractive index of the fiber core. Its working principle mainly utilizes total internal reflection. By changing the grating pitch and its refractive index, the reflectivity, bandwidth, and spectral characteristics of the reflected light can be adjusted. When incident light propagates into the grating region, light satisfying the center wavelength condition will return, while the remaining light waves can continue to propagate until they are transmitted out. The peak value of the reflected wavelength is expressed as: (2) in, The effective refractive index of the optical fiber core. The period is the grating period. The fiber grating is typically arranged on a vibration pickup structure. Under acceleration, the vibration pickup device causes the fiber to deform, resulting in a change in the phase difference of the grating's center wavelength. Therefore, for a known fiber optic accelerometer, acceleration can be measured by capturing the wavelength shift, expressed as... (3) Where Δλ represents the phase difference change between the two gratings, and S is the sensitivity of the fiber optic accelerometer. However, besides the wavelength shift of the fiber grating caused by acceleration, temperature changes also lead to changes in the effective refractive index of the fiber core and the FBG period. Therefore, considering the effects of vibration and temperature, the fiber grating offset is expressed as: (4) in, The change in acceleration The proposed fiber optic accelerometer structure is a push-pull structure, with a fiber grating on each side of the diaphragm. Under acceleration, the mass block oscillates periodically, causing the fiber to deform. During this process, the fiber gratings at both ends undergo opposite deformations. When the upper fiber grating is stretched, the lower fiber grating is compressed, meaning the wavelength shift caused by acceleration occurs in opposite directions at both ends. Furthermore, the effect of temperature change is consistent in both fiber gratings; that is, the temperature-induced wavelength shift is in the same direction. Ideally, both should be equal. Therefore, the wavelength shifts of the two gratings can be expressed as follows: (5) To obtain the wavelength shift caused by acceleration, the wavelength shifts of the two fiber gratings need to be subtracted. Since the wavelength shift caused by acceleration occurs in opposite directions, the resulting wavelength shift is twice that of one side. Furthermore, this subtraction process can cancel out the wavelength shift caused by temperature, thereby eliminating the interference of temperature changes. The response of this fiber acceleration to the vibration signal can be approximately expressed as: (6) The stiffness of the system consists of three main parts, expressed as: (7) , , These represent the stiffness level of the elastic diaphragm, the stiffness introduced by the spring, and the additional stiffness introduced by the optical fiber, respectively. The resonant frequency of this fiber optic accelerometer can be expressed as: (8).

[0036] In this application, the center wavelength shifts of the two fiber Bragg gratings caused by vibration are opposite. The output response of the fiber optic accelerometer is obtained by subtracting the wavelength shifts of the upper and lower fiber Bragg gratings. Compared with a single fiber grating as a sensing unit, the push-pull structure can achieve twice the sensitivity.

[0037] Since the thermal expansion coefficient and thermo-optic coefficient of the optical fiber are constant, the wavelength shift of the two FBGs caused by temperature changes has the same trend and is similar in degree. In the process of obtaining the final response by subtraction, temperature-induced crosstalk can be significantly suppressed.

[0038] In this application, part of the stiffness of the accelerometer is contributed by the spring assembly. Changes in the spring parameters alter the stiffness level it provides, thereby changing the resonant frequency and resonant frequency of the entire sensor structure. An increase in the resonant frequency will effectively expand the frequency detection range of the fiber optic accelerometer, while a decrease in sensitivity will correspondingly expand the upper limit of the amplitude of acceleration that can be measured.

[0039] Compared with existing technologies, this invention utilizes FBG as the sensing unit, eliminating the need to weld optical components inside the sensor. This allows for a fully fiber-optic optical structure within the fiber optic accelerometer, facilitating sensor miniaturization and weight reduction, and lowering costs and manufacturing complexity. Based on wavelength division multiplexing (WDM), the push-pull structure significantly improves the sensitivity of the fiber optic accelerometer and significantly reduces the impact of temperature changes on the fiber optic sensor, thereby ensuring the accuracy of acceleration measurements.

[0040] Composed of two fiber gratings with different center wavelengths (e.g., 1545 nm and 1555 nm), it employs wavelength division multiplexing (WDM) demodulation technology. It can simultaneously and independently track the wavelength shift of the two FBGs; avoid signal crosstalk problems when the grating spacing is small; and support the construction of multi-point sensor networks.

[0041] Although the above embodiments have been described, those skilled in the art, once they understand the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the above descriptions are merely embodiments of the present invention and do not limit the scope of patent protection of the present invention. Any equivalent structural or procedural transformations made using the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A push-pull fiber optic accelerometer with crosstalk self-compensation based on FBG, characterized in that: Includes an optical fiber (11), both ends of which pass through a housing (13) and are fixedly connected to the housing (13). An elastic diaphragm (21) is fixed inside the housing (13). A first mass block (22) is fixed to the upper side of the elastic diaphragm (21), and a second mass block (23) is fixed to the lower side of the elastic diaphragm (21). A first spring (24) is coaxially arranged outside the optical fiber (11) on the upper side of the first mass block (22), and a second spring (24) is coaxially arranged outside the optical fiber (11) on the lower side of the second mass block (23). Two springs (25), the optical fiber (11) passes through the first mass block (22), the elastic diaphragm (21) and the second mass block (23) from top to bottom, and the middle region of the optical fiber is fixedly connected to the first mass block (22), the elastic diaphragm (21) and the second mass block (23). A first fiber Bragg grating (31) is formed on the optical fiber (11) located on the upper side of the first mass block (22), and a second fiber Bragg grating (32) is formed on the optical fiber (11) located on the lower side of the second mass block (23).

2. The push-pull fiber optic accelerometer with crosstalk self-compensation based on FBG as described in claim 1, characterized in that: Both ends of the optical fiber (11) are fixed to the outer shell (13) by a fastener (12).

3. The push-pull fiber optic accelerometer with crosstalk self-compensation based on FBG as described in claim 1, characterized in that: The outer shell (13) includes an upper shell and a lower shell, which are made of metal or high-strength engineering plastic. The upper and lower shells clamp the edge of the elastic diaphragm (21) and contain a mass block and a spring inside, providing overall mechanical support for it.

4. The push-pull fiber optic accelerometer with crosstalk self-compensation based on FBG as described in claim 1, characterized in that: The elastic diaphragm (21) is a thin sheet elastic structure with an optical fiber insertion hole in its center. Its edge is fixed between the upper and lower shells of the outer shell (13), and its center is fixedly connected to the first mass block (22) and the second mass block (23) to provide flexible support for them, allowing the first mass block (22) and the second mass block (23) to generate displacement under vibration, while introducing part of the system stiffness.

5. The push-pull fiber optic accelerometer with crosstalk self-compensation based on FBG as described in claim 1, characterized in that: The first spring (24) and the second spring (25) are replaceable helical springs or disc springs, which are placed between the first mass block (22) and the upper cover of the outer shell (13) and the second mass block (23) and the lower bottom of the outer shell (13), arranged symmetrically to provide adjustable system stiffness. The resonant frequency can be adjusted by replacing springs with different stiffnesses.

6. The push-pull fiber optic accelerometer with crosstalk self-compensation based on FBG as described in claim 1, characterized in that: The first mass block (22) and the second mass block (23) are made of high-density metal material, and have optical fiber insertion holes in their centers for optical fibers (11) to pass through. Under vibration, they generate inertial force, which drives the optical fiber (11) to generate periodic strain.

7. The push-pull fiber optic accelerometer with crosstalk self-compensation based on FBG as described in claim 1, characterized in that: The first fiber Bragg grating (31) and the second fiber Bragg grating (32) are inscribed on the optical fiber (11) and are composed of two fiber gratings with different center wavelengths. They are demodulated using wavelength division multiplexing technology.

8. The push-pull fiber optic accelerometer with crosstalk self-compensation based on FBG as described in claim 1, characterized in that: The diameter of the fiber optic insertion hole at the center of the first mass block (22), the second mass block (23), and the elastic diaphragm (21) is slightly larger than the diameter of the fiber (11), which is used for the insertion and exit of the fiber (11) and to fix the fiber region between the two fiber Bragg gratings in the fiber optic insertion hole.

9. The push-pull fiber optic accelerometer with crosstalk self-compensation based on FBG as described in claim 1, characterized in that: Under vibration excitation, the mass block generates periodic displacement; when the mass block moves upward, the upper optical fiber is compressed and the lower optical fiber is stretched. As the mass block moves downwards, the upper optical fiber is stretched and the lower optical fiber is compressed.

10. The push-pull fiber optic accelerometer with crosstalk self-compensation based on FBG as described in claim 1, characterized in that: The method for calculating the resonant frequency of the fiber optic accelerometer includes: Under the action of a simple harmonic external force with amplitude F=ma, the force analysis of the mass block yields the following results: （1） In the formula, m represents the sum of the masses of the two mass blocks, c represents the damping coefficient, k represents the spring stiffness, x represents the displacement of the mass block relative to the lower shell, and ω represents the angular frequency of the excitation source. When the incident light propagates into the grating region, the light that meets the center wavelength condition will return, and the remaining light waves can continue to propagate until they are transmitted out. The peak value of the reflected wavelength is represented as: (2) in, Let Λ be the effective refractive index of the fiber core and Λ be the grating period; acceleration is measured by capturing the wavelength shift, expressed as: (3) Where Δλ is the phase difference change between the two gratings, and S is the sensitivity of the fiber optic accelerometer; the offset of the fiber optic grating is expressed as: (4) Where da is the change in acceleration and dT is the change in temperature; The wavelength shifts of the two gratings are expressed as follows: (5) This push-pull fiber optic accelerometer obtains its response to acceleration signals by subtracting the wavelength offsets of the two gratings, thus doubling its sensitivity. This subtraction process cancels out temperature-induced wavelength offsets, thereby eliminating interference from temperature changes. The fiber optic accelerometer's response to vibration signals can be approximated as follows: （6） The stiffness of a system mainly consists of three parts, expressed as: （7） , , Given the stiffness level of the elastic diaphragm, the stiffness introduced by the spring, and the additional stiffness introduced by the optical fiber, the resonant frequency of this fiber optic accelerometer can be expressed as: （8）。

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