# Structural Design and Test of a Piezoelectric Flextensional Transducer for Passive Detection of Frogmen

Authors: Yuchen Sun; Weiyi Chen; Zongji Li; Pingbo Wang; Li Dong; Yongyong Zhu; Shizhe Wang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

A piezoelectric flextensional transducer was designed using the finite element method (FEM) for the passive detection of underwater frogmen. By studying the main performance parameters of sonar transducers for the detection of frogmen around the world, this paper presents the advantages of active and passive sonar in this task and proposes a passive method for the detection of frogmen. Subsequently, a Cymbal transducer was selected considering the needs of the research. After introducing the principles and methods of the FEM analysis, the acoustic and electromechanical characteristics of the Cymbal transducer were verified under the influence of structural dimensions, e.g., resonance frequency, conductance, and susceptance. The electromechanical performance of the Cymbal transducer was simulated with a FEM to study how it is affected by static water pressure and processing errors and to demonstrate the feasible application of the Cymbal transducer in practical applications. In the end, a Cymbal prototype was tested to verify that the designed Cymbal transducer performs in compliance with the requirements and can be used for the passive detection of underwater frogmen with open-circuit breathing.


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## Body

## 1. Introduction

For security surveillance in water, radar and similar equipment are often used to ensure a nearly warning on the water surface, but few measures are available for underwater detection. In recent years, underwater frogmen and minisubmarines have been gradually introduced; these can infiltrate sensitive waters such as wharves, seaports, offshore exploration platforms, ship anchorage areas, and reefs for reconnaissance or sabotage. At present, sonar is mainly employed to detect such underwater targets [1, 2]. However, a frogman is a small target that causes little underwater noise and infrequent signal. In ports and coastal water where they are often deployed, many backscattering objects and boundaries exist such as ship wreckage, port walls, sea beds, and water surfaces. Additionally, these environments have severe noises and reverberations [3], making it difficult to design the sonar for detection.Active sonar depends mainly on the echo from a frogman to identify the target, whereas passive sonar detects a frogman based on the underwater breathing characteristics of the diver. They have different ranges of frequency in the detection of underwater frogmen.Active sonar can identify a small underwater frogman under a high-frequency acoustical signal or expand its detection distance through a higher intensity of the transmitted wave. At present, high-frequency active sonar technology is often used to detect underwater frogmen in many countries. The operating frequency ranges from 60 kHz to 100 kHz, and the longest detection distance is 400 m to 1200 m as shown in Table1 [4–9]. It is mainly fixed or suspended in the water to one side of a ship or the sidewall of a wharf for port bases, large ships, or high-value offshore facilities.Table 1
Main performance of active sonar for frogman detection in several countries.
No.CountryModelOperating frequency range (Hz)Longest detection distance (m)1BritainCerberus 360100 k8002BritainCerberus Mod270 k–130 k9003BritainEchoscope-SD80 k7404BritainSentinel IDS70 k9005IsraelAqua shield DDS60 k1000–12006IsraelPoint shield portable DDS70 k7007BritainX-type100 k10008CanadaCSDS-8580 k15009Turkey—80 k120010RussiaPALLADA100 k400Under the effects of passive sonar, breathing provides an important basis for the detection and identification of underwater frogmen. A frogman with open-circuit breathing has an underwater acoustic radiation signal frequency ranging from 200 Hz to 13 kHz within the period consistent with the person’s underwater physiological respiration cycle (approximately 3s to 5s). The energy is mainly concentrated in the frequency range of 2 kHz to 13 kHz while inhaling and in a low-frequency range, 200 Hz to 2 kHz, while exhaling. The signal characteristic of inhaling is noticeably at a higher frequency and contains standard components, so it is the ideal frequency range for passive detection [10]. Stolkin et al. [11, 12] from the Stevens Institute of Technology used passive sonar to detect the periodical characteristics of the acoustic radiation signals generated by a frogman with open-circuit breathing. Based on the characteristic signals, two kinds of underwater passive detection systems have been developed in the United States and the Netherlands; they are the SPADES and Delphinus System, with detection distances up to 350 m, respectively.For frogman detection with a passive sonar, a low operating frequency range may require a large and heavy transducer, whereas the weak radiation signal makes the unit’s detection distance shorter than the active sonar. Hence, passive sonar is rarely produced and purchased around the world. Nevertheless, passive detection offers a great number of advantages. Compared with active sonar, passive sonar is more robust, environmentally friendly, invisible, and energy-efficient. Especially when deployed around a large military ship, passive sonar is difficult for opposing forces to detect. Moreover, it can identify a target more easily based on the various acoustical characteristics of different targets [2, 13]. For this reason, a low frequency, small, very sensitive, and low-cost transducer should be designed to improve the detection of underwater frogmen.The low-frequency passive underwater acoustic transducer is generally complex in structure or large in size, and the production cost is high, while the ordinary standard hydrophone has a low receiving sensitivity, which leads to a short distance for passive detection of frogmen. These reasons seriously restrict the large-scale application of passive detection sonar for frogmen. To solve the problem of high production cost, the structure of the transducer should be simple and the volume should be small. To increase the passive detection distance of the frogman, it is necessary to select a transducer with high sensitivity. Therefore, taking advantage of the high sensitivity and simple structure of the flextensional transducer, we designed a Cymbal hydrophone with a diameter of 0.05 m by using the FEM and introduced a new batch manufacturing scheme of the transducer prototype. Combined with the experimental analysis, the prepared transducer has the advantages of simple structure, small volume, and high sensitivity. It is expected to provide a transducer scheme for passive detection of frogmen in a long distance for the industry.In this project, we analyzed the underwater acoustic signal characteristics of frogmen, demonstrated the advantages and disadvantages of active and passive systems used to detect underwater frogmen, and determined to explore the passive acoustical detection of underwater frogmen. Based on the acoustic signal characteristics of underwater frogmen, the generation V flextensional transducer Cymbal was selected in the research. The finite element method (FEM) was used to determine how the electromechanical parameters of the Cymbal transducer were affected by the dimensional parameters. The simulation was carried out for the Cymbal based on the need for detection to determine the needed structural dimensions of the Cymbal. It revealed that the electromechanical characteristics of the designed Cymbal were suitable for the frogman detection in practical conditions, e.g., resistance to pressure, resonance frequency, and receiving sensitivity. Considering the structural dimensions of the designed Cymbal, a prototype was fabricated for the practical detection of underwater frogmen. Compared with the common transducers, the transducer designed in this paper has several advantages such as using a low frequency and having a small size, high sensitivity, simple structure, and is easily produced in batches.


## 2. Design and Analysis of the Transducer

### 2.1. Design Basis

This paper will design a piezoelectric transducer of simple structure and small size with relatively low production cost and convenient application. The designed transducer will operate at the frequency that falls in the range of frequencies produced by the acoustic signal of underwater frogmen with open-circuit breathing (200 Hz to 13 kHz) and basically at the middle and lower frequency section of the range. Additionally, the transducer will be very sensitive in the operating frequency range to increase its range in detecting frogmen.


### 2.2. Selection of a Transducer

To increase the detection distance while reducing the volume and weight of a passive sonar unit, this paper analyzed the generation V flextensional transducer Cymbal [14–16]. The transducer has a “Sandwich” rotary designed and symmetrical structure (Figure 1). In this 3D image, the Cymbal consists of a top and a bottom metal cap along with a central piezoelectric ceramic disk. The 2D profile of Cymbal is presented in Figure 2. In the figure, the structural dimensions of Cymbal are defined as follows: dp is the diameter of Cymbal; de1 is the diameter at the top of the cavity in the metal cap; de2 is the diameter at the bottom of the metal cap; tp is the thickness of the piezoelectric ceramic disk; tc is the thickness of the metal caps; h is the depth of the cavity in the metal cap.Figure 1
3D image of the Cymbal transducer.Figure 2
2D profile of the Cymbal transducer.The “Sandwich” circular and symmetrical structure allows the Cymbal transducer to realize the piezoelectric and inverse piezoelectric effects satisfactorily. When a force caused by the external oscillation of acoustic pressure is applied to the Cymbal transducer, the Cymbal transducer serves as a sensor and a flextensional vibration mode is generated on the caps. The radial vibration overlaps on the ceramic disk, leading to higher radial displacement, which therefore improves the sensitivity of the receiver. Moreover, a Cymbal transducer has several advantages such as having a simple structure, being convenient to produce, having low cost, and being easy to produce in batches. At the resonance frequency of 5 kHz, the Cymbal transducer weights only 1/100 of Langevin.After deciding on the shape of the transducer, calculations were carried out to determine the materials needed and the structural dimensions of these parts, so that the detection performance of the transducer meets the actual needs.


### 2.3. Design Method

In most cases, a higher-order partial differential equation is used to design and analyze an underwater acoustic transducer, but its computation and analysis are very difficult to implement. To simplify the analysis and computation, it is now a common practice to analogically replace the mathematic model with any other model. The common methods include the analytic method, equivalent circuit method, and finite element method.The analytic method is the theoretical basis for other analysis methods, but a large amount of work will be required to perform the analytic computation for many theories including acoustics, electricity, and vibration involved in the working principles of transducers. Numerous calculations have to be repeated if any change is made to the parameters. For this reason, the analytic method is typically quite time-consuming. A piezoelectric transducer is an element that operates for the constant conversion of electromechanical energy so that it constitutes a typical electromechanical coupling system. To integrate the characteristics of acoustics, vibration, and electricity in a transducer, mechanical vibration is analogically regarded as a circuit network. After that, the equivalent circuit method is habitually used.This method can vividly illustrate the working principles of a transducer; it is convenient to build a model and the model is easy to compute, but it is troubled by large differences [17]. To eliminate the differences, the finite element method is often introduced [18]. Compared with the analytic method, the finite element method can basically control the actual difference within 5% [19], and this allows convenient calculation of the higher-order resonance frequency of transducers.The finite element method adopted in this paper has the computation that is used based on a piezoelectric equation. Under normal circumstances, the operation of a transducer can be regarded as an adiabatic process that ignores some variables such as temperature and entropy and is regarded as the low-amplitude vibration of a linear elastomer [20]. Currently, (1) provides the piezoelectric equation:(1)TD=C−eteεSSE,where T is the stress, S is the strain, E is the electric intensity, D is the electric displacement, C is the elastic constant component of the constant electric field, e is the piezoelectric constant component, et is the transposition of e, and εS is the dielectric constant component of the constant strain.Based on (1) and Hamilton’s principle, the finite element method can be used to calculate the electromechanical characteristic parameters of a transducer while satisfying the basic relationship and boundary conditions in mechanical and electrical theories.The electromechanical and acoustic characteristics of the Cymbal transducer are significantly affected by the material used and its structural dimensions. Therefore, its performance can be regulated by selecting appropriate materials and adjusting the structural dimensions. After learning from what James F. Tressler et al. achieved [18, 21, 22], the same FEM has been extensively performed by the research team to analyze the frequency, conductance, susceptance, etc. of the Cymbal transducer and obtain the following results [20, 23].(1)
Brass is more suitable for metal caps than the common materials such as titanium alloy and carbon steel. With the same size, a Cymbal transducer made of brass offers lower frequency. Moreover, brass is easy to find in the market and easy to process.(2)
At present, the common piezoelectric materials in the market are PZT-4, PZT-5A, and PZT-8. Among them, PZT-5A provides a lower resonance frequencyfr and a higher equivalent conductance and susceptance of the Cymbal transducer, so it is a more suitable material for producing receiving transducers.(3)
The resonance frequencyfr of the Cymbal transducer decreases with the increase of its diameter dp but increases with the decrease of cap thickness tc and cavity depth h.(4)
The transmitting voltage response levelTVR of the Cymbal transducer is lower when the diameter dp or ceramic disk thickness tp of the transducer increases but higher when the cap cavity depth h increases.(5)
The free-field voltage sensitivity level FFVS of the Cymbal transducer becomes higher when thedp, cap thickness tc, or h of the transducer increases.(6)
The effective electromechanical coupling coefficientkeff of the Cymbal transducer goes up with an increase of its dp but goes down with the increase of tp and tc.Considering the performance requirements and complex fabrication of transducers, we preliminarily decided to use the brass for metal caps and PZT-5A for the piezoelectric ceramic disk. These two materials could meet the requirements for performance, be easily found in the market, have well-developed technology, and are easy to process. According to the variation laws of transducer performance with structural dimensions mentioned above in this paper, we had tried many calculations through the FEM for the frogman detection transducer, and the dimensions of the designed Cymbal transducer were preliminarily determined, in which the diameter of the Cymbal transducerdp was 50 mm.


## 2.1. Design Basis

This paper will design a piezoelectric transducer of simple structure and small size with relatively low production cost and convenient application. The designed transducer will operate at the frequency that falls in the range of frequencies produced by the acoustic signal of underwater frogmen with open-circuit breathing (200 Hz to 13 kHz) and basically at the middle and lower frequency section of the range. Additionally, the transducer will be very sensitive in the operating frequency range to increase its range in detecting frogmen.


## 2.2. Selection of a Transducer

To increase the detection distance while reducing the volume and weight of a passive sonar unit, this paper analyzed the generation V flextensional transducer Cymbal [14–16]. The transducer has a “Sandwich” rotary designed and symmetrical structure (Figure 1). In this 3D image, the Cymbal consists of a top and a bottom metal cap along with a central piezoelectric ceramic disk. The 2D profile of Cymbal is presented in Figure 2. In the figure, the structural dimensions of Cymbal are defined as follows: dp is the diameter of Cymbal; de1 is the diameter at the top of the cavity in the metal cap; de2 is the diameter at the bottom of the metal cap; tp is the thickness of the piezoelectric ceramic disk; tc is the thickness of the metal caps; h is the depth of the cavity in the metal cap.Figure 1
3D image of the Cymbal transducer.Figure 2
2D profile of the Cymbal transducer.The “Sandwich” circular and symmetrical structure allows the Cymbal transducer to realize the piezoelectric and inverse piezoelectric effects satisfactorily. When a force caused by the external oscillation of acoustic pressure is applied to the Cymbal transducer, the Cymbal transducer serves as a sensor and a flextensional vibration mode is generated on the caps. The radial vibration overlaps on the ceramic disk, leading to higher radial displacement, which therefore improves the sensitivity of the receiver. Moreover, a Cymbal transducer has several advantages such as having a simple structure, being convenient to produce, having low cost, and being easy to produce in batches. At the resonance frequency of 5 kHz, the Cymbal transducer weights only 1/100 of Langevin.After deciding on the shape of the transducer, calculations were carried out to determine the materials needed and the structural dimensions of these parts, so that the detection performance of the transducer meets the actual needs.


## 2.3. Design Method

In most cases, a higher-order partial differential equation is used to design and analyze an underwater acoustic transducer, but its computation and analysis are very difficult to implement. To simplify the analysis and computation, it is now a common practice to analogically replace the mathematic model with any other model. The common methods include the analytic method, equivalent circuit method, and finite element method.The analytic method is the theoretical basis for other analysis methods, but a large amount of work will be required to perform the analytic computation for many theories including acoustics, electricity, and vibration involved in the working principles of transducers. Numerous calculations have to be repeated if any change is made to the parameters. For this reason, the analytic method is typically quite time-consuming. A piezoelectric transducer is an element that operates for the constant conversion of electromechanical energy so that it constitutes a typical electromechanical coupling system. To integrate the characteristics of acoustics, vibration, and electricity in a transducer, mechanical vibration is analogically regarded as a circuit network. After that, the equivalent circuit method is habitually used.This method can vividly illustrate the working principles of a transducer; it is convenient to build a model and the model is easy to compute, but it is troubled by large differences [17]. To eliminate the differences, the finite element method is often introduced [18]. Compared with the analytic method, the finite element method can basically control the actual difference within 5% [19], and this allows convenient calculation of the higher-order resonance frequency of transducers.The finite element method adopted in this paper has the computation that is used based on a piezoelectric equation. Under normal circumstances, the operation of a transducer can be regarded as an adiabatic process that ignores some variables such as temperature and entropy and is regarded as the low-amplitude vibration of a linear elastomer [20]. Currently, (1) provides the piezoelectric equation:(1)TD=C−eteεSSE,where T is the stress, S is the strain, E is the electric intensity, D is the electric displacement, C is the elastic constant component of the constant electric field, e is the piezoelectric constant component, et is the transposition of e, and εS is the dielectric constant component of the constant strain.Based on (1) and Hamilton’s principle, the finite element method can be used to calculate the electromechanical characteristic parameters of a transducer while satisfying the basic relationship and boundary conditions in mechanical and electrical theories.The electromechanical and acoustic characteristics of the Cymbal transducer are significantly affected by the material used and its structural dimensions. Therefore, its performance can be regulated by selecting appropriate materials and adjusting the structural dimensions. After learning from what James F. Tressler et al. achieved [18, 21, 22], the same FEM has been extensively performed by the research team to analyze the frequency, conductance, susceptance, etc. of the Cymbal transducer and obtain the following results [20, 23].(1)
Brass is more suitable for metal caps than the common materials such as titanium alloy and carbon steel. With the same size, a Cymbal transducer made of brass offers lower frequency. Moreover, brass is easy to find in the market and easy to process.(2)
At present, the common piezoelectric materials in the market are PZT-4, PZT-5A, and PZT-8. Among them, PZT-5A provides a lower resonance frequencyfr and a higher equivalent conductance and susceptance of the Cymbal transducer, so it is a more suitable material for producing receiving transducers.(3)
The resonance frequencyfr of the Cymbal transducer decreases with the increase of its diameter dp but increases with the decrease of cap thickness tc and cavity depth h.(4)
The transmitting voltage response levelTVR of the Cymbal transducer is lower when the diameter dp or ceramic disk thickness tp of the transducer increases but higher when the cap cavity depth h increases.(5)
The free-field voltage sensitivity level FFVS of the Cymbal transducer becomes higher when thedp, cap thickness tc, or h of the transducer increases.(6)
The effective electromechanical coupling coefficientkeff of the Cymbal transducer goes up with an increase of its dp but goes down with the increase of tp and tc.Considering the performance requirements and complex fabrication of transducers, we preliminarily decided to use the brass for metal caps and PZT-5A for the piezoelectric ceramic disk. These two materials could meet the requirements for performance, be easily found in the market, have well-developed technology, and are easy to process. According to the variation laws of transducer performance with structural dimensions mentioned above in this paper, we had tried many calculations through the FEM for the frogman detection transducer, and the dimensions of the designed Cymbal transducer were preliminarily determined, in which the diameter of the Cymbal transducerdp was 50 mm.


## 3. Simulation of Characteristics

After selecting the materials and determining the structural dimensions of the Cymbal transducer, the finite element method was employed in this section to analyze the characteristics of the designed transducer in four aspects. The four aspects include the analysis of the designed transducer’s resistance to water pressure under the practical operating environment, the calculation of its electromechanical parameters including electrical conductance and susceptance, the calculation of its receiving sensitivity, and the influence of dimensional difference on its main performance.The Cymbal transducer was designed with an axially symmetrical structure; the external loads applied vertically onto the top of the caps are also axially symmetrical. Consequently, the stress and strain caused by the Cymbal array under the loads are also axially symmetric by the transducer’s rotary axis of symmetry. To reduce the need for calculations and enhance the computational accuracy, a two-dimensional 1/2 axisymmetrical model was built for the Cymbal transducer, which simplifies the finite element analysis [24, 25]. Its main boundary conditions were pasting the metal parts with the piezoelectric disk, limiting the displacement in the Y direction of the x-axis of symmetry and the displacement in the X direction of the Y-axis of symmetry, and applying 1 V voltage to the positive pole of the piezoelectric disk and 0 V voltage to the negative pole of the piezoelectric disk, and the positive and negative poles of the piezoelectric disk were, respectively, voltage coupled.To meet the requirements of calculation accuracy, the side length of finite element mesh should not be greater than 1/20 of the acoustic wavelength, and the length-width ratio cannot be too large. The maximum frequency range of the transducer simulation in this paper is 5 kHz, and the corresponding grid side length should not be greater than 15 mm, while the grid size used in this paper was 0.5 mm for calculation accuracy.In Figures3 and 4, the construction of a 2D axisymmetric model of the Cymbal transducer is shown using the dimensional parameters preliminarily determined and then gridded.Figure 3
2D axisymmetric finite element analysis (FEA) model of the Cymbal transducer.Figure 4
2D axisymmetric finite element analysis (FEA) model of the Cymbal transducer in the water.With the performance parameters of piezoelectric ceramic materials provided by ceramic material manufacturers, in the 2D axisymmetric model of the Cymbal transducer, the polarization direction of the PZT-5A ceramic is perpendicular to the plane of the piezoelectric ceramic disk, so that the parameters are as follows:(1)
The density of PZT-5A ceramic is 7750 kg/m3.(2)
The relative dielectric constant matrix of PZT-5A ceramic is(2)ξr=ξr11000ξr33000ξr11=916000830000916.(3)
The piezoelectric stress constant matrix of PZT-5A ceramic is(3)T=0T3100T3300T31000T15000T1500=0−5.40015.800−5.400012.300012.300Cm2.(4)
The elastic stiffness coefficient matrix of PZT-5A ceramic is(4)C=C11C13C12000C13C33C13000C12C13C11000000C44000000C66000000C44=12.17.527.540007.5211.17.520007.547.5212.10000002.110000002.260000002.11×1010Nm2. The parameters of the material for metal caps are as follows:(1)
The density of brass is 8600 kg/m3.(2)
Poisson’s ratio of brass is 0.37.(3)
Young’s modulus of elasticity of brass is 10.4 × 1010 N/m2.After building and gridding the model and inputting the diameters of materials, the simulation calculation of the Cymbal transducer was then presented in the abovementioned four aspects including resistance to water pressure, electrical conductance and susceptance, receiving sensitivity, and influence of dimensional difference on performance. In the calculation process, we used the Sparse Direct Solver, which is very powerful. We set the convergence tolerance of force to 10−6 m, which can well solve the problem of convergence [26].


### 3.1. Resistance to Water Pressure

In practical applications, a transducer should be placed at a certain depth in water, so that it is meaningful to study which part of the Cymbal transducer is deformed and how much the deformation occurs at a certain water depth. When the Cymbal transducer is placed at 1 m deep in water, it is exposed to the external water pressure of around 10,000 pa. The external static loading on the Cymbal transducer was analyzed with the finite element method (Figure5).Figure 5
Static loading chart.As shown in Figure6, the analysis results reveal that the maximum amount of deformation occurs near the top of the metal cap of the Cymbal transducer under the effect of external static water pressure.Figure 6
Deformation direction vector.To explore the deformation characteristics of the Cymbal transducer underwater pressure, this paper presented the maximum deformation at different water depths from 10 to 200 m by eliminating the influence of factors such as the air inside the Cymbal cavity and the strength of the adhesive. As shown in Figure7, basically a linear relationship exists between the maximum deformation of the Cymbal transducer and the water depth that is below 200 m. According to Hooke’s law, the Cymbal transducer experiences an elastic deformation under static water pressure at a depth of less than 200 m, which does not easily cause a structural collapse. Hence, the designed Cymbal transducer is suitable for most offshore areas in shallow seas.Figure 7
Maximum deformation curve of the transducer with water depth.When a Cymbal transducer is commonly placed at a water depth of around 10 m, it is not covered by any material; deformation mainly occurs to its metal cap cavity depthh, but the maximum deformation is only 1.62 × 10−5 m, which is very small compared with the transducer size 10−3 m. During production, transducers are normally coated with acoustic transparent rubber or other waterproof packaging material. Thanks to the tension of such a coating, transducers will have relatively small deformation at the same water depth [20], and water depth causes very little disturbance to their performance.


### 3.2. Electrical Conductance and Susceptance

Electrical conductance and susceptance are the major parameters that affect the performance of transducers. The characteristic curve of electrical conductance and susceptance can be obtained as the basis for the calculation of other electromechanical characteristics such as bandwidth, mechanical quality factor, and the effective electromechanical coupling coefficient. Therefore, it is possible to understand the practical performance of transducers in an all-around way.After repeated calculations [18, 19, 21], we found that the resonance frequency of the Cymbal transducer ranged from 3k to 4 kHz when it was placed in water, which met the actual expectations. Figure 8 presents the characteristic curve of electrical conductance and susceptance of the designed Cymbal transducer in the water. The analysis reveals that the frequency at the maximum and minimum electrical susceptance B was f(Bmax) = 3224 Hz and f(Bmin) = 3512 Hz, respectively. The frequency at the maximum electrical conductance G was f(Gmax) = 3350 Hz in which the maximum electrical conductance was Gmax = 7.88e−5 S. Therefore, half of the maximum electrical conductance is Gmax/2 = 3.94e−5 S. The electrical conductance corresponds with two frequencies, i.e., f1 = 3152 Hz and f2 = 3566 Hz.Figure 8
Characteristic curve of conductance and susceptance of the Cymbal transducer in the water.On this basis, the main electromechanical parameters of the Cymbal transducer in water can be calculated as follows [17]:(1)
Mechanical quality factorQm is a physical quantity to measure the energy loss of the piezoelectric vibrator, which indicates the ratio of the mechanical energy stored by the vibrator to the lost mechanical energy in one cycle:(5)Qm=fGmaxfBmin−fBmax=11.6.(2)
−3 dB bandwidth in water Δf is(6)Δf=f2−f1=414Hz,where f1 and f2 are the frequencies corresponding with Gmax/2 mentioned above.(3)
Mechanical quality factor at −3 dB band pass in waterQmd is(7)Qmd=fGmaxf2−f1=8.1.(4)
Electrical quality factorQe is the ratio of the electric energy stored by piezoelectric materials to the electric energy consumed. It reflects the amount of electric energy consumed by piezoelectric materials and transformed into heat energy under the action of alternating voltage:(8)Qe=BSGmax=3.1.where the electrical susceptance corresponding with the maximum electrical conductance Gmax is BS = 2.44e−4 S.(5)
Dynamic branch equivalent resistanceReq is(9)Req=1Gmax=12690.4Ω.(6)
Dynamic branch equivalent capacitanceCeq is(10)Ceq=12πfGmaxQmdReq=4.6e−10F.(7)
Dynamic branch equivalent inductanceLeq is(11)Leq=QmdReq2πfGmax=4.9H.(8)
Effective electromechanical coupling coefficientKeff is(12)Keff=11+QmQe=1−fGmax2fa2=0.16. Therefore, the antiresonance frequency of the Cymbal transducer in water can be calculated to be fa = 3396.3 Hz.The electromechanical characteristics of the Cymbal transducer can be calculated including bandwidth, mechanical quality factor, and effective electromechanical coupling coefficient after obtaining the characteristic curve of its electrical conductance and susceptance. The calculated electromechanical characteristics meet the expectation in the design of the Cymbal transducer.


### 3.3. Receiving Sensitivity

The Cymbal transducer has a great advantage in that it has a relatively high receiving sensitivity, which can increase the target detection distance. In the calculations, a node in the far-field acoustic axis is taken to determine its acoustic pressurep. The distance from the node to the acoustic receiving center is r. The electric charge Q of the node is measured at the positive pole of the ceramic disk. Therefore, the current is [27](13)I=∂Q∂t=jωQ=j2πfQ,where t stands for time, j is an imaginary sign, and f is the vibration frequency of acoustic waves.The transmitting current response level SIL is(14)SIL=Re20logprI+120=20logprI+120.It is measured in dB, where Re represents the real number of the equation. While the acoustic pressurep is complex, its modulus is taken as |p|.Following the spherical wave reciprocity principle, the Cymbal transducer satisfies(15)Js=MfSI=2ρf,where Mf is the free-field voltage sensitivity, SI is the transmitting current response, ρ is the density of the medium, and the ratio JS is a constant.Therefore, the free-field receiving voltage sensitivity level FFVS is(16)FFVS=20log2ρf+SIL−240,=20log2prρfI−120.It is measured in dB.Based on the calculation with the finite element method, the relationship between the receiving voltage sensitivity level FFVS of the Cymbal transducer and the frequencyf is shown in Figure 9.Figure 9
Receiving sensitivity of the transducer.The analysis shows that the receiving sensitivity at the frequencyf = 3320 Hz is the highest, i.e., FFVS = −164.9 dB, while the resonance frequency fr is around 3350 Hz. As for the upper and lower frequencies of the −3 dB bandwidth, there is FFVS1 = −167.3 dB at fs1 = 3152 Hz and FFVS2 = −169.2 dB at fs2 = 3566 Hz. At the frequency range of −3 dB bandwidth, the receiving sensitivity level remains high, and the performance is very good.


### 3.4. Influence of Dimensional Differences on Performance

The actual dimensions of transducers can never remain consistent with their theoretical values because of their unavoidable processing error in production and deformation under static water pressure. The structural deformation inevitably affects the detection performance of transducers. Based on static simulation analysis, the maximum deformation of the Cymbal transducer was 4.87 ×e−5 m when it is under the static water pressure at 30 m, and deformation mainly occurs to the metal cap cavity at depth h. At present, most Chinese factories have a metal processing accuracy of 1 × e−5 m. Deformation errors mainly exist in the metal caps produced during pressing [20].Therefore, this paper took the greater pressure deformation and machining error for research. We assumed that the metal cap cavity depthh of the Cymbal transducer decreased by 4.87 × e−5 m at the water depth of 30 m, but other structural dimensions remained unchanged. The calculations reveal that the performance of the designed Cymbal transducer varies before and after deformation as shown in Figures 10 and 11.Figure 10
Electrical conductance and susceptance of the Cymbal transducer after deformation.Figure 11
Receiving sensitivity of the Cymbal transducer before and after deformation.Note. FFVS, free-field voltage sensitivity level.The electromechanical characteristics of the Cymbal transducer before and after deformation are calculated as shown in Table2.Table 2
Electromechanical parameters before and after deformation.
ItemSymbolBefore deformationAfter deformationDifferential modulusRate of varianceResonance frequency (Hz)fr33503290601.8%Antiresonance frequency (Hz)fa33963330661.9%Mechanical quality factorQm11.612.81.210.3%−3 dB bandwidth (Hz)Δf414402122.9%Mechanical quality factor at −3 dB band passQmd8.18.20.11.2%Electrical quality factorQe3.13.20.13.2%Dynamic branch equivalent resistance (Ω)Req12690.413550.1859.76.8%Dynamic branch equivalent capacitance (F)Ceq4.6e−104.4e−100.2e−104.3%Dynamic branch equivalent inductance (H)Leq4.95.40.510.2%Effective electromechanical coupling coefficientKeff0.160.150.016.3%After comparing the performance parameters of the Cymbal transducer, we found that its main parameters including resonance frequencyfr, bandwidth Δf, electrical quality factor Qe, and equivalent capacitance Ceq vary slightly at a rate of less than 5%. Moreover, its equivalent resistance Req and effective electromechanical coupling coefficient Keff change at a rate of 6%, having little influence on the performance of the unit. However, the highest rate of variance happens to the mechanical quality factor Qm and equivalent inductance Leq. The receiving sensitivity of FFVS is not significantly affected, but its curve shifts slightly toward a low frequency.Obviously, processing accuracy and water pressure do not significantly affect most electromechanical properties of transducers in practice, but some electromechanical properties are very sensitive to the variation of cap cavity depth. To improve the Cymbal transducer’s resistance to pressure and deformation, the influence of deformation can be offset by filling the cavity with special oil or silica gel, adding a pressure-resisting coating, forming an array with a shared baffle plate, or adjusting the size of the transducer based on the water depth at which it is used.


## 3.1. Resistance to Water Pressure

In practical applications, a transducer should be placed at a certain depth in water, so that it is meaningful to study which part of the Cymbal transducer is deformed and how much the deformation occurs at a certain water depth. When the Cymbal transducer is placed at 1 m deep in water, it is exposed to the external water pressure of around 10,000 pa. The external static loading on the Cymbal transducer was analyzed with the finite element method (Figure5).Figure 5
Static loading chart.As shown in Figure6, the analysis results reveal that the maximum amount of deformation occurs near the top of the metal cap of the Cymbal transducer under the effect of external static water pressure.Figure 6
Deformation direction vector.To explore the deformation characteristics of the Cymbal transducer underwater pressure, this paper presented the maximum deformation at different water depths from 10 to 200 m by eliminating the influence of factors such as the air inside the Cymbal cavity and the strength of the adhesive. As shown in Figure7, basically a linear relationship exists between the maximum deformation of the Cymbal transducer and the water depth that is below 200 m. According to Hooke’s law, the Cymbal transducer experiences an elastic deformation under static water pressure at a depth of less than 200 m, which does not easily cause a structural collapse. Hence, the designed Cymbal transducer is suitable for most offshore areas in shallow seas.Figure 7
Maximum deformation curve of the transducer with water depth.When a Cymbal transducer is commonly placed at a water depth of around 10 m, it is not covered by any material; deformation mainly occurs to its metal cap cavity depthh, but the maximum deformation is only 1.62 × 10−5 m, which is very small compared with the transducer size 10−3 m. During production, transducers are normally coated with acoustic transparent rubber or other waterproof packaging material. Thanks to the tension of such a coating, transducers will have relatively small deformation at the same water depth [20], and water depth causes very little disturbance to their performance.


## 3.2. Electrical Conductance and Susceptance

Electrical conductance and susceptance are the major parameters that affect the performance of transducers. The characteristic curve of electrical conductance and susceptance can be obtained as the basis for the calculation of other electromechanical characteristics such as bandwidth, mechanical quality factor, and the effective electromechanical coupling coefficient. Therefore, it is possible to understand the practical performance of transducers in an all-around way.After repeated calculations [18, 19, 21], we found that the resonance frequency of the Cymbal transducer ranged from 3k to 4 kHz when it was placed in water, which met the actual expectations. Figure 8 presents the characteristic curve of electrical conductance and susceptance of the designed Cymbal transducer in the water. The analysis reveals that the frequency at the maximum and minimum electrical susceptance B was f(Bmax) = 3224 Hz and f(Bmin) = 3512 Hz, respectively. The frequency at the maximum electrical conductance G was f(Gmax) = 3350 Hz in which the maximum electrical conductance was Gmax = 7.88e−5 S. Therefore, half of the maximum electrical conductance is Gmax/2 = 3.94e−5 S. The electrical conductance corresponds with two frequencies, i.e., f1 = 3152 Hz and f2 = 3566 Hz.Figure 8
Characteristic curve of conductance and susceptance of the Cymbal transducer in the water.On this basis, the main electromechanical parameters of the Cymbal transducer in water can be calculated as follows [17]:(1)
Mechanical quality factorQm is a physical quantity to measure the energy loss of the piezoelectric vibrator, which indicates the ratio of the mechanical energy stored by the vibrator to the lost mechanical energy in one cycle:(5)Qm=fGmaxfBmin−fBmax=11.6.(2)
−3 dB bandwidth in water Δf is(6)Δf=f2−f1=414Hz,where f1 and f2 are the frequencies corresponding with Gmax/2 mentioned above.(3)
Mechanical quality factor at −3 dB band pass in waterQmd is(7)Qmd=fGmaxf2−f1=8.1.(4)
Electrical quality factorQe is the ratio of the electric energy stored by piezoelectric materials to the electric energy consumed. It reflects the amount of electric energy consumed by piezoelectric materials and transformed into heat energy under the action of alternating voltage:(8)Qe=BSGmax=3.1.where the electrical susceptance corresponding with the maximum electrical conductance Gmax is BS = 2.44e−4 S.(5)
Dynamic branch equivalent resistanceReq is(9)Req=1Gmax=12690.4Ω.(6)
Dynamic branch equivalent capacitanceCeq is(10)Ceq=12πfGmaxQmdReq=4.6e−10F.(7)
Dynamic branch equivalent inductanceLeq is(11)Leq=QmdReq2πfGmax=4.9H.(8)
Effective electromechanical coupling coefficientKeff is(12)Keff=11+QmQe=1−fGmax2fa2=0.16. Therefore, the antiresonance frequency of the Cymbal transducer in water can be calculated to be fa = 3396.3 Hz.The electromechanical characteristics of the Cymbal transducer can be calculated including bandwidth, mechanical quality factor, and effective electromechanical coupling coefficient after obtaining the characteristic curve of its electrical conductance and susceptance. The calculated electromechanical characteristics meet the expectation in the design of the Cymbal transducer.


## 3.3. Receiving Sensitivity

The Cymbal transducer has a great advantage in that it has a relatively high receiving sensitivity, which can increase the target detection distance. In the calculations, a node in the far-field acoustic axis is taken to determine its acoustic pressurep. The distance from the node to the acoustic receiving center is r. The electric charge Q of the node is measured at the positive pole of the ceramic disk. Therefore, the current is [27](13)I=∂Q∂t=jωQ=j2πfQ,where t stands for time, j is an imaginary sign, and f is the vibration frequency of acoustic waves.The transmitting current response level SIL is(14)SIL=Re20logprI+120=20logprI+120.It is measured in dB, where Re represents the real number of the equation. While the acoustic pressurep is complex, its modulus is taken as |p|.Following the spherical wave reciprocity principle, the Cymbal transducer satisfies(15)Js=MfSI=2ρf,where Mf is the free-field voltage sensitivity, SI is the transmitting current response, ρ is the density of the medium, and the ratio JS is a constant.Therefore, the free-field receiving voltage sensitivity level FFVS is(16)FFVS=20log2ρf+SIL−240,=20log2prρfI−120.It is measured in dB.Based on the calculation with the finite element method, the relationship between the receiving voltage sensitivity level FFVS of the Cymbal transducer and the frequencyf is shown in Figure 9.Figure 9
Receiving sensitivity of the transducer.The analysis shows that the receiving sensitivity at the frequencyf = 3320 Hz is the highest, i.e., FFVS = −164.9 dB, while the resonance frequency fr is around 3350 Hz. As for the upper and lower frequencies of the −3 dB bandwidth, there is FFVS1 = −167.3 dB at fs1 = 3152 Hz and FFVS2 = −169.2 dB at fs2 = 3566 Hz. At the frequency range of −3 dB bandwidth, the receiving sensitivity level remains high, and the performance is very good.


## 3.4. Influence of Dimensional Differences on Performance

The actual dimensions of transducers can never remain consistent with their theoretical values because of their unavoidable processing error in production and deformation under static water pressure. The structural deformation inevitably affects the detection performance of transducers. Based on static simulation analysis, the maximum deformation of the Cymbal transducer was 4.87 ×e−5 m when it is under the static water pressure at 30 m, and deformation mainly occurs to the metal cap cavity at depth h. At present, most Chinese factories have a metal processing accuracy of 1 × e−5 m. Deformation errors mainly exist in the metal caps produced during pressing [20].Therefore, this paper took the greater pressure deformation and machining error for research. We assumed that the metal cap cavity depthh of the Cymbal transducer decreased by 4.87 × e−5 m at the water depth of 30 m, but other structural dimensions remained unchanged. The calculations reveal that the performance of the designed Cymbal transducer varies before and after deformation as shown in Figures 10 and 11.Figure 10
Electrical conductance and susceptance of the Cymbal transducer after deformation.Figure 11
Receiving sensitivity of the Cymbal transducer before and after deformation.Note. FFVS, free-field voltage sensitivity level.The electromechanical characteristics of the Cymbal transducer before and after deformation are calculated as shown in Table2.Table 2
Electromechanical parameters before and after deformation.
ItemSymbolBefore deformationAfter deformationDifferential modulusRate of varianceResonance frequency (Hz)fr33503290601.8%Antiresonance frequency (Hz)fa33963330661.9%Mechanical quality factorQm11.612.81.210.3%−3 dB bandwidth (Hz)Δf414402122.9%Mechanical quality factor at −3 dB band passQmd8.18.20.11.2%Electrical quality factorQe3.13.20.13.2%Dynamic branch equivalent resistance (Ω)Req12690.413550.1859.76.8%Dynamic branch equivalent capacitance (F)Ceq4.6e−104.4e−100.2e−104.3%Dynamic branch equivalent inductance (H)Leq4.95.40.510.2%Effective electromechanical coupling coefficientKeff0.160.150.016.3%After comparing the performance parameters of the Cymbal transducer, we found that its main parameters including resonance frequencyfr, bandwidth Δf, electrical quality factor Qe, and equivalent capacitance Ceq vary slightly at a rate of less than 5%. Moreover, its equivalent resistance Req and effective electromechanical coupling coefficient Keff change at a rate of 6%, having little influence on the performance of the unit. However, the highest rate of variance happens to the mechanical quality factor Qm and equivalent inductance Leq. The receiving sensitivity of FFVS is not significantly affected, but its curve shifts slightly toward a low frequency.Obviously, processing accuracy and water pressure do not significantly affect most electromechanical properties of transducers in practice, but some electromechanical properties are very sensitive to the variation of cap cavity depth. To improve the Cymbal transducer’s resistance to pressure and deformation, the influence of deformation can be offset by filling the cavity with special oil or silica gel, adding a pressure-resisting coating, forming an array with a shared baffle plate, or adjusting the size of the transducer based on the water depth at which it is used.


## 4. Fabrication and Experiment

To verify the correctness of the performance parameters of the Cymbal transducer in the above simulation, a corresponding prototype was fabricated using the structural dimensions calculated in the simulation, and relevant performance tests were conducted with the help of Wuhan Tianjin Technology Co., Ltd.


### 4.1. Fabrication of Prototype

A mold is needed to fabricate the metal caps. The mold consists of two parts, i.e., upper and lower parts. The upper and lower parts are used in the forming to fix the shape and size of the metal caps. The mold was made of steelCr12. The image of the mold is presented in Figure 12.Figure 12
Forming mold (the upper part on the left and the lower part on the right).A single metal cap was formed by pressing the metal three times under a pressure of 15°t. After each pressing, the cap should be rotated by 120° to guarantee even pressing. In batch production, three or more molds could be used simultaneously and fixed at a certain angle on the same straight line. Three brass pieces can be pressed from different angles at the same time when they are conveyed on the belt. Each brass piece passes through three molds progressively to be formed into the cap. The formed cap needs to be polished with 200-mesh abrasive paper for deburring. Subsequently, the cap is immersed in alcohol or acetone for cleaning to facilitate the subsequent bonding. At present, the polishing technology for piezoelectric ceramic pieces and metal devices has reached the hyperfine level. In other words, the machining accuracy is up to 0.1μm, and the surface roughness is less than 0.02 to 0.01 μm. Moreover, some new technological methods have been developed such as abrading in liquid, mechanical-chemical abrading, chemical-mechanical polishing, and nondestructive surface polishing, which is beneficial to eliminate the influence of dimensional errors on the performance of Cymbal.The Cymbal transducer had its piezoelectric ceramic and metal caps bonded by the KingStar K-818 conductive silver paint adhesive. The bonding technique exerts a very noticeable effect on such characteristics of the Cymbal transducer as it changes its sensitivity to static water pressure and impedance frequency [20]. The research team designed a silk screen printing method. In this method, the prepared adhesive is evenly distributed on a special dust-free plate and then covered by a piece of clean gauze. The ceramic disk is placed flatly on the gauze and pushed properly and evenly to uniformly smear it with the adhesive. In addition, the adhesive thickness may be controlled within 10 μm to guarantee that the conductance is uniform between the ceramic disk and the caps. This method is easy to perform and applicable to the batch production of Cymbal transducers. After bonding the Cymbal transducer, a special holder may be used to hold it together against any internal stress and it should be precured at room temperature for 15 minutes and then be placed within a 40°C drying oven for 15 minutes. This can make a thinner and create a more uniform bonding layer and finally be baked at 60 °C for 30 minutes. After being precured, the hydrostatic piezoelectric properties of the Cymbal transducer can nearly double [20].The final Cymbal prototype as fabricated by the research team is presented in Figure13.Figure 13
The Cymbal prototype before (a) and after (b) encapsulation experiment.In the experiment, this paper mainly tests the electrical conductance and susceptance as well as the receiving sensitivity of the prototype. The simulation results were compared with the results obtained in the test to determine whether the designed Cymbal transducer is reliable based on its resistance to pressure and the influence of dimensional errors.


### 4.2. Measured Electrical Conductance and Susceptance

We measured the electrical conductance and susceptance of the prototype as shown in Figure14 by using the cylindrical wave emitted by the standard transmitting transducer in the anechoic pool [28]. The test instrument is an HP4294 A impedance analyzer. We found that the encapsulated prototype had a frequency at the maximum electrical conductance of f(Gmaxp) = 3503 Hz, which was 4.5% higher than its calculated value in the simulation which was f(Gmax) = 3350 Hz. This difference was acceptable. We, therefore, inferred that the other electromechanical characteristics of the prototype in the test were not much different from the calculated values in the simulation. This difference was mainly attributed to the uneven application or insufficient curing of the adhesive in the manufacturing process. In addition, the acoustic transmission characteristics of the prototype packaging layer and the effect of its tension would also cause the frequency error, loss of sensitivity, and other characteristics of the transducer [20].Figure 14
Measured conductance and susceptance characteristic curve of the prototype in water.


### 4.3. Measured Receiving Sensitivity

In this paper, the free-field comparison method was employed to measure the receiving sensitivity of the prototype at five frequency points. According to the test report of the prototype, the measured receiving sensitivity of the Cymbal transducer reached −173.1 dB at the frequency off = 3150 Hz, but its calculated value in the simulation was −167.3 dB at the same frequency as shown in Figure 15. The difference was 5.8 dB. When the frequency f was 4000 Hz, the receiving sensitivity reached FFVS = −176.6 dB, and the calculated value in the simulation was −176.8 dB. The difference was 0.2 dB. There was not much difference between the calculated and measured values, and such difference was acceptable. In other words, the designed transducer actually had a high receiving sensitivity, which could help increase the detection distance of frogmen in practical applications. The difference might be caused by the interference of noise around the test environment, the drift of the test devices, or the imprecision in the fabrication of the prototype.Figure 15
Simulated and experimental sensitivities of the transducer.The test results of the prototype’s electrical conductance and susceptance as well as receiving sensitivity were highly consistent with the calculated values in the simulation, and the performance of the prototype met our expectations. This proved the correctness of the finite element method and its calculation results. On this basis, we inferred that the calculation results could reliably reflect how the performance of the Cymbal transducer was affected by the resistance to pressure and dimensional differences.A prototype was used to detect a frogman with open-circuit breathing in a rectangular swimming pool, and the R62 standard hydrophone (−209 dB@ 1 kHz) of Wuhan Tianjin Technology Company was used for the comparative test. The pool used in the test is 10 m long, 5 m wide, and 3 m deep. The two hydrophones were horizontally in the same position, with a distance of 0.1 m between them as shown in Figure16. They were arranged at the bottom of the pool using brackets, about 0.3 m from the bottom of the pool and the side pool wall. When a frogman was snorkeling, the distance from both sides of the pool wall was basically equal, and the frogman swam back and forth at a water depth of about 2 m. The distance between the swimming route and the two hydrophones was 2.2 m.Figure 16
Layout of the test environment.The collected frogman signal was amplified by the front end of 40 dB and showed obvious breathing cycles, which was consistent with the experimental results of Alexander Sutin of Stevens Institute of Technology and Lohrasbipeydeh of Victoria University in Canada. It can be seen from the time-domain diagrams of the two transducers as shown in Figure17 that the designed Cymbal transducer’s received signal voltage amplitude was about 10 times (20 dB) that of the standard hydrophone, which showed that the sensitivity of the designed Cymbal transducer is significantly higher than the standard hydrophone used, which was conducive to increasing the detection range of the frogman. However, while using the prototype to collect the frogman's breathing signal, there were other chaotic signal waveforms in the time-domain diagram, which may be the bottom noise of the produced prototype or other noises such as the frogman's rowing, which need to be further analyzed in the subsequent signal processing.Figure 17
Frogman time-domain signals received by two hydrophones.


## 4.1. Fabrication of Prototype

A mold is needed to fabricate the metal caps. The mold consists of two parts, i.e., upper and lower parts. The upper and lower parts are used in the forming to fix the shape and size of the metal caps. The mold was made of steelCr12. The image of the mold is presented in Figure 12.Figure 12
Forming mold (the upper part on the left and the lower part on the right).A single metal cap was formed by pressing the metal three times under a pressure of 15°t. After each pressing, the cap should be rotated by 120° to guarantee even pressing. In batch production, three or more molds could be used simultaneously and fixed at a certain angle on the same straight line. Three brass pieces can be pressed from different angles at the same time when they are conveyed on the belt. Each brass piece passes through three molds progressively to be formed into the cap. The formed cap needs to be polished with 200-mesh abrasive paper for deburring. Subsequently, the cap is immersed in alcohol or acetone for cleaning to facilitate the subsequent bonding. At present, the polishing technology for piezoelectric ceramic pieces and metal devices has reached the hyperfine level. In other words, the machining accuracy is up to 0.1μm, and the surface roughness is less than 0.02 to 0.01 μm. Moreover, some new technological methods have been developed such as abrading in liquid, mechanical-chemical abrading, chemical-mechanical polishing, and nondestructive surface polishing, which is beneficial to eliminate the influence of dimensional errors on the performance of Cymbal.The Cymbal transducer had its piezoelectric ceramic and metal caps bonded by the KingStar K-818 conductive silver paint adhesive. The bonding technique exerts a very noticeable effect on such characteristics of the Cymbal transducer as it changes its sensitivity to static water pressure and impedance frequency [20]. The research team designed a silk screen printing method. In this method, the prepared adhesive is evenly distributed on a special dust-free plate and then covered by a piece of clean gauze. The ceramic disk is placed flatly on the gauze and pushed properly and evenly to uniformly smear it with the adhesive. In addition, the adhesive thickness may be controlled within 10 μm to guarantee that the conductance is uniform between the ceramic disk and the caps. This method is easy to perform and applicable to the batch production of Cymbal transducers. After bonding the Cymbal transducer, a special holder may be used to hold it together against any internal stress and it should be precured at room temperature for 15 minutes and then be placed within a 40°C drying oven for 15 minutes. This can make a thinner and create a more uniform bonding layer and finally be baked at 60 °C for 30 minutes. After being precured, the hydrostatic piezoelectric properties of the Cymbal transducer can nearly double [20].The final Cymbal prototype as fabricated by the research team is presented in Figure13.Figure 13
The Cymbal prototype before (a) and after (b) encapsulation experiment.In the experiment, this paper mainly tests the electrical conductance and susceptance as well as the receiving sensitivity of the prototype. The simulation results were compared with the results obtained in the test to determine whether the designed Cymbal transducer is reliable based on its resistance to pressure and the influence of dimensional errors.


## 4.2. Measured Electrical Conductance and Susceptance

We measured the electrical conductance and susceptance of the prototype as shown in Figure14 by using the cylindrical wave emitted by the standard transmitting transducer in the anechoic pool [28]. The test instrument is an HP4294 A impedance analyzer. We found that the encapsulated prototype had a frequency at the maximum electrical conductance of f(Gmaxp) = 3503 Hz, which was 4.5% higher than its calculated value in the simulation which was f(Gmax) = 3350 Hz. This difference was acceptable. We, therefore, inferred that the other electromechanical characteristics of the prototype in the test were not much different from the calculated values in the simulation. This difference was mainly attributed to the uneven application or insufficient curing of the adhesive in the manufacturing process. In addition, the acoustic transmission characteristics of the prototype packaging layer and the effect of its tension would also cause the frequency error, loss of sensitivity, and other characteristics of the transducer [20].Figure 14
Measured conductance and susceptance characteristic curve of the prototype in water.


## 4.3. Measured Receiving Sensitivity

In this paper, the free-field comparison method was employed to measure the receiving sensitivity of the prototype at five frequency points. According to the test report of the prototype, the measured receiving sensitivity of the Cymbal transducer reached −173.1 dB at the frequency off = 3150 Hz, but its calculated value in the simulation was −167.3 dB at the same frequency as shown in Figure 15. The difference was 5.8 dB. When the frequency f was 4000 Hz, the receiving sensitivity reached FFVS = −176.6 dB, and the calculated value in the simulation was −176.8 dB. The difference was 0.2 dB. There was not much difference between the calculated and measured values, and such difference was acceptable. In other words, the designed transducer actually had a high receiving sensitivity, which could help increase the detection distance of frogmen in practical applications. The difference might be caused by the interference of noise around the test environment, the drift of the test devices, or the imprecision in the fabrication of the prototype.Figure 15
Simulated and experimental sensitivities of the transducer.The test results of the prototype’s electrical conductance and susceptance as well as receiving sensitivity were highly consistent with the calculated values in the simulation, and the performance of the prototype met our expectations. This proved the correctness of the finite element method and its calculation results. On this basis, we inferred that the calculation results could reliably reflect how the performance of the Cymbal transducer was affected by the resistance to pressure and dimensional differences.A prototype was used to detect a frogman with open-circuit breathing in a rectangular swimming pool, and the R62 standard hydrophone (−209 dB@ 1 kHz) of Wuhan Tianjin Technology Company was used for the comparative test. The pool used in the test is 10 m long, 5 m wide, and 3 m deep. The two hydrophones were horizontally in the same position, with a distance of 0.1 m between them as shown in Figure16. They were arranged at the bottom of the pool using brackets, about 0.3 m from the bottom of the pool and the side pool wall. When a frogman was snorkeling, the distance from both sides of the pool wall was basically equal, and the frogman swam back and forth at a water depth of about 2 m. The distance between the swimming route and the two hydrophones was 2.2 m.Figure 16
Layout of the test environment.The collected frogman signal was amplified by the front end of 40 dB and showed obvious breathing cycles, which was consistent with the experimental results of Alexander Sutin of Stevens Institute of Technology and Lohrasbipeydeh of Victoria University in Canada. It can be seen from the time-domain diagrams of the two transducers as shown in Figure17 that the designed Cymbal transducer’s received signal voltage amplitude was about 10 times (20 dB) that of the standard hydrophone, which showed that the sensitivity of the designed Cymbal transducer is significantly higher than the standard hydrophone used, which was conducive to increasing the detection range of the frogman. However, while using the prototype to collect the frogman's breathing signal, there were other chaotic signal waveforms in the time-domain diagram, which may be the bottom noise of the produced prototype or other noises such as the frogman's rowing, which need to be further analyzed in the subsequent signal processing.Figure 17
Frogman time-domain signals received by two hydrophones.


## 5. Conclusions

We analyzed the performance parameters of mainstream sonar transducers for the detection of underwater frogmen in the world and demonstrated the advantages and disadvantages of active and passive detection methods. Next, we chose the passive detection method. To achieve a satisfying detection, we selected a Cymbal transducer featuring simple structure, low frequency, small size, and high sensitivity in the research. After introducing its principles, the finite element method was employed to explore how the Cymbal transducer’s acoustic and electromechanical characteristics were affected by the structural and dimensional parameters of the transducer. On this basis, the electromechanical characteristics of the designed Cymbal transducer in water were calculated such as resonance frequency 3350 Hz, bandwidth 414 Hz, and maximum receiving sensitivity −164.9 dB. Additionally, the calculation results revealed that the electromechanical properties of the designed transducer were not significantly affected by the pressure at the water depth of fewer than 200 m and had a processing error of 1 ×e−5 m, proving its feasibility in practical applications. The effectiveness of the finite element method was demonstrated by performing a test with the fabricated prototype. It showed that the designed Cymbal transducer could be used in the passive detection of underwater frogmen with open-circuit breathing. The research in this paper provides some references for the industry. However, whether the bandwidth is suitable for detection, the measures to reduce the bottom noise, the consistency in the production process of the prototype, and the influence law of the environment on the service life are the key problems that limit the practical application of the transducer, which is worthy of further research.



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*Source: 7438749-2022-06-16.xml*