DING Ke,WANG Yong-sheng,WEI Ying-san

(Department of Mechanical Engineering,Naval University of Engineering,Wuhan 430033,China)

1 Introduction

With the development of detectability technology and the need of modern war,the stealth performance of submarine is becoming more and more important to navy of different countries.The U.S.Navy report-Technology for the United States Navy and Marine Corps,2000-2035,listed 6 kinds of key technology,the stealth technology is the first one.Last decades,China developed submarine stealth technology energetically,has got great advance,but still was distanced by Europe,the U.S.and Russia.

Submarine noise is categorized into three main components-machine noise,propeller noise,and hydrodynamic noise.This paper mainly studies the second component.Submarine moves through the water,creates asymmetric wake at the tail because of the sail,tails and other appendix structures.Vibration modes of a submarine hull are excited from the transmission of fluctuating forces through the shaft and thrust bearings due to the propeller rotating in an unsteady fluid[1].Pan[2]thought that the structural vibration arisen by the propeller fluctuating forces through the thrust bearing is the main noise source of the low frequency underwater ra-diated noise.Dylejko[3]investigated the influence of resonance changer by the transmission matrix approach.Kinns[4-5]studied the excitation of the hull vibration resulting from transmission through the propeller-shafting system.Feng[6]used the FEM+BEM to study the characteristics of the submarine tail vibra-noise,and drew the conclusion that the thrust bearing pedestal is the main transmission route under the longitudinal excitation.Cao,Zhang,Li et al.also investigated the longitudinal vibration of propeller-shafting system.But,only few people thought to change the structure form of thrust bearing pedestal.Cao and Zhang[7]used the bulkheads replace the thrust bearing pedestal,and obtained a result that it could reduce the longitudinal vibration.Zhang[8]advanced that to use flanged thrust bearing pedestal instead of Michell(common pedestal),and used FEM analyze the vibration transmission of propellershafting system,but his paper had not introduced the vibration response and radiated noise of submarine hull under the propeller fluctuating force.Considering the scale effect and real propeller fluctuating forces,this paper uses FEM+BEM and real scale of Suboff model investigate the influence of thrust bearing pedestal form on vibration and underwater radiated noise of submarine.

2 Basic theory

2.1 Fluid-structure interaction theory

When the structure is placed in fluid,there is interaction between fluid and structure at their interface.The voice pressure acts on the structure as surface force.Then the vibration matrix equation of fluid-structure interaction is:

where,［Ms］,［Cs］and［Ks］are the mass matrix,damp matrix and stiffness matrix of structure,respectively.［Mf］,［Cf］and［Kf］are the equivalent mass matrix,equivalent damp matrix and equivalent stiffness matrix of fluid,respectively.［R］ is the interaction matrix between fluid and structure,{Fs}is the load force of structure,{U}and{P} are the displacement and pressure of element nodes.

When structure is acted on by external force,the structure is excited to vibrate,the vibration of the structure causes the surrounding fluid’s interaction,it causes fluctuating pressure,the fluctuating pressure acts on the structure again and affects the structure vibration,and this is the fluid-structure interaction phenomenon.At low frequency,it presents added fluid effect;at high frequency,it presents damp effect.

2.2 Acoustic radiation theory

Because of the structure vibration,the surface of structure and fluid causes interaction which causes the fluid vibrating,and makes part of vibration energy transmit to surrounding,namely,forms the underwater radiated noise.Although FEM can be used to predict the underwater radiated noise,its size is very large,and has high requirement on computer.But BEM reduces the dimensions efficiently,only divides at the surface,then reduces the requirement on computer.

For the monochromatic voice field,if the surface of structure is smooth and the boundary normal vibration velocity is known,then Helmholtz integral equation[9]is:

where,E,S and I are the exterior,surface and interior of structure,P and Q are the observation point and the integral point on the surface of structure,G（P,Q）=e-jkR/4πR is the Green function of free space,k=ω/c is the wave number,is the normal vibration velocity,ω is the circular frequency,and ρ is the density of fluid.

After the discreteness of Helmholtz integral equation,the boundary element solution equation is:

where,A and B are the coefficient matrices.

The paper uses ANSYS to analyze the Suboff model,taking all the nodes vibration displacement of hull,and uses SYSNOISE to analyze the underwater radiated noise field.

3 Calculation of the submarine structure vibration response

This paper sets up a model of single shell submarine based on the database of the Suboff.The total length is 78.408 m,it concludes 6 cabins divided by 5 bulkheads,and is reinforced with ring stiffeners,longitudinal stiffeners and flat boards and the sail and tails are reinforced with beams and bars,as shown in Fig.1(a).This paper considers two cases.The Case 1 is flanged thrust bearing pedestal,as shown in Fig.1(a)and Fig.1(b).The Case 2 is common thrust bearing pedestal,as shown in Fig.1(c)and Fig.1(d).Fig.1(e)and Tab.1 show that how the Suboff submarine structure elements mesh.

Fig.1 Submarine element meshing

The fluctuating force used in this paper comes from the former result[10].The Suboff is matched with a propeller,then a numerical calculation of self-propulsion is run,and get the self-propulsion point.The propeller fluctuating thrust force at the speed of 6 kns is shown in Fig.2,three wave crests are Axial Passing Frequency(APF),Blade Passing Frequency(BPF),and Double Blade Passing Frequency(2BPF).

Fig.2 Propeller fluctuating thrust force calculated by CFD

Tab.1 Element meshing

Fig.3 shows that the quad velocity and react power of submarine hull under the fluctuating force,represents the vibration intensity of hull and the distributing of vibration power at different frequency.As shown in Fig.3,both flanged and common thrust bearing form have wave crest at the frequencies of APF,BPF and 2BPF.Below 60 Hz except 28 Hz,the response of flanged form is smaller than the common form,it represents that the flanged thrust bearing pedestal reacts smaller response than the common form because the flanged thrust bearing pedestal transfers the propeller fluctuating force equally to the submarine hull along the circumference,which mainly causes longitudinal vibration,only the head and tail of the hull are caused normal vibration,but the common one causes not only the longitudinal vibration but also the lateral vibration.

Fig.3 Vibration and radiated noise of submarine hull by unit force

Fig.4 shows the vibration and radiated noise of submarine hull by unit force,it mainly represents the nature frequencies of the hull.As shown in Fig.4,the vibration power mainly distributes in frequencies of 0-300 Hz because the vibration of submarine hull is mainly affected by stiffness impedance in low frequency;in middle-high frequency,it is damping impedance;at the critical frequency,it is mass impedance.The radiated noise power of common form is the biggest at 2BPF,but the flanged form is at 28 Hz,which explains that why the responses of flanged form under fluctuating force is bigger than the common form’s.

Fig.4 Vibration and radiated noise of submarine hull by fluctuating thrust force

Line spectrum 1 in Fig.3(a),(b)corresponds with the 1 in Fig.4(a),(b),it is the nature frequency of common form;line spectrum 2,3 in Fig.3(a),(b)corresponds with the 1 in Fig.2;line spectrum 4 in Fig.3(a),(b)corresponds with the 2 in Fig.4(a),(b),it is the nature frequency of common form;line spectrum 5 in Fig.3(a),(b)corresponds with the 3 in Fig.4(a),(b),it is the nature frequency of flanged form;4,5 and 6 in Fig.4(a),(b)are the nature frequencies of flanged and common form.

4 Calculation of submarine radiated noise

As shown in Fig.3 at 2BPF and 28 Hz,the vibration of the Case 1 and the Case 2 is intense,so their surface pressure color maps are shown in Fig.5.

Fig.5 Case 1(Flanged Pedestal)surface pressure color map

Fig.6 Case 2(Common Pedestal)surface pressure color map

The hull structure of flanged thrust bearing pedestal has better symmetry than common pedestal,the color maps show clearly,the Case 1 mainly presents the vibration of the whole hull,but the Case 2 presents the vibration of the tail.The flanged thrust bearing pedestal transfers the propeller fluctuating force equally to the submarine hull along the circumference,it mainly causes longitudinal vibration of the whole hull.The common pedestal firstly causes the vibration of the hull combined with it,then transfers to other parts.So,flanged thrust bearing pedestal has better vibration property.

5 Conclusions

This paper uses FEM+BEM and real scale of single shell submarine investigate influence of thrust bearing pedestal form on vibration and underwater radiated noise of submarine under the excitation of propeller fluctuating force,the conclusions are as follows:

(1)The vibration property of hull of the flanged thrust bearing pedestal form is better than common form in low frequency(below 300 Hz),and has no difference in medium and high frequency.

(2)The flanged thrust bearing pedestal transfers the propeller fluctuating force equally to the submarine hull along the circumference,so its response of hull is better than common form’s.

In sum,the flanged thrust bearing pedestal can replace the common pedestal.But,of course,the hole in flanged bulkhead,the combination with hull,and etc should be considered in application process.

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