LIUJunfengjournal16.magtechjournal.com/jwk_zgjcyj/fileup/PingShen/... · 2017. 11. 9. · downloaded from Received：2016-07-28 Supportedby：NationalNaturalScienceFoundationofChina(51239007)

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Received2016 - 07 - 28Supported byNational Natural Science Foundation of China (51239007)Author(s)LIU Junfeng male born in 1993 master candidate Research interest ship collision and stranding E-mail

liujunfengsjtueducnHU Zhiqiang (Corresponding author) male born in 1975 Ph D associate professor Research interests ship collisionand stranding marine renewable energy dynamics performance of marine engineering structures E-mail zhqhusjtueducn

CHINESE JOURNAL OF SHIP RESEARCHVOL12NO2APR 2017DOI103969jissn1673-3185201702011Translated fromLIU J FHU Z Q 3D analytical method for the external dynamics of ship collisions and investigation of the

coefficient of restitution［J］ Chinese Journal of Ship Research201712（2）84-91

http englishship-researchcom

0 Introduction

Ship collision is a highly nonlinear process In order to analyze the collision process the collisionmechanism is generally divided into two independent processes for research external dynamics andinternal dynamics[1] The external dynamics mainlyuses the rigid body motion theory to analyze the motion attitude of the striking ship and the struck shipas well as the energy dissipation in the collision process The internal dynamics mainly uses the elasticplastic mechanics theory to solve the problems ofstructural deformation resistance deformation energy dissipation and structural damage of the strikingship and the struck ship

Ship collision will lead to disastrous consequences therefore many scholars have carried out research on ship collision In the study of external dynamics Minorsky[2] carried out pioneering researchIt is assumed that fully plastic deformation occurs onthe struck ship By the law of conservation of momentum the effect of the surrounding additional water isconsidered as additional mass and not changed inthe collision process so as to estimate the energy dissipation in ship collision Pedersen et al[3] proposedthe shock dynamics model of ship collision and obtained the energy dissipation and impulse changevalue in each direction by integrating the contactforce and relative displacement in each directionHowever the model can only be applied to two-di

3D analytical method for the external dynamics ofship collisions and investigation of the coefficient

of restitution

LIU Junfeng12 HU Zhiqiang12

1 State Key Laboratory of Ocean Engineering Shanghai Jiao Tong University Shanghai 200240 China2 Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration Shanghai 200240 ChinaAbstract The analytical method for predicting the dynamic responses of a ship in a collision scenario features speedand accuracy and the external dynamics constitute an important part A 3D simplified analytical method is implemented by MATLAB and used to calculate the energy dissipation of ship-ship collisions The results obtained by the proposed method are then compared with those of a 2D simplified analytical method The total dissipated energy can be obtained through the proposed analytical method and the influence of the collision heights angles and locations on thedissipated energy is discussed on that basis Furthermore the effects of restitution on the conservative coefficients andthe effects of conservative coefficients on energy dissipation are discussed It is concluded that the proposed 3D analysis yields a less energy dissipation than the 2D analysis and the collision height has a significant influence on the dissipated energy In using the proposed simplified method it is not safe to simplify the conservative coefficient as zerowhen the collision angle is greater than 90 degrees In the future research to get more accurate energy dissipation it isa good way to adopt the 3D simplified analytical method instead of the 2D methodKey words ship collisions external dynamics 3D analytical method energy dissipation restitution coefficientCLC number U66143

61


mensional plane space and since the equation is established in the global coordinate system it is difficult to be extended to three-dimensional space because of its complexity Stronge[4] proposed athree-dimensional collision solution scheme but themodel only deals with the solution of velocity and acceleration of the collision objects On the basis of theresearch of Stronge[4] Liu et al[5] proposed thethree-dimensional dynamic model of ship collisionand obtained the energy dissipation and impulsechange value in each direction The main characteristic of this method is that all the equations are established in the local coordinate system and the closedsolution of the energy dissipation values in the localcoordinate system along each coordinate axis can beobtained On the other hand in order to truly simulate the ship collision process some scholars studythe dissipation process of collision energy in time domain Petersen[6] presented an analytical method fortwo-dimensional external dynamics of ship collisionin time domain Based on the ships horizontal motion equation the side of the struck ship is simplified into 4 nonlinear springs then the ships motionresponse energy dissipation and damage depth inthe ship collision are obtained using numerical integration of time Aiming at the ship collision processand combining the data of actual ship and model experiment Tabri et al[7-9] proposed an analytical method for the ship motion in ship collision based on theship maneuvering model Using the calculation module of the explicit nonlinear finite element softwareLS_DYNA Yu et al[10] presented a method of external and internal dynamics coupling by adding hydrodynamic through subprogram and calculating collision force by LS_DYNA

In the study of internal dynamics Luumltzen et al[11]used the super element method to estimate the deformation resistance and energy dissipation in ship collision which considered the influence of side structure and the shape of the bow Kitamura[12] used FEMto discuss the problems that are neglected in manysimplified analytical methods including the lateralbending of ship hull girder the equivalent failurestrain the forward speed and collision angle of thestruck ship etc Haris et al[13] proposed a simplifiedanalytical method that can quickly estimate the damage and energy dissipation in ship collision whichhas been verified by the numerical results of LS_DYNA A simplified method proposed by Sun et al[14]can estimate the deformation resistance and energy

dissipation of side plates stiffeners and web girdersso as to obtain the deformation resistance and energydissipation of the whole side structure

In the simplified analytical method of external dynamics the restitution coefficient has a direct impacton the value of collision energy but the detail research results are rare at present Pedersen et al[3]proposed a fast estimation method for the energy dissipation and collision impulse of two-dimensionalship collision and this method has closed solution Inthe study restitution coefficient value e ranges in 0leele1 For fully plastic collision the restitution coefficient is 0 and the restitution coefficient is 1 for thefully elastic collision however the method of selecting the restitution coefficient was not explained indetail Liu et al[5] proposed a three-dimensional model of the external dynamics of ship collision andused it to calculate the force of the ship-ice collision but the selection of the restitution coefficientwas also not discussed in depth only set to 0 for calculation Restitution coefficient is an important parameter of external dynamics model which determines the relation of relative velocity between twoships before and after the collision It is generally believed that if the restitution coefficient is 0 the striking ship will not be bounced off by the side of thestruck ship after the collision the strain energy isthe largest at the moment and the energy dissipationis the largest which is conservative If the restitutioncoefficient is 1 the striking ship will be bounced offand the energy dissipation is the least which is dangerous In the case the restitution coefficient is notknown we can simply take the restitution coefficientof 0 But in fact the restitution coefficient of 0 is notconservative For different collision scenarios conservative restitution coefficient (here defined as therestitution coefficient that makes energy dissipationmaximum and ranges in 0leele 1) is different

In this paper we will use the MATLAB program torealize the three-dimensional simplified analyticalmethod for external dynamics of ship collision anddiscuss the impact of the collision height angle andlocation on the collision energy In addition we willalso discuss the influence of collision scenario on therestitution coefficient and compare the new collisionenergy calculated by the conservative restitution coefficient (ie energy dissipation in the collision process) with the collision energy corresponding to restitution coefficient of 0

62


1 Three-dimensional analyticalmethod for external dynamics

11 Coordinate system

The definition of the global coordinate system(fixed coordinate system) and the local coordinatesystem is shown in Fig 1 The global coordinate system is an inertial system with the origin located atthe center of gravity of the ship which is aright-handed coordinate system The X axis is alongthe bow direction and the Z axis is upward The origin of the local coordinate system is located at thecollision point C and its 3 mutually perpendicularunit vectors are denoted as n1 n2 and n3 The vectors n1 and n2 are located at the tangent plane ofcollision and the vector n3 is perpendicular to thetangent plane In order to elaborate more conveniently the body-fixed coordinate system is introducedwhich coincides with the global coordinate systeminitially

12 Motion equation of ship collision

In the process of ship collision the ship is regarded as a rigid body so the Newton-Euler equationcan be used to describe the motion of the rigid bodyThe Newton-Euler equation for the general motion ofa rigid body is

M dvdt

+ Mω acute v = F （1）J dω

dt+ω acute Jω = G （2）

where ω is the angular velocity vector of the rigidbody in the local coordinate system v is the velocity vector of the rigid body at the center of gravity inthe local coordinate system M is the mass matrixin the local coordinate system F is the force vectorin the local coordinate system J is the rotational inertia matrix in the local coordinate system and G isthe moment vector

In the collision the influence of hydrodynamicforce on the collision process was simplified by considering the additional mass and additional inertia in

the mass matrix and the rotational inertia matrixFormulas (1) and (2) are nonlinear and inconve

nient to solve It is assumed that the collision timewas very short then Mω acute v and ω acute Jω weresmall quantities and the linear Formulas (3) and (4)are obtained

Mdv = Fdt （3）Jdω = r acute Fdt （4）

In the formulas r represents the location vectorfrom the center of gravity to the collision point

The symbol was used to distinguish between thestriking ship and the struck ship The physical quantity with refers to the striking ships physical quantity otherwise it represents the physical quantity ofthe struck ship In the process of collision the collision force was assumed constant at collision point Cand impulses dPi and dP primei of the two ships are expressed as

dPi = Fidt （5）dP primei = F primeidt （6）

Then the ships equations of motion in the tensorform are

M ijdV j = dPi （7）M primeijdV primej = dP primei （8）

Iijdω j = εijk r jdPk （9）I primeijdωprimej = εijk rprimejdP primek （10）

In Formulas (7)-(10) the repeatedly emergent subscripts represent the summation and εijk is the permutation matrix When the subscripts of εijk were arranged clockwise the value was + 1 when arrangedcounterclockwise the value was -1 and the valuewas 0 when there were repeated subscriptsM ijM primeij Iij and I primeij respectively represent massmatrix and inertia matrix of the two ships in the localcoordinate system r j and rprimej respectively representthe location vectors of the two ships from their centerof gravity to the collision point V j and V primej respectively represent velocities at the center of gravity

The above Formulas (7)-(10) are consistent withthe three-dimensional collision model proposed byStronge[4] which can be solved by the same processas Liu et al[5]2 Example analysis

MATLAB was used to compile the program to realize the three-dimensional simplified analytical method for the external dynamics of ship collision andthe energy dissipation in the ship collision was obtained

Fig1 Global and local coordinate systems［5］

X

YZ

COG

Ship

rn2

n1

n3

CF = f1n1 + f2n2 + f3n3

63


21 Collision scenario

In this paper we used the example of Ref[15]The forward speed of the two supply ships was both45 ms and the two ships was 825 m in length 188 min breadth 76 m in draft and 4 000 t in displacement The additional mass coefficients in the X andY directions were 005 and 085 respectively Theadditional rotational inertia coefficient of yawing wastaken as 1 The inertia radius was 025 of the corresponding ship length In order to compare with the results of the example the friction coefficient μ0 ofthe two ships was equal to that of the example taking the value of 06

In order to analyze the effect of different collisionlocations on the collision results we selected 24points from the bow to the stern of the struck ship asthe collision points The location coordinates in theXYZ global coordinate system are shown in Table 1where α is waterline angle representing the curvature of waterline of the struck ship The collision location of the striking ship was selected at the bow ofthe striking ship as shown in Fig 2 In addition inorder to consider the influence of different collisionangles θ on the collision results the values of θ

were taken as 30deg 60deg 90deg 120deg and 150deg

In the example of this paper the above two supplyships were selected as the analysis object and theaddition mass inertia coefficient and turning radiuswere obtained by empirical formulas[16] In the two-dimensional collision the influence of vertical direction is neglected that is the vertical coordinates Zc

and Z primec of the collision points of the striking ship Aand the struck ship B are assumed to be 0 Therefore there are only heave sway and yaw motions inthe results of the calculation The influence of vertical height of the collision points needs to be considered in the 3D collision The vertical coordinate Zc

of collision point at struck ship A changes in therange of 0-1Rxx where Rxx is the turning radius of rollmotion of ship A and the range is obtained based onthe assumption that the vertical coordinates of thecenter of gravity of the ship is half of the draft In thecalculation it was assumed that the vertical coordinates Zc of the collision points on the struck ship Awere 0 025Rxx 05Rxx 075Rxx and 1Rxx and the vertical coordinate Z primec of the collision points on thestriking ship B was 05Rprimexx The coordinates Xc andYc of collision points on the struck ship A in theglobal coordinate system and the coordinates X primecand Y primec of collision point on the striking ship B arethe same as those in the two-dimensional collisionscenarios The collision angles of the two ships were30deg 60deg 90deg 120deg and 150deg respectively Therefore there were a total of 120 collision locations and600 collision scenarios22 Results analysis

The energy dissipation rate of collision (the ratioof energy dissipation to initial energy) of the 600 collision scenarios was calculated and the curves forthe change of energy dissipation rate of collision withthe collision location along ship length at specifiedcollision angle θ and in the vertical collision location scenarios were drawn (Fig 3)

It can be seen from Figs 3 (a)-(e) that the collision height has a great influence on the energy dissipation rate When the coordinates Xc and Yc of collision location were determined and the collision an

Collision point1（bow）

23456789101112

13（mid）14151617181920212223

24（stern）

XcL050048046043039034029024019015010005000-005-010-015-019-024-029-034-039-043-048-050

Xcm403853663463082723119315411677390

-39-77-116-154-193-231-27-308-346-385-40

Ycm0264156759949494949494949494949494949494949494

α （deg）90453753252171447300000000000000000

Table 1 Collision locations and waterline angles［3］

Note L in the table refers to the length of the struck ship

Fig2 Collision locations along ship length

23 21 19 17 11 9 7 53 1 X

α

Y

θ

64


gle was given the energy dissipation rate of collisiondecreased with increasing collision height Zc Especially in the mid-ship collision the phenomenonwas more obvious This is because the larger the Zc the larger the induced roll motion and the smallerthe energy dissipation that is the larger the energydissipation rate of collision With the same height ofcollision strong yaw and roll motion would becaused when the collision location is near the bow orstern when the collision location is in mid-ship rollmotion caused by the collision height accounts forthe major part and yaw motion is small Thereforein the mid-ship collision the effect of collisionheight is obvious Figs 3(a)-3(e) also give thetwo-dimensional results of the Ref[15] It can beseen that the collision energy obtained by thethree-dimensional analytical method was less thanthat by the two-dimensional analytical methodWhen the collision height was equal to 0 the resultsobtained by the three-dimensional method were similar to those by the two-dimensional method

（e）θ=150deg

Energy

dissip

ationra

teofco

llision

096088080072064056048040032024016008-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location

Collision heightZcRxx=0ZcRxx=025ZcRxx=05ZcRxx=075ZcRxx=1Ref［15］

（d）θ=120deg

Energy

dissip

ationra

teofco

llision

072064056048040032024016-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location


（f）Overall picture of Figs 3（a）-3（e）

Energy

dissip

ationra

teofco

llision

-05 -04 -03 -02 -01 0 01 02 03 04 05Collision location

100908070605040302010

ZcRxx=0ZcRxx=075

ZcRxx=025ZcRxx=1

ZcRxx=05

150deg

120deg

90deg

60deg30deg

Fig3 Relationships between energy dissipation and collisionlocation with different impact angles and verticalimpact heights

（c）θ=90deg

Energy

dissip

ationra

teofco

llision

048044040036032028024020016012-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location


（a）θ=30deg

Energy

dissip

ationra

teofco

llision

0040

0036

0032

0028

0024

0020

0016-05 -04 -03 -02 -01 0 01 02 03 04 05Collision location


（b）θ=60deg

Energy

dissip

ationra

teofco

llision

018

016

014

012

010

008



65


As can be seen from Fig 3(f) the influence of collision angle and collision location is also obvious onthe energy dissipation rate of collision When the collision angle was 0-120deg the energy dissipation rateof collision increased with the increase of the collision angle When the collision angle was about120deg-150deg the energy dissipation rate of collisiondecreased with the increase of the collision angleBecause when the collision angle increases to a certain value relative motion occurs between the twoships making the energy dissipation decrease In addition when the collision angles were 120deg and150deg collision energy at the bow of ship A was significantly greater than the corresponding collision energy at the stern of the ship and the greater the collision angle the more obviously bow collision energyincreases The reason is that the curvature of the bowof the ship A is not 0 which makes the collisionclose to the frontal collision3 Effect of restitution coefficient

The value of restitution coefficient may be relatedto the characteristics of the two ships (the side structure length and breadth of ship draft and ship type)and collision scenario parameters (velocities of thestriking ship and the struck ship collision angle andcollision location) In this section we will discussthe impact of collision scenarios and the characteristics of the two ships on the conservative restitutioncoefficient and the influence of the conservative restitution coefficient on the collision energy31 Influence of collision scenario and

characteristics of the two ships on theconservative restitution coefficient

In order to study the influence of collision scenario on the conservative restitution coefficient keepingother values unchanged the velocities of the strikingship and the struck ship collision angle and collision location were adjusted respectively to obtaindifferent energy dissipation-restitution coefficientcurves as shown in Figs 4-7 The point at which thex is marked in the figure represents the highestpoint of the curve and its abscissa corresponds tothe conservative restitution coefficient In the title ofthe figure v_stru represents the velocity of the struckship and v_stri represents the velocity of the strikingship

As can be seen from Fig 4 in the case of the collision angle less than 90deg energy dissipation was thelargest when the restitution coefficient was equal to

0 Because the smaller the restitution coefficient thesmaller the part of the struck ships internal energy (ie strain energy) that was restituted to the kinetic energy the larger the energy dissipation For the caseof collision angle greater than 90deg such as the colli

Fig4 Relationship between energy dissipation and restitutioncoefficient with different collision angles（mid-shipcollisionv_stru=v_stri=45 ms）

0 02 04 06 08 10Restitution coefficient

4540353025201510050

times107

Energy

dissip

ationJ

Collision angleθ=30degθ=60degθ=90degθ=120degθ=150deg

Fig5 Relationship between energy dissipation and restitutioncoefficient with different collision locations（θ=120degv_stru=v_stri=45 ms）


4540353025201510050

times107

Energy

dissip

ationJ

XcL=039XcL=024XcL=015XcL=0XcL=-015XcL=-024XcL=-039

Collision location

Fig6 Relationship between energy dissipation and restitutioncoefficient with different velocities of the struck ship（mid-ship collisionθ=60deg v_stri=45 ms）


40353025201510050

times107

Energy

dissip

ationJ

v_stru=2 msv_stru=4 msv_stru=6 msv_stru=8 ms

Velocity of thestruck ship

66


sion angles of 120deg and 150deg however the maximumvalue was not obtained when the restitution coefficient was equal to 0 This is due to that the energydissipation is composed of the friction energy (tangential force work) and internal energy (normal forcework) In order to verify this interpretation the corresponding friction energy and internal energy are calculated at 60deg and 120deg respectively

From Figs 8 and 9 it can be seen that at 60deg thefriction energy was significantly smaller than the internal energy Because the collision angle was lessthan 90deg velocity directions of the striking ship andstruck ship were at an acute angle the relative sliding distance of the tangential force along the contactsurface was small and work of friction force wassmall the change of the energy dissipation was thesame as that of the internal energy At 120deg the friction energy was equivalent to the internal energyeven greater than the internal energy Because thecollision angle was greater than 90deg the relative sliding distance of the tangential force along the contactsurface was large and work of friction force waslarge the changes of energy dissipation were different from the change of internal energy It can be seenfrom Figs 5-7 that the collision location the velocity of the struck ship and the velocity of the strikingship also have an influence on the selection of theconservative restitution coefficient

In addition to the collision scenarios the influence of the respective characteristics of the two ships(length breadth draft displacement and block coefficient) on the conservative restitution coefficient canbe obtained by using similar methods It is found inresearch that the influence of the characteristics ofthe two ships is very small on the conservative resti

tution coefficient respectively This is because the influence of the restitution coefficient depends on therelative size of friction energy and internal energyThe friction energy is mainly related to the relativesliding distance while the influence of the characteristics of the two ships on the sliding distance respectively can be ignored

32 Influence of the conservative restitu-tion coefficient on the collision energy

In order to analyze the influence of the conservative restitution coefficient on the collision resultsZxx = 05Rxx and Zc = 05Rc are taken to obtain theenergy dissipation rate of collision at two kinds ofspeed The calculation process is shown in Fig 10The calculation program is divided into the main program and subprogram The main program calculatesthe energy dissipation in the collision scenario andthe subprogram calculates the conservative restitution coefficient in the specific collision scenarioWhen the conservative restitution coefficient was tak

Fig7 Relationship between energy dissipation and restitutioncoefficient with different velocities of the striking ship（mid-ship collisionθ=60degv_stru=45 ms）


1816141210080604020

times107

Energy

dissip

ationJ

Velocity of thestriking shipv_stri=2 msv_stri=4 msv_stri=6 msv_stri=8 ms

Fig8 Relationship between energy and restitution coefficient（θ=60deg）


12

10

08

06

04

02

0

times107

Energy

dissip

ationJ

Internal energyFriction energyEnergy dissipation

Fig9 Relation between energy and restitution coefficient（θ=120deg）


4540353025201510050

times107

Energy

dissip

ationJ Internal energy

Friction energyEnergy dissipation

67


en as the restitution coefficient it is necessary to callthe subprogram The calculation process of the subprogram is shown in Fig 10 and the calculated results are shown in Figs 11 and 12

From Figs 11 and 12 it can be seen that for thecollision scenario with the collision angle greaterthan 90deg restitution coefficient of 0 is not conservative or not safe In particular the bigger the collision angle is the bigger the gap of the correspondingenergy dissipation rate is between the conservativerestitution coefficient and the restitution coefficientof 0 For the case where the collision angle was lessthan 90deg the curves of energy dissipation rate of collision with the two kinds of restitution coefficientsare nearly the same In Fig 12 the correspondingcurve of 60deg rises in the bow because the velocityvector direction of the struck ship relative to thestriking ship forms a small angle with the tangentialdirection of the bow waterline a larger relative slid

ing is obtained leading to larger friction energy andincrease of the collision energy dissipation

The corresponding conservative restitution coefficients of each collision scenario of Figs 11 and 12were given in Tables 2 and 3 It can be seen thatwhen the collision angle was close to 90deg most of theconservative restitution coefficients were close to 0and most of the conservative restitution coefficientswere close to 1 at about 150deg

Fig10 Flow chart of analysis

Start

Solution oflinear Formulas（7）~（10）

Subprogram for calculatingconservative restitution

coefficientSpecific collisionangle location andcollision velocity

Restitutioncoefficiente=0 Restitutioncoefficient e=0∶1 cycling

Energydissipation matrixTotal energydissipation Total energy

dissipation

Comparison

End

Extraction of ecorresponding tothe maximumenergy dissipation

Fig11 Relation between energy dissipation and collisionlocation when the velocities of both ships are 45 ms

Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg

Conservative restitution coefficientRestitution coefficient is 0

Fig12 Relation between energy dissipation and collisionlocation when the velocities of the struck ship andthe striking ship are 45 ms and 6 ms separately

Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg


Collisionlocation050048046043039034029024019015010005000-005-010-015-019-024-029-034-039-043-048-050

Collision angle θ（deg）30095000000000101010101501501501501501501502020202

6008500000000000

0150202020202000000

9006500000000000000000000

0050101

12000000010306055050450404040404045045050550606065065

1500001025071111111111111111111

Table 2 Selection of the conservative restitution coefficientwhen the velocities of both ships are 45 ms

68


4 Conclusion

In this paper a set of analytical methods and procedures for three-dimensional ship collision are presented Compared with the two-dimensional analytical method of ship collision 3D analytical method ofship collision proposed in this paper considers theroll pitch and heave motions so the calculated collision energy was less than the result of 2D ship collision

By analyzing the results of different collision scenarios the conclusions are obtained as follows

1) The collision height has obvious impact on thecollision energy When mid-ship collision occursthe impact is particularly evident

2) The collision location and collision angle haveobvious influence on the collision results Especiallywhen the frontal collision occurs bow collision willproduce greater energy dissipation

3) For the scenario when collision angle is greaterthan 90deg it is not safe to simply take 0 as the restitution coefficient The program presented in this papercan be used to calculate the corresponding conserva

tive restitution coefficient for each specific collisionscenarioReferences［1］ WANG Z LGU Y N Motion lag of struck ship in colli

sion［J］ Shipbuilding of China200142（2）56-64（in Chinese）

［2］ MINORSKY V U An analysis of ship collisions withreference to protection of nuclear power plants［R］New YorkSharp（George G）Inc1958

［3］ PEDERSEN P TZHANG S M On impact mechanicsin ship collisions［J］ Marine Structures199811（10）429-449

［4］ STRONGE W J Impact mechanics［M］ CambridgeCambridge University Press2004

［5］ LIU Z HAMDAHL J A new formulation of the impact mechanics of ship collisions and its application toa ship-iceberg collision［J］ Marine Structures201023（3）360-384

［6］ PETERSEN M J Dynamics of ship collisions［J］OceanEngineering19829（4）295-329

［7］ TABRI KBROEKHUIJSEN JMATUSIAK Jet alAnalytical modelling of ship collision based onfull-scale experiments［J］ Marine Structures200922（1）42-61

［8］ TABRI KMAumlAumlTTAumlNEN JRANTA J Model-scaleexperiments of symmetric ship collisions［J］ Journal ofMarine Science and Technology200813（1）71-84

［9］ TABRI KVARSTA PMATUSIAK J Numerical andexperimental motion simulations of nonsymmetric shipcollisions［J］ Journal of Marine Science and Technology201015（1）87-101

［10］ YU Z LAMDAHL J RSTORHEIM M A new approach for coupling external dynamics and internalmechanics in ship collisions［J］ Marine Structures201645110-132

［11］ LUumlTZEN MPEDERSEN P T Ship collision damage［D］ DenmarkTechnical University of Denmark2002

［12］ KITAMURA O FEM approach to the simulation ofcollision and grounding damage［J］ Marine Structures200215（45）403-428

［13］ HARIS SAMDAHL J Analysis of ship-ship collision damage accounting for bow and side deformationinteraction［J］ Marine Structures20133218-48

［14］ SUN BHU Z QWANG G An analytical method forpredicting the ship side structure response in rakedbow collisions［J］ Marine Structures 2015 41288-311

［15］ ZHANG S M The mechanics of ship collisions［D］DenmarkTechnical University of Denmark1999

［16］ POPOV Y NFADDEEV O VKHEISIN D Eet alStrength of ships sailing in ice［R］ DTIC DocumentWashingtonDCArmy Foreign Science amp Technology Center1969



09509507507507507508508509509509509509509509502020303030303

601

045025005000

005005005005005005005005005005005010101010101

9009500000000000000000000000

120025000000204504030302502502025025030303503504045045045

1500001020609111111111111111111

Table 3 Selection of the conservative restitution coefficientwhen the velocities of the struck ship and strikingship are 45 ms and 6 ms separately

69


船舶碰撞机理三维解析法实现及恢复系数研究

刘俊峰 12胡志强 12

1 上海交通大学海洋工程国家重点实验室上海 2002402 高新船舶与深海开发装备协同创新中心上海 200240

摘要［目的目的］采用解析方法分析船舶碰撞动力特性较为快速和准确其中外部动力学分析十分重要［方法方法］

为此运用MATLAB程序实现船舶碰撞外部机理三维简化解析方法计算两艘船舶碰撞的动能损失并与二维

解析方法的计算结果进行比对在实现船舶碰撞动能损失快速计算解析方法的基础上讨论碰撞高度角度和

位置对动能损失的影响此外还研究碰撞场景对保守恢复系数的影响和保守恢复系数对动能损失的影响

［结果结果］结果表明三维解析方法得到的动能损失小于二维解析方法碰撞高度对于动能损失有明显的影响简

化解析方法中对于碰撞角度大于 90deg的场景恢复系数简单地取 0并不安全［结论结论］在今后的外部动力学分析

中为了使动能损失的计算值更加准确可以使用三维解析方法代替二维解析方法

关键词船舶碰撞外部动力学三维解析法能量耗散恢复系数

126-129（in Chinese）［3］ ZHU W WWANG W FGUO B Cet al A practical

symmetric aerofoil with high effectiveness［J］ Journalof Shanghai Jiaotong University199630（10）35-40（in Chinese）

［4］ CHEN W M The effect of rudder forms on ship maneuverability［J］ Journal of SSSRI200225（1）40-43（in Chinese）

［5］ YU H X The numerical simulation and experimentalresearch of ichthyoid rudder steady lift［D］ HarbinHarbin Engineering University2003（in Chinese）

［6］ YANG J M Prediction of performance of the shillingrudder behind a propeller［J］ Journal of Hydrodynamics199914（2）162-168（in Chinese）

［7］ MA Y CLIN J XZHAO Y 敞水舵水动力数值计算

及分析［J］ China Water Transport20088（12）

1-3（in Chinese）［8］ LI S ZZHAO FYANG L Multi-objective optimiza

tion for airfoil hydrodynamic performance design basedon CFD techniques［J］ Journal of Ship Mechanics201014（11）1241-1248（in Chinese）

［9］ GIM O SLEE G W Flow characteristics and tip vortexformation around a NACA 0018 foil with an end plate［J］ Ocean Engineering20136028-38

［10］ XIONG Z YSUN H XZHU X Q 船尾伴流场与螺

旋桨低频噪声相关性研究［C］Proceedings of theFourteenth Symposium on Ship Underwater NoiseChongqingChinese Society of Naval Architects andMarine Engineers2013282-288（in Chinese）

高效翼型舵在潜艇上的应用

周轶美张书谊卢溦何汉保中国舰船研究设计中心湖北武汉 430064

摘要［目的目的］现代潜艇对操纵面设计的要求越来越高使得设计者们需要不断研究新的舵型以提高操纵面

的效率而高效翼型舵是提高操纵面效率的有效措施之一［方法方法］为此在比较分析各种翼型优缺点的基础

上提出一种优化的高效翼型舵并采用数值计算的方法比较分析潜艇上应用这种高效翼型舵与常规 NACA舵的水动力特性和对尾部伴流场的影响规律同时在拖曳水池中开展模型测力试验发现试验结果与仿真计算

结果一致性良好误差不超过 10［结果结果］研究结果表明高效翼型舵的舵效比常规舵高 40以上但对艇体总

阻力的影响则与常规舵相当不超过 4采用高效翼型舵带来的升力效益要比其对艇体总阻力的影响大得

多［结论结论］表明高效翼型舵在提高操纵效率方面优势明显有着较好的应用前景

关键词潜艇高效翼型舵水动力特性尾部伴流场

[Continued from page 60]10509051050905105090510509051050905105090510509051050905105090510509051050905105090510509051050905105090510509051050905105090510509051050905105090510509051050905105090510509051050905105090510509051050905

70


mensional plane space and since the equation is established in the global coordinate system it is difficult to be extended to three-dimensional space because of its complexity Stronge[4] proposed athree-dimensional collision solution scheme but themodel only deals with the solution of velocity and acceleration of the collision objects On the basis of theresearch of Stronge[4] Liu et al[5] proposed thethree-dimensional dynamic model of ship collisionand obtained the energy dissipation and impulsechange value in each direction The main characteristic of this method is that all the equations are established in the local coordinate system and the closedsolution of the energy dissipation values in the localcoordinate system along each coordinate axis can beobtained On the other hand in order to truly simulate the ship collision process some scholars studythe dissipation process of collision energy in time domain Petersen[6] presented an analytical method fortwo-dimensional external dynamics of ship collisionin time domain Based on the ships horizontal motion equation the side of the struck ship is simplified into 4 nonlinear springs then the ships motionresponse energy dissipation and damage depth inthe ship collision are obtained using numerical integration of time Aiming at the ship collision processand combining the data of actual ship and model experiment Tabri et al[7-9] proposed an analytical method for the ship motion in ship collision based on theship maneuvering model Using the calculation module of the explicit nonlinear finite element softwareLS_DYNA Yu et al[10] presented a method of external and internal dynamics coupling by adding hydrodynamic through subprogram and calculating collision force by LS_DYNA

In the study of internal dynamics Luumltzen et al[11]used the super element method to estimate the deformation resistance and energy dissipation in ship collision which considered the influence of side structure and the shape of the bow Kitamura[12] used FEMto discuss the problems that are neglected in manysimplified analytical methods including the lateralbending of ship hull girder the equivalent failurestrain the forward speed and collision angle of thestruck ship etc Haris et al[13] proposed a simplifiedanalytical method that can quickly estimate the damage and energy dissipation in ship collision whichhas been verified by the numerical results of LS_DYNA A simplified method proposed by Sun et al[14]can estimate the deformation resistance and energy

dissipation of side plates stiffeners and web girdersso as to obtain the deformation resistance and energydissipation of the whole side structure

In the simplified analytical method of external dynamics the restitution coefficient has a direct impacton the value of collision energy but the detail research results are rare at present Pedersen et al[3]proposed a fast estimation method for the energy dissipation and collision impulse of two-dimensionalship collision and this method has closed solution Inthe study restitution coefficient value e ranges in 0leele1 For fully plastic collision the restitution coefficient is 0 and the restitution coefficient is 1 for thefully elastic collision however the method of selecting the restitution coefficient was not explained indetail Liu et al[5] proposed a three-dimensional model of the external dynamics of ship collision andused it to calculate the force of the ship-ice collision but the selection of the restitution coefficientwas also not discussed in depth only set to 0 for calculation Restitution coefficient is an important parameter of external dynamics model which determines the relation of relative velocity between twoships before and after the collision It is generally believed that if the restitution coefficient is 0 the striking ship will not be bounced off by the side of thestruck ship after the collision the strain energy isthe largest at the moment and the energy dissipationis the largest which is conservative If the restitutioncoefficient is 1 the striking ship will be bounced offand the energy dissipation is the least which is dangerous In the case the restitution coefficient is notknown we can simply take the restitution coefficientof 0 But in fact the restitution coefficient of 0 is notconservative For different collision scenarios conservative restitution coefficient (here defined as therestitution coefficient that makes energy dissipationmaximum and ranges in 0leele 1) is different

In this paper we will use the MATLAB program torealize the three-dimensional simplified analyticalmethod for external dynamics of ship collision anddiscuss the impact of the collision height angle andlocation on the collision energy In addition we willalso discuss the influence of collision scenario on therestitution coefficient and compare the new collisionenergy calculated by the conservative restitution coefficient (ie energy dissipation in the collision process) with the collision energy corresponding to restitution coefficient of 0

62







M dvdt


















X

YZ

COG

Ship

rn2

n1

n3

CF = f1n1 + f2n2 + f3n3

63












23456789101112

13（mid）14151617181920212223

24（stern）

XcL050048046043039034029024019015010005000-005-010-015-019-024-029-034-039-043-048-050

Xcm403853663463082723119315411677390

-39-77-116-154-193-231-27-308-346-385-40

Ycm0264156759949494949494949494949494949494949494

α （deg）90453753252171447300000000000000000




23 21 19 17 11 9 7 53 1 X

α

Y

θ

64



（e）θ=150deg

Energy

dissip

ationra

teofco

llision

096088080072064056048040032024016008-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location


（d）θ=120deg

Energy

dissip

ationra

teofco

llision

072064056048040032024016-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location



Energy

dissip

ationra

teofco

llision


100908070605040302010

ZcRxx=0ZcRxx=075

ZcRxx=025ZcRxx=1

ZcRxx=05

150deg

120deg

90deg

60deg30deg


（c）θ=90deg

Energy

dissip

ationra

teofco

llision

048044040036032028024020016012-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location


（a）θ=30deg

Energy

dissip

ationra

teofco

llision

0040

0036

0032

0028

0024

0020



（b）θ=60deg

Energy

dissip

ationra

teofco

llision

018

016

014

012

010

008



65










4540353025201510050

times107

Energy

dissip

ationJ




4540353025201510050

times107

Energy

dissip

ationJ


Collision location



40353025201510050

times107

Energy

dissip

ationJ



66










1816141210080604020

times107

Energy

dissip

ationJ




12

10

08

06

04

02

0

times107

Energy

dissip

ationJ




4540353025201510050

times107

Energy

dissip



67







Start






dissipation

Comparison

End



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg




6008500000000000

0150202020202000000

9006500000000000000000000

0050101

12000000010306055050450404040404045045050550606065065

1500001025071111111111111111111


68


4 Conclusion

























09509507507507507508508509509509509509509509502020303030303

601

045025005000

005005005005005005005005005005005010101010101

9009500000000000000000000000

120025000000204504030302502502025025030303503504045045045

1500001020609111111111111111111


69



































70







M dvdt


















X

YZ

COG

Ship

rn2

n1

n3

CF = f1n1 + f2n2 + f3n3

63












23456789101112

13（mid）14151617181920212223

24（stern）

XcL050048046043039034029024019015010005000-005-010-015-019-024-029-034-039-043-048-050

Xcm403853663463082723119315411677390

-39-77-116-154-193-231-27-308-346-385-40

Ycm0264156759949494949494949494949494949494949494

α （deg）90453753252171447300000000000000000




23 21 19 17 11 9 7 53 1 X

α

Y

θ

64



（e）θ=150deg

Energy

dissip

ationra

teofco

llision

096088080072064056048040032024016008-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location


（d）θ=120deg

Energy

dissip

ationra

teofco

llision

072064056048040032024016-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location



Energy

dissip

ationra

teofco

llision


100908070605040302010

ZcRxx=0ZcRxx=075

ZcRxx=025ZcRxx=1

ZcRxx=05

150deg

120deg

90deg

60deg30deg


（c）θ=90deg

Energy

dissip

ationra

teofco

llision

048044040036032028024020016012-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location


（a）θ=30deg

Energy

dissip

ationra

teofco

llision

0040

0036

0032

0028

0024

0020



（b）θ=60deg

Energy

dissip

ationra

teofco

llision

018

016

014

012

010

008



65










4540353025201510050

times107

Energy

dissip

ationJ




4540353025201510050

times107

Energy

dissip

ationJ


Collision location



40353025201510050

times107

Energy

dissip

ationJ



66










1816141210080604020

times107

Energy

dissip

ationJ




12

10

08

06

04

02

0

times107

Energy

dissip

ationJ




4540353025201510050

times107

Energy

dissip



67







Start






dissipation

Comparison

End



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg




6008500000000000

0150202020202000000

9006500000000000000000000

0050101

12000000010306055050450404040404045045050550606065065

1500001025071111111111111111111


68


4 Conclusion

























09509507507507507508508509509509509509509509502020303030303

601

045025005000

005005005005005005005005005005005010101010101

9009500000000000000000000000

120025000000204504030302502502025025030303503504045045045

1500001020609111111111111111111


69



































70












23456789101112

13（mid）14151617181920212223

24（stern）

XcL050048046043039034029024019015010005000-005-010-015-019-024-029-034-039-043-048-050

Xcm403853663463082723119315411677390

-39-77-116-154-193-231-27-308-346-385-40

Ycm0264156759949494949494949494949494949494949494

α （deg）90453753252171447300000000000000000




23 21 19 17 11 9 7 53 1 X

α

Y

θ

64



（e）θ=150deg

Energy

dissip

ationra

teofco

llision

096088080072064056048040032024016008-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location


（d）θ=120deg

Energy

dissip

ationra

teofco

llision

072064056048040032024016-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location



Energy

dissip

ationra

teofco

llision


100908070605040302010

ZcRxx=0ZcRxx=075

ZcRxx=025ZcRxx=1

ZcRxx=05

150deg

120deg

90deg

60deg30deg


（c）θ=90deg

Energy

dissip

ationra

teofco

llision

048044040036032028024020016012-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location


（a）θ=30deg

Energy

dissip

ationra

teofco

llision

0040

0036

0032

0028

0024

0020



（b）θ=60deg

Energy

dissip

ationra

teofco

llision

018

016

014

012

010

008



65










4540353025201510050

times107

Energy

dissip

ationJ




4540353025201510050

times107

Energy

dissip

ationJ


Collision location



40353025201510050

times107

Energy

dissip

ationJ



66










1816141210080604020

times107

Energy

dissip

ationJ




12

10

08

06

04

02

0

times107

Energy

dissip

ationJ




4540353025201510050

times107

Energy

dissip



67







Start






dissipation

Comparison

End



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg




6008500000000000

0150202020202000000

9006500000000000000000000

0050101

12000000010306055050450404040404045045050550606065065

1500001025071111111111111111111


68


4 Conclusion

























09509507507507507508508509509509509509509509502020303030303

601

045025005000

005005005005005005005005005005005010101010101

9009500000000000000000000000

120025000000204504030302502502025025030303503504045045045

1500001020609111111111111111111


69



































70



（e）θ=150deg

Energy

dissip

ationra

teofco

llision

096088080072064056048040032024016008-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location


（d）θ=120deg

Energy

dissip

ationra

teofco

llision

072064056048040032024016-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location



Energy

dissip

ationra

teofco

llision


100908070605040302010

ZcRxx=0ZcRxx=075

ZcRxx=025ZcRxx=1

ZcRxx=05

150deg

120deg

90deg

60deg30deg


（c）θ=90deg

Energy

dissip

ationra

teofco

llision

048044040036032028024020016012-05 -04 -03 -02 -01 0 01 02 03 04 05

Collision location


（a）θ=30deg

Energy

dissip

ationra

teofco

llision

0040

0036

0032

0028

0024

0020



（b）θ=60deg

Energy

dissip

ationra

teofco

llision

018

016

014

012

010

008



65










4540353025201510050

times107

Energy

dissip

ationJ




4540353025201510050

times107

Energy

dissip

ationJ


Collision location



40353025201510050

times107

Energy

dissip

ationJ



66










1816141210080604020

times107

Energy

dissip

ationJ




12

10

08

06

04

02

0

times107

Energy

dissip

ationJ




4540353025201510050

times107

Energy

dissip



67







Start






dissipation

Comparison

End



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg




6008500000000000

0150202020202000000

9006500000000000000000000

0050101

12000000010306055050450404040404045045050550606065065

1500001025071111111111111111111


68


4 Conclusion

























09509507507507507508508509509509509509509509502020303030303

601

045025005000

005005005005005005005005005005005010101010101

9009500000000000000000000000

120025000000204504030302502502025025030303503504045045045

1500001020609111111111111111111


69



































70










4540353025201510050

times107

Energy

dissip

ationJ




4540353025201510050

times107

Energy

dissip

ationJ


Collision location



40353025201510050

times107

Energy

dissip

ationJ



66










1816141210080604020

times107

Energy

dissip

ationJ




12

10

08

06

04

02

0

times107

Energy

dissip

ationJ




4540353025201510050

times107

Energy

dissip



67







Start






dissipation

Comparison

End



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg




6008500000000000

0150202020202000000

9006500000000000000000000

0050101

12000000010306055050450404040404045045050550606065065

1500001025071111111111111111111


68


4 Conclusion

























09509507507507507508508509509509509509509509502020303030303

601

045025005000

005005005005005005005005005005005010101010101

9009500000000000000000000000

120025000000204504030302502502025025030303503504045045045

1500001020609111111111111111111


69



































70










1816141210080604020

times107

Energy

dissip

ationJ




12

10

08

06

04

02

0

times107

Energy

dissip

ationJ




4540353025201510050

times107

Energy

dissip



67







Start






dissipation

Comparison

End



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg




6008500000000000

0150202020202000000

9006500000000000000000000

0050101

12000000010306055050450404040404045045050550606065065

1500001025071111111111111111111


68


4 Conclusion

























09509507507507507508508509509509509509509509502020303030303

601

045025005000

005005005005005005005005005005005010101010101

9009500000000000000000000000

120025000000204504030302502502025025030303503504045045045

1500001020609111111111111111111


69



































70







Start






dissipation

Comparison

End



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg



Energy

dissip

ationra

teofco

llision


100908070605040302010

150deg

120deg

90deg60deg30deg




6008500000000000

0150202020202000000

9006500000000000000000000

0050101

12000000010306055050450404040404045045050550606065065

1500001025071111111111111111111


68


4 Conclusion

























09509507507507507508508509509509509509509509502020303030303

601

045025005000

005005005005005005005005005005005010101010101

9009500000000000000000000000

120025000000204504030302502502025025030303503504045045045

1500001020609111111111111111111


69



































70


4 Conclusion

























09509507507507507508508509509509509509509509502020303030303

601

045025005000

005005005005005005005005005005005010101010101

9009500000000000000000000000

120025000000204504030302502502025025030303503504045045045

1500001020609111111111111111111


69



































70



































70

Documents

LIUJunfengjournal16.magtechjournal.com/jwk_zgjcyj/fileup/PingShen/... · 2017. 11. 9. · downloaded from Received：2016-07-28 Supportedby：NationalNaturalScienceFoundationofChina(51239007)