Design of a Broadband Cavity Baffle Bender Transducer

Abstract

As low-frequency and broadband acoustic emission capability is beneficial to the detection range and acoustic communication speed of small scale autonomous underwater vehicles (AUV), this type of transducer is required, especially in cases of complex acoustic environments. A broadband bender transducer with cavity baffle that suits small scale AUV is proposed. Rather than additional benders, a passive cavity baffle, which would be capable of providing mutual radiation and a fluid cavity mode, is introduced to a single bender. The bending resonant frequency is reduced by the mutual radiation between the bender and the cavity baffle, the cavity baffle extends the lower limit of the available frequency band of the transducer, the liquid resonant frequency behind the former expands the higher limit, then the cavity baffle bender transducer fills the role of radiating low-frequency and broadband emissions through multimode coupling. The finite element method is used to analyze the acoustic performance of the transducer under different baffle conditions. Then, a prototype of the broadband cavity baffle bender transducer is developed according to the optimized parameters of simulation. The acoustic parameters of the prototype were measured in an anechoic pool. The resonant frequency measured in water of the bender itself is 3 kHz, and the −3dB bandwidth is 560 Hz. The prototype test results show that the cavity baffle scheme can improve the −3dB bandwidth of the bender from 560 Hz to 1000 Hz, which fundamentally realizes the expectations of the prototype design.

1. Introduction

AUVs are a type of underwater vehicle that can carry various loads. They have been unprecedentedly developed in the fields of chart drawing, acoustic communication, and marine environmental monitoring [1]. To fulfill communication, navigation, and detection functions, AUVs are equipped with acoustic systems commonly used for underwater information exchange. Typical devices include communication and navigation sonar based on free-flooded ring transducers [2,3] and detection sonar based on longitudinal vibration transducers [4,5]. Sonar technique applications present the principal need for underwater sound transducers and the main motivation for new transducer developments [6]. As low-frequency and broadband acoustic emission capability helps to improve the detection range of the system [7], low-frequency and broadband acoustic sources are one of the current research directions for transmitting transducers [8], and the demand for such acoustic sources in ocean acoustic tomography [9], acoustic countermeasures [10], and acoustic communication [11,12] is growing, especially in the case of complex acoustic environments [13,14].

Since the resonant frequency of the transducer is usually inversely proportional to its geometric size [15], it is inconvenient for small-scale AUVs to carry large-scale low-frequency transducers as acoustic loads [16,17]. Owing to the low bending stiffness of the metal disc, the bender transducer has the characteristics of low frequency and small size synchronously [18,19,20], and it is a type of transducer with a high space utilization ratio. Therefore, the bender is an available technical method to realize small size, low weight, and low frequency for sound sources loaded on small and medium-scale AUVs. Due to the high Q value, the bandwidth does not meet the requirements of broadband emission. Researchers have carried out a series of experiments on the bender, improved its structure or combined it with other forms of transducers, and expanded its bandwidth by multimode coupling.

John L. Delany [21] proposed a bender structure with an air cavity to suppress back radiation and improve efficiency and pressure-resistant capacity. Ajesh Kumar et al. [22] analyzed the influence of structural size on the acoustic performance of benders and calculated the theoretical source level under static pressure. Daisuke Watanabe et al. [23] proposed a transducer supported by a radial movable bearing, which is conducive to the smooth change of the resonant frequency corresponding to different excitation frequencies. This structure broadens the bandwidth of the transducer by 4.6 times. Through the mutual radiation introduced by the close-packed axial mechanical series of vertical transducer elements(modular projector system, MPS), B. Armstrong and James Crawford [24] achieve the purpose of low-frequency, high-power radiation by the bender. Mitsuru Yamamoto et al. [25] combined six bender elements with different sizes and piezoelectric ceramic excitation modes to form a close-packed vertical array which realized the bandwidth expansion of the system. Mo X.P. [26] developed a new type of broadband transducer based on a free-flooded cavity and a phase-driving technique. Three groups of vibration pairs are in axial mechanical series and placed in the barrel. When the phase difference between the vibration pairs of the bender is 270°, the transmitting voltage response (TVR) fluctuation of the transducer is less than 10 dB in the frequency range of 750 Hz to 4000 Hz.

Most of the above use a method to extend the bandwidth through the mutual radiation introduced by multiple benders, whereas there are few studies that maintain a relatively small volume on the bandwidth expansion of a single bender. In this paper, the design idea of multimode coupling is adopted to broaden the bandwidth of a single bender. In the transducer—rather than additional benders—a cavity baffle, which would be capable of providing mutual radiation and a fluid cavity mode is introduced to a single bender. The bender is placed concentrically in the center of the cavity baffle, and there is a gap between them. Then, a bending mode of the bender and a fluid cavity mode are available to realize multimode coupling once they are set in suitable positions. The first-order bending resonance frequency of the bender can be reduced by the mutual radiation between the bender and the cavity baffle, and the coupling with the liquid cavity resonance is beneficial to the bandwidth expansion. The reduction in bending resonant frequency extends the lower limit of the available frequency band of the transducer, and a liquid resonant frequency behind the former expands the higher limit. Then, the cavity baffle bender transducer gains low-frequency and broadband radiation abilities, and the cavity baffle conforms easily to the submarine, which is helpful in improving the acoustic detection capability of AUVs.

2. Vibration and Radiation Characteristics

Figure 1 shows the schematic diagram of the transducer, which contains an air-backing bender, a cavity baffle, and a spare diaphragm. In the bender, two thickness-polarized piezoelectric ceramics are bonded to the outside of the two metal discs, the non-piezoelectric ceramic side of the metal disc is connected, and the whole structure is wrapped in flexible waterproof material. When the polarization directions of the two piezoelectric ceramics are the same, the circuit is connected in series, and if they are contrary, it is connected in parallel. The two piezoelectric ceramics vibrate along an external normal direction when excited, and they drive the bending vibration of the overall structure and then radiate sound waves outward. There is a large gap between the bender and the baffle. When the two radiation surfaces of the bender are separated by a diaphragm in the gap, the transmission voltage response of the vibration system is almost unchanged. This indicates that the mutual radiation between the two radiation surfaces of the bender does not play a leading role in the calculation frequency band when the bender is in the center of the baffle.

The equivalent circuit diagram of the transducer could be drawn as Figure 2, where $C_0$ is static capacitance of the bender; $R_m$, $C_m$, and $M_m$ are mechanical impedances of the bender; $R_r$ and $M_r$ are radiation impedances of the bender. The variation of the radiation impedance of the bender after the introduction of the baffle can be expressed by the difference between the piston end impedance of the piston driver in the open-ended unflanged pipe driven by a planar piston [27] and the radiation impedance of the bender itself shown in Equation (1), where $r_b$, $S_b$ are the radius and cross-sectional area of the baffle, respectively; $r$, $S$ are the radius and area of the radiating surface of the bender, respectively; and the mutual radiation effect between the bender and the baffle is feasibly equivalent to the mutual radiation resistance $\Delta R_r$ and the mutual radiation mass reactance $\Delta X_r$, which are combined equivalently with the radiation impedance of the bender itself in the acoustic end. The effectiveness of the baffle and the liquid cavity is equivalent to the acoustic resistance $R_a$, the acoustic mass $M_a$ and $M_b$, and the acoustic compliance $C_a$ and $C_b$ of the radiation impedance branch of the bender paralleled by the transformer [28,29]. Then, a resonant branch which provides the possibility for the transducer to realize multimode coupling is introduced to the circuit when the two resonant frequencies are relatively close. The frequency of the bending mode $f_1$ related to the mutual radiation mass reactance $\Delta X_r$ is given by Equation (2). In other words, the resonant frequency of the bending mode will move forward if $\Delta X_r$ is positive, and it shall extend the lower limit of the available frequency band of the transducer. If the resonant frequency of the liquid cavity mode with an elastic cavity baffle can be solved by Equation (3) [28], then it is possible to achieve coupling of the bending mode and fluid cavity mode as the Janus-Helmholtz Bell transducer does to a certain extent when the latter is properly placed [30].

$$\Delta Z_r=\Delta R_r+j\Delta X_r=2{\rho }_0{c}_0\left(S_b\frac{\left({\left(k{r}_b/2\right)}^2+j0.6k{r}_b\right)+j\tan \frac{kl}{2}}{1+j\left({\left(k{r}_b/2\right)}^2+j0.6k{r}_b\right)\tan \frac{kl}{2}}-S\left(1-\frac{2J_1\left(2kr\right)}{2kr}+j\frac{K_1\left(2kr\right)}{2{\left(kr\right)}^2}\right)\right),$$

(1)

$$f_1=\frac{1}{2\pi }{\left(\frac{1}{C_m(M_m+M_r+\Delta X_r}\right)}^{1/2},$$

(2)

$${\omega }_2={\left(M_a\left(C_a+\frac{C_b}{1-{\omega }_2{}^2{M}_b{C}_b}\right)\right)}^{-1/2},$$

(3)

The finite element software is used to analyze the acoustic properties of the transducer because the equivalent circuit is inconvenient for showing the effectiveness of the mode coupling. If in the one-fourth two-dimensional axisymmetric finite element modal shown in Figure 3, structural details such as adhesive layer and waterproof layer that have little effect on vibration are neglected and the main structures are wrapped in nearby fluid whose element type consists of the degree of structural freedom, then the structural motion and fluid pressure at the interface will be coupled and the fluid without a degree of structural freedom whose radius is two times the wavelength of the low-frequency end of the interested band is applied outside the nearby fluid to simulate the far-field fluid domain. Moreover, the boundary line realizes a second-order-absorbing boundary condition so that an outgoing pressure wave reaching the boundary of the modal is absorbed with minimal reflections back into the fluid domain. Due to the symmetrical structure of the transducer, only one-half or even onefourth of the plane model needs to be established. After applying the symmetrical boundary conditions to the bottom line, it can be equivalent to a complete model. Regarding materials, the piezoelectric ceramics are lead zirconate titanate(PZT), the disc uses titanium alloy, and the baffles uses steel.

The resonant frequency of the bender itself is 3 kHz. After the baffle is introduced, there are two resonant peaks, which are located on both sides of the resonant peak of the bender itself. The sound pressure and displacement distribution of the two-order resonant frequency with and without baffle calculated by the finite element model are shown in Figure 4. The first-order resonant frequency is 2740 Hz, and it is slightly lower than that of the bender itself. The vibration mode is the first-order bending mode of the bender. Around the first-order resonant frequency, the impedance difference of the transducer with and without the baffle is positive, as shown in Figure 5, where $\Delta R$ and $\Delta X$ are the real part and imaginary part of the impedance difference between the transducer with baffle and the bender itself, respectively. Combined with the equivalent circuit, it could be considered that the decrease in the first-order resonant frequency is due to the increase in the mutual radiation resistance caused by the mutual radiation between the bender and the baffle. Regarding the second-order vibration mode, the second-order resonant frequency is 3700 Hz, which is lower than the resonant frequency of the free-flooded breathing mode of the cavity baffle calculated by Equation (4) of 4990 Hz, and it is similar to the estimated liquid cavity resonant frequency calculated by Equation (3) of 3347 Hz when the cavity volume is occupied by the bender, which, if unconsidered, will increase the resonant frequency. The estimated frequency is 3861 Hz after the change introduced by the volume of the bender is brought into the intermediate variable related to the volume of the liquid cavity in the equation, and it is closer to the second-order resonant frequency of 3700 Hz modelled by the finite element model. In contrast, the sound pressure distribution approximates liquid cavity resonance where the pressure decreases from the center to both ends gradually, and the sound pressure in the 0° and 180° directions of the transducer is merely slightly lower, as shown in Figure 6, which is the distribution image of sound pressure, which is contrary to the directivity of the free-flood breathing vibration of the cavity baffle. While the sound pressure distribution has no obvious gradient change at the two frequencies of the bender itself as there is a large interval between the first and the second resonant frequencies, it would vibrate in its first-order vibration form in a wide frequency range near the first resonant frequency, and the fluctuations of the directivity diagrams of the bender itself at two frequencies are less than 1 dB. Taking the analysis above into consideration, it can be approximated that the second-order mode is the liquid cavity resonance under the conditions of elastic baffling. There is a large gap between the bender and the cavity baffle in the transducer when the length and radius of the baffle are approximate, thus it is inaccurate to analogize the excitation source with the planar piston. Its form and sound pressure distribution are different from those of the Helmholtz resonator, and there is no obvious ‘∞’-shaped directivity similar to that of the Helmholtz resonator at the second resonance. The vibration of the cavity may also have great influence on the circumferential acoustic radiation of the transducer.

The resonant frequency of the free-flood breathing mode of a ring is given by [30]:

$$f_r=\frac{c}{2\pi r_b}{\left(1+\frac{{\rho }_0\sqrt{r_{b}L/2}}{\rho t}\right)}^{-1/2},$$

(4)

where $r_b$ is radius, $L$ is length, $t$ is thickness, $\rho$ is density, $c$ is ring longitudinal wave velocity of the ring, and ${\rho }_0$ is fluid density. The resonance frequency of the baffle is far away from the bending vibration resonance frequency of the bender, and the effect of the vibration in the research calculation range can be ignored.

3. The Influences of Structural Parameters of the Transducer

The radius and length of the baffle determine the sound mass and capacitance of the semi-closed space, and the thickness and material decide the cavity elasticity, thereby affecting the second-order vibration. The influence of size parameters of the baffle on the bandwidth of the transducer will be mainly discussed below. The bender has been prototyped with a diameter of 150 mm. As shown in Figure 7, the resonant frequency in water of the bender is 3 kHz, the maximum TVR is 135 dB, and its −3 dB bandwidth is 560 Hz.

The curves simulated by finite element modal shown in Figure 3 of the circumferential TVR of the transducer with various baffle sizes are shown in Figure 8. Compared with free space, the equivalent acoustic impedance of the mutual radiation between the radiation surface of the bender and the baffle is attached to the radiation impedance of the bender, and the increase in the radiation impedance decreases the resonant frequency of the vibration system. Then, the first-order resonance peak moves forward relative to that of the bender itself. The equivalent mass resistance of mutual radiation is inversely proportional to the source–image distance and is proportional to the effective surface area S₂ in the range of 0.15–0.2 λ, where λ is the wavelength of the sound wave in the fluid.

Regarding the first-order resonant frequency, with the increase in radius of the baffle, the source–image distance and S₂ increase, the two factors affect the mutual radiation reactance oppositely, and the mutual radiation reactance and the first-order resonant frequency are almost unchanged. When the radius is 150 mm, which is larger than 0.5 λ, the mutual radiation reactance varies quickly, the variation of first-order resonance frequency is complicated, and the power may be absorbed, a valley may appear between the first two resonant frequencies when the mutual radiation reactance is negative. When the length increases, the source–image distance is constant, S₂ increases, and the mutual radiation reactance increases, then the first-order resonant frequency decreases.

Regarding the second-order resonant frequency, the baffle radius and length are proportional to the sound mass and volume of the liquid cavity and are inversely proportional to the resonant frequency of the liquid cavity, which is as same as that of Helmholtz resonator. With the increase in baffle size, the sound mass and volume increases, the second-order resonant frequency gradually moves forward. The dimension can change the position of the second-order resonant peak in a large range and will affect the coupling degree of the two modes further.

The variation curve of the TVR of the transducer with the baffle thickness is shown in Figure 8c. The main influencing factors of the first-order resonant frequency under mutual radiation are the source–image distance and the equivalent area, which show that the first-order resonant peak almost does not change with the thickness of the baffle. The equivalent acoustic impedance introduced by baffle elasticity can reduce the resonant frequency of the resonant branch of the liquid cavity, resulting in the decrease in the second-order resonant frequency with the decrease in the thickness. In addition, the equivalent acoustic mass and equivalent force order of the baffle are related to the density and Young’ s modulus in the material properties, and the scattering ability of different materials in the sound field will also be different.

4. Prototype Test

Taking all analysis above into consideration, the optimization of the design of the baffle is carried out, and the effective coupling of two-order vibration modes is realized. The radius of the steel baffle is 100 mm, the length is 100 mm, and the thickness is 5 mm. The structural parameters of the transducer are shown in

Table 1. Structural parameters of the transducer.

Parameter	Dimension (mm)	Material
Piezoelectric ceramic disc radius	50	PZT
Piezoelectric ceramic disc thickness	4
Metal disc radius	70	titanium alloy
Metal disc thickness	12
Cavity baffle radius	100	steel
Cavity baffle height	100
Cavity baffle thickness	5

and PZT is selected as piezoelectric material.

The acoustic parameters of the prototype were tested in an anechoic pool where the depth was 10 m. The framework of the test system is shown in Figure 9, where the signal source is Keysight 33220A (Keysight Technologies, Santa Rosa, CA, USA), the power amplifier is instrument L2 (INSTRUMENTS, INC. San Diego, CA, USA) whose −3 dB working band can cover from 400 Hz to 150 kHz, the oscilloscope is Keysight MSOX3104T (Keysight Technologies, Santa Rosa, US, USA), and the hydrophone is a SPHR-080 whose free-field sound pressure sensitivity level is −198 dB re 1 V/μPa from 2 kHz to 5 kHz, demarcated in the underwater acoustic metering station. During the test, the sine wave signal with a pulse width of 4 ms and duty ratio of 0.1 produced by the signal source will be input to the power amplifier. The signal amplified by the power amplifier stimulates the transducer to work. Then, the hydrophone converts the acoustic energy radiated by the transducer into an electrical signal and outputs it to the oscilloscope. Finally, the oscilloscope signal is measured and calculated.

The prototype and hydrophone were spaced 4 m apart and were located at 5 m of depth in the anechoic pool to meet the far-field distance condition and to ensure that the time difference between the direct wave and the wave reflected by the water surface reaches the hydrophone could cover the sine wave signal pulse width of 4 ms. The measured conductance curves with and without baffle by the impedance analyzer Agilent 4294A are shown in Figure 10b. The equivalent conductance of the dynamic branch is 0.4 mS at the resonant frequency 3 kHz of the bender itself, and the resonant frequencies measured with the baffle are found to be 2.8 kHz and 3.7 kHz, which are on both sides of the original frequency, and the equivalent conductance at two resonant frequencies are 0.2 mS and 0.25 mS, respectively. The test data above verifies that the baffle can move forward the first-order resonance and introduce the cavity mode. The comparison curves of TVR with and without the baffle are shown in Figure 10c. The simulation and test curves of the bender without baffle agree well. The maximum value of TVR is 132.5 dB, and the −3 dB bandwidth is 1000 Hz when the baffle is introduced. The maximum value of the TVR is slightly lower and the bandwidth is broader compared with the single bender transducer. While the two peaks of the TVR curve are not presented clearly due to the limited water depth and low simulation damping. Figure 10d shows the directivity diagrams at two resonant frequencies, and they are basically consistent with those in the simulation. Comparison of acoustic parameters is listed in

Table 2. Acoustic parameters of the transducer.

Characteristic	Modelled	Measured
The first-order resonant frequency	2740 Hz	2800 Hz
The second-order resonant frequency	3700 Hz	3700 Hz
Conductance at the first-order resonant frequency	0.2 mS	0.2 mS
TVR at the second-order resonant frequency	0.3 mS	0.25 mS
TVR at the first-order resonant frequency	133.6 dB	131.4 dB
TVR at the second-order resonant frequency	133.4 dB	128.8 dB
Directivity fluctuation at the first-order resonant frequency	5 dB	4 dB
Directivity fluctuation at the second-order resonant frequency	8 dB	7 dB

.

5. Conclusions

A broadband transducer that suits AUVs is developed. The first-order resonant frequency of the bender transducer is moved forward by the mutual radiation effect, and the liquid cavity mode placed behind the first-order mode is introduced via the baffle. The coupling of the two-order vibration modes realizes the −3 dB bandwidth expansion from 560 Hz to 1000 Hz of the bender.

• A broadband bender transducer which uses the mutual radiation between the bender and the baffle to reduce the resonant frequency of the vibration system and realizes broadband emission by liquid cavity resonant mode is proposed. The mutual radiation introduced by the baffle increases the radiation impedance of the bender radiation surface and reduces its first-order bending resonance frequency. The coupling of the bending mode and the liquid cavity mode broadens the available bandwidth of the transducer.
• The size of the baffle has a significant indigenous effect on the response curve of the vibration system. By adjusting the size, the bandwidth performance of the transducer can be optimized. When the thickness of the baffle or the Young’s modulus is small, the elasticity of the baffle is obvious. At this time, the scattering of the baffle has a large interference on the sound field, and there is a clear valley between the two resonant peaks.
• The size of the baffle which can achieve broadband effect is negatively correlated with the resonant frequency of the bender. When the resonant frequency of the bender is low, the size of the baffle is relatively large. In order to achieve the goal of small size and low frequency sound source, further research is needed to reduce the size of the baffle.
• The measured curves of conductance and directivity prove that the design is effective, while the test result of the TVR is slightly different from that of the simulation, and further research will be conducted on this issue.