Dynamic Characteristics of the Rotating Penetrating ...

Research ArticleDynamic Characteristics of the Rotating Penetrating Missile forAttacking Warship Vertically

Dong-ze Qin and Pei-hang Li

School of Mechatronic Engineering North University of China Taiyuan 030051 China

Correspondence should be addressed to Dong-ze Qin apo1981126com

Received 26 March 2021 Accepted 5 July 2021 Published 20 July 2021

Academic Editor Francesco Tornabene

Copyright copy 2021 Dong-ze Qin and Pei-hang Li is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

e paper aimed to analyze the dynamic response of a new type penetrating missile in rotary attacking warship e dynamicresponse characteristics of the penetrator become more complex when attacking the ship target due to the special materials of thedeck such as stiffeners erefore different from attacking other targets the article reveals the design rules of precessionpenetration ammunition and fuze A physical model of the missile target is established to study the numerical simulation of thepenetration process of rotating projectile into a stiffened target based on finite element analysis (FEA) software We studied thedynamic response characteristics of different projectile positions rotational speeds and positions that act in precession pen-etration As experimental results show the residual velocity of the precession penetrator decreases with the distance between theprojectile point and stiffenerWhen the projectile penetrates the second target plate the acceleration is greater than that in the firstlayer It is proved that the deflection angle of the shell body is affected by comprehensive factors e rotational speed in theprojectile has less contribution to precession penetration ammunition In addition the change of acceleration in the missilersquoscentral section can be significantly perceived in the direction perpendicular to the penetration direction

1 Introduction

11 Background e rotating penetrating projectile is notonly a new type of penetration ammunition but also aneffective supplement when it is applied to attack ship targetsWith the improvement of the warshiprsquos armor structuredesign the antipenetrating effectiveness of the deck isshowing a substantial promotion Unlike the traditionalhomogeneous target plate the special design of the ship deck(eg transverse or longitudinal T-stiffener) will have a greatinfluence on the performance of the projectile

Literature [1] introduced a high rotating speed missilepenetrating into moving vehicle doors at a different incidentangle Literature [2] introduced rotating penetrating missilenumerical simulation and experimental in bunker buster

Literature [3] introduced an investigation of the penetrationresistance of monolithic and double-layered steel platesLiterature [4] introduced an experimental and numericalinvestigation on the ballistic resistance of double-layeredsteel plates Literature [5] introduced a computational in-vestigation of ballistic impact behavior and penetrationresistance of a nacre-like ceramicpolymer-laminatedcomposite Literature studies [6ndash11] introduced the responseof different protective materials during penetration andrevealed the relevant laws Literature studies [12ndash16] in-troduced the analysis and experiments of antiship targetpenetration and revealed relevant laws

e results of the relevant literature show that the nu-merical analysis method for penetration is mature Howeverit can be seen that there is relatively little research in the ship

HindawiJournal of EngineeringVolume 2021 Article ID 9953866 9 pageshttpsdoiorg10115520219953866

of the rotating penetrating and the relevant laws are notclearly understood which has caused certain constraints onthe design of the rotating penetrating missile

12 Contributions

(1) In this paper we established the physical model ofmissile into the target Under different workingconditions the numerical simulation is applied toanalyze the penetration process of the projectile tothe stiffened target by FEA

(2) is research provides five contributions e residualspeed of the novel rotating penetrating missile de-creases with the reduction of the distance of theprojectile point relative to the reinforcing ribs eacceleration of themissile penetrating the second targetis larger than that of the first onee combined factorsaffect the deflection angle of the missile e rotationalspeed of the projectile affects the penetration of pre-cession ammunition weakly Finally the accelerationchange perpendicular to the penetration direction ismore obvious in the middle of the missile

2 Simulation Model

21 Procedure As follows the research is based on ANSYSworkbench LS-DYNA for simulation analysis

Step 1 3D modeling software was used to build asimulation geometry modelStep 2 call the LS-DYNA module on the ANSYSWORKBENCH add geometric models and set ma-terial parametersStep 3 preprocessing specifically including meshingdefining contact applying loads and boundary con-ditions etcStep 4 solve e LS-DYNA module is used to solve itwith its own solverStep 5 postprocessing the relevant result file generatedafter step 4 is solved imported into LS-POST post-processing software and generated the required dataand chartsStep 6 analysis of simulation results

22 Finite Element Model Assuming the target is a warshipthe steel is HY-80 its characteristics are comparable with the921A steel so choose the 921A steel in the software materiallibrary [14 16] Target plate size settings 1400mm long1000mm wide deck thickness 152mm large rib height68mm width 152mm small rib height 26mm width7mm small rib spacing 125mm large rib spacing 600mmas shown in Figure 1

emissile is chosen to cut the truncated ogive noseeintercepting diameter (d) is about 15 of the projectile di-ameter (D) e truncated ogive nosersquos head is a wall-to-wallthick head shell gradually thinning from the apex axis to theldquofirst-columnrdquo excessive area the thickest at the top is 5

times the thickness of the wall and the wall thickness of thecolumn segment is 10mm minus 14mm e missile body is370mm long the projectile diameter is 105mm the missilehead is egg-cut the cut head diameter is 20mm and the arcradius of the missile body is 180mm e projectile materialis 30CrMnSiNi2A and the explosives and fuze in themissiles are treated with elastic material Among them theloading density is 17gcm3 the fuze density is 38 cm3 andthe total mass of the missile body is 16 kg

In order to reduce the calculation the target analysisprocess is assumed to be two-layered on the basis of gen-erality e finite element model of the target and the missileis shown in Figure 2

e structure of this article is modeled and analyzedusing 3D solid164 units Taking into account the accuracyand timeliness of the calculation the mesh is dense and themesh in the rest of the area is sparse in the 200mm squarearea with a 200mm square length at the center edge of thetarget board On the intersection of the dense and sparseareas of the mesh the mesh performs a good transitionwhich avoids the reflection of the stress wave on the tran-sition e grid size convergence analysis shows that thecalculation is stable at a fixed level and the duration is ac-ceptable Each calculation takes about 6 hours Table 1 showsthe grid size of each part

e cell grid ratio is within the normal range and is denseand reasonable and the mesh quality is higher is shape andsize mesh is used for calculation and the results are reliable

23 Constitutive Equations Since both 921A steel and30CrMnSiNi2A are temperature-sensitive materials theJohnsonndashCookmodel is usede equation for this structure is[14ndash16]

σy A + Bεnp1113872 1113873(1 + C ln ε

middotlowast) 1 minus T

lowastm( 1113857 (1)

where A B C n andm is the material in the formula εnp is

an equivalent plastic strain εmiddotlowast

εp

middotmiddot ε0

middotis the plastic strain

ratio generally taken ε0 10 sminus 1 Tlowast (T minus Tr)(Tm minus Tr) isthe relative temperatureTr is the room temperature and Tm

is the melting point temperature

1000

1400152600

125

7

Figure 1 Target plate structure diagram

2 Journal of Engineering

Break strain is

εf D1 + D2 exp D3σlowast

( 1113857 1 + D4 ln εglowast

1113874 1113875 1 + D5Tlowast

( 1113857 (2)

where σlowast pσ

radicis the ratio of hydrostatic pressure to

equivalent stress and Di is a constant in the formulaWhen defining a material with the JohnsonndashCook

model it is necessary to combine the Gruneisen stateequation which can define the relationship between thepressure volume in two ways to determine whether thematerial is compressed or expanded e Gruneisen stateequation with a three-dimensional impact velocity of oneparticle defines the pressure of the compressed material asfollows

P ρ0C

2μ 1 + 1 minus c02( 11138571113858 1113859μ minus a2μ2

[1 minus (S minus 1)μ]2 + c0 + aμ( 1113857E (3)

In the formula C is the intercept of the ]S minus ]P curve S isthe vs minus vp slope coefficient c0 is the Gruneisen constantand a is the first-order volume correction of μ ρρminus 1

0 ematerial model parameters of the target system are set inTables 2 and 3

231 Boundary Condition Settings A fixed restraint is usedon the four sides of the reinforced rib target plate For thestructure the type of the contact set is CONTACT_AUTOMATIC_GENERAL which ensures effective contactbetween individual components and between componentsIn the calculation of complex structural contact nodes andsurfaces are difficult to predict and the contact type is in-troduced to avoid penetration by unpredictable contacte type of contact between the missile and the target boardis CONTACT_ERODING_SINGLE_SURFACE Erosioncontact is a common method in simulation calculationDuring the invasion the phenomenon of fragmentation ofthe missile and target plate is obvious and the failed unit isdeleted in large numbers thus causing the original contactinterface to be destroyed To make the surface unit be largelydeleted the internal unit can still effectively contact do notpenetrate use erosion contact and can effectively solve thecontact problem

232 Time Integration Scenario e calculation time is setto 12ms e maximum energy errorrsquos value is 0 e timestep safety factor is 06

Table 2 921A steel JohnndashCook material model constant [14 15 16]

ρ (kgm) E (GPa) U Tr (K) Tm (k) A (MPa) B (MPa) N7800 205 028 298 1765 490 807 073C m D1 D2 D3 D4 D500114 094 08 1732 minus 054 minus 0015 0

Table 3 30CrMnSiNi2A steel JohnndashCook material model constant [14 15 16]

ρ (kgm) E (GPa) U Tr (K) Tm (k) A (MPa) B (MPa) N7850 211 03 298 1798 1269 81018 0479C m D1 D2 D3 D4 D50040 1 0239 8593 7867 0009 0

Figure 2 Reinforcing rib plate and missilersquos finite element model

Table 1 Unit size of each part

Parts Target plate dense area Target plate sparse area Bullet LoadingRegional (mm) 8 10 5 5

Journal of Engineering 3

3 Numerical Simulation Results and Analysis

31 Impact of Missile Position e target deck composed ofstiffeners is heterogeneous which leads to the differentimpact points of the projectile relative to the targeterefore the forces on the structure of the missile are alsodifferent e relative position relationship between theprojectile point target plate reinforcement is shown inFigure 3 Table 4 describes the six main working conditionsof the impact point Because most warships use the verticalskeleton type the spacing of the horizontal reinforcing ribs isusually large the probability of working conditions 2 and 4 isrelatively small and is not the most dangerous case of targetplate breakage failure erefore this paper mainly studiesthe dynamic response characteristics of the cyclones underworking conditions 1 3 5 and 6

It is assumed that the impact velocity of the missilepenetrating the target is 1300ms and the rotation velocity is10000 rmin When the missile is hitting the target plate theabove four conditions (condition 1 condition 3 condition 5and condition 6) are simulated respectively

Figure 4 shows a stress cloud map of the missile in fourworking conditions that have just penetrated through thesecond target plate It can be seen that the target plateprojectile hole is approximately oval the missile hole di-ameter is slightly larger than the projectile body diameterthe edge of the projectile hole on the back of the target plateforms a turned lip (the front of the target petal deformation)and the area of the missile hole collapse is slightly larger thanthe cross-sectional area of the missile body As shown inFigure 5 when the truncated surface of the missile pene-trates into the stiffener in the working conditions 5 and 6the stiffener struck by the projectile during the penetrationprocess will produce obvious bending deformation away

from the direction of it under its impact is phenomenonis induced by the intrusion of themissile Under the action ofcompressive resistance the target plate material in theminimum resistance direction produces plastic flow whichmakes the back surface of the target bulge in the direction ofpenetrationen cracks are formed so that the missile bodyis exposed from the bulge to form the lip behind the targetAt the same time on the stiffeners perpendicular to the planeof the target plate the bending phenomenon tends to deviatefrom the direction of the projectile

Figures 6 7 and 8 show the time curve of the speedacceleration and ballistic offset angle changes in the Z-di-rection of the missile centroid under the above four workingconditions

As can be seen from Figure 6 that when penetrating thereinforcing rib target plate the projectile point position isdifferent and the speed drop of the body also has obviousdifferences It is caused by the different positions of themissile relative to the plate and the corresponding differentequivalent penetration thickness e equivalent penetra-tion thickness of the missile to the stiffener is inverselyproportional to the residual velocity of the projectileFigure 7 shows the graph of the acceleration in the Z-di-rection during the penetrating of speed fixing From Fig-ure 7 it can be seen that the overall trend of accelerationchanging over time in the four working conditions is thesame while the acceleration when the missile body pen-etrates the second target plate is significantly greater thanthe acceleration when penetrating the first target plate ereason of this phenomenon is the plastic deformation of themissile in the process of penetrating the target plate whichmakes the warhead blunt Because of the increase of thecontact area between the projectile and the target thepenetration resistance of the missile is forced to increase

Table 4 Schedule of work

Working condition 1 Workingcondition 2

Workingcondition 3

Workingcondition 4 Working condition 5 Working condition 6

Missileposition

Hitting the platebetween the

reinforcing ribs

Hitting thebig ribs

Hitting thelittle ribs

Hitting the size ribintersection point

Intercepting the arc ofthe head penetrate the

big ribs


small ribs

Working condition 3

Working condition 4

Working condition 5

Working condition 2

Working condition 1

Working condition 6

Figure 3 Missile position


during the penetration of the second target plate In ad-dition due to the different impact points the erosion andpier thickness of the warhead are different when the missilepenetrates the first target plate erefore the accelerationdifference is obvious when the body penetrates the secondone Figure 8 shows speed fixed when the trajectory de-flection angle changes the time graph A number of factorswork together to determine the angle of deflection of themissile When the projectile body impacts the flat part ofthe target plate in the forward direction the overturningtorque of the missile is small due to the uniform equivalentpenetration thickness e main performance of the systemis the gyro stability and the deflection angle of the missile

body is the minimum simultaneously When the truncatedsurface invades the stiffener the flip torque produced bythe projectile is greater than the gyro stabilization effecterefore the ballistic offset angle increases which is dueto the different equivalent penetration thickness on bothsides of the missile

32 Speed Effects It is the most common phenomenon thatthe curved part of the truncated body penetrates the rein-forcing ribs of the target In order to study the influence ofrotational speed on precession penetration the abovecondition (5) is simulated as the research object Among

(a) (b)

Figure 5 Target plate missile hole structure (a) Working condition 5 (b) Working condition 6

1168e + 03

Effective stress (vndashm)

Time = 000078399Contours of effective stress (vndashm)min = 378084 at elem 53297max = 11678 at elem 130305

1051e + 039350e + 028186e + 027022e + 025858e + 024694e + 023530e + 022366e + 021202e + 023781e + 00

(a)

1197e + 03



1077e + 039579e + 028384e + 027189e + 025995e + 024800e + 023605e + 022410e + 021216e + 022097e + 00

(b)

1189e + 03



1070e + 039516e + 028331e + 027145e + 025959e + 024773e + 023587e + 022401e + 021215e + 022883e + 00

(c)

1172e + 03



1055e + 039381e + 028212e + 027044e + 025876e + 024708e + 023540e + 022371e + 021203e + 023494e + 00

(d)

Figure 4 Target plate stress cloud chart (a) Working condition 1 (b) Working condition 3 (c) Working condition 5 (d) Workingcondition 6


them the initial velocity of the missile is 1300ms and therotational angular velocity is 0 rmin 5000 rmin 10000 rmin and 20000 rmin

Figures 9 10 and 11 shows the time curve of the velocityacceleration and ballistic offset angle changing in the Z-

direction of the missile at different speed It can be seen thatthe rotational speed has a little effect on the penetrationprocess when it penetrates the first target e variation ofvelocity acceleration and trajectory deviation angle with

13201300128012601240122012001180116011401120Re

sulta

nt ri

gid

body

vel

ocity

(ms

)

0 01 02 03t (ms)

04 05 06

0 rs5000 rs

10000 rs20000 rs

Figure 9 Intrusive speed graph when the speed changes

Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

0 rmin5000 rmin

20E + 05

00E + 00

ndash20E + 05

ndash40E + 05

ndash60E + 05

ndash80E + 05

ndash10E + 06

ndash12E + 06

ndash14E + 06

10000 rmin20000 rmin

Figure 10 Invasive acceleration graph when the speed changes

7

6

5

4

3

2

1

0

ndash1

Balli

stic d

eflec

tion

angl

e (deg)

0 01 02 03t (ms)

04 05 06

0 rmin5000 rmin


Figure 11 Ballistic offset angle changes over time when the speedchanges

1320130012801260

Resu

ltant

rigi

d bo

dy v

eloc

ity (m

s)

1240122012001180116011401120

0 01 02 03t (ms)

04 05

Working condition 1Working condition 3


Figure 6 e change of projectile speed

20E + 500E + 0

ndash20E + 5ndash40E + 5ndash60E + 5ndash80E + 5ndash10E + 6ndash12E + 6ndash14E + 6ndash16E + 6Z-

rigid

bod

y ac

cele

ratio

n (m

s2 )

0 01 02 03t (ms)

04 05 06

Working condition 1Working condition 3Working condition 5Working condition 6

Figure 7 e change of the acceleration of the missile body

876543210

ndash1

Balli

stic d

eflec

tion

angl

e (deg)

0 01 02 03t (ms)

04 05 06



Figure 8 Ballistic offset angle change of the missile body


time is similar and the curves coincide approximatelyWhen the projectile penetrates the second target plate theresidual velocity of the missile increases and the speeddecrease and the acceleration change curve closes Ballisticoffset angle is the maximum at 5000 rmin and minimum at20000 rmin and the ballistic offset angle of themissile at 0 rmin and 10000 rmin is approximately equal between thetwo working conditions above is is due to the length ofthe penetrating missile far greater than the thickness of themetal target plate the penetrating process can be regarded asthe projectile body penetration of the metal sheet processand the form of destruction is ductility perforated armorWhen the missile body heads through the target plate theprojectile hole will be further expanded e missile holediameter is slightly larger than the projectile body diameterWith the penetrating the sidewall of the missile body will nolonger be in direct contact with the metal target plate At thistime the missile body was penetrated resistance and the fliptorque disappeared the body only under the original dy-namic energy and gravity acceleration in the missile body tobreak through the first target plate before the second targetplate of this process and the projectile bodyrsquos velocity andapproximate acceleration remain unchanged e ballisticoffset angle continues to increase with the speed directionafter the first target plate is broken and this process cor-responds to the curve between 012 and 028ms in Figures 910 and 11 As the penetration proceeds the penetrationprocess starts again when the head of the missile touchesthe second plate After the missile penetrated the firsttarget the warhead will erode and the pier will be thickWhen the warhead becomes blunt the velocity decreasesand the acceleration increases obviously e accumulationof trajectory offset angle will lead to further increase ofoffset angle e above process corresponds to the curveafter t 028ms

33 Changes in Parameters at Different Positions of theMissileBody As the acceleration sensor of the fuze is arranged indifferent positions the penetrating parameters obtained arealso different To understand the design law of rotatingpenetrating projectile the following simulation analysis iscarried out on this problem

Condition 5 is still selected as the research object efront middle and back positions on the projectile axis areselected as the measurement points as shown Figure 12

Figures 13 14 and 15 show the acceleration change slotover time in the X Y and Z directions of the differentpositions of the missile As can be seen from Figures 13 and14 the acceleration of the missile in the direction per-pendicular to the penetration direction is obvious at pointsA and C showing two obvious peaks and the direction ofthe two points is opposite e reason is that in the processof penetration there will be an approximate deflectionaround the center of mass and the deflection of its headand tail is opposite resulting in the opposite accelerationdirection of the two parts in the same direction simulta-neously When the deflection angle acceleration of theprojectile is constant the deflection acceleration is larger at

the position far away from the centroid because the cen-troid of the missile is close to point B Far away from themissile body the center position is subjected to deflectionand acceleration is larger so the head and tail of the missile

Pid = 5

Pid = 3

Pid = 6

A

B

C

Figure 12 Missile parameter measurement point

X-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

60E + 05

40E + 05

20E + 05

00E + 00

ndash20E + 05

ndash40E + 05

ndash60E + 05

ndash80E + 05

C

Figure 13 Acceleration curve in the X-direction at different po-sitions of the missile


perpendicular to the direction of the acceleration changesensing are more obvious As plotted in Figure 15 theacceleration curve of the B in the middle of the missileshows two distinct peaks in the Z-direction which cor-respond to the acceleration of the two target layers whenthe missile invades and the point A and C accelerationmutations are relatively not obvious

is is due to the fact that the missile in the process ofpenetrating will be around its own deflection the head andtail in the Z-direction of the acceleration component issignificantly larger than the middle By the accelerationvector synthesis principle the missile deflection of the twoparts of the acceleration interference in the Z-direction islarger and the central position is relatively small ereforethe central position of the missile body is more obvious tothe acceleration of the body in the direction of penetrationFurthermore when swirling into the arrangement of the fuzeaccelerometer of the intrusive ammunition the acceler-ometer should be arranged as far as possible in the positionof the relatively ballistic center

4 Conclusions

e numerical results showed that (1) the residual velocity ofrotating penetrator decreases with the compression of therelative distance between missile point and reinforcing ribs(2) e acceleration of the missile penetrating the secondtarget is larger than that of the first layer (3) e deflectionballistic offset angle is affected by comprehensive factors (4)e rotational speed of missile has less effect on precessionpenetration ammunition (5)e acceleration perpendicularto the penetration direction is obviously perceived in themiddle of the missile e research results will provide areference for the design of the rotating penetrating missileand fuze obtained above

In this paper vertical penetration is mainly consideredwhile oblique penetration and composite deck are rarelyconsidered For the problems we will study them in anotherresearch

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the Key Laboratory OpenResearch Fund Project of the Advanced ManufacturingTechnology Laboratory in Shanxi under the grantXJZZ201704

References

[1] J Li X J Li and Z Zhao ldquoSimulation on projectile with highrotating speed penetrating into the moving vehicular doorrdquo5eoretical and Applied Fracture Mechanics vol 47 no 2pp 113ndash119 2007

[2] S Fan Z-G Chen and X Hou ldquoNumerical simulations andexperimental study penetrating projectile on novel rotatingrdquoJournal of Projectiles Rockets Missiles and Guidance vol 22013

[3] J Cui X Chen A Tian et al ldquoInvestigation of the penetrationresistance of monolithic and double-layered steel platesrdquoInternational Journal of Modern Physics B vol 33 Article ID1940005 2019

[4] S Dey T Boslashrvik X Teng T Wierzbicki andO S Hopperstad ldquoOn the ballistic resistance of double-layered steel plates an experimental and numerical investi-gationrdquo International Journal of Solids and Structures vol 44no 20 pp 6701ndash6723 2007

[5] M Grujicic S Ramaswami and J Snipes ldquoComputationalinvestigation of ballistic-impact behavior and penetrationresistance of a nacre-like ceramicpolymer laminated com-positerdquo International Journal of Structural Integrity vol 8no 1 pp 79ndash107 2017

[6] O A Kudryavtsev and S B Sapozhnikov ldquoNumerical sim-ulations of ceramic target subjected to ballistic impact using

Y-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

80E + 0460E + 0440E + 0420E + 0400E + 00

ndash20E + 04ndash40E + 04ndash60E + 04ndash80E + 04ndash10E + 05ndash12E + 05

C

Figure 14 Acceleration curve in the Y-direction at different po-sitions of the missile

Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

45E + 0640E + 0635E + 0630E + 0625E + 0620E + 0615E + 0610E + 0650E + 0500E + 00

C

Figure 15 Z-directional acceleration curve at different positions ofthe missile


combined DEMFEM approachrdquo International Journal ofMechanical Sciences vol 114 pp 60ndash70 2016

[7] C-Y Huang and Y-L Chen ldquoDesign and impact-resistantanalysis of functionally graded Al2O3-ZrO2 ceramic com-positerdquo Materials amp Design vol 91 pp 294ndash305 2015

[8] P J Hazell G J Appleby-omas and S Toone ldquoBallisticcompaction of a confined ceramic powder by a non-deforming projectile experiments and simulationsrdquoMaterialsand Design vol 56 pp 943ndash952 2014

[9] H Mei L Zhang and H Xu ldquoDamage mechanism of acarbon-fiber ceramic composite during the step-loading in-dentation and its effect on the mechanical propertiesrdquoComposites Part B Engineering vol 56 pp 142ndash148 2014

[10] B G Compton E A Gamble and F W Zok ldquoFailure ini-tiation during the impact of metal spheres onto ceramictargetsrdquo International Journal of Impact Engineering vol 55pp 11ndash23 2012

[11] W A Gooch and R G OrsquoDonnell ldquoStudy of fragmentation inthe ballistic impact of ceramicsrdquo International Journal ofImpact Engineering vol 15 no 5 pp 605ndash618 1994

[12] Y Li H-L Yu and X-T Rui ldquoNumerical study on pene-tration of rotating projectile into steel platerdquo Fire Control ampCommand Control vol 39 no 12 pp 31ndash35+39 2014

[13] X Li and L Jiang ldquoNumerical study on penetration of a high-speed-rotating bullet into the moving sheet-metal platerdquoExplosion and Shock Waves vol 1 pp 57ndash61 2008

[14] Z Zhang and F Huang 5e Numerical Simulation for Semi-armor-piecing Anti-ship WarheadPenetrating the StructuralTarget with Rebar pp 406ndash410 Transaction of Beijing In-stitute of Technology Beijing China 2003

[15] Z Duan ldquoExperimental and theoretical study on the endballistics of semi-piercing projectiles on the penetration ofreinforced targetsrdquo Explosion and Shock Waves vol 6pp 547ndash552 2005

[16] R L Woodward and S J Cimpoeru ldquoA study of the per-foration of aluminum laminate targetsrdquo International Journalof Impact Engineering vol 21 no 3 1998


of the rotating penetrating and the relevant laws are notclearly understood which has caused certain constraints onthe design of the rotating penetrating missile

12 Contributions

(1) In this paper we established the physical model ofmissile into the target Under different workingconditions the numerical simulation is applied toanalyze the penetration process of the projectile tothe stiffened target by FEA

(2) is research provides five contributions e residualspeed of the novel rotating penetrating missile de-creases with the reduction of the distance of theprojectile point relative to the reinforcing ribs eacceleration of themissile penetrating the second targetis larger than that of the first onee combined factorsaffect the deflection angle of the missile e rotationalspeed of the projectile affects the penetration of pre-cession ammunition weakly Finally the accelerationchange perpendicular to the penetration direction ismore obvious in the middle of the missile

2 Simulation Model

21 Procedure As follows the research is based on ANSYSworkbench LS-DYNA for simulation analysis

Step 1 3D modeling software was used to build asimulation geometry modelStep 2 call the LS-DYNA module on the ANSYSWORKBENCH add geometric models and set ma-terial parametersStep 3 preprocessing specifically including meshingdefining contact applying loads and boundary con-ditions etcStep 4 solve e LS-DYNA module is used to solve itwith its own solverStep 5 postprocessing the relevant result file generatedafter step 4 is solved imported into LS-POST post-processing software and generated the required dataand chartsStep 6 analysis of simulation results

22 Finite Element Model Assuming the target is a warshipthe steel is HY-80 its characteristics are comparable with the921A steel so choose the 921A steel in the software materiallibrary [14 16] Target plate size settings 1400mm long1000mm wide deck thickness 152mm large rib height68mm width 152mm small rib height 26mm width7mm small rib spacing 125mm large rib spacing 600mmas shown in Figure 1

emissile is chosen to cut the truncated ogive noseeintercepting diameter (d) is about 15 of the projectile di-ameter (D) e truncated ogive nosersquos head is a wall-to-wallthick head shell gradually thinning from the apex axis to theldquofirst-columnrdquo excessive area the thickest at the top is 5

times the thickness of the wall and the wall thickness of thecolumn segment is 10mm minus 14mm e missile body is370mm long the projectile diameter is 105mm the missilehead is egg-cut the cut head diameter is 20mm and the arcradius of the missile body is 180mm e projectile materialis 30CrMnSiNi2A and the explosives and fuze in themissiles are treated with elastic material Among them theloading density is 17gcm3 the fuze density is 38 cm3 andthe total mass of the missile body is 16 kg

In order to reduce the calculation the target analysisprocess is assumed to be two-layered on the basis of gen-erality e finite element model of the target and the missileis shown in Figure 2

e structure of this article is modeled and analyzedusing 3D solid164 units Taking into account the accuracyand timeliness of the calculation the mesh is dense and themesh in the rest of the area is sparse in the 200mm squarearea with a 200mm square length at the center edge of thetarget board On the intersection of the dense and sparseareas of the mesh the mesh performs a good transitionwhich avoids the reflection of the stress wave on the tran-sition e grid size convergence analysis shows that thecalculation is stable at a fixed level and the duration is ac-ceptable Each calculation takes about 6 hours Table 1 showsthe grid size of each part

e cell grid ratio is within the normal range and is denseand reasonable and the mesh quality is higher is shape andsize mesh is used for calculation and the results are reliable

23 Constitutive Equations Since both 921A steel and30CrMnSiNi2A are temperature-sensitive materials theJohnsonndashCookmodel is usede equation for this structure is[14ndash16]

σy A + Bεnp1113872 1113873(1 + C ln ε

middotlowast) 1 minus T

lowastm( 1113857 (1)

where A B C n andm is the material in the formula εnp is

an equivalent plastic strain εmiddotlowast

εp

middotmiddot ε0

middotis the plastic strain

ratio generally taken ε0 10 sminus 1 Tlowast (T minus Tr)(Tm minus Tr) isthe relative temperatureTr is the room temperature and Tm

is the melting point temperature

1000

1400152600

125

7

Figure 1 Target plate structure diagram


Break strain is


( 1113857 1 + D4 ln εglowast

1113874 1113875 1 + D5Tlowast

( 1113857 (2)

where σlowast pσ




P ρ0C
























Workingcondition 3


Missileposition


reinforcing ribs

Hitting thebig ribs




big ribs


small ribs

Working condition 3

Working condition 4

Working condition 5

Working condition 2

Working condition 1

Working condition 6






(a) (b)


1168e + 03



1051e + 039350e + 028186e + 027022e + 025858e + 024694e + 023530e + 022366e + 021202e + 023781e + 00

(a)

1197e + 03



1077e + 039579e + 028384e + 027189e + 025995e + 024800e + 023605e + 022410e + 021216e + 022097e + 00

(b)

1189e + 03



1070e + 039516e + 028331e + 027145e + 025959e + 024773e + 023587e + 022401e + 021215e + 022883e + 00

(c)

1172e + 03



1055e + 039381e + 028212e + 027044e + 025876e + 024708e + 023540e + 022371e + 021203e + 023494e + 00

(d)






13201300128012601240122012001180116011401120Re

sulta

nt ri

gid

body

vel

ocity

(ms

)

0 01 02 03t (ms)

04 05 06

0 rs5000 rs

10000 rs20000 rs


Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

0 rmin5000 rmin

20E + 05

00E + 00

ndash20E + 05

ndash40E + 05

ndash60E + 05

ndash80E + 05

ndash10E + 06

ndash12E + 06

ndash14E + 06



7

6

5

4

3

2

1

0

ndash1

Balli

stic d

eflec

tion

angl

e (deg)

0 01 02 03t (ms)

04 05 06

0 rmin5000 rmin



1320130012801260

Resu

ltant

rigi

d bo

dy v

eloc

ity (m

s)

1240122012001180116011401120

0 01 02 03t (ms)

04 05




20E + 500E + 0


rigid

bod

y ac

cele

ratio

n (m

s2 )

0 01 02 03t (ms)

04 05 06



876543210

ndash1

Balli

stic d

eflec

tion

angl

e (deg)

0 01 02 03t (ms)

04 05 06










Pid = 5

Pid = 3

Pid = 6

A

B

C


X-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

60E + 05

40E + 05

20E + 05

00E + 00

ndash20E + 05

ndash40E + 05

ndash60E + 05

ndash80E + 05

C





4 Conclusions



Data Availability




Acknowledgments


References







Y-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

80E + 0460E + 0440E + 0420E + 0400E + 00


C


Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

45E + 0640E + 0635E + 0630E + 0625E + 0620E + 0615E + 0610E + 0650E + 0500E + 00

C















Break strain is


( 1113857 1 + D4 ln εglowast

1113874 1113875 1 + D5Tlowast

( 1113857 (2)

where σlowast pσ




P ρ0C
























Workingcondition 3


Missileposition


reinforcing ribs

Hitting thebig ribs




big ribs


small ribs

Working condition 3

Working condition 4

Working condition 5

Working condition 2

Working condition 1

Working condition 6






(a) (b)


1168e + 03



1051e + 039350e + 028186e + 027022e + 025858e + 024694e + 023530e + 022366e + 021202e + 023781e + 00

(a)

1197e + 03



1077e + 039579e + 028384e + 027189e + 025995e + 024800e + 023605e + 022410e + 021216e + 022097e + 00

(b)

1189e + 03



1070e + 039516e + 028331e + 027145e + 025959e + 024773e + 023587e + 022401e + 021215e + 022883e + 00

(c)

1172e + 03



1055e + 039381e + 028212e + 027044e + 025876e + 024708e + 023540e + 022371e + 021203e + 023494e + 00

(d)






13201300128012601240122012001180116011401120Re

sulta

nt ri

gid

body

vel

ocity

(ms

)

0 01 02 03t (ms)

04 05 06

0 rs5000 rs

10000 rs20000 rs


Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

0 rmin5000 rmin

20E + 05

00E + 00

ndash20E + 05

ndash40E + 05

ndash60E + 05

ndash80E + 05

ndash10E + 06

ndash12E + 06

ndash14E + 06



7

6

5

4

3

2

1

0

ndash1

Balli

stic d

eflec

tion

angl

e (deg)

0 01 02 03t (ms)

04 05 06

0 rmin5000 rmin



1320130012801260

Resu

ltant

rigi

d bo

dy v

eloc

ity (m

s)

1240122012001180116011401120

0 01 02 03t (ms)

04 05




20E + 500E + 0


rigid

bod

y ac

cele

ratio

n (m

s2 )

0 01 02 03t (ms)

04 05 06



876543210

ndash1

Balli

stic d

eflec

tion

angl

e (deg)

0 01 02 03t (ms)

04 05 06










Pid = 5

Pid = 3

Pid = 6

A

B

C


X-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

60E + 05

40E + 05

20E + 05

00E + 00

ndash20E + 05

ndash40E + 05

ndash60E + 05

ndash80E + 05

C





4 Conclusions



Data Availability




Acknowledgments


References







Y-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

80E + 0460E + 0440E + 0420E + 0400E + 00


C


Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

45E + 0640E + 0635E + 0630E + 0625E + 0620E + 0615E + 0610E + 0650E + 0500E + 00

C
























Workingcondition 3


Missileposition


reinforcing ribs

Hitting thebig ribs




big ribs


small ribs

Working condition 3

Working condition 4

Working condition 5

Working condition 2

Working condition 1

Working condition 6






(a) (b)


1168e + 03



1051e + 039350e + 028186e + 027022e + 025858e + 024694e + 023530e + 022366e + 021202e + 023781e + 00

(a)

1197e + 03



1077e + 039579e + 028384e + 027189e + 025995e + 024800e + 023605e + 022410e + 021216e + 022097e + 00

(b)

1189e + 03



1070e + 039516e + 028331e + 027145e + 025959e + 024773e + 023587e + 022401e + 021215e + 022883e + 00

(c)

1172e + 03



1055e + 039381e + 028212e + 027044e + 025876e + 024708e + 023540e + 022371e + 021203e + 023494e + 00

(d)






13201300128012601240122012001180116011401120Re

sulta

nt ri

gid

body

vel

ocity

(ms

)

0 01 02 03t (ms)

04 05 06

0 rs5000 rs

10000 rs20000 rs


Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

0 rmin5000 rmin

20E + 05

00E + 00

ndash20E + 05

ndash40E + 05

ndash60E + 05

ndash80E + 05

ndash10E + 06

ndash12E + 06

ndash14E + 06



7

6

5

4

3

2

1

0

ndash1

Balli

stic d

eflec

tion

angl

e (deg)

0 01 02 03t (ms)

04 05 06

0 rmin5000 rmin



1320130012801260

Resu

ltant

rigi

d bo

dy v

eloc

ity (m

s)

1240122012001180116011401120

0 01 02 03t (ms)

04 05




20E + 500E + 0


rigid

bod

y ac

cele

ratio

n (m

s2 )

0 01 02 03t (ms)

04 05 06



876543210

ndash1

Balli

stic d

eflec

tion

angl

e (deg)

0 01 02 03t (ms)

04 05 06










Pid = 5

Pid = 3

Pid = 6

A

B

C


X-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

60E + 05

40E + 05

20E + 05

00E + 00

ndash20E + 05

ndash40E + 05

ndash60E + 05

ndash80E + 05

C





4 Conclusions



Data Availability




Acknowledgments


References







Y-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

80E + 0460E + 0440E + 0420E + 0400E + 00


C


Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

45E + 0640E + 0635E + 0630E + 0625E + 0620E + 0615E + 0610E + 0650E + 0500E + 00

C


















(a) (b)


1168e + 03



1051e + 039350e + 028186e + 027022e + 025858e + 024694e + 023530e + 022366e + 021202e + 023781e + 00

(a)

1197e + 03



1077e + 039579e + 028384e + 027189e + 025995e + 024800e + 023605e + 022410e + 021216e + 022097e + 00

(b)

1189e + 03



1070e + 039516e + 028331e + 027145e + 025959e + 024773e + 023587e + 022401e + 021215e + 022883e + 00

(c)

1172e + 03



1055e + 039381e + 028212e + 027044e + 025876e + 024708e + 023540e + 022371e + 021203e + 023494e + 00

(d)






13201300128012601240122012001180116011401120Re

sulta

nt ri

gid

body

vel

ocity

(ms

)

0 01 02 03t (ms)

04 05 06

0 rs5000 rs

10000 rs20000 rs


Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

0 rmin5000 rmin

20E + 05

00E + 00

ndash20E + 05

ndash40E + 05

ndash60E + 05

ndash80E + 05

ndash10E + 06

ndash12E + 06

ndash14E + 06



7

6

5

4

3

2

1

0

ndash1

Balli

stic d

eflec

tion

angl

e (deg)

0 01 02 03t (ms)

04 05 06

0 rmin5000 rmin



1320130012801260

Resu

ltant

rigi

d bo

dy v

eloc

ity (m

s)

1240122012001180116011401120

0 01 02 03t (ms)

04 05




20E + 500E + 0


rigid

bod

y ac

cele

ratio

n (m

s2 )

0 01 02 03t (ms)

04 05 06



876543210

ndash1

Balli

stic d

eflec

tion

angl

e (deg)

0 01 02 03t (ms)

04 05 06










Pid = 5

Pid = 3

Pid = 6

A

B

C


X-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

60E + 05

40E + 05

20E + 05

00E + 00

ndash20E + 05

ndash40E + 05

ndash60E + 05

ndash80E + 05

C





4 Conclusions



Data Availability




Acknowledgments


References







Y-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

80E + 0460E + 0440E + 0420E + 0400E + 00


C


Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

45E + 0640E + 0635E + 0630E + 0625E + 0620E + 0615E + 0610E + 0650E + 0500E + 00

C


















13201300128012601240122012001180116011401120Re

sulta

nt ri

gid

body

vel

ocity

(ms

)

0 01 02 03t (ms)

04 05 06

0 rs5000 rs

10000 rs20000 rs


Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

0 rmin5000 rmin

20E + 05

00E + 00

ndash20E + 05

ndash40E + 05

ndash60E + 05

ndash80E + 05

ndash10E + 06

ndash12E + 06

ndash14E + 06



7

6

5

4

3

2

1

0

ndash1

Balli

stic d

eflec

tion

angl

e (deg)

0 01 02 03t (ms)

04 05 06

0 rmin5000 rmin



1320130012801260

Resu

ltant

rigi

d bo

dy v

eloc

ity (m

s)

1240122012001180116011401120

0 01 02 03t (ms)

04 05




20E + 500E + 0


rigid

bod

y ac

cele

ratio

n (m

s2 )

0 01 02 03t (ms)

04 05 06



876543210

ndash1

Balli

stic d

eflec

tion

angl

e (deg)

0 01 02 03t (ms)

04 05 06










Pid = 5

Pid = 3

Pid = 6

A

B

C


X-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

60E + 05

40E + 05

20E + 05

00E + 00

ndash20E + 05

ndash40E + 05

ndash60E + 05

ndash80E + 05

C





4 Conclusions



Data Availability




Acknowledgments


References







Y-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

80E + 0460E + 0440E + 0420E + 0400E + 00


C


Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

45E + 0640E + 0635E + 0630E + 0625E + 0620E + 0615E + 0610E + 0650E + 0500E + 00

C




















Pid = 5

Pid = 3

Pid = 6

A

B

C


X-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

60E + 05

40E + 05

20E + 05

00E + 00

ndash20E + 05

ndash40E + 05

ndash60E + 05

ndash80E + 05

C





4 Conclusions



Data Availability




Acknowledgments


References







Y-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

80E + 0460E + 0440E + 0420E + 0400E + 00


C


Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

45E + 0640E + 0635E + 0630E + 0625E + 0620E + 0615E + 0610E + 0650E + 0500E + 00

C

















4 Conclusions



Data Availability




Acknowledgments


References







Y-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

80E + 0460E + 0440E + 0420E + 0400E + 00


C


Z-rig

id b

ody

acce

lera

tion

(ms

2 )

0 01 02 03t (ms)

04 05 06

AB

45E + 0640E + 0635E + 0630E + 0625E + 0620E + 0615E + 0610E + 0650E + 0500E + 00

C















Dynamic Characteristics of the Rotating Penetrating ...

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Transcript of Dynamic Characteristics of the Rotating Penetrating ...