Low-frequency FBG acceleration sensor based on symmetric cantilever beam and manufacturing method thereof

Abstract

The present invention discloses a low-frequency FBG acceleration sensor based on a symmetric cantilever beam and a manufacturing method thereof, relating to the technical field of optical fiber sensing. The acceleration sensor includes: a cantilever beam, a mass block, and an FBG. First, according to the mechanical model of the sensor structure, expressions for the sensitivity and natural frequency of the sensor are derived; then, the structural parameters of the sensor are optimized, and static stress and modal analysis of the sensor are performed using ANSYS Workbench; finally, the sensor is manufactured according to the analysis results. The natural frequency of the sensor is 72 Hz, the sensitivity is 681.7 pm / g, the anti-lateral interference degree is less than 4.9%, and the volume is only 6.48 cm3, which can be used for real-time monitoring of low-frequency weak vibration signals below 50 Hz.

Description

Technical Field

[0001] The present invention relates to the technical field of fiber optic sensing, and particularly to a low-frequency FBG accelerometer based on a symmetric cantilever beam and a manufacturing method thereof. Background Art

[0002] The statements in this section merely provide background technical information related to the present invention and do not necessarily constitute prior art.

[0003] Real-time monitoring of low-frequency vibrations is of great significance for carrying out monitoring research in fields such as engineering seismology, bridge dams, and oil and gas exploration. In recent years, accelerometers, as one of the key devices for dynamically collecting vibration signals, have been widely used in the monitoring of large structures and environmental safety. However, traditional electronic accelerometers have limited application ranges due to their susceptibility to electromagnetic interference. Fiber Bragg gratings are optical sensing elements with advantages such as small size, high stability, electromagnetic interference resistance, and high measurement accuracy, enabling them to replace electronic accelerometers in fields such as seismic wave detection, large structure health monitoring, and oil and gas exploration, and improving the ability of remote online monitoring in harsh environments.

[0004] In recent years, extensive and in-depth research has been conducted on low-frequency fiber Bragg grating (FBG) accelerometers at home and abroad, such as flexible hinge type, diaphragm type, and cantilever beam type. Mohd.M.Khan et al. designed a temperature self-compensated FBG accelerometer based on an improved cantilever beam. The mass block and the cantilever beam structure were integrally designed, resulting in a volume of approximately 25 cm 3 , and two fiber Bragg gratings were pasted on the strain-sensitive area of the beam, effectively improving the sensitivity of the sensor. Kok-Sing Lim et al. designed a horizontal cantilever beam fiber Bragg grating accelerometer with a magnetic damper. The sensor used a magnet as the mass block, which formed a magnetic damper with a U-shaped groove. The FBG was pasted on the surface of the cantilever beam, and the overall structure volume was approximately 70 cm 3Jianzhi Li et al. proposed an FBG low-frequency acceleration sensor based on a rotating support beam. The main structure of this sensor is compact and simple, easy to install and has good low-frequency characteristics. Experiments show that the working frequency range of this sensor is 0.5 - 20 Hz, and the sensitivity is as high as 1495.2 pm / g, but the mass block is relatively heavy. Qinpeng Liu et al. proposed an FBG acceleration sensor with a double-bending cantilever beam. The structure of this sensor mainly consists of two bending cantilever beams and an inertial mass. The results show that the sensitivity of this sensor is 651.0 - 850.5 pm / g, and the corresponding fluctuation within the range of 1 - 70 Hz is less than 2.2 dB. However, the mass of only the mass block of this sensor reaches 57.6 g, making the overall size relatively large. Although a series of fruitful results have been achieved in low-frequency FBG acceleration sensors in recent years, low sensitivity and large volume have always been the bottleneck problems hindering the practical engineering application of low-frequency FBG acceleration sensors. Summary of the Invention

[0005] Aiming at the problems of low sensitivity and large volume of existing low-frequency FBG acceleration sensors, the purpose of the present invention is to provide a low-frequency FBG acceleration sensor based on a symmetric cantilever beam and its manufacturing method. According to the mechanical model of the sensor structure, the expressions of the sensitivity and natural frequency of the sensor are derived; then the structural parameters of the sensor are optimized, and static stress and modal analysis of the sensor are carried out using ANSYS Workbench; finally, the sensor is manufactured according to the analysis results.

[0006] To achieve the above purpose, the present invention is realized through the following technical solutions:

[0007] The first aspect of the present disclosure provides a low-frequency FBG acceleration sensor based on a symmetric cantilever beam, including: a housing, a mass block, a sensing element, and two FBGs. The housing is divided into two parts, namely an upper housing and a lower housing arranged up and down. There are two mass blocks, which are placed up and down and are exactly the same. The two mass blocks are symmetrically placed on the upper and lower surfaces of the cantilever beam respectively, constituting a spring-mass inertial vibration system. The cantilever beam is embedded in the center of the sensor, and the FBGs are symmetrically pasted on the outer surface of the mass block.

[0008] Furthermore, the upper housing is designed with 6 bolt holes for assembling and cooperating with the sensing element and the lower housing; the upper housing is designed in the shape of a pillar with a cover. The four pillars leave enough space between the top cover part of the upper housing and the upper mass block for pasting two FBGs, and the FBGs are pasted on the edge of the top cover.

[0009] Furthermore, the lower housing is designed with 6 screw holes for fixing with the upper housing and the sensing element, and a screw hole is designed at the lowermost end for fixing with the vibration table, so that the mass block swings up and down while keeping the outer shell unchanged during vibration, and the signal changes of the FBGs are recorded.

[0010] Furthermore, the sensing element is designed with four cantilever beams and four wing spans. One screw hole is provided on each of two wing spans, and two screw holes are provided on each of the other two wing spans, all of which are used for assembling and fixing with the upper and lower shells. Two screw holes are designed in the central part of the sensing element for fixing with the upper and lower mass blocks. Moreover, the sensing element is designed with a hollow structure. While the cantilever beams are well preserved, the remaining area in the middle is made to have the same upper and lower surface areas as the upper and lower mass blocks, which is for better force application and assembly.

[0011] Furthermore, two screw holes are respectively designed on the two mass blocks for assembling the two mass blocks with the sensing element, so that the two mass blocks are located at the central position inside the shell and have a certain distance from the inside of the shell without any contact.

[0012] The second aspect of the present disclosure provides a manufacturing method of a low-frequency FBG acceleration sensor based on symmetric cantilever beams, including the following steps:

[0013] According to the mechanical model of the sensor structure, the expressions of the sensitivity and natural frequency of the sensor are derived;

[0014] Optimize the structural parameters of the sensor;

[0015] Manufacture the acceleration sensor based on the optimized structural parameters.

[0016] Furthermore, the mechanical model of the sensor structure is:

[0017]

[0018] where λ is the central wavelength of the FBG, P e ≈0.22 is the elasto-optic coefficient, ε is the strain generated by the FBG, Δλ is the wavelength drift of the FBG caused by the strain; F is the inertial force received by the mass block, E is the elastic modulus of the cantilever beam material; H, L, and B are the thickness, length, and width of the cantilever beam in sequence.

[0019] Even further, the sensitivity expression is:

[0020]

[0021] where S is the sensitivity and M is the mass of the sensor mass block.

[0022] Even further, the expression of the natural frequency of the sensor is:

[0023]

[0024] where F0 is the natural frequency of the sensor and ω0 is the natural angular frequency.

[0025] Furthermore, the optimized structural parameters are as follows: the material of the cantilever beam is 65Mn spring steel, with Young's modulus E = 201 GPa and Poisson's ratio μ = 0.28. The material of the mass block is H62 brass, and the mass of a single mass block is 0.7 g.

[0026] The beneficial effects of the above embodiments of the present invention are as follows:

[0027] First, based on the mechanical model of the sensor structure, the present invention derives the expressions for the sensitivity and natural frequency of the sensor; then, it optimizes the structural parameters of the sensor and uses ANSYS Workbench to perform static stress and modal analysis on the sensor; finally, it manufactures the sensor according to the analysis results and studies the performance of the sensor through experiments. The natural frequency of this sensor is 72 Hz, the sensitivity is 681.7 pm / g, the anti-lateral interference degree is less than 4.9%, and the volume is only 6.48 cm3, which can be used for real-time monitoring of low-frequency weak vibration signals below 50 Hz.

[0028] The low-frequency FBG acceleration sensor based on a symmetric cantilever beam in the present invention is small in volume, light in weight, strong in stability and high in sensitivity, solving the problems of low sensitivity and large volume of existing low-frequency FBG acceleration sensors, and laying a solid technical foundation for low-frequency vibration measurement applications. Description of the Drawings

[0029] The specification drawings forming a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention.

[0030] Figure 1 It is a cross-sectional view of the overall structure of the low-frequency FBG acceleration sensor in Embodiment 1 of the present invention;

[0031] Figure 2 It is a structural diagram of the sensitive element of the low-frequency FBG acceleration sensor in Embodiment 1 of the present invention;

[0032] Figure 3 It is a three-dimensional view of the overall structure of the low-frequency FBG acceleration sensor in Embodiment 1 of the present invention;

[0033] Figure 4(a) is a front view of the equivalent model of the low-frequency FBG acceleration sensor in Embodiment 2 of the present invention;

[0034] Figure 4(b) is a top view of the equivalent model of the low-frequency FBG acceleration sensor in Embodiment 2 of the present invention;

[0035] Figure 5 It is a relationship curve graph of the sensitivity and natural frequency of the low-frequency FBG acceleration sensor in Embodiment 2 of the present invention changing with the length of the cantilever beam;

[0036] Figure 6 It is the relationship curve graph of the sensitivity and natural frequency of the low-frequency FBG acceleration sensor in the second embodiment of the present invention varying with the width of the cantilever beam;

[0037] Figure 7 It is the relationship curve graph of the sensitivity and natural frequency of the low-frequency FBG acceleration sensor in the second embodiment of the present invention varying with the thickness of the cantilever beam;

[0038] Figure 8 It is the reflection spectrum graph of the low-frequency FBG acceleration sensor in the second embodiment of the present invention;

[0039] Figure 9 It is the schematic diagram of the low-frequency vibration experimental test platform in the second embodiment of the present invention;

[0040] Figure 10 It is the amplitude-frequency response curve graph of the low-frequency FBG acceleration sensor in the second embodiment of the present invention;

[0041] Figure 11(a) is the curve graph of the wavelength drift varying with acceleration of the low-frequency FBG acceleration sensor in the second embodiment of the present invention under the linearity of 20 Hz;

[0042] Figure 11(b) is the curve graph of the wavelength drift varying with acceleration of the low-frequency FBG acceleration sensor in the second embodiment of the present invention under the linearity of 40 Hz;

[0043] Figure 12 It is the linear response curve graph of the low-frequency FBG acceleration sensor in the second embodiment of the present invention;

[0044] Figure 13 It is the lateral anti-interference characteristic curve graph of the low-frequency FBG acceleration sensor in the second embodiment of the present invention;

[0045] Figure 14 It is the impact response characteristic curve graph of the low-frequency FBG acceleration sensor in the second embodiment of the present invention;

[0046] Wherein, 1. housing, 2. FBG, 3. mass block, 4. cantilever beam, 5. wing. Detailed implementation manners

[0047] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further descriptions of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0048] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof;

[0049] Embodiment 1:

[0050] Embodiment 1 of the present disclosure provides a low-frequency FBG acceleration sensor based on a symmetric cantilever beam. As Figure 1-2 shown, it includes: a housing 1, a mass block 3, a sensing element, and two fiber Bragg gratings FBG 2. The housing 1 is divided into two parts, namely an upper housing and a lower housing arranged up and down, and the material of both is 304 stainless steel. The mass block 3 is composed of two identical parts placed one above the other. Except for the fiber Bragg grating being pasted to the housing 1 and the upper mass block 3 with UV glue for fixation, the assembly of the remaining components is fixed by bolts.

[0051] As a further technical solution, the upper housing is designed with 6 bolt holes for assembling and cooperating with the sensing element and the lower housing. The upper housing is designed in the shape of a pillar with a cover. The function of the four pillars is to leave enough space between the top cover part of the upper housing and the upper mass block for pasting two optical fibers, so that the grating parts of the two optical fibers are suspended in the middle without affecting the measured data, and it is also convenient for the work during fixed cooperation. The edge of the top cover is used for pasting the optical fibers.

[0052] As a further technical solution, the lower housing is also designed with 6 screw holes for facilitating fixation with the upper housing and the sensing element, and a screw hole is designed at the lowermost end for fixation with a vibration table, so that the mass block swings up and down while keeping the outer housing unchanged during vibration, and the signal change of the fiber Bragg grating is recorded.

[0053] As a further technical solution, the sensing element is designed with four cantilever beams 4 and four wingspans 5. One screw hole is respectively provided on two of the wingspans 5, and two screw holes are respectively provided on the other two wingspans 5, all for assembling and fixing with the upper and lower housings. The four cantilever beams 4 are important parts for bearing force, and the length, width, and height of the cantilever beams 4 have different effects on the performance of the sensor. Two screw holes are designed in the central part of the sensing element for fixing with the upper and lower mass blocks 3, and the sensing element is designed with a hollow-out structure. While keeping the cantilever beams intact, the area left in the middle is the same as the upper and lower surface areas of the upper and lower mass blocks, for better force bearing and assembly.

[0054] As a further technical solution, the upper and lower mass blocks 3 are respectively designed with two screw holes for assembling the two mass blocks 3 with the sensing element, so that the two mass blocks 3 are located at the central position inside the housing and have a certain distance from the inside of the housing without any contact.

[0055] The working principle of the sensor is as follows: After all components of the sensor are assembled, the sensor is fixed to the vibration table. Due to the existence of the cantilever beam inside, the two mass blocks 3 and the sensing element form a spring-mass inertial vibration system of the acceleration sensor. When the sensor is excited by external vibration, the mass block 3 at the free end will vibrate vertically up and down with the inertial force, while the housing 1 part remains unchanged. Then the upper end of the fiber Bragg grating is fixed and unchanged, and the lower end changes with the up and down swing of the mass block, so that the central wavelength of the fiber Bragg grating changes to obtain the required data.

[0056] Preferably, the material of the cantilever beam selected in the manufacture of the sensor is 65Mn spring steel. The length L of the cantilever beam is 6.5 mm, the width B of the cantilever beam is 0.6 mm, and the thickness H of the cantilever beam is 0.1 mm. The effective length l of the optical fiber is 5 mm, the outer diameter D of the optical fiber is 0.125 mm, and the Young's modulus E1 of the optical fiber is 72.9×10 9 Pa. The central wavelength λ B of the FBG is 1560 nm, the cross-sectional area A f of the light is 1.23×10-8 m2, and the effective elasto-optic coefficient P e of the optical fiber is 0.22. The Young's modulus E of the cantilever beam spring steel is 201 GPa, the Poisson's ratio μ is 0.28, the material of the mass block is H62 brass, and the calculated mass of a single mass block is only 0.7 g.

[0057] The working principle of the FBG acceleration sensor in this embodiment is as follows:

[0058] As Figure 1 can be seen, the cantilever beams on both sides of the sensor are strictly symmetrical, clamping the mass block at the center of the sensor to improve its axial sensitivity. When vibrating at a low frequency, the mass block at the free end of the sensor will vibrate vertically with the inertial force, converting the vibration displacement amplitude into the axial strain value of the FBG, thereby changing the central wavelength of the reflected spectrum in the FBG. Thus, a mathematical relationship between the drift amount of the central wavelength of the reflected spectrum and the acceleration can be established, and the magnitude of the acceleration can be obtained by measuring the drift amount of the central wavelength of the reflected spectrum, realizing low-frequency vibration measurement.

[0059] Embodiment 2:

[0060] The present disclosure provides a method for manufacturing a low-frequency FBG acceleration sensor based on a symmetric cantilever beam, including the following steps:

[0061] According to the mechanical model of the sensor structure, the expressions for the sensitivity and natural frequency of the sensor are derived.

[0062] Preferably, the mechanical model of the sensor structure is obtained based on the strain generated by the forced vibration of the mass block on the cantilever beam and the change in the central wavelength caused by the longitudinal deformation of the fiber Bragg grating. The specific process is as follows:

[0063] Since the sensor is a symmetric structure and the cantilever beam is on the outside of the mass block, the sensor can be equivalently regarded as a second-order single-degree-of-freedom forced vibration model composed of a cantilever beam and a mass block, as shown in Figures 4(a) and 4(b).

[0064] H, L, and B are the thickness, length, and width of the cantilever beam in sequence, M is the mass of the sensor mass block, and y is the micro-displacement generated by the vibration. Among them, the value of the equivalent elastic stiffness K of the cantilever beam mainly depends on the material and size of the processed cantilever beam and plays an important role in determining the sensitivity and natural frequency of the sensor. In the coordinate system shown in Figure 4(a), the motion equation of the mass block is:

[0065]

[0066] In the formula, M is the mass of the mass block, y is the absolute displacement of the mass block, γ is the damping constant of the vibration system, K is the equivalent elastic coefficient of the vibration system, and a is the acceleration of the vibration signal received by the sensor.

[0067] The strain ε generated by the forced vibration of the mass block on the cantilever beam is:

[0068]

[0069] In the formula, F is the inertial force received by the mass block, and E is the elastic modulus of the cantilever beam material. Since the stretching or compression of the FBG will change the period of the core refractive index, and thus cause the reflection peak to shift. Therefore, the fiber Bragg grating pasted between the fixed support and the mass block will be longitudinally deformed, thereby causing a change in the central wavelength, and its change amount is:

[0070] Δλ=λ(1 - P e )ε (3)

[0071] In the formula, λ is the central wavelength of the FBG, P e ≈0.22 is the elasto-optic coefficient, ε is the strain generated by the FBG, and Δλ is the wavelength drift amount of the FBG caused by the strain.

[0072] Since the cantilever beam and the FBG are in the same plane, the deformation generated by the cantilever beam can be approximately regarded as the deformation of the FBG. Substituting Equation (2) into Equation (3) gives:

[0073]

[0074] Equation (4) shows the mathematical model between the measured acceleration a and the wavelength drift Δλ of the FBG reflection spectrum. Therefore, the strain of the cantilever beam can characterize the magnitude of the acceleration, and there is a linear relationship between the acceleration a and the wavelength drift Δλ of the FBG reflection spectrum. Therefore, the measured acceleration can be obtained by measuring the wavelength drift of the FBG reflection spectrum.

[0075] In order to better measure low-frequency vibration signals, the sensor needs to have better sensitivity in the flat area of the frequency band. By combining Equation (4) with F = ma and S = Δλ / a, the sensitivity of the acceleration sensor can be obtained as:

[0076]

[0077] It can be seen from Equation (5) that the magnitude of the sensor sensitivity is related to the magnitude of the strain generated when the sensor sensitive element is forced to vibrate. The sensitivity referred to in this article is the peak-to-peak value, that is, 2S.

[0078] The measurable frequency band range of the vibration signal to be measured is determined by the natural frequency of the FBG acceleration sensor. The natural frequency of the sensor is:

[0079]

[0080] Among them, F0 is the natural frequency of the sensor, and ω0 is the natural angular frequency. It can be seen from Equation (5) and Equation (6) that once the structural parameters of the cantilever beam are determined, its natural frequency and sensitivity are both determined, and the length of the encapsulated optical fiber is also limited. Therefore, it is necessary to optimize the design of the cantilever beam structure to balance the natural frequency, sensitivity and sensor volume.

[0081] Optimize the structural parameters of the sensor. The specific process is as follows:

[0082] Due to its low frequency, long duration, large influence range and difficulty to avoid, engineering vibration causes relatively large direct and indirect hazards to large buildings. In order to enable a small-volume FBG acceleration sensor to effectively capture low-frequency vibration signals, it is necessary to optimize the design of the cantilever beam structure, and try to find a suitable value among reducing the volume, increasing the sensitivity S and reducing the natural frequency F0 as much as possible to ensure high low-frequency response characteristics under the condition of a small-volume sensor. From the results of theoretical analysis, it can be seen that the length L, width B and thickness H of the cantilever beam are the key parameters affecting the sensor sensitivity S and natural frequency F0. Therefore, with other parameters fixed, Solidworks is used to model cantilever beams of different sizes, and ANSYS Workbench is used for static stress and modal simulation analysis to study the effects of these three key parameters on the sensor sensitivity and natural frequency respectively.

[0083] First, due to the size of the volume-sensitive element of the probe, the size of the sensitive element is changed by reducing the size of a single cantilever beam and increasing the number of cantilever beams. Since the sensor structure is centrosymmetric, taking a single cantilever beam as an example, the influence of the change of the cantilever beam length L within 5 - 8 mm on the sensor sensitivity S and the natural frequency F0 is discussed. The simulation results and their fitting curves are as Figure 5 shown. When the cantilever beam L changes within a small range, the sensor sensitivity is positively correlated with the cantilever beam length, while the natural frequency is negatively correlated with the cantilever beam length. Considering that the design goal of this sensor is to reduce the sensor volume and collect engineering vibration signals, the sensor natural frequency F0 is selected to be greater than 60 Hz. Moreover, the sensor sensitivity S should not be too low. Therefore, the cantilever beam length can be selected as 6 mm < L < 7 mm.

[0084] Secondly, the influence of the change of the cantilever beam width B within 0.5 - 1 mm on the sensor sensitivity S and the natural frequency F0 is analyzed. The simulation results and their fitting curves are as Figure 6 shown. The sensor sensitivity S decreases with the increase of the cantilever beam width B, and the natural frequency F0 increases with the increase of the cantilever beam width B. To obtain a higher sensitivity, the cantilever beam width B should be as small as possible. Considering the material selection of the cantilever beam and the limitations of actual processing conditions, B = 0.6 mm can be taken.

[0085] Finally, the influence of the change of the cantilever beam height H within 0.1 - 1 mm on the sensor sensitivity S and the natural frequency F0 is considered. The simulation results and their fitting curves are as Figure 7 shown. The sensor sensitivity S decreases with the increase of the cantilever beam thickness H, and the natural frequency F0 increases with the increase of the cantilever beam thickness H. When H ≤ 0.2 mm, with the increase of H, the downward trend of the sensitivity S curve is obvious; when 0.2 mm < B < 0.5 mm, the downward trend tends to be stable. To meet the requirements of the sensor for sensitivity and natural frequency and facilitate the manufacture and experimental operation of the sensor, H = 0.1 mm is taken.

[0086] An acceleration sensor is manufactured based on the optimized structural parameters.

[0087] By analyzing the influence of three key parameters on the sensor sensitivity and natural frequency, considering material selection and processing conditions, the structural parameters of the manufactured sensor are shown in Table 1:

[0088] Table 1. Sensor Structural Parameter Table

[0089] Structural parameter Numerical value Mass m of a single mass block 0.7g Length L of the cantilever beam 6.5 mm Width B of the cantilever beam 0.6 mm Thickness H of the cantilever beam 0.1 mm <![CDATA[Young's modulus E1 of optical fiber]]> <![CDATA[72.9×10 9 Pa]]> Effective length l of the optical fiber 5 mm Outer diameter D of the optical fiber 0.125 mm <![CDATA[FBG central wavelength λ B > 1560 nm <![CDATA[Cross-sectional area A of the optical fiber f > <![CDATA[1.23×10 -8 m 2 > <![CDATA[Effective elasto-optic coefficient P of optical fiber e > 0.22

[0090] Preferably, the cantilever beam material selected in the manufacture of the sensor is 65Mn spring steel, with a Young's modulus E = 201 GPa and a Poisson's ratio μ = 0.28. Limited by the volume and processing cost of the sensor, the mass block is required to have a small volume and a large mass. Therefore, H62 brass with a relatively large density is selected as the material of the mass block. It is calculated that the mass of a single mass block is only 0.7 g.

[0091] In order to further study the dynamic response characteristics of the symmetric cantilever beam miniaturized low-frequency FBG acceleration sensor, the finite element simulation software ANSYS Workbench is used to perform static stress and modal simulations on the sensor. The mass block, cantilever beam, and FBG constitute the measurement element of the sensor and are the main components affecting its dynamic characteristics. According to the size parameters provided in Table 1, the Solidworks software is used to perform solid modeling on the sensor, and the modeling results are imported into the ANSYS Workbench software for simulation analysis.

[0092] First, a fixed constraint is applied to the bottom of the sensor model, the connection between each component is set as a fully bonded support constraint, and an external load of the standard earth gravity acceleration g is applied to the entire sensor. Through hexahedral mesh division, a static stress simulation analysis of the model is carried out to obtain the strain nephogram of the sensor model. The deformation generated at the free end of the sensor is the largest and gradually decreases towards the fixed end. The maximum deformation at the free end is approximately 0.047 mm.

[0093] Based on the static stress analysis results, a modal analysis is performed on the sensor model. The first two-order modal natural frequencies are 73.19 Hz and 86.36 Hz respectively, and the main vibration mode diagrams of the first two orders are extracted. The first-order mode of the sensor is a simple harmonic vibration, indicating that the sensor model vibrates along the Y-axis under the action of an external excitation. The second-order mode of the sensor is a swinging vibration mode, indicating that the sensor model swings along the Z-axis under the action of an external excitation. From the ANSYS simulation results, it can be seen that the difference between the first and second-order natural frequencies of this sensor is relatively small, indicating that the ability of this structure to resist cross-interference is weak, especially the vibration excitation in the X-axis direction may pose a risk of cross-interference to the sensor.

[0094] In order to further verify the test performance of the sensor, the sensor in this embodiment is experimentally tested:

[0095] The FBG used in the sensor is two optical fiber Bragg gratings of the same batch, with a central wavelength of 1550.2 nm, a reflectivity ≥ 90%, and a grating region length of 5 mm. When the sensor is packaged, a certain prestress is applied to it to cause a drift in its central wavelength. The reflected spectrum diagram after packaging is as Figure 8 shown.

[0096] The low-frequency vibration experimental test platform is as Figure 9As shown, the signal function generator uses the DG1000Z model of Protek Precision Electronics Co., Ltd., which has 160 arbitrary waveforms built-in and a sampling rate of 200 MSa / s; the signal amplifier uses the ZT-5702 model of Yangzhou Zhenzhong Testing Technology Co., Ltd., with a frequency response range of 0 - 10 kHz, a signal-to-noise ratio greater than 80 dB, and can amplify the function signal when paired with the signal function generator. The vibration table also selects the ZT-JZ-200T standard vibration table of Yangzhou Zhenzhong Testing Technology Co., Ltd., with an excitation frequency range of DC - 5 kHz, meeting the needs of low-frequency vibration testing. This vibration table has a standard accelerometer built-in for calibrating the FBG accelerometer. The acquisition and analysis of the output signal of the standard accelerometer use the ZT-U8204I type dynamic signal analyzer of Yangzhou Zhenzhong Testing Technology Co., Ltd., which has 4-channel high-precision A / D and a sampling frequency of 128 kHz. The fiber Bragg grating demodulator uses the MWY-FBG-CS800 model of Beijing Weiyun Technology Co., Ltd., with a maximum sampling frequency of up to 1 kHz, and a laser light source built-in. The light wave emitted by it is transmitted through the optical fiber to the double-tilted cantilever beam low-frequency accelerometer on the vibration table system. At the same time, the fiber Bragg grating demodulator receives the reflected spectrum of the FBG and completes spectral analysis and data acquisition inside it. Due to the strain and temperature cross-sensitivity characteristics of the FBG, the entire experiment is carried out at a room temperature of 27°C. During the experiment, the temperature changes slowly, and the influence of ambient temperature fluctuations on the measurement results can be ignored. Use this platform to study the performance of the sensor such as amplitude-frequency response characteristics, linear response characteristics, anti-lateral interference characteristics, and impulse response characteristics, and obtain the actual performance parameters of the sensor.

[0097] First, in the experiment, adjust the signal generator to make the vibration table output a sine excitation signal with an acceleration amplitude of 0.1g (g = 10 m / s²), and conduct a sweep frequency test on the sensor. According to the results, the sweep frequency range is selected as 1 - 100 Hz, and the step size is 10 Hz. Determine the approximate range of the natural frequency of the sensor, and then repeat the experiment with a step size of 2 Hz. During the experiment, record the central wavelength offset of the FBG at different frequencies in real time. After processing the experimental data, obtain the amplitude-frequency characteristic curve of the sensor, as Figure 10 shown. The natural frequency of the sensor is approximately 72 Hz, and the response is relatively flat in the frequency range of 8 - 52 Hz. The experimental measurement value of the natural frequency is close to the simulation calculation value, and the small error may be due to the too long vibration time during the experiment, resulting in creep of some of the cured ultraviolet glue.

[0098] To obtain the sensitivity characteristics of the sensor under different frequency excitations, when the vibration frequencies are 20 Hz and 40 Hz respectively, adjust the signal generator to increase the acceleration amplitude of the excitation signal from 0.1 g to 0.6 g with a step size of 0.1 g. Record the wavelength drift of the sensor. Each group of experiments is repeated three times to obtain the curves of wavelength drift versus acceleration at different frequencies, as shown in Figures 11(a) and 11(b). When the frequencies of the excitation signals are 20 Hz and 40 Hz respectively, the acceleration measurement sensitivities of the sensor are 678.8 pm / g and 684.7 pm / g respectively, and the repeatability errors of the sensor are 1.58% and 2.31% respectively. It can be seen that the sensitivities at the two frequencies are not very different, and individual points deviate, which may be related to the stability of the demodulation system or may be affected by external signals.

[0099] The sources of engineering vibration are mostly point vibration sources and line vibration sources, and their vibration signal amplitudes are small and decay quickly. Therefore, it is necessary to discuss the magnitude of the minimum acceleration amplitude that the sensor can measure. Through experiments, it is found that when the sensor is static on the vibration isolation platform, the central wavelength drift of its reflection spectrum is about 2.4 pm, as Figure 12 shown. Considering the above-mentioned sensor sensitivity and possible errors, the minimum acceleration amplitude that the sensor can measure is calculated to be about 0.03 g.

[0100] The dynamic range is an important parameter index of the sensor. For the FBG acceleration sensor, the dynamic range D R is related to the maximum wavelength drift amount λ max and the minimum wavelength drift amount λ min that the sensor can detect, and its relational expression is:

[0101]

[0102] The maximum wavelength drift value λ max is mainly restricted by the elastic deformation range of the sensor elastic element and the prestress of the grating, and the minimum wavelength drift value λ min is mainly determined by the resolution of the FBG demodulation system. In the sensitivity test experiment of this sensor, the maximum wavelength drift amount output by the sensor is 415 pm, and the resolution of the FBG demodulator used in the experiment is 0.1 pm. It can be calculated that the dynamic range of the sensor can reach 72 dB, which basically meets the requirements of the dynamic range of Class C acceleration sensors in the Advanced National Seismic System (ANSS) of the United States National Seismic Monitoring Network.

[0103] The anti-lateral interference characteristic is also an important performance index for a single-degree-of-freedom acceleration sensor. In the structural design of this sensor, the anti-interference ability of the sensor has been improved as much as possible. For example, the cantilever beam adopts a small and multi-piece design scheme, and the mass block is clamped at the center of the sensor to ensure that the deformation of the FBG is reduced, so as to achieve the purpose of weakening the lateral crosstalk. In the experimental test, the sensor is rotated 90° and installed longitudinally along the sensor, so that the main vibration direction of the sensor is perpendicular to the vibration direction of the vibration table for sensitivity testing, as Figure 13 shown. Under the action of the same excitation frequency and amplitude, the wavelength drift of the sensor in the Y-axis direction is about 3.2 pm, the wavelength drift in the Z-axis direction is about 7 pm, and the wavelength drift in the X-axis direction is about 16 pm. It shows that the lateral interference degree of the sensor in the Z-axis direction is less than 2.2%, and the lateral interference degree in the X-axis direction is less than 4.9%, which is the same as the modal simulation result, indicating that the sensor has good anti-lateral interference ability.

[0104] Compared with the excitation signal, the impact signal is a non-steady transient signal and contains relatively rich vibration information, which can fully reflect the response characteristics of the acceleration sensor. In the experiment, the impact signal was simulated by instantaneously tapping the vibration table surface, and the impact response test is as Figure 14 shown. The symmetric cantilever beam miniaturized low-frequency FBG acceleration sensor can effectively identify the impact signal and generate a large wavelength drift. At the same time, the sensor can quickly return to a stable state when subjected to an impact.

[0105] Aiming at the problems of low sensitivity and large volume of the existing low-frequency FBG acceleration sensors, a miniaturized low-frequency FBG acceleration sensor based on a symmetric cantilever beam is proposed. First, according to the mechanical model of the sensor structure, the expressions of the sensitivity and natural frequency of the sensor are derived; then, the structural parameters of the sensor are optimized, and the static stress and modal analysis of the sensor are carried out using ANSYS Workbench; finally, the sensor is manufactured according to the analysis results, and the amplitude-frequency response, sensitivity characteristics, lateral

[0106] anti-interference ability and impact response of the sensor are studied through experiments. The experimental results show that the natural frequency of the sensor is 72 Hz, the sensitivity is 681.7 pm / g, the anti-lateral interference degree is less than 4.9%, and the volume is only 6.48 cm3, which can be used for real-time monitoring of low-frequency weak vibration signals below 50 Hz.

[0107] Each step involved in the above Embodiment 2 corresponds to that in Method Embodiment 1, and the specific implementation manner can refer to the relevant description part of Embodiment 1.

[0108] Those skilled in the art should understand that the above-mentioned modules or steps of the present invention can be implemented by a general-purpose computer device. Optionally, they can be implemented by program codes executable by a computing device. Thus, they can be stored in a storage device and executed by the computing device, or they can be separately fabricated into individual integrated circuit modules, or multiple modules or steps among them can be fabricated into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0109] Although the specific implementation manners of the present invention have been described above in conjunction with the accompanying drawings, it is not a limitation on the protection scope of the present invention. Those skilled in the art should understand that various modifications or deformations that can be made without creative efforts on the basis of the technical solution of the present invention are still within the protection scope of the present invention.

Claims

1. A low-frequency FBG acceleration sensor based on a symmetric cantilever beam, characterized in that, Including: A housing, mass blocks, a sensing element, and two FBGs. The housing is divided into two parts, namely an upper housing and a lower housing which are arranged vertically. There are two mass blocks which are placed vertically and are identical. The two mass blocks are symmetrically placed on the upper and lower surfaces of the cantilever beam respectively, forming a spring-mass inertial vibration system. The cantilever beam is embedded in the center of the sensor, and the FBGs are symmetrically pasted on the outer surfaces of the mass blocks. The upper housing is designed with 6 bolt holes for assembling and cooperating with the sensing element and the lower housing. The upper housing is designed in the shape of a pillar with a cover. The four pillars leave enough space between the top cover part of the upper housing and the upper mass block for pasting two FBGs. The FBGs are pasted on the edge of the top cover. The sensing element is designed with four cantilever beams and four wing spans. One of the two wing spans is respectively provided with a screw hole, and the other two wing spans are respectively provided with two screw holes, all of which are used for assembling and fixing with the upper and lower housings. The center part of the sensing element is designed with two screw holes for fixing with the upper and lower mass blocks. And the sensing element is designed with a hollow-out structure. While keeping the cantilever beams intact, the area left in the middle is the same as the upper and lower surface areas of the upper and lower mass blocks. In the manufacturing process of the low-frequency FBG acceleration sensor based on symmetric cantilever beams, according to the mechanical model of the sensor structure, the expressions of the sensitivity and natural frequency of the sensor are derived. The structural parameters of the sensor are optimized to balance the natural frequency, sensitivity, and sensor volume. The acceleration sensor is manufactured based on the optimized structural parameters. The length L of the cantilever beam is 6 mm - 7 mm, the width B of the cantilever beam is 0.5 - 1 mm, and the thickness H of the cantilever beam is 0.1 - 1 mm.

2. The low-frequency FBG acceleration sensor based on a symmetric cantilever beam according to claim 1, wherein The lower housing is designed with 6 screw holes for facilitating the fixation with the upper housing and the sensing element, and there is a screw hole at the lowermost end for fixing with the vibration table, so that the mass block swings up and down while keeping the outer housing unchanged during vibration.

3. The low-frequency FBG acceleration sensor based on a symmetric cantilever beam according to claim 1, characterized in that Each of the two mass blocks is designed with two screw holes for assembling the two mass blocks with the sensing element, so that the two mass blocks are located at the center position inside the housing and have a certain distance from the inside of the housing without any contact.

4. The manufacturing method of the low-frequency FBG acceleration sensor based on a symmetric cantilever beam according to the foregoing claim 1, characterized in that, The mechanical model of the sensor structure is: where λ is the central wavelength of the FBG, P e is the photoelastic coefficient, and Δλ is the wavelength drift of the FBG caused by strain; F is the inertial force acting on the mass, and E is the elastic modulus of the cantilever beam material; H, L, and B are the thickness, length, and width of the cantilever beam, respectively.

5. The manufacturing method of the low-frequency FBG acceleration sensor based on a symmetric cantilever beam according to claim 4, characterized in that, The expression of the sensitivity is: Among them, S is the sensitivity, and M is the mass of the mass block of the sensor.

6. The manufacturing method of the low-frequency FBG acceleration sensor based on a symmetric cantilever beam according to claim 4, characterized in that, The expression of the natural frequency of the sensor is: Among them, F0 is the natural frequency of the sensor, and ω0 is the natural angular frequency.

7. The manufacturing method of the low-frequency FBG acceleration sensor based on a symmetric cantilever beam according to claim 4, characterized in that The optimized structural parameters are: the material of the cantilever beam is 65Mn spring steel, the Young's modulus E = 201 GPa, the Poisson's ratio μ = 0.28, the material of the mass block is H62 brass, and the mass of a single mass block is 0.7 g.

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