Pressure-resistant hydrophone based on piezoelectric ceramic spherical shell

Based on the pressure resistance of piezoelectric ceramic spherical shell itself, a pressure-resistant.hydrophone was designed and fabricated by using radially poled air backing piezoelectric ceramic spherical shell.transducer as acoustic sensitive element. Firstly, the acoustic characteristics such as low frequency open circuit.receiving sensitivity and vibration frequency were analyzed, and simulated by finite element method. Then the pressure-resistant performance such as strength and stability were analyzed, also simulated with FE software.Finally, its acoustic performance and pressure resistance were tested. Test results show that the diameter of the pressure-resistant hydrophone is 36 mm, and its working frequency range is from 50 Hz to 10 kHz. The low frequency pressure sensitivity is 198:4 dB (0 dB ref 1 V/Pa), the noise spectrum level is 46.5 dB at 1 kHz,and its working depth is 3000 m. This pressure-resistant hydrophone provides a reference for the design of deep water hydrophones and has important application value in the field of deep water acoustics.

 

introduction

 

Since entering the 21st century, deep-sea research and development have received more and more attention and have become a hot area for competition among countries. Pressure-resistant hydrophones are indispensable equipment for deep-sea development. In addition, with the rapid development of military technology in various countries, various underwater equipment such as submarines, torpedoes, underwater unmanned aerial vehicles (UUV), underwater gliders (UUG), underwater robots (ROV), submersible targets, etc. With increasing depth, these deep-water equipment usually need to be equipped with pressure-resistant hydrophones that can meet their working depths. In order to withstand the effects of high hydrostatic pressure, pressure-resistant hydrophones usually adopt special pressure-resistant structures or internal and external pressure balance designs, such as pressure relief or pressure compensation structures, oil-filled, overflow structures, etc. Oil-filled and overflow structures can theoretically withstand the static pressure of the whole sea depth, and are the most commonly used pressure-resistant structures for pressure-resistant hydrophones. The pressure-resistant hydrophones of these two structures generally use piezoelectric ceramic tube as the receiving transducer. This piezoelectric ceramic tube hydrophone has the advantages of simple structure and technology, but also has the advantages of low low-frequency open circuit voltage sensitivity. Disadvantages. The radially polarized piezoelectric tube is slit to improve the receiving sensitivity, but it also greatly narrows the working frequency band, which is only 10/200 Hz. If the receiving frequency band of the piezoelectric ceramic round tube hydrophone is near its resonance frequency, although the sensitivity can be improved, its working frequency band will be severely limited, and the flatness of the sensitivity curve will be lost. In addition to piezoelectric round tube transducers, piezoelectric spherical shell transducers are also commonly used receiving transducers for acoustic pressure hydrophones. The piezoelectric spherical shell transducer has many advantages such as simple structure and process, high sensitivity, good omnidirectionality, and bandwidth of working frequency. More importantly, the characteristics of the material and structure determine that the piezoelectric ceramic spherical shell itself has high resistance. In addition to the oil-filled or overflow structure, this provides another possibility for the design of pressure-resistant hydrophones, that is, the use of an air-backed piezoelectric spherical shell as the receiving transducer of the pressure-resistant hydrophone.

 

1 Acoustic receiving characteristics of piezoelectric spherical shell transducer

 

 Low frequency receiving sensitivity

 

Restricted by shape and processing technology, piezoelectric ceramic spherical shells usually have only one polarization mode: radial polarization, and the positive and negative electrodes are respectively on the inner and outer surfaces of the spherical shell. For a piezoelectric spherical shell transducer with an inner radius of a and an outer radius of b, when subjected to a sound pressure p0 whose frequency is much lower than its intrinsic frequency, a potential difference V will be generated between the inner and outer electrodes of the piezoelectric spherical shell. The receiving sensitivity of a hydrophone is generally expressed by the free-field receiving sensitivity Me. Me is defined as the ratio of the open-circuit voltage at the output of the hydrophone to the free-field sound pressure at the position of the hydrophone in the sound field. Its decibel form is the free-field receiving sensitivity. . Therefore, the low-frequency open-circuit receiving voltage sensitivity of the air-backed piezoelectric spherical shell. Under the premise that the piezoelectric material is the material used in this article, when t is constant, the larger b is, that is, the larger the outer diameter of the piezoelectric spherical shell, the higher the sensitivity; When b is certain and t 0.36, the sensitivity is the smallest, and this point should be avoided in design; when b is certain and t <0:36, the smaller t, that is, the thinner the piezoelectric spherical shell, the higher the sensitivity.

 

1.2 Resonant frequency

 

For a thin piezoelectric spherical underwater acoustic transducer, its resonant frequency in air. It can be seen that the resonance frequency of the thin piezoelectric spherical shell is only its average radius r and the density of the material s, Young's modulus Y E11 It is related to Poisson's ratio, which is equivalent to simplifying it to a spherical shell of isotropic elastic material. It can be seen that when the piezoelectric material is determined, the larger the average radius r of the spherical shell, the higher the resonance point and the wider the working bandwidth. When in water, due to the increased radiation impedance of the piezoelectric spherical shell transducer, its resonant frequency will be slightly lower than the resonant frequency in air. When the piezoelectric spherical hydrophone is used for low-frequency reception, in order to ensure the flatness of its sensitivity, its working frequency is far away from its resonance frequency. In engineering, it is generally required that its resonance frequency be at least 5 times the upper limit frequency of its working.

 

 

 

2 Analysis of pressure resistance performance of piezoelectric spherical shell transducer

 

The failure modes of pressure-resistant structures mainly include strength failure, stiffness failure, stability failure and corrosion failure. For large depth hydrophones, the load it bears is mainly external water pressure, and its failure modes are mainly strength failure and stability failure. The two failure situations of the piezoelectric spherical shell transducer are discussed below.

 

2.1 Strength failure analysis

Strength failure refers to the phenomenon that irreversible deformation or fracture occurs after the maximum stress in the container exceeds the yield limit, causing the container to lose its load-bearing capacity. Corresponding to the strength failure is the maximum allowable pressure of the piezoelectric spherical shell transducer. According to the moment-free theory of the rotating shell, under the action of the external pressure p, the spherical shell will produce axial tensile stress z and hoop tensile stress, and the two are equal in value. Among them, D0 is outside the spherical shell Diameter, the unit is mm; is the thickness of the spherical shell, the unit is mm. According to the theory of maximum principal stress, the pressure-resistant structure design must be satisfied. Among them, is the allowable stress. According to my country's national standard GB 150.3, for the material standard normal temperature yield strength Rel, the safety factor is ns = 1:5. The normal temperature yield strength of the piezoelectric ceramic material P-51 used in the piezoelectric spherical shell is Rel = 137:9 MPa, so the allowable stress of the material [] = Rel/ns = 91:9 MPa. Substituting the parameter t, the maximum allowable pressure of the piezoelectric spherical shell transducer can be obtained as it is easy to know that the larger the ratio t of the spherical shell thickness to the outer diameter, the stronger the piezoelectric spherical shell's strength and pressure resistance capability.

 

2.2 Stability failure analysis

Stability failure refers to the phenomenon that the container changes from a stable equilibrium state to another unstable state under the action of external load, and its shape changes suddenly and loses its normal working ability. Corresponding to the stability failure is the critical instability allowable pressure of the piezoelectric spherical shell transducer. According to the theory of small deformation, the critical instability pressure pcr of the spherical shell under external force has a large error for this formula, so a large safety factor is often used to compensate. According to GB 150.3, the stability safety factor is taken as m = 14:25, so the allowable critical pressure for circumferential instability [p] = pcr/m. Substituting the parameter t in the same way, the allowable critical pressure for circumferential instability of the piezoelectric spherical shell transducer is easy to know. When the piezoelectric material is determined, the larger the ratio t of the spherical shell thickness to the outer diameter, the greater the pressure The stability and pressure resistance of the electric ball shell is stronger.

 

3 Finite element simulation

From the above analysis, for the sensitivity and working frequency of the piezoelectric spherical shell, the larger the outer diameter, the thinner the better; and for its pressure resistance, the smaller the outer diameter, the thicker the thickness. it is good. That is, the acoustic performance and the pressure resistance performance are mutually opposed. Considering the requirements of acoustic performance and pressure resistance, as well as the difficulty and cost of spherical shell processing (usually the larger the outer diameter, the greater the thickness, the greater the processing difficulty and the higher the cost), the outer radius of the design spherical shell b = 15 mm, Thickness = 3 mm. The piezoelectric material used in the spherical shell is P-51, its piezoelectric coefficient g33 = 25: 6 10 3 V m/N, g31 = 9: 6 10 3 V m/N, density s = 7600 kg/m3, Young's modulus Y E11 = 6:0 1010 Pa, Poisson's ratio = 0:36.

 

3.1 Simulation of acoustic characteristics of piezoelectric spherical shell

In order to verify the correctness of the analysis of the acoustic receiving characteristics of the piezoelectric spherical shell transducer, the finite element analysis method is used to model and simulate it, and the simulation software COMSOL5.4 is used.

 

3.1.1 Receiving sensitivity simulation

First create a three-dimensional spherical shell structure model. In order to simplify the modeling geometry and speed up the solution, the model only creates 1/8 piezoelectric spherical shells and uses 3 plane symmetry constraints to achieve a complete spherical shell. Create a piezoelectric material radial polarization coordinate system in spherical coordinates and use the material parameters of piezoelectric material P-51. Set the boundary load as 0.1 MPa pressure on the outer surface and no pressure on the inner surface. By performing frequency domain analysis, it is solved as a steady-state problem. Figure 2 shows the simulation results of the potential distribution of the piezoelectric spherical shell when subjected to a pressure with a frequency of 500 Hz and a pressure of 0.1 MPa.

Substituting the size and material parameters of the piezoelectric spherical shell into the formula, the theoretical open circuit when it is subjected to a low-frequency sound pressure of 0.1 MPa can be obtained

The output voltage is 11.646 V. It can be seen from Figure 2 that when the piezoelectric spherical shell is subjected to a sound pressure of 0.1 MPa@500 Hz, the simulation result of its output voltage is 11.632 V, which is consistent with the theoretical value. At this time its sensitivity is 198.7 dB@500 Hz (0 dB = 1 V/ Pa).

 

3.1.2 Resonance frequency simulation

The following also uses the finite element simulation method to simulate the resonance frequency of the piezoelectric ceramic spherical shell, and the simulation frequency band is 1 Hz/200 kHz. First, the material of the piezoelectric spherical shell is simplified into an isotropic elastic material, and the frequency sweep analysis is performed on it, and the frequency response curve of its deformation is shown in Figure 3. According to formula (3), the resonant frequency fa of the piezoelectric spherical shell in the air is derived to be 58.557 kHz. From Fig. 3, it can be seen that the simulated value of the resonant frequency is 58.9 kHz, which is basically consistent with the theoretical value. It should be noted that the formula (3) is only a simplified calculation for the isotropic thin spherical shell, and the piezoelectric spherical shell material is not isotropic, and the thickness is relatively thick, directly applying the formula (3) will have certain errors. If the complete parameters of the piezoelectric ceramics are substituted in, the frequency response curve of the open circuit voltage sensitivity is shown in Figure 4. It can be seen from Figure 4 that in the 1 Hz 10 kHz frequency band, the sensitivity curve of the piezoelectric spherical shell is very flat, with a sensitivity of 198.7 dB, which is consistent with the theoretical analysis. The resonant frequency becomes 72.1 kHz, which is slightly larger than the calculation result of formula (3), but it does not affect the validity of the formula in engineering applications. Since the relevant damping coefficient of the piezoelectric material cannot be obtained, the flexibility matrix loss factor and the piezoelectric matrix loss factor in the model are set to 0, which leads to the simulation that the sensitivity of the piezoelectric spherical shell at the resonance frequency is 155 dB, in fact the sensitivity should be less than this value.

3.2 Simulation of pressure resistance performance of piezoelectric spherical shell

The theoretical calculation formula of pressure resistance in section 2 is a simplified formula summarized for the convenience of engineering application, and the actual piezoelectric spherical shell.Holes will be opened due to installation needs, which may cause the actual pressure capacity to be inconsistent with the theoretical calculation results. In order to obtain the pressure capability of the piezoelectric spherical shell transducer as accurately as possible, the structure static simulation and the eigenvalue buckling simulation were carried out respectively through the finite element analysis software Workbench.

 

3.2.1 Structural static simulation

Structural static simulation can obtain the stress distribution throughout the structure when the structure is under load. Therefore, the maximum allowable stress of the known material is

The maximum allowable pressure it can bear can be simulated. A three-dimensional model of the spherical shell is established, and mounting holes are set on the spherical shell model. Adopt the spherical shell

The hexahedron method is used to divide the grid, and roller supports are set on the cylindrical surface and the lower plane of the mounting hole, and pressure is applied to the outer surface of the piezoelectric spherical shell transducer.

Constantly change the size of the pressure, and carry out structural static analysis on it. The simulation found that when the pressure applied on the outer surface reaches 28 MPa, the piezoelectric

The maximum stress of the spherical shell is 151 MPa, and its stress distribution is shown in Figure 5 (In order to facilitate the observation of the internal stress, the piezoelectric spherical shell is cut along the center line to show

Show). It should be noted that the maximum stress only occurs at the boundary line of the fillet on the mounting hole, and the maximum stress in the remaining other places is less than this

The safe allowable stress of the piezoelectric material is 91.9 MPa, so the maximum allowable pressure of the piezoelectric spherical shell can reach 28 MPa according to the simulation. And the root

According to formula (6), the maximum allowable pressure of the piezoelectric spherical shell transducer can be obtained as 36.8 MPa. It can be seen that the compressive strength of the spherical shell after perforation is lower than that of the complete

The theoretical strength of the entire spherical shell. In the simulation, the stress concentration phenomenon that appears in a few places at the mounting hole exceeds the safety allowable stress, and whether it affects the pressure resistance of the piezoelectric spherical shell remains to be verified by the pressure test.

 

3.2.2 Eigenvalue buckling simulation

The eigenvalue buckling simulation can obtain the buckling modes of thin-shell structures and their corresponding critical buckling pressures. A pressure of 1 MPa was applied to the outer surface of the piezoelectric spherical shell transducer, and its eigenvalue buckling analysis was performed. The simulation results show that the first-order buckling mode is shown in Figure 6, and the first-order wavenumber n = 4, which is consistent with the instability characteristics of the spherical shell. The first-order buckling load factor is 3379, so its first-order critical load is 3379 MPa. Since the first order is the lowest value of the buckling load, this means that the piezoelectric spherical shell structure will not be stable until the theoretical pressure reaches 3379 MPa. According to formula (7), the critical pressure of circumferential instability of the piezoelectric spherical shell transducer can be obtained as 2970 MPa, which is basically consistent with the simulation results. The finite element simulation results show that the maximum allowable pressure of the piezoelectric spherical shell transducer is 28 MPa, and its critical buckling pressure is 3379 MPa, which indicates that when the external pressure continues to increase, the piezoelectric spherical shell changes The first occurrence of the energy device is strength failure, which also shows that its safe withstand voltage depth is 2800 m.

 

4 Development and performance test of spherical pressure hydrophone

4.1 Development of spherical pressure-resistant hydrophone

In this paper, a radially polarized air-backed piezoelectric spherical shell transducer is used as the acoustic receiving sensor, and a spherical pressure-resistant hydrophone is designed and fabricated. The outer radius of the piezoelectric spherical shell used in the spherical pressure-resistant hydrophone is 15 mm, the thickness of the spherical shell is 3 mm, and the piezoelectric ceramic material used for the spherical shell is P-51. The inside of the piezoelectric spherical shell is a cavity, and the outermost layer is potted with a layer of sound-permeable rubber to insulate, seal and protect. The thickness of the sound-permeable rubber is 3 mm. The physical object of a spherical pressure-resistant hydrophone. The diameter of the entire hydrophone is 36 mm.

 

 

4.2 Performance test of spherical pressure hydrophone

 

4.2.1 Receiving sensitivity test

The finished spherical pressure-resistant hydrophone is placed in a standing wave tube, and its low-frequency open-circuit receiving sensitivity is tested by the comparison method. Ball-resistant

The pressure hydrophone and the standard hydrophone are hung at the same height in the standing wave tube at the same time, changing the emission frequency of the standing wave tube sound source, and recording both at the same time

Through the comparison method, the receiving sensitivity of the spherical pressure-resistant hydrophone is obtained. The standing wave tube used can only produce a combination of 50 1000 Hz

Grid standing wave, so the measurement frequency band this time is 50 1000 Hz. The measured results of the sensitivity curve of the spherical pressure-resistant hydrophone are shown in Figure 8. by

The test result shows that the sensitivity of the spherical pressure-resistant hydrophone in the 50 1000 Hz frequency band is about 198.4 dB, which is basically consistent with the theoretical value. in

In the range of 50 1000 Hz, the sensitivity fluctuation does not exceed 0.5 dB. The standing wave tube can only be calibrated below 1 kHz. For the 1 kHz to 10 kHz frequency band, the measurement is carried out in an anechoic tank. Put the finished spherical pressure-resistant hydrophone and the standard hydrophone in the same position of the anechoic tank, use the sound source to play single-frequency signals of different frequencies, and use the comparison method to complete the receiving sensitivity measurement. The measured results of the sensitivity curve of the spherical pressure-resistant hydrophone at 1 kHz and 10 kHz are shown in Fig. 9. It can be seen from the test results that the sensitivity of the spherical pressure-resistant hydrophone in the frequency band of 1 kHz and 10 kHz is about 198 dB, which is basically consistent with the theoretical value. In the range of 1 kHz to 10 kHz, the sensitivity fluctuation does not exceed 1.4 dB.

 

4.2.2 Self-noise test

 

In order to ensure that the hydrophone can pick up weak sound signals, the hydrophone is required to have a lower equivalent self-noise. Spherical pressure hydrophone

It is placed in a vacuum tank with electromagnetic shielding, damping and vibration reduction, and the self-noise test is carried out on the BK-3050 signal acquisition card with extremely low noise.

The equivalent self-noise spectrum of the spherical pressure-resistant hydrophone is shown in the red solid line in Figure 10. The black dotted line in Figure 10 is the earliest research on ocean noise.The 0-level sea state ocean background noise spectrum level summarized by Kundson [9]. According to the Kundson curve, the ocean background noise under sea state 0.The sound spectrum level is about 44 dB@1 kHz. It should be noted that this data is a research result in 1948. In recent years, as the global shipping

With rapid development, ocean background noise is increasing year by year. The blue dotted line in Figure 10 is the background noise spectrum level of the South China Sea in 2013 at level 0 sea conditions Line , it can be seen that the equivalent self-noise spectrum level of the spherical pressure-resistant hydrophone is lower than or equal to the level 0 sea state in the range of 10 1500 Hz.The scene noise is slightly higher than the 0 level sea state ocean background noise in the range of 1500 5000 Hz. Its equivalent self-noise spectrum at 1000 Hz.The level is 46.5 dB.

 

4.2.3 Withstand voltage performance test

In order to verify the pressure resistance capability of the spherical pressure-resistant hydrophone, a sample of the spherical pressure-resistant hydrophone was put into an autoclave for a pressure test. To ensure safety, the test system is pressurized with high-pressure water. According to the previous analysis, its safe pressure resistance capacity is 28 MPa, which is under 1.5 times of safety factor

The result obtained, that is to say its theoretical ultimate pressure capability is 42 MPa. In order to balance safety and ease of use, here is rounded to

30 MPa for testing. During the test, first pressurize to 30 MPa, hold the pressure for 3 hours, release the pressure, and check the hydrophone; then pressurize again to 30 MPa, and repeat the test 3 times. No significant pressure drop occurred during the entire pressurization process. After each pressurization, check the hydrophone to be tested. The appearance is not damaged. The weighing is consistent before and after the test. Then the sensitivity is tested again in the standing wave tube. The test result shows that the sensitivity is basically the same as the sensitivity before the pressurization. This proves that it can withstand 3000 m water pressure.

 

5 Conclusion

In this paper, a combination of theoretical formula and finite element simulation is used, and the piezoelectric spherical shell structure and material have the pressure resistance capability, and the radially polarized air-backed piezoelectric spherical shell transducer is used as the acoustic receiving sensitive element. And made a spherical pressure-resistant hydrophone. The diameter of the spherical pressure-resistant hydrophone is 36 mm, the working frequency band is 50 Hz 10 kHz, the low-frequency sensitivity is 198.4 dB, the equivalent self-noise spectrum level is 46.5 dB@1 kHz, and the working depth is 3000 m. The air-backed piezoelectric spherical shell scheme used in this paper has obtained a certain pressure resistance capacity under the condition of high sensitivity. If the pressure resistance depth is to be continuously improved, the sensitivity must be lost at the cost. This solution can achieve relatively limited pressure resistance. If the hydrophone needs to obtain a greater pressure resistance (such as full sea depth), it is better to choose an oil-filled or overflow solution.