Optimal Design of Spherical Shell of Co-vibration Vector Hydrophone(1)

Abstract: Aiming at the structural pressure problem of deep-water vector hydrophones, the maximum stress formula of the external pressure spherical shell is derived, and the influence of the materials and dimensions of the co-vibrating spherical vector hydrophone on its acoustic performance and pressure performance is analyzed here. Based on this, a design method of minimum average density thin-walled pressure-resistant spherical shell is given. The typical deep-sea engineering materials are studied, aluminum alloy material is selected, and a co-vibration spherical vector hydrophone with a designed pressure resistance depth of 3000m is produced. The pressure-resistant structure of the hydrophone was simulated by finite element method, and its sensitivity, directivity and pressure-resistant ability were tested. The results show that the vector hydrophone has good cosine directivity, the sensitivity is -188 dB@500 Hz, and it can withstand 37.5MPa external pressure. This verifies the design method and engineering of the minimum average density thin-walled pressure-resistant spherical shell given in this paper. The rationality and feasibility of the prototype design

 

Introduction

 

The co-vibration vector hydrophone can measure the vibration velocity vector information in the sound field medium, and a single vector hydrophone can complete the direction finding of the acoustic target. It also has the advantages of small size, low power consumption, high sensitivity, moderate frequency band, and is very suitable for installation on underwater unmanned platforms such as underwater gliders and profile buoys to perform tasks such as target detection and marine environmental noise monitoring. At present, with the development of pressure-resistant technology, the working depth of various underwater unmanned platforms is increasing, which puts forward higher requirements for the pressure-resistant capability of vector hydrophones. The United States, Russia and other countries have developed vector hydrophones with a working depth of 5000~6000 m. Domestically, it is still in the initial stage of research. The vector hydrophone with a pressure resistance depth of 1000 m was made by using epoxy resin and glass microbead composite material potting and metal shell oil filling. The sensitivity and directivity of the hydrophone are unsatisfactory; the double-layer shell scheme of the outer composite shell and the inner aluminum alloy shell is used to design a vector hydrophone with a pressure resistance depth of 2000 m. Due to its large size, its high The upper frequency limit is only 1000 Hz; the pressure-resistant composite co-vibration vector hydrophone was designed and manufactured with a metal shell covered with a polyurethane shell. Diving test, the maximum diving depth is 1200 m. The design of a capsule-shaped aluminum alloy thin shell design realizes a co-vibration vector hydrophone with a pressure resistance of 20 MPa. In this paper, the relevant theory of pressure vessel design is applied to the design of a large depth vector hydrophone, and a single-layer thin-walled spherical shell made of high-strength metal materials is directly used as the resistant shell of the vector hydrophone. The process of this scheme is relatively simple, and can reach a large withstand voltage depth. In this scheme, how to select the spherical shell material and design the spherical shell size so that the acoustic performance of the vector hydrophone can be improved as much as possible on the premise that the pressure resistance performance meets the requirements is the key to the design of the pressure spherical shell of the vector hydrophone.

 

1 Influencing factors of acoustic performance of co-vibrating spherical vector hydrophone

 

When the co-vibrating low frequency vector hydrophone works in the underwater sound field, it will vibrate under the action of the sound field. Set its vibration velocity to v. In addition, set the position of the original hydrophone geometric center when the hydrophone is not placed in the sound field. If the vibration velocity of the medium particle is v0, the precondition of the following relationship (3) can be expressed as the frequency of sound wave fc 2 π R. It can be seen from equation (3) that when the upper limit of the working frequency of the co-oscillating spherical vector hydrophone is much smaller than oc 2 π R, the smaller the average density of the hydrophone, the smaller the vibration velocity amplitude v and the vibration of the water quality point in the sound field. The greater the absolute value of the ratio of velocity amplitude, the greater the sensitivity of hydrophone vibration velocity, and the phase difference between the hydrophone vibration velocity and the vibration velocity of the water quality point approaches zero. Since the co-vibration vector hydrophone is also equipped with vibration pickup sensors, signal conditioning circuits and other additional structures, it is difficult to realize that the average density vr of the vector hydrophone is less than the density ρ0 of water. Engineering generally pursues that the average density of the hydrophone is close to the density of the water medium. At this time, the hydrophone can pick up the vibration velocity of the water quality point in the sound field approximately 1:1, and the upper limit of the working frequency of the hydrophone can be the same-vibration vector water. The acoustic performance of the listener mainly includes sensitivity, directivity and working frequency band. When the sensitivity of the internal vibration pickup sensor is constant, the sensitivity of the hydrophone is determined by its average density. The smaller the average density, the higher the sensitivity of the hydrophone. The directivity of a hydrophone is mainly determined by the lateral sensitivity of the internal vibration pickup sensor. The shape of the hydrophone will also affect the directivity. The closer the hydrophone is to a standard spherical shape, the less interference it will have on the directivity. Since the upper frequency limit of the internal vibration pickup sensor is generally high, the upper limit of the hydrophone's working frequency band is generally determined by the outer radius Ro of the hydrophone. The smaller the outer radius, the higher the upper limit of the hydrophone's working frequency. Therefore, when designing the pressure-resistant spherical shell of the co-vibration vector hydrophone, in order to maximize the acoustic performance of the hydrophone, it is necessary to make the average density r of the spherical shell as small as possible under the premise of satisfying the pressure-resistant performance. At the same time, make the outer radius Ro as small as possible. The upper frequency limit of the co-vibrating spherical vector hydrophone requires the smaller the outer radius, the better; the sensitivity of the co-vibrating spherical vector hydrophone requires the smaller the average density, the better; the smaller the outer radius is when the material and thickness are unchanged , The average density increases instead, which is a contradiction. The pressure performance of the co-vibrating spherical vector hydrophone requires the smaller the outer radius, the larger the thickness, and the higher the material strength, the better. The smaller the outer radius and the greater the thickness, the greater the average density, which is also a contradiction. The pressure resistance and acoustic performance of the co-vibrating spherical vector hydrophone requires the design of its spherical shell to be as small as possible (high sensitivity) and outer radius as small as possible (high frequency upper limit) on the premise of reaching the pressure resistance requirements), these restrictions restrict each other. The following will study the relationship between the material, outer radius and thickness of the spherical shell of the co-vibrating spherical vector hydrophone and its pressure resistance, sensitivity and high frequency upper limit, in order to find the vector with the best acoustic performance under the premise of satisfying the pressure performance. The design scheme of the pressure-resistant spherical shell of the hydrophone.

 

2 Failure analysis of thin-walled spherical shell under external pressure

 

When the co-vibrating spherical vector hydrophone works normally underwater, its pressure-resistant spherical shell is subjected to external hydrostatic pressure. It is an external pressure vessel. Without considering the corrosion failure, there are two main failure modes: strength failure and Stability failure.

 

2.1 Strength failure

Strength failure means that when the maximum stress of a material in a pressure vessel exceeds its yield point, the material changes from elastic deformation to plastic deformation, resulting in irreversible deformation or fracture. According to the maximum principal stress theory and elastic failure criterion, if the external pressure spherical shell does not have strength failure, the maximum stress T should be less than or equal to the strength failure allowable stress of the material used in the spherical shell. In the field of pressure vessel design, people use the maximum stress formula when designing external pressure spherical shells. This formula is a summary formula of engineering experience. The calculation is simple, but the prerequisite for its establishment is that the spherical shell is a thin-walled shell, that is, Ro/Ri is required. ≤1.35, where Ro is the outer radius of the spherical shell and Ri is the inner radius. The solution obtained by using this formula belongs to the local optimal solution. Therefore, the maximum stress of the external pressure spherical shell is re-derived. Let p be the external pressure on the spherical shell and δ be the thickness of the spherical shell. According to the moment-free theory of the rotating shell, the radial stress inside the thin-walled spherical shell under external pressure is very small, and only the axial compressive stress Tzz and the circumferential compressive stress Tθθ are considered. Since the geometric shape of the spherical shell is symmetrical with respect to the center of the sphere, the axial compressive stress and the circumferential compressive stress are equal in value. On the section passing through the center of the sphere, the resultant force of the external pressure p on the section of the spherical shell is Fs=pπRo2, and the cross-sectional area of the shell material Ss=π(Ro2-Ri2), so the Tzz and Tθθ of the external pressure spherical shell are the spherical shell The strength failure maximum allowable external pressure pi must meet

 

2.2 Stability failure

Stability failure refers to the failure of the pressure vessel from a stable equilibrium state to an unstable state under the action of an external load, and suddenly loses its original geometric shape. When the thickness of the spherical shell is very thin, the instability failure often occurs before the strength failure. For a thin-walled spherical shell under external pressure, the calculation formula of the critical buckling pressure pcr is derived from the theory of small deformation, where E is the Young's modulus of the spherical shell material and is the Poisson's ratio of the material. The calculation of the small deformation theoretical critical pressure formula is relatively simple, but the error is relatively large, which can be compensated by a larger safety factor m. GB 150.3 stipulates m=14.52. Then the maximum allowable external pressure ps for the stability failure of the thin-walled spherical shell must be satisfied.

 

3 Optimization design of pressure-resistant spherical shell of vector hydrophone

 

The pressure-resistant spherical shell of the vector hydrophone transducer does not fail and needs to meet the maximum allowable external pressure p=min(pi, ps). In addition to the parameters of the material itself, the maximum allowable external pressure p of the spherical shell is only related to Ri/Ro . Define a variable X=Ri/Ro. It is easy to know that X is the ratio of the inner and outer radius of the spherical shell, X∈(0,1), this variable is dimensionless, the larger the X, the thinner the spherical shell. After the allowable stress T of a given material and the maximum allowable external pressure p of the spherical shell, the maximum value of X that the spherical shell meets the strength requirements is obtained, which is recorded as Xi. Similarly, the Young's modulus E, After the Poisson's ratio μ and the maximum allowable external pressure p of the spherical shell, the maximum value of X that the spherical shell meets the stability requirements can be obtained according to the formula, which is recorded as Xs. The co-vibrating spherical vector hydrophone can withstand external static water The function of pressure p without failure, and the pressure-resistant spherical shell is required to meet the conditions of no strength failure and stability failure at the same time, and the maximum value of X that meets the requirements at the same time is X = min X, X (12) Xmax is determined Later, the minimum average density of the spherical shell can be further obtained. It is easy to know that the volume of the spherical shell material is Vc=4π(Ro3-Ri3)/3. The mass of the spherical shell mc=ρVc, where ρ is the density of the spherical shell material. The volume of water discharged by the spherical shell is Vs=4πRo3/3. Then the average density of the spherical shell r is ρ is the density of the material, which is a positive constant; the (1-X3) term X∈(0,1) is always a positive value and monotonously decreases. The minimum average density of the spherical shell that meets the pressure requirements. Therefore, to obtain the optimal design of the pressure-resistant spherical shell of the co-vibration vector hydrophone, firstly, the pressure requirements p and the properties of the material should be substituted into the formula to calculate Xmax ; Substituting Xmax into the formula can get the minimum average density of the spherical shell that meets the pressure requirements. Assuming the total mass of the vibration pickup sensor, signal conditioning circuit and other additional structures inside the co-vibration vector hydrophone, the minimum value of the average density of the hydrophone is a certain value; in the case where the spherical shell material and the pressure resistance requirement p are determined Below, it is also a definite value. For the vector hydrophone, Ro determines the upper limit fmax of the working frequency of the vector hydrophone. The upper limit of the working frequency of the vector hydrophone is selected and the outer radius Ro of the spherical shell of the vector hydrophone is determined. Then the minimum average density of the hydrophone can be obtained, and the vibration velocity sensitivity of the vector hydrophone can be obtained. Similarly, if the vibration velocity sensitivity of the vector hydrophone is selected, the average density of the hydrophone can be obtained according to equation (3), and the outer radius of the spherical shell of the hydrophone at this time can be obtained, and the vector can be obtained The upper limit of the working frequency of the hydrophone. Through the above steps, we can find the most suitable material and the theoretical optimal solution of the size parameters such as the outer radius and thickness of the pressure-resistant spherical shell. And based on the basic size data of the pressure-resistant spherical shell, the next detailed design is carried out. After the design is completed, the finite element simulation software is used to conduct stress distribution analysis and buckling analysis of the designed pressure-resistant shell to ensure that the shell does not have strength failure and stability failure under the design pressure.

 

4 Design example of pressure-resistant spherical shell of vector hydrophone

At present, the working depth of domestic mainstream underwater gliders, profile buoys and other underwater unmanned platforms has reached the level of 2000 m. In order to provide a certain safety margin, the design pressure resistance depth of the hydrophone is set to 3000 m, that is, p=30 MPa.

 

4.1 Shell material optimization

First, we must select the best metal material for the pressure-resistant spherical shell of the co-vibration vector hydrophone. Table 1 lists the mechanical properties of several commonly used deep-sea engineering materials such as 304, 316L stainless steel, 6061T6, 7075T6 aluminum alloy, TC4 titanium alloy and H90 brass. There may be slight differences in the relevant values of the materials). Substituting the pressure requirements p and the properties of various materials in Table 1 into the formula can be used to obtain these engineering materials that meet the strength requirements of Xi, the stability requirements of Xs, and both of them Xmax; substitute the obtained Xmax into the formula , The minimum average density that can be achieved by a spherical shell made of each material that meets the pressure requirements can be obtained. If a certain material meets the strength requirements Xi is less than the stability requirements Xs, then the material is made into a ball that meets the strength requirements In the case of a shell, its stability is surplus; similarly, if the Xi of a certain material is greater than Xs, when the material is made into a spherical shell that meets the stability requirements, its strength is surplus. The closer the values of Xi and Xs are, the more balanced the strength and stability of the spherical shell made of this material. Among the several materials shown in Table 2, Xi of TC4 titanium alloy is greater than Xs, indicating that the strength of the spherical shell made of this material is surplus when it meets the stability requirements. Except for TC4, the Xi of the remaining materials are all smaller than Xs, indicating that the stability of the spherical shell made of these materials is surplus when meeting the strength requirements. Among the materials in Table 2, Xi and Xs of 7075T6 aluminum alloy and TC4 titanium alloy are relatively close, indicating that the strength and stability of the spherical shell made of these two materials are relatively balanced. It can be seen from Table 2 that under the premise of meeting the pressure resistance of 30 MPa, among the several commonly used engineering materials listed in the table, the average density of the spherical shell made of aluminum alloy and TC4 titanium alloy can achieve a density close to or less than that of water, which is consistent with The design requirements of the co-vibrating spherical vector hydrophone. Among them, TC4 titanium alloy material has the largest Xmax, that is, the thinnest pressure-resistant spherical shell made of this material. The pressure-resistant spherical shell made of 7075T6 material can achieve the smallest average density, leaving the largest mass margin for other internal structures. In addition, aluminum alloy has greater advantages than TC4 titanium alloy in terms of material cost and processing cost. Therefore, aluminum alloy is the best material for making vector hydrophone pressure-resistant spherical shells.

 

4.2 Size design of pressure-resistant spherical shell

The aluminum alloy material is selected to make a hydrophone spherical shell with a pressure resistance of 30 MPa, and the minimum average density of the spherical shell that meets the pressure requirements is 0.64×103 kg/m3, and X=0.9177 at this time. If the vibration velocity sensitivity of the vector hydrophone |v/v0| is allowed to 0.8, the actual design of the hydrophone spherical shell should be designed in two halves to facilitate the installation of internal components. It is assumed that the two hemispherical shells of the hydrophone are assembled The additional mass of the measured hydrophone, the accelerometer, the mounting bracket, the signal conditioning circuit, and the watertight penetrating chamber used in the actual hydrophone has a mass sum of 99.5 g, so the sum of the additional mass me=149.5 g. The outer radius Ro=36.48 mm of the spherical shell of the hydrophone is obtained. X=Ri/Ro=0.9177, the inner radius of the spherical shell Ri=33.48 mm, the thickness of the spherical shell=3.00 mm, for the convenience of calculation, drawing and processing, the inner radius of the spherical shell Ri is rounded down to 33 mm, the outer radius Ro is 36mm.

 

4.3 Check of withstand voltage performance

After obtaining the size data of the pressure-resistant spherical shell, in order to ensure that it can meet the pressure-resistant requirements, the pressure-resistant performance is checked, and the two cases of strength failure and stability failure are mainly considered.

 

4.3.1 Strength failure

It can be seen from Table 1 that the allowable stress of aluminum alloy used for the spherical shell is 190 MPa, which is combined with the spherical shell size parameters to obtain the strength failure allowable pressure of the spherical shell is 30.4 MPa, which is greater than 30 MPa, which meets the pressure requirements .

 

4.3.2 Stability failure

The Poisson's ratio of aluminum alloy μ=0.33, the Young's modulus E=7.2×1010 Pa, and the stability system m=14.52. Substituting the material data and the spherical shell size into equations (8) and (9), the critical circumferential instability pressure pcr=611.6 MPa is calculated, and the allowable circumferential instability pressure is 42.1 MPa, which is greater than 30 MPa, which meets the pressure requirements . It can be seen that the pressure-resistant spherical shell of the vector hydrophone can withstand the external hydrostatic pressure of 30 MPa. And the allowable pressure for circumferential instability is greater than the allowable pressure for strength failure. If the pressure continues to increase outside the spherical shell, the strength effect will happen first.

 

4.4 Engineering design of vector hydrophone pressure shell

After determining the basic data such as the material, outer radius and thickness of the pressure-resistant spherical shell of the vector hydrophone, the detailed design of the vector hydrophone shell can be carried out. This paper uses the 3D modeling software to carry out the auxiliary design of the large-depth spherical co-vibration vector hydrophone. The cross-sectional view of the vector hydrophone structure is shown in Figure 1.