Research ArticleEffect of Bird YawPitch Angles on Soft Impact Damage of aFan Assembly

Junjie Li 12 Yunfeng Lou 3 Gaoyuan Yu 12 Tong Li 12 and Xianlong Jin 12

1School of Mechanical Engineering Shanghai Jiao Tong University Shanghai 200240 China2State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong University Shanghai 200240 China3Department of Structural Design Aerospace System Engineering Shanghai Shanghai 201108 China

Correspondence should be addressed to Xianlong Jin jxlongsjtueducn

Received 15 September 2020 Revised 4 December 2020 Accepted 24 December 2020 Published 16 January 2021

Academic Editor Ning Wang

Copyright copy 2021 Junjie Li et al+is is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

+is paper presents a numerical investigation of bird attitude angles affecting the soft-impact damage of a full fan assembly Firstlyconsidering the geometry of a mallard a real bird model is established by the Smoothed Particle Hydrodynamics (SPH) methodand calibrated with available test data +en complying with airworthiness requirements simulations of a full-bladed fan as-sembly subjected to a real bird were conducted to determine the critical ingestion parameters (CIP) Furthermore a real bird withdifferent attitude angles aimed at a full fan assembly was simulated Results show that attitude angles of the bird produce asignificant impact on the effect of the bird strike on rotating blades and would increase the possibility of blade failures especiallyfor the yaw angle of -45deg and the pitch angle of minus 60deg It is invaluable for commercial airlines and engine manufactures to providesafe flight and landing by adopting the real bird model with critical yaw and pitch angles in the design for resistance tobird ingestion

1 Introduction

Bird strikes have been presenting the main threat to aircraftssince the beginning of aviation history All available statisticsindicate that the bird-strike hazard is increasing dramati-cally due to the significant expansion of wild bird pop-ulations as well as to some extent because of the steadyincrease in air transport [1] +erefore aviation authoritiesrequire that all forward facing components need to prove acertain level of bird-strike resistance in certification testsbefore they are allowed for operational use [2] Howeveraccording to a large number of reported bird-strike inci-dents substantial damage to aircraft structures occurs eventhough the involved energies of the bird did not achieve theaircraft certification standard It indicates that only takingthe mass and impact speed of the bird into account is farfrom enough

Initially early studies were commonly based on theo-retical and experimental studies Wilbeck [3 4] conducted acomprehensive set of experimental studies on bird impacts

on various structures regarding different bird sizes initialvelocities bird substitutes and oblique impacts It was foundthat real birds behave as fluids during impact at velocitieslarger than 100ms and the impact process consists of fourtypical phases In recent times much effort and significantprogress have been done to get better insight into simulatingthe process of bird-strike events involving substitute birdmodels [5 6] numerical methods [7ndash9] and materialmodels [10 11] It can be concluded that the substitutemodel with bird shapes namely ellipsoid and hemispher-ical-ended cylinder (aspect ratio of 2) is recommendedassociated with material properties of homogenized fluidicmaterials +e equation of state is used to describe thecompressibility characteristics of bird material

However the values of Hugoniot pressure obtained fromtheoretical and experimental results are so far from eachother especially at lower velocities [12] Meanwhile thevalues obtained from numerical results calculated by dif-ferent authors are in a wide range between the experimentaland theoretical values [2 12] +erefore some scholars

HindawiComplexityVolume 2021 Article ID 8879874 13 pageshttpsdoiorg10115520218879874

shifted the focus to the real bird model Lakshmi [13] used amultimaterial bird model with a more realistic bird shape tocapture a more detailed impact load spectrum McCallumet al [14] developed a physically representative birdmodel ofa Canadian goose +e results show that compared with thetraditional model the physically representative bird modelproduces a lower Hugoniot pressure and higher magnitudeof peak impact force with longer duration Hedayati et al[12 15] established a real bird model based on the mallardCT-scan image data +ey found that the numerical resultsof the realistic bird model are closer to the available ex-perimental results than those in the case of the traditionalmodel

Bird strikes are the major factor of blade damage foraircraft engines [16] It is worth noting that in a largenumber of incidents the involved bird energy was lowerthan the magnitude of impact energy in certificationwhereas aircraft structures can be substantially damaged[17] In a typical field-event of the bird strike it is commonto observe a single bird coming into contact with multipleblades with respect to arbitrary attitude angle Projectile yawduring impact would result in a variation in the impactloading history [4] On that point several research workshave been done to capture the amount of damage imposedon blades due to bird impact considering bird orientation orpitchyaw angles [18ndash20] +e results reveal that bird ori-entation has a significant effect on the impact force How-ever with respect to a realistic bird shape not only is the birdattitude far more complicated but also the effect of birdorientation on rotating blades during the bird strike isdifferent for yaw and pitch angles Moreover it is difficultand complicated to record attitude angles of bird both inphysical tests and in a field-event of bird strikes +e high-pressure gas cannon is not capable of firing a real bird or asubstitute bird with arbitrary yawpitch angle Biologicallyinspired motion modelling and control algorithms [21ndash25]may seem like a good choice to determine the bird attitudewhich is urgent to study Attitude angles in our research areassumed in a wide range from 0deg to 60deg

+e study presented in this paper aims to focus on at-titude angels of a realistic bird affecting soft impact damageof jet engine blades Considering the shape of a real mallardin a published literature [12] a new bird model wasestablished using the SPH approach and validated againstthe latest published experimental results [26] To determinethe influence of bird orientation on the blade damage therealistic bird model with various attitude angles targeted at afan assembly has been developed +e simulations wereperformed based on Magic Cubic-II of Shanghai Super-computer Centre using LS-DYNA FE code

2 Theoretical Background

21 Soft Impact+eory Figure 1 shows the main stages andthe pressure profile of a typical bird-strike process a normalimpact of a flat cylinder on a rigid plate At the moment ofimpact in Figure 1 the bird material is rapidly deceleratedand a shock wave is initiated at the bird-target interfaceresulting in a sharp rise in pressure +e shockwave pressure

exceeds the strength of bird material to a large extentConsequently as the shockwave propagates through the birdbody in Figure 1 it rapidly breaks the internal bonds ofbirds generating a transition from a solid towards a fluidphase +e bird material is transitioned to a fluid-like me-dium +e high-pressure gradient across the free surface ofbird and the surrounding air forces out shocked materialradially [27] +is behavior is known as shock release Withthe propagation of release waves towards the center of thebird the pressure of the bird material gradually decays to thefluid pressure As the bird strike progresses in Figure 1 thebird material is progressively forced out of the original birdvolume and spreads outwards nonlinearly With the bird tailapproaching the target the bird-strike pressure decays tozero Figure 1 shows the pressure at the center of the impact

+e shockwave pressure (Hugoniot pressure PH) at theinitial impact (see Figure 1) is determined by [28]

PH ρ0]S]0 (1)

in which

]S (1 minus z) C + S1]0( 1113857 + z]a (2)

where ρ0 is the initial density of the bird ]S ]0 and ]arepresent the speed of shock wave impact speed of the birdand sound speed respectively z represents bird porosity Cand S1 are coefficients of the relationship between the shockand particle velocities

+e stagnation pressure PS during the liquid impact (seeFigure 1) is given by the following equation [28]

Pres

sure

at th

e im

pact

cent

erTime

Hugoniot pressure (PH)

Steady-flow pressure (PS)

(a) (b)

(d)

(c)

Figure 1 Main phases and pressure profile of a bird strike event(a) Solid-structure impact (b) Solid-fluid transition (c) Fluid-structure impact (d) Impact pressure profile

2 Complexity

PS k

1 minus zρ0]

20 (3)

where the constant k is 05 for an incompressible fluid [27]

22 Loads on Blades during Impact In a practical fan bladeapplication the impact progress is far more complex Fig-ure 2 indicates the bird-slicing action during the impact +ebird is represented as a flat cylinder As soon as a bird comesinto contact with blades it undergoes cut into several slicesby the blade leading edge in the direction of the relativevelocity VRelative

Blades subjected to a bird are invariably an ldquoobliqueimpactrdquo event consisting of two phases [29] the bird-slicingaction by multiple rotating blades each individual bird slicetravelling along the blade airfoil +us the impact generatesboth a slicing-impact load on the blade leading edge and abird-slice turning load acting on the concave surface whichcan be expressed as [29]

FBirdminus slice Fslicing + Ftravel (4)

At the moment of the leading edge slicing a bird pro-jectile it produces a high-intensity shock wave For theinitial impact area on the concave surface is almost a pointthe effective load generated by the shock-wave pressure isnot significant and thus its contribution is ignored [29]+us the slicing-impact load is determined by the slicingstagnation pressure [29]

Fslicing(t) Ba(t)Pstagnation (5)

in which the slicing stagnation pressure is determined by

Pstagnation 12ρ0 ]impact1113872 1113873

2 (6)

where Ba(t) denotes the bird-foot-print area on the bladeleading edge ]impact represents the normal component of therelative velocity VRelative (see Figure 2) on the blade leadingedge

23 Airworthiness Standards of Aircraft EnginesCurrently aviation authorities require that all new com-mercial aero-engines must substantiate physical certificationtests before operational use +ese requirements are com-piled in the Federal Aviation Regulations (FAR) ChineseCivil Aviation Regulations (CCAR) and the CertificationSpecifications (CS) of the European Aviation Safety Agency(EASA) [2] According to airworthiness standards of FARsect3376 [30] for the inlet throat area 237m2 of the jet enginepresented in this study it must be substantiated that the fanassembly is subjected to a medium bird of 115 kg under FARsect3376(c) (3) aimed at the most critical location outboard ofthe primary core flow path [30] Figure 3 indicates the lo-cation of target point on the first exposed rotating stage ofthe engine +e airfoil height is measured at the leading edgeof the blade+e target point for bird ingestion is determinedby impact loading on rotating blades as well as the possi-bility of blade failures [31]

3 Bird Modelling

31 +e SPHMethod +e SPH method is increasingly usedin bird-strike simulations as it has already been proved to bequite capable of simulating high deforming matter withdefragmentation [14] With the SPH technique the bird wasrepresented as a set of discrete particles in which the in-teraction between particles was achieved through a kernelfunction rather than a structured mesh [12] +e SPHmethod is recommended in the simulation of the bird-strikeprocess because of its high stability low cost and goodcorrelation with experimental observations in terms ofscattering particles [2] +erefore the SPH approach wasadopted to model a real bird of mallard

32 Geometry of a Real Bird According to the reported birdstrike incidents resulting in substantial damage to civil aircraftcomponents in the period 1990ndash2017 [32] the waterfowl hadbeen the most threatened species for civil aviation safety

mS

L S

v0v0prime

Direction of rotation

Engine axis

D

LChord direction

Slice direction

Bird

Blades

VBlade

VRelative

x

z

Figure 2 +e bird slicing action by the blade leading edge

Secondary flow

Fan

blad

e hei

ght

Engine axis

Primary flow

Bird mass115kg Most critical location

Direction of airflow

z

y

Figure 3 Location of target point on the leading edge of a fanblade

Complexity 3

accounting for 28 of the total specified species +erefore themallard (a typical species of waterfowl) is represented as ageneral realistic bird model Since a real bird consists of severalinternal cavities bone structures etc with complex geometrythe presented bird model can reflect the bird shape to someextent not exactly the same as the real one+emain geometriccharacteristics are given as follows (1) Wilbeck [3] found thatbone effect of a bird can be assumed negligible and thus auniform density of the real bird model is used (2) the head issimplified to be an ellipsoid and the neck was considered as acircular-conical-frustum [19] (3) geometric parameters of thebird torso were modelled considering the geometry of a realmallard bird in Ref [12] (4) the mass of bird wings accountedfor 19 of the total mass in accordance with Ref [14] +einterparticular distance is 2mm and the amount of SPHparticles is 153621 as shown in Figure 4

33 Bird Material Constitutive Model With a general ma-terial model for both solids and fluids to describe the fluidicbehavior of the bird material the Cauchy stress tensor isdivided into a hydrostatic part and a deviatoric part [16]

σij minus Pδij + sij (7)

in which the hydrostatic pressure P is written as

P minusσkk

3

minus σ11 + σ22 + σ33( 1113857

3 (8)

where σij represents stress tensor and sij represents devia-toric stress tensor Variable δij represents Kronecker deltasymbol

Since the compression of bird material during impactinduces a change in the bird density [27] theMiendashGruneisen equation of state (EOS) was used to reflectthe relationship between the pressure and the density [15]

P ρ0C

2μ 1 + 1 minus c02( 1113857( 1113857μ minus (a2)μ21113960 1113961

1 minus S1 minus 1( 1113857μ minus S2 μ2μ + 11113872 1113873 minus S3 μ3(μ + 1)2

1113872 11138731113960 11139612

+ c0 + aμ( 1113857E

(9)

A linear EOS is adopted for the bird material model [26]and equation (9) can be written as

P ρ0C

2μ1 minus S1 minus 1( 1113857μ1113858 1113859

2 (10)

where C S1 S2 and S3 are coefficients of the relationshipbetween the shock and particle velocities and c0 representsMiendashGruneisen gamma a is the first-order volume cor-rection to c0 μ represents the relative change in density

Porcine gelatinewith 10porosity is used instead of the birdmaterial [26] Parameters of porcine gelatine can be obtainedfrom Ref [33] +us for the developed bird model parametersare given as follows ρ0 954kgm3 C 1447ms S1 177

34 Attitude Angle Description In this research work birdattitude was defined based on the TaitndashBryan angles +eTaitndashBryan angles are three angles named as yaw angle αpitch angle β and roll angle c +ey were introduced todescribe the orientation of a bird As shown in Figure 5 aright-handed Cartesian coordinate system was defined in thecenter of bird gravity and any bird attitude can be pa-rameterized by three TaitndashBryan angles α β and c

In a field event of the bird strike it is difficult andcomplicated to record the TaitndashBryan angles of bird in-gestion Attitude angles of the real bird are assumed in a widerange from 0deg to 60deg and the orientation of bird based on anindividual TaitndashBryan angle was studied at a time Con-sidering the weight of wings accounting for about 19 birdmass [14] the effect of the roll angle on the slicing action of abird is relatively small +erefore bird attitude based on theroll angle was neglected Yaw angle α and pitch angle β wereselected as plusmn15deg plusmn30deg plusmn45degand plusmn60deg respectively Figure 6shows the attitude angles of a realistic bird where the at-titude angle is represented as the angle between the roll axisand the impact velocity

4 Numerical Model of a Fan Assembly

41 Fan Assembly Model +e fan assembly consists of 24equally spaced (15deg) wide-chord blades and a fan disc +efan assembly was modelled with 8-noded solid elementsBending is the basic mode of load carrying capacity forblades during impact With a single-point integration atthe element centroid solid elements can carry membranestresses only [34] +us blades were assigned 3 layers ofsolid elements through the thickness A tied-contact re-lationship was assumed to represent the attachment be-tween the blade and the fan hub Fixed boundaryconstraints of z-displacement direction were defined onthe side of the hub component To restrict nonphysicaldeformations relevant to zero energy modes stiffnesshourglass control with exact volume integration [34] wasapplied to the simulation model Figure 7 shows the finiteelement model of the fan assembly +e fan assemblyconsists of 165200 solid elements with a total of 222912nodes +e minimum element size of the fan assemblymodel was 042mm at the tip of the blade leading edgeand the corresponding time step for explicit dynamicsimulation was 406E-8 s In addition Figure 7 givesnumbers to fan blades during slicing a bird so that it canidentify the blade damage in the simulation of the impacton a fully bladed fan rotor

42 Blade Material Constitutive Model Bird strike eventscan be described as high strains and high strain rates in shortduration with considerable intensity [35] +erefore theempirical JohnsonndashCook relation was selected [36]

σy A + Bεn( 1113857 1 + C ln _εlowast( 1113857 1 minus T

lowastm( 1113857 (11)

in which

4 Complexity

Tlowast

T minus Troom( 1113857 Tmelt minus Troom( 1113857 (12)

where σy represents the equivalent von Mises stress εrepresents the equivalent plastic strain and _εlowast represents thenormalized equivalent plastic strain rate +e parameters AB C m and n are material constants T Tmelt and Troomrepresent the metal temperature melting temperature androom temperature respectively

Material fracture is determined by a cumulative damagelaw a function of mean stress strain rate and temperature[36]

D 1113944Δεεf

(13)

in which Figure 5 Definition of the TaitndashBryan angles

426 mm

(a)

340 m

m

(b)

86 mm

86 m

m

(c)

(d)

Figure 4 A realistic birdmodel by the SPHmethod (a) Left view (b) Front view (c) Bottom view (d) A real mallard compared to the SPHmodel

Complexity 5

εf D1 + D2 exp D3σlowast

( 11138571113858 1113859 1 + D4 ln _εlowast1113858 1113859 1 + D5Tlowast

1113858 1113859

(14)

where ∆ε is the increment of equivalent plastic strain and σlowastis the mean normalized by the equivalent stress D1 D2 D3D4 and D5 are damage constants Failures are assumed tooccur when D 1

+e fan assembly is made of titanium alloy Ti-6Al-4Vand material parameters are derived from Ref [37] as listedin Table 1 In addition the MiendashGruneisen EOS (equation(3)) was defined in conjunction with the material consti-tutive model and parameters for Ti-6Al-4V are as followsC 513times103ms S1 1028 c0 123 and a 017 [35]

43 Stress Initialization +e rotating fan assembly un-dergoes a constant centrifugal force resulting in significantdeformation and initial stresses prior to impact It is nec-essary to evaluate the prestress of the rotating componentsespecially for blades [16] +us a preload analysis procedurewas conducted by assigning rotational velocity of 542 radsin an implicit solution+e initial stress of blades assembly isshown in Figure 8

5 Results and Discussion

51 Bird Model Calibration +e effect of the high-intensityshock wave on the blade damage can be ignored for the

z

x

v0α

(a)

z

x

v0α

(b)

z

y

v0β

(c)

z

y

v0β

(d)

Figure 6 Schematic of yaw and pitch angles (a) Positive yaw angle α (b) Negative yaw angle α (c) Positive pitch angle β (d) Negative pitchangle β

Tip on the leadingedge of fan blade

v0

EnlargedBird

Axis of rotary

Fan assembly

Back view

Mos

t crit

ical

loca

tion

Bottom view

1

2

3

4

56

XX

Y

ZZ

Y

ω = 542 rads

Figure 7 FE model of a fan assembly subjected to a bird

6 Complexity

reason that the initial bird loading area is almost like a pointloading [29] +e focus of blade damage analysis needs to beon accurately capturing the steady stagnation pressure phaseof impact [27] +us the stagnation pressure is representedas a criterion to calibrate bird models Numerical simulationof a normal impact on a rigid plate was established in ac-cordance with the experimental setup in Ref [26] A seg-ment sensor was assigned at the center of the plate to extractthe impact pressure +e stagnation pressures were esti-mated by averaging the pressure between T03 and 2T03[26] where T0 denotes the duration of the bird strike event+e theoretical curve of the stagnation pressure was de-termined by equation (3) and test data was derived fromRef [26] as shown in Figure 9+e numerical results were ina range between theoretical and experimental values +estagnation pressures captured by simulation of the real birdwere in closer agreement with the test data than those in thecase of the hemispherical-ended cylinder

52MostCritical IngestionParameters +e critical ingestionparameters are required to be identified for the specified birdingestion [30] In this section simulations of a full fan as-sembly subjected to a real bird were performed to determinethe critical location and ingestion speed under FARsect3376(c) (1) and FAR sect3376(c) (3)

521 Most Critical Ingestion Speed Complying with FARsect3376(c)(1) the critical ingestion speed is required to reflectthe most severe situation within the range of speeds used fornormal flight operations up to 460m (1500 feet) but not lessthan V1 minimum for airplanes [30] +erefore simulationsof the bird ingested at different speeds were performedaimed at the fan blade height of 80 Figure 10(a) shows theeffect of ingestion speed on impact loading history +e peakvalues of impact force generated by a real bird targeted atspeeds of 60ms 65ms 70ms 80ms 105ms and 130ms are 18335KN at 395ms 18253KN at 397ms 19891 KNat 348ms 21096KN at 348ms 21216KN at 299ms and17095KN at 250ms respectively As the speed increasesthe impact duration becomes shorter It is also found that thehigher the impact speed is the earlier the peak force occursAs the normalized sum of effective plastic strains shown inFigure 10(b) the ingestion speed of 65ms caused the mostsevere plastic strain+erefore 65ms was represented as themost critical speed

522 Most Critical Exposed Location To find out the mostcritical location under FAR sect3376(c)(1) the real bird aimedat different target points on the leading edge of blades wasevaluated at a speed of 65ms Figure 11(a) shows the effectof target location on the time histories of impact force +epeak values of impact force generated by a real bird aimed at

the fan blade height of 50 70 75 80 85 and 90are 16379KN at 384ms 16825KN at 430ms 17730KN at392ms 18253KN at 397ms 15592KN at 439ms and17169KN at 485ms respectively It can be observed thatthe impact location of 80 blade height reaches the max-imum value of peak impact force As the blade damageindicated in Figure 11(b) with the single medium birdtargeted at the fan blade height of 80 it occurs to the most

Table 1 Material properties of Ti-6Al-4V

Material ρ (kgm3) A (MPa) B (MPa) C m n D1 D2 D3 D4 D5

Ti-6Al-4V 44times103 1098 1092 0014 11 093 -009 025 -05 014 387

Effective stress (v ndash m)

6529e + 02

5804e + 02

5080e + 02

4355e + 02

3631e + 02

2906e + 02

2182e + 02

1457e + 02

7330e + 01

8491e ndash 01

7253e + 02

Figure 8 von Mises stress (MPa) of the fan assembly

Stag

natio

n pr

essu

re (M

Pa)

Theoretical pressure(z = 01)Hemispherical endedcylinderReal bird (mallard)

Experiment (pigeons)Experiment (porousgelatine)

0

2

4

6

8

10

12

110 120 130 140 150100Impact velocity (ms)

Figure 9 Calibration of stagnation pressures

Complexity 7

severe blade plastic strain As a result the most criticallocation for a middle-sized bird should be aimed at 80 ofthe fan blade height

53 Effect of Attitude Angles on Soft-Impact DamageFigure 12 shows the deformation of bird oriented along theengine axis As expected it can be clearly observed that priorto the impact of the bird torso the real bird was sliced intomore pieces +e orientation of bird has a direct effect on

slicing action of fan blades With respect to different atti-tudes the contact area and duration of bird strikes changeresulting in a significant impact on the effect of the birdstrike on rotatory blades and the possibility of blade failures

Figure 13 shows the effect of the yaw angle on impactloading history As shown in Figure 13(a) peak values ofimpact force generated by a real bird with respect to yawangle of 15deg 30deg 45deg and 60deg are 20153KN at 397ms17052KN at 431ms 17634KN at 433ms and 18697 KNat 428ms respectively As shown in Figure 13(b) the peak

Impa

ct fo

rce (

KN)

2 4 6 8 100Time (ms)

0

50

100

150

200

250

60 ms65 ms70 ms

80 ms105 ms130 ms

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

60 ms65 ms70 ms

80 ms105 ms130 ms

(b)

Figure 10 Effect of ingestion speed on the impact loading history and blade damage (a)+e impact loading history (b) Normalized sum ofeffective plastic strains

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

507075

808590

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

507075

808590

(b)

Figure 11 Effect of target location on the impact loading history and blade damage (a) +e impact loading history (b) Normalized sum ofeffective plastic strains

8 Complexity

values of impact force derived from a real bird with yawangle of minus 15deg minus 30deg minus 45deg and minus 60deg are 15732KN at 522ms13799KN at 433ms 20647KN at 370ms and 24666KNat 485ms respectively It can be concluded that a yaw angleof the bird would generate a variation in the impact loadinghistory and a negative yaw angle has a more significant effecton the impact loading history

Figure 14 shows the effect of pitch angle on the timehistories of impact loads As shown in Figure 14(a) withrespect to pitch angles of 15deg 30deg 45deg and 60deg the peakimpact loads are 20515KN at 435ms 22720 KN at 391ms26147 KN at 433ms and 26940 KN at 392ms respectivelyObviously the peak impact force increases as the positivepitch angle increases As shown in Figure 14(b) peak valuesof impact loading obtained from a real bird model with pitchangles of minus 15deg minus 30deg minus 45deg and minus 60deg are 16073KN at 393ms

16828KN at 390ms 18485KN at 386ms and 22406 KNat 385ms respectively It is observed that a negative yawangle would result in a variation in the impact loadinghistory

Figure 15 shows effective plastic strains of a single bladewhich undergoes the most severe plastic deformation duringimpact Obviously with the change of the bird attitude anglethe blade undergoes more severe plastic deformation Es-pecially as subjected to a real bird with a yaw angle of minus 45deg ora pitch angle of minus 60deg the blade suffers more than twice themagnitude of effective plastic strain compared with a realbird oriented along the engine centerline It can be con-cluded that attitude angles would increase the possibility offan blade failure Moreover the yaw angle of bird ingestionhas a significant effect on the location of the blade with themost severe plastic deformation

9972e + 02 1244e + 03 1255e + 031129e + 031004e + 038782e + 027527e + 026273e + 025018e + 023764e + 022509e + 021255e + 020000e + 00

1335e + 031314e + 031293e + 031163e + 031034e + 039049e + 027756e + 026463e + 025171e + 023878e + 022585e + 021293e + 020000e + 00

1182e + 031051e + 039197e + 027883e + 026569e + 025255e + 023942e + 022628e + 021314e + 020000e + 00

1202e + 031069e + 039351e + 028017e + 026683e + 025349e + 024015e + 022681e + 021347e + 021243e + 00

1120e + 039951e + 028707e + 027464e + 026220e + 024976e + 023732e + 022488e + 021244e + 020000e + 00

8975e + 027977e + 026980e + 025983e + 024986e + 023989e + 022992e + 021994e + 029972e + 010000e + 00

t = 10 ms t = 20 ms t = 25 ms

t = 45 mst = 35 mst = 30 ms

z

x

(a)

Figure 12 Bird deformation during the slicing action

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 13 Yaw angle effect on impact loading history (a) Positive yaw angle α (b) Negative yaw angle α

Complexity 9

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

300

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)Im

pact

forc

e (KN

)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 14 Pitch angle effect on impact loading history (a) Positive pitch angle β (b) Negative pitch angle β

Effec

tive p

lasti

c str

ains

0deg15deg on 3 blade30deg on 4 blade45deg on 4 blade60deg on 4 blade

ndash15deg on 6 bladendash30deg on 5 bladendash45deg on 3 bladendash60deg on 5 blade

2 4 6 8 10Time (ms)

00

12

24

36

48

60

(a)

Effec

tive p

lasti

c str

ains

of t

he b

lade

3

12

24

36

48

60

4 6 8 10Time (ms)

0deg15deg30deg45deg60deg

ndash15degndash30degndash45degndash60deg

00

2

(b)

Figure 15 Attitude angle effect on blade damage (a) Yaw angle α (b) Pitch angle β

10 Complexity

Figure 16 shows the effective plastic strains of the fanassembly It can be seen that a ldquocusprdquo plastic deformationoccurs at the leading edge and the maximum plastic strainoccurred to the impact location Compared with the plasticdeformation of a fan assembly during a normal impact (seeFigure 16(a)) subjected to a bird with an attitude angle ofα minus 45deg and β minus 60deg fan blade failure occurs at the impactlocation and the plastic deformation at the root of the fanblade leading edge is more significant which would increasethe risk of a fan blade release event

6 Conclusions

Considering a geometric shape similar to what has alreadybeen published as a real mallard [12] a real bird model wasdeveloped +en this paper discusses the effect of attitudeangles of the realistic bird model on the soft impact damageof a full fan assembly Besides the stagnation pressure isrepresented as a criterion to calibrate the developed bird

model Results show a good correlation with available testdata [26]

In accordance with certification requirements the mostcritical ingestion parameters for the new bird model wereinvestigated It is found that the real bird aimed at the fanblade height of 80 with an ingestion speed of 65msproduces the most severe damage to the full fan assembly

Complying with the critical ingestion parameters of thebird simulations of a full fan assembly subjected to a realbird with respect to various attitude angles reveal that bothyaw and pitch angles of the bird have a significant effect onthe impact loading history +e blade that undergoes thehighest magnitude of effective plastic strain would beconfronted with a more plastic deformation than that in thecase of a normal impact (attitude angle 0deg) even though theimpact loading decreases Especially as subjected to a realbird with yaw angle of minus 45deg or pitch angle of minus 60deg the bladesuffers more than twice the magnitude of effective plasticstrain compared with that of attitude angle 0deg and the plastic

1898e ndash 01

1705e ndash 01

1512e ndash 01

1319e ndash 01

1125e ndash 01

9323e ndash 02

7392e ndash 02

5460e ndash 02

3529e ndash 02

1598e ndash 02

ndash3332e ndash 032

3 4

(a)

3294e ndash 01

2960e ndash 01

2627e ndash 01

2294e ndash 01

1960e ndash 01

1627e ndash 01

1294e ndash 01

9605e ndash 02

6272e ndash 02

2939e ndash 02

ndash3947e ndash 033

(b)

2032e ndash 01

1825e ndash 01

1617e ndash 01

1410e ndash 01

1202e ndash 01

9950e ndash 02

7876e ndash 02

5803e ndash 02

3729e ndash 02

1655e ndash 02

ndash4189e ndash 033

(c)

Figure 16 Effective plastic strain contours at time t 10ms (a) 0deg (b) α minus 45deg (c) β minus 60deg

Complexity 11

deformation at the root of the leading edge is more sig-nificant which would increase the risk of a fan blade releaseevent

Moreover it is invaluable to ensure the safety of com-mercial airlines and engine manufacture by adopting therealistic bird model with the dangerous attitude angle in thecertification of engine designs for resistance to bird strikeswhich will provide sufficient resistance in actual bird-strikeevents However attitude angles of the bird were set upbased on the assumption in this paper If the bird attitudecould be determined through experiments or control al-gorithms [38ndash42] it is of great significance to investigate theeffect of bird attitude on soft impact damage as well as thedistribution of flocking bird

Data Availability

All data included in this study are available from the cor-responding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is research was supported by the National Key Researchand Development Program of China (Grant no2016YFB0201800) and the National Natural Science Foun-dation of China (Grant no 11772192)

References

[1] R H Mao S A Meguid and T Y Ng ldquoTransient threedimensional finite element analysis of a bird striking a fanbladerdquo International Journal of Mechanics and Materials inDesign vol 4 no 1 pp 79ndash96 2008

[2] S Heimbs ldquoComputational methods for bird strike simula-tions a reviewrdquo Computers amp Structures vol 89 no 23-24pp 2093ndash2112 2011

[3] J S Wilbeck Impact Behavior of Low Strength Projectiles AirForce Materials Lab Ohio AFFDL-TR-75-5 1978

[4] J S Wilbeck and J L Rand ldquo+e development of a substitutebird modelrdquo Journal of Engineering for Power vol 103 no 4pp 725ndash730 1981

[5] A Airoldi and B Cacchione ldquoModelling of impact forces andpressures in Lagrangian bird strike analysesrdquo InternationalJournal of Impact Engineering vol 32 no 10 pp 1651ndash16772006

[6] M A Lavoie A Gakwaya M N Ensan D G Zimcik andD Nandlall ldquoldquoBirdrsquos substitute test results and evaluation ofavailable numerical methodsrdquo International Journal of ImpactEngineering vol 36 no 10-11 pp 1276ndash1287 2009

[7] M Guida F Marulo M Meo and M Riccio ldquoEvaluation andvalidation of multi-physics FE methods to simulate bird strikeon a wing leading edgerdquo in Proceedings of the 13th EuropeanConference on Composite Materials (ECCM) StockholmSweden June 2008

[8] M A Lavoie A Gakwaya M N Ensan and D G ZimcikldquoReview of existing numerical methods and validation pro-cedure available for bird strike modellingrdquo International

Journal of Applied Mathematics and Computer Science vol 2no 4 pp 111ndash118 2007

[9] M A Lavoie A Gakwaya M Nejad Ensan and D G ZimcikldquoValidation of available approaches for numerical bird strikemodeling toolsrdquo International Review of Mechanical Engi-neering vol 1 no 4 pp 380ndash389 2007

[10] M A McCarthy J R Xiao C T McCarthy et al ldquoModellingof bird strike on an aircraft wing leading edge made from fibremetal laminates-part 2 modelling of impact with SPH birdmodelrdquo Applied Composite Materials vol 11 no 5pp 317ndash340 2004

[11] L Nizampatnam and W Horn ldquoInvestigation of equation ofstate models for predicting bird impact loadsrdquo in Proceedingsof the 46th AIAA Aerospace Sciences Meeting and Exhibitpp 7ndash10 2013

[12] R Hedayati M Sadighi and M Mohammadi-Aghdam ldquoOnthe difference of pressure readings from the numerical ex-perimental and theoretical results in different bird strikestudiesrdquo Aerospace Science and Technology vol 32 no 1pp 260ndash266 2014

[13] L S Nizampatnam Models and Methods for Bird Strike LoadPredictions Wichita State University Wichita Kansas 2007

[14] S McCallum H Shoji and H Akiyama ldquoDevelopment of anadvanced multi-material bird-strike model using thesmoothed particle Hydrodynamics methodrdquo InternationalJournal of Crashworthiness vol 18 no 6 pp 579ndash597 2013

[15] R Hedayati and S Ziaei-Rad ldquoA new bird model and theeffect of bird geometry in impacts from various orientationsrdquoAerospace Science and Technology vol 28 no 1 pp 9ndash202013

[16] A Serge ldquoSoft impacts on aerospace structuresrdquo Progress inAerospace Sciences vol 81 pp 1ndash17 2016

[17] J Kou F Xu S Ji and X Zhang ldquoInfluence of bird yawpitchorientation on bird-strike resistance of aircraft structuresrdquoExplosion and Shock Waves vol 37 no 5 pp 937ndash944 2017

[18] Z Zhang L Li and D Zhang ldquoEffect of arbitrary yawpitchangle in bird strike numerical simulation using SPHmethodrdquoAerospace Science and Technology vol 81 pp 284ndash293 2018

[19] D Zhang and Q Fei ldquoEffect of bird geometry and impactorientation in bird striking on a rotary jet-engine fan analysisusing SPH methodrdquo Aerospace Science and Technologyvol 54 pp 320ndash329 2016

[20] R H Mao S A Meguid and T Y Ng ldquoEffects of incidenceangle in bird strike on integrity of aero-engine fan bladerdquoInternational Journal of Crashworthiness vol 14 no 4pp 295ndash308 2009

[21] C Yang C Chen N Wang et al ldquoBiologically inspiredmotion modeling and neural control for robot learning fromdemonstrationsrdquo IEEE Transactions on Cognitive and De-velopmental Systems vol 11 no 2 pp 281ndash291 2019

[22] C Yang C Chen W He R Cui and Z Li ldquoRobot learningsystem based on adaptive neural control and dynamicmovement primitivesrdquo IEEE Transactions on Neural Networksand Learning Systems vol 30 no 3 pp 777ndash787 2019

[23] C Yang D Huang W He and L Cheng ldquoNeural control ofrobot manipulators with trajectory tracking constraints andinput saturationrdquo IEEE Transactions on Neural Networks andLearning Systems pp 1ndash12 2020

[24] H Huang T Zhang C Yang and C L P Chen ldquoMotorlearning and generalization using broad learning adaptiveneural controlrdquo IEEE Transactions on Industrial Electronicsvol 67 no 10 pp 8608ndash8617 2020

12 Complexity

[25] H Huang C Yang and C L P Chen ldquoOptimal robot-envi-ronment interaction under broad fuzzy neural adaptive controlrdquoIEEE Transactions on Cybernetics pp 1ndash12 2020

[26] F Allaeys G Luyckx W Van Paepegem and J DegrieckldquoNumerical and experimental investigation of the shock andsteady state pressures in the bird material during bird strikerdquoInternational Journal of Impact Engineering vol 107pp 12ndash22 2017

[27] M Kim A Zammit A Siddens and J Bayandor ldquoAn ex-tensive crashworthiness methodology for advanced pro-pulsion systems part I soft impact damage assessment ofcomposite fan stage assembliesrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting Including the New HorizonsForum and Aerospace Exposition Orlando Florida January2011

[28] R Hedayati and M Sadighi Bird Strike An Experimental+eoretical and Numerical Investigation Woodhead Pub-lishing in Mechanical Engineering Elsevier AmsterdamNetherlands 978-0-08-100093-9 2016

[29] S K Sinha K E Turner and N Jain ldquoDynamic loading onturbofan blades due to bird-strikerdquo Journal of Engineering forGas Turbines and Power vol 133 no 12 Article ID 1225042011

[30] Federal Aviation Administration ldquoElectronic code of federalRegulationsrdquo Title 14 Aeronautics and Space National Ar-chives and Records Administration Washington DC USAChapter I Subchapter C Part 33-Airworthiness StandardsAircraft Engines Section 3376 2020

[31] Federal Aviation Administration ldquoBird ingestion certificationstandardsrdquo Advisory Circular Federal Aviation Administra-tion Wasington DC USA 3376-1A 2009

[32] R A Dolbeer S E Wright J R Weller and M J BegierWildlife Strikes to Civil Aircraft in the United States 1990-2017National Wildlife Strike Database Washington DC USA2018

[33] C J Shepherd G J Appleby-+omas P J Hazell andD F Allsop ldquo+e dynamic behaviour of ballistic gelatinrdquo AIPConference Proceedings vol 1195 pp 1399ndash1402 2009

[34] J O Hallquist LS-DYNA+eory Manual Livermore SoftwareTechnology Corporation Livermore CA USA 2007

[35] R Vignjevic M Orłowski T De Vuyst and J C CampbellldquoA parametric study of bird strike on engine bladesrdquo Inter-national Journal of Impact Engineering vol 60 pp 44ndash572013

[36] G R Johnson and W H Cook ldquoFracture characteristics ofthree metals subjected to various strains strain rates tem-peratures and pressuresrdquo Engineering Fracture Mechanicsvol 21 no 1 pp 31ndash48 1985

[37] D Leseur Experimental Investigations of Material Models forTi-6A1-4V and 2024-T3 Lawrence Livermore National LabLivermore CA USA UCRL-ID-134691 1999

[38] C Yang Y Jiang W He J Na Z Li and B Xu ldquoAdaptiveparameter estimation and control design for robot manipu-lators with finite-time convergencerdquo IEEE Transactions onIndustrial Electronics vol 65 no 10 pp 8112ndash8123 2018

[39] C Yang G Peng L Cheng J Na and Z Li ldquoForce sensorlessadmittance control for teleoperation of uncertain robotmanipulator using neural networksrdquo IEEE Transactions onSystems Man and Cybernetics Systems pp 1ndash11 2019

[40] G Peng C Yang W He and C L P Chen ldquoForce sensorlessadmittance control with neural learning for robots with ac-tuator saturationrdquo IEEE Transactions on Industrial Elec-tronics vol 67 no 4 pp 3138ndash3148 2020

[41] C Yang H Wu Z Li W He N Wang and C-Y Su ldquoMindcontrol of a robotic arm with visual fusion technologyrdquo IEEETransactions on Industrial Informatics vol 14 no 9pp 3822ndash3830 2018

[42] H Lin T Zhang Z Chen H Song and C Yang ldquoAdaptivefuzzy Gaussian mixture models for shape approximation inrobot graspingrdquo International Journal of Fuzzy Systemsvol 21 no 4 pp 1026ndash1037 2019

Complexity 13

PS k

1 minus zρ0]

20 (3)

where the constant k is 05 for an incompressible fluid [27]

22 Loads on Blades during Impact In a practical fan bladeapplication the impact progress is far more complex Fig-ure 2 indicates the bird-slicing action during the impact +ebird is represented as a flat cylinder As soon as a bird comesinto contact with blades it undergoes cut into several slicesby the blade leading edge in the direction of the relativevelocity VRelative

Blades subjected to a bird are invariably an ldquoobliqueimpactrdquo event consisting of two phases [29] the bird-slicingaction by multiple rotating blades each individual bird slicetravelling along the blade airfoil +us the impact generatesboth a slicing-impact load on the blade leading edge and abird-slice turning load acting on the concave surface whichcan be expressed as [29]

FBirdminus slice Fslicing + Ftravel (4)

At the moment of the leading edge slicing a bird pro-jectile it produces a high-intensity shock wave For theinitial impact area on the concave surface is almost a pointthe effective load generated by the shock-wave pressure isnot significant and thus its contribution is ignored [29]+us the slicing-impact load is determined by the slicingstagnation pressure [29]

Fslicing(t) Ba(t)Pstagnation (5)

in which the slicing stagnation pressure is determined by

Pstagnation 12ρ0 ]impact1113872 1113873

2 (6)

where Ba(t) denotes the bird-foot-print area on the bladeleading edge ]impact represents the normal component of therelative velocity VRelative (see Figure 2) on the blade leadingedge

23 Airworthiness Standards of Aircraft EnginesCurrently aviation authorities require that all new com-mercial aero-engines must substantiate physical certificationtests before operational use +ese requirements are com-piled in the Federal Aviation Regulations (FAR) ChineseCivil Aviation Regulations (CCAR) and the CertificationSpecifications (CS) of the European Aviation Safety Agency(EASA) [2] According to airworthiness standards of FARsect3376 [30] for the inlet throat area 237m2 of the jet enginepresented in this study it must be substantiated that the fanassembly is subjected to a medium bird of 115 kg under FARsect3376(c) (3) aimed at the most critical location outboard ofthe primary core flow path [30] Figure 3 indicates the lo-cation of target point on the first exposed rotating stage ofthe engine +e airfoil height is measured at the leading edgeof the blade+e target point for bird ingestion is determinedby impact loading on rotating blades as well as the possi-bility of blade failures [31]

3 Bird Modelling

31 +e SPHMethod +e SPH method is increasingly usedin bird-strike simulations as it has already been proved to bequite capable of simulating high deforming matter withdefragmentation [14] With the SPH technique the bird wasrepresented as a set of discrete particles in which the in-teraction between particles was achieved through a kernelfunction rather than a structured mesh [12] +e SPHmethod is recommended in the simulation of the bird-strikeprocess because of its high stability low cost and goodcorrelation with experimental observations in terms ofscattering particles [2] +erefore the SPH approach wasadopted to model a real bird of mallard

32 Geometry of a Real Bird According to the reported birdstrike incidents resulting in substantial damage to civil aircraftcomponents in the period 1990ndash2017 [32] the waterfowl hadbeen the most threatened species for civil aviation safety

mS

L S

v0v0prime

Direction of rotation

Engine axis

D

LChord direction

Slice direction

Bird

Blades

VBlade

VRelative

x

z

Figure 2 +e bird slicing action by the blade leading edge

Secondary flow

Fan

blad

e hei

ght

Engine axis

Primary flow

Bird mass115kg Most critical location

Direction of airflow

z

y

Figure 3 Location of target point on the leading edge of a fanblade

Complexity 3

accounting for 28 of the total specified species +erefore themallard (a typical species of waterfowl) is represented as ageneral realistic bird model Since a real bird consists of severalinternal cavities bone structures etc with complex geometrythe presented bird model can reflect the bird shape to someextent not exactly the same as the real one+emain geometriccharacteristics are given as follows (1) Wilbeck [3] found thatbone effect of a bird can be assumed negligible and thus auniform density of the real bird model is used (2) the head issimplified to be an ellipsoid and the neck was considered as acircular-conical-frustum [19] (3) geometric parameters of thebird torso were modelled considering the geometry of a realmallard bird in Ref [12] (4) the mass of bird wings accountedfor 19 of the total mass in accordance with Ref [14] +einterparticular distance is 2mm and the amount of SPHparticles is 153621 as shown in Figure 4

33 Bird Material Constitutive Model With a general ma-terial model for both solids and fluids to describe the fluidicbehavior of the bird material the Cauchy stress tensor isdivided into a hydrostatic part and a deviatoric part [16]

σij minus Pδij + sij (7)

in which the hydrostatic pressure P is written as

P minusσkk

3

minus σ11 + σ22 + σ33( 1113857

3 (8)

where σij represents stress tensor and sij represents devia-toric stress tensor Variable δij represents Kronecker deltasymbol

Since the compression of bird material during impactinduces a change in the bird density [27] theMiendashGruneisen equation of state (EOS) was used to reflectthe relationship between the pressure and the density [15]

P ρ0C

2μ 1 + 1 minus c02( 1113857( 1113857μ minus (a2)μ21113960 1113961

1 minus S1 minus 1( 1113857μ minus S2 μ2μ + 11113872 1113873 minus S3 μ3(μ + 1)2

1113872 11138731113960 11139612

+ c0 + aμ( 1113857E

(9)

A linear EOS is adopted for the bird material model [26]and equation (9) can be written as

P ρ0C

2μ1 minus S1 minus 1( 1113857μ1113858 1113859

2 (10)

where C S1 S2 and S3 are coefficients of the relationshipbetween the shock and particle velocities and c0 representsMiendashGruneisen gamma a is the first-order volume cor-rection to c0 μ represents the relative change in density

Porcine gelatinewith 10porosity is used instead of the birdmaterial [26] Parameters of porcine gelatine can be obtainedfrom Ref [33] +us for the developed bird model parametersare given as follows ρ0 954kgm3 C 1447ms S1 177

34 Attitude Angle Description In this research work birdattitude was defined based on the TaitndashBryan angles +eTaitndashBryan angles are three angles named as yaw angle αpitch angle β and roll angle c +ey were introduced todescribe the orientation of a bird As shown in Figure 5 aright-handed Cartesian coordinate system was defined in thecenter of bird gravity and any bird attitude can be pa-rameterized by three TaitndashBryan angles α β and c

In a field event of the bird strike it is difficult andcomplicated to record the TaitndashBryan angles of bird in-gestion Attitude angles of the real bird are assumed in a widerange from 0deg to 60deg and the orientation of bird based on anindividual TaitndashBryan angle was studied at a time Con-sidering the weight of wings accounting for about 19 birdmass [14] the effect of the roll angle on the slicing action of abird is relatively small +erefore bird attitude based on theroll angle was neglected Yaw angle α and pitch angle β wereselected as plusmn15deg plusmn30deg plusmn45degand plusmn60deg respectively Figure 6shows the attitude angles of a realistic bird where the at-titude angle is represented as the angle between the roll axisand the impact velocity

4 Numerical Model of a Fan Assembly

41 Fan Assembly Model +e fan assembly consists of 24equally spaced (15deg) wide-chord blades and a fan disc +efan assembly was modelled with 8-noded solid elementsBending is the basic mode of load carrying capacity forblades during impact With a single-point integration atthe element centroid solid elements can carry membranestresses only [34] +us blades were assigned 3 layers ofsolid elements through the thickness A tied-contact re-lationship was assumed to represent the attachment be-tween the blade and the fan hub Fixed boundaryconstraints of z-displacement direction were defined onthe side of the hub component To restrict nonphysicaldeformations relevant to zero energy modes stiffnesshourglass control with exact volume integration [34] wasapplied to the simulation model Figure 7 shows the finiteelement model of the fan assembly +e fan assemblyconsists of 165200 solid elements with a total of 222912nodes +e minimum element size of the fan assemblymodel was 042mm at the tip of the blade leading edgeand the corresponding time step for explicit dynamicsimulation was 406E-8 s In addition Figure 7 givesnumbers to fan blades during slicing a bird so that it canidentify the blade damage in the simulation of the impacton a fully bladed fan rotor

42 Blade Material Constitutive Model Bird strike eventscan be described as high strains and high strain rates in shortduration with considerable intensity [35] +erefore theempirical JohnsonndashCook relation was selected [36]

σy A + Bεn( 1113857 1 + C ln _εlowast( 1113857 1 minus T

lowastm( 1113857 (11)

in which

4 Complexity

Tlowast

T minus Troom( 1113857 Tmelt minus Troom( 1113857 (12)

where σy represents the equivalent von Mises stress εrepresents the equivalent plastic strain and _εlowast represents thenormalized equivalent plastic strain rate +e parameters AB C m and n are material constants T Tmelt and Troomrepresent the metal temperature melting temperature androom temperature respectively

Material fracture is determined by a cumulative damagelaw a function of mean stress strain rate and temperature[36]

D 1113944Δεεf

(13)

in which Figure 5 Definition of the TaitndashBryan angles

426 mm

(a)

340 m

m

(b)

86 mm

86 m

m

(c)

(d)

Figure 4 A realistic birdmodel by the SPHmethod (a) Left view (b) Front view (c) Bottom view (d) A real mallard compared to the SPHmodel

Complexity 5

εf D1 + D2 exp D3σlowast

( 11138571113858 1113859 1 + D4 ln _εlowast1113858 1113859 1 + D5Tlowast

1113858 1113859

(14)

where ∆ε is the increment of equivalent plastic strain and σlowastis the mean normalized by the equivalent stress D1 D2 D3D4 and D5 are damage constants Failures are assumed tooccur when D 1

+e fan assembly is made of titanium alloy Ti-6Al-4Vand material parameters are derived from Ref [37] as listedin Table 1 In addition the MiendashGruneisen EOS (equation(3)) was defined in conjunction with the material consti-tutive model and parameters for Ti-6Al-4V are as followsC 513times103ms S1 1028 c0 123 and a 017 [35]

43 Stress Initialization +e rotating fan assembly un-dergoes a constant centrifugal force resulting in significantdeformation and initial stresses prior to impact It is nec-essary to evaluate the prestress of the rotating componentsespecially for blades [16] +us a preload analysis procedurewas conducted by assigning rotational velocity of 542 radsin an implicit solution+e initial stress of blades assembly isshown in Figure 8

5 Results and Discussion

51 Bird Model Calibration +e effect of the high-intensityshock wave on the blade damage can be ignored for the

z

x

v0α

(a)

z

x

v0α

(b)

z

y

v0β

(c)

z

y

v0β

(d)

Figure 6 Schematic of yaw and pitch angles (a) Positive yaw angle α (b) Negative yaw angle α (c) Positive pitch angle β (d) Negative pitchangle β

Tip on the leadingedge of fan blade

v0

EnlargedBird

Axis of rotary

Fan assembly

Back view

Mos

t crit

ical

loca

tion

Bottom view

1

2

3

4

56

XX

Y

ZZ

Y

ω = 542 rads

Figure 7 FE model of a fan assembly subjected to a bird

6 Complexity

reason that the initial bird loading area is almost like a pointloading [29] +e focus of blade damage analysis needs to beon accurately capturing the steady stagnation pressure phaseof impact [27] +us the stagnation pressure is representedas a criterion to calibrate bird models Numerical simulationof a normal impact on a rigid plate was established in ac-cordance with the experimental setup in Ref [26] A seg-ment sensor was assigned at the center of the plate to extractthe impact pressure +e stagnation pressures were esti-mated by averaging the pressure between T03 and 2T03[26] where T0 denotes the duration of the bird strike event+e theoretical curve of the stagnation pressure was de-termined by equation (3) and test data was derived fromRef [26] as shown in Figure 9+e numerical results were ina range between theoretical and experimental values +estagnation pressures captured by simulation of the real birdwere in closer agreement with the test data than those in thecase of the hemispherical-ended cylinder

52MostCritical IngestionParameters +e critical ingestionparameters are required to be identified for the specified birdingestion [30] In this section simulations of a full fan as-sembly subjected to a real bird were performed to determinethe critical location and ingestion speed under FARsect3376(c) (1) and FAR sect3376(c) (3)

521 Most Critical Ingestion Speed Complying with FARsect3376(c)(1) the critical ingestion speed is required to reflectthe most severe situation within the range of speeds used fornormal flight operations up to 460m (1500 feet) but not lessthan V1 minimum for airplanes [30] +erefore simulationsof the bird ingested at different speeds were performedaimed at the fan blade height of 80 Figure 10(a) shows theeffect of ingestion speed on impact loading history +e peakvalues of impact force generated by a real bird targeted atspeeds of 60ms 65ms 70ms 80ms 105ms and 130ms are 18335KN at 395ms 18253KN at 397ms 19891 KNat 348ms 21096KN at 348ms 21216KN at 299ms and17095KN at 250ms respectively As the speed increasesthe impact duration becomes shorter It is also found that thehigher the impact speed is the earlier the peak force occursAs the normalized sum of effective plastic strains shown inFigure 10(b) the ingestion speed of 65ms caused the mostsevere plastic strain+erefore 65ms was represented as themost critical speed

522 Most Critical Exposed Location To find out the mostcritical location under FAR sect3376(c)(1) the real bird aimedat different target points on the leading edge of blades wasevaluated at a speed of 65ms Figure 11(a) shows the effectof target location on the time histories of impact force +epeak values of impact force generated by a real bird aimed at

the fan blade height of 50 70 75 80 85 and 90are 16379KN at 384ms 16825KN at 430ms 17730KN at392ms 18253KN at 397ms 15592KN at 439ms and17169KN at 485ms respectively It can be observed thatthe impact location of 80 blade height reaches the max-imum value of peak impact force As the blade damageindicated in Figure 11(b) with the single medium birdtargeted at the fan blade height of 80 it occurs to the most

Table 1 Material properties of Ti-6Al-4V

Material ρ (kgm3) A (MPa) B (MPa) C m n D1 D2 D3 D4 D5

Ti-6Al-4V 44times103 1098 1092 0014 11 093 -009 025 -05 014 387

Effective stress (v ndash m)

6529e + 02

5804e + 02

5080e + 02

4355e + 02

3631e + 02

2906e + 02

2182e + 02

1457e + 02

7330e + 01

8491e ndash 01

7253e + 02

Figure 8 von Mises stress (MPa) of the fan assembly

Stag

natio

n pr

essu

re (M

Pa)

Theoretical pressure(z = 01)Hemispherical endedcylinderReal bird (mallard)

Experiment (pigeons)Experiment (porousgelatine)

0

2

4

6

8

10

12

110 120 130 140 150100Impact velocity (ms)

Figure 9 Calibration of stagnation pressures

Complexity 7

severe blade plastic strain As a result the most criticallocation for a middle-sized bird should be aimed at 80 ofthe fan blade height

53 Effect of Attitude Angles on Soft-Impact DamageFigure 12 shows the deformation of bird oriented along theengine axis As expected it can be clearly observed that priorto the impact of the bird torso the real bird was sliced intomore pieces +e orientation of bird has a direct effect on

slicing action of fan blades With respect to different atti-tudes the contact area and duration of bird strikes changeresulting in a significant impact on the effect of the birdstrike on rotatory blades and the possibility of blade failures

Figure 13 shows the effect of the yaw angle on impactloading history As shown in Figure 13(a) peak values ofimpact force generated by a real bird with respect to yawangle of 15deg 30deg 45deg and 60deg are 20153KN at 397ms17052KN at 431ms 17634KN at 433ms and 18697 KNat 428ms respectively As shown in Figure 13(b) the peak

Impa

ct fo

rce (

KN)

2 4 6 8 100Time (ms)

0

50

100

150

200

250

60 ms65 ms70 ms

80 ms105 ms130 ms

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

60 ms65 ms70 ms

80 ms105 ms130 ms

(b)

Figure 10 Effect of ingestion speed on the impact loading history and blade damage (a)+e impact loading history (b) Normalized sum ofeffective plastic strains

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

507075

808590

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

507075

808590

(b)

Figure 11 Effect of target location on the impact loading history and blade damage (a) +e impact loading history (b) Normalized sum ofeffective plastic strains

8 Complexity

values of impact force derived from a real bird with yawangle of minus 15deg minus 30deg minus 45deg and minus 60deg are 15732KN at 522ms13799KN at 433ms 20647KN at 370ms and 24666KNat 485ms respectively It can be concluded that a yaw angleof the bird would generate a variation in the impact loadinghistory and a negative yaw angle has a more significant effecton the impact loading history

Figure 14 shows the effect of pitch angle on the timehistories of impact loads As shown in Figure 14(a) withrespect to pitch angles of 15deg 30deg 45deg and 60deg the peakimpact loads are 20515KN at 435ms 22720 KN at 391ms26147 KN at 433ms and 26940 KN at 392ms respectivelyObviously the peak impact force increases as the positivepitch angle increases As shown in Figure 14(b) peak valuesof impact loading obtained from a real bird model with pitchangles of minus 15deg minus 30deg minus 45deg and minus 60deg are 16073KN at 393ms

16828KN at 390ms 18485KN at 386ms and 22406 KNat 385ms respectively It is observed that a negative yawangle would result in a variation in the impact loadinghistory

Figure 15 shows effective plastic strains of a single bladewhich undergoes the most severe plastic deformation duringimpact Obviously with the change of the bird attitude anglethe blade undergoes more severe plastic deformation Es-pecially as subjected to a real bird with a yaw angle of minus 45deg ora pitch angle of minus 60deg the blade suffers more than twice themagnitude of effective plastic strain compared with a realbird oriented along the engine centerline It can be con-cluded that attitude angles would increase the possibility offan blade failure Moreover the yaw angle of bird ingestionhas a significant effect on the location of the blade with themost severe plastic deformation

9972e + 02 1244e + 03 1255e + 031129e + 031004e + 038782e + 027527e + 026273e + 025018e + 023764e + 022509e + 021255e + 020000e + 00

1335e + 031314e + 031293e + 031163e + 031034e + 039049e + 027756e + 026463e + 025171e + 023878e + 022585e + 021293e + 020000e + 00

1182e + 031051e + 039197e + 027883e + 026569e + 025255e + 023942e + 022628e + 021314e + 020000e + 00

1202e + 031069e + 039351e + 028017e + 026683e + 025349e + 024015e + 022681e + 021347e + 021243e + 00

1120e + 039951e + 028707e + 027464e + 026220e + 024976e + 023732e + 022488e + 021244e + 020000e + 00

8975e + 027977e + 026980e + 025983e + 024986e + 023989e + 022992e + 021994e + 029972e + 010000e + 00

t = 10 ms t = 20 ms t = 25 ms

t = 45 mst = 35 mst = 30 ms

z

x

(a)

Figure 12 Bird deformation during the slicing action

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 13 Yaw angle effect on impact loading history (a) Positive yaw angle α (b) Negative yaw angle α

Complexity 9

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

300

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)Im

pact

forc

e (KN

)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 14 Pitch angle effect on impact loading history (a) Positive pitch angle β (b) Negative pitch angle β

Effec

tive p

lasti

c str

ains

0deg15deg on 3 blade30deg on 4 blade45deg on 4 blade60deg on 4 blade

ndash15deg on 6 bladendash30deg on 5 bladendash45deg on 3 bladendash60deg on 5 blade

2 4 6 8 10Time (ms)

00

12

24

36

48

60

(a)

Effec

tive p

lasti

c str

ains

of t

he b

lade

3

12

24

36

48

60

4 6 8 10Time (ms)

0deg15deg30deg45deg60deg

ndash15degndash30degndash45degndash60deg

00

2

(b)

Figure 15 Attitude angle effect on blade damage (a) Yaw angle α (b) Pitch angle β

10 Complexity

Figure 16 shows the effective plastic strains of the fanassembly It can be seen that a ldquocusprdquo plastic deformationoccurs at the leading edge and the maximum plastic strainoccurred to the impact location Compared with the plasticdeformation of a fan assembly during a normal impact (seeFigure 16(a)) subjected to a bird with an attitude angle ofα minus 45deg and β minus 60deg fan blade failure occurs at the impactlocation and the plastic deformation at the root of the fanblade leading edge is more significant which would increasethe risk of a fan blade release event

6 Conclusions

Considering a geometric shape similar to what has alreadybeen published as a real mallard [12] a real bird model wasdeveloped +en this paper discusses the effect of attitudeangles of the realistic bird model on the soft impact damageof a full fan assembly Besides the stagnation pressure isrepresented as a criterion to calibrate the developed bird

model Results show a good correlation with available testdata [26]

In accordance with certification requirements the mostcritical ingestion parameters for the new bird model wereinvestigated It is found that the real bird aimed at the fanblade height of 80 with an ingestion speed of 65msproduces the most severe damage to the full fan assembly

Complying with the critical ingestion parameters of thebird simulations of a full fan assembly subjected to a realbird with respect to various attitude angles reveal that bothyaw and pitch angles of the bird have a significant effect onthe impact loading history +e blade that undergoes thehighest magnitude of effective plastic strain would beconfronted with a more plastic deformation than that in thecase of a normal impact (attitude angle 0deg) even though theimpact loading decreases Especially as subjected to a realbird with yaw angle of minus 45deg or pitch angle of minus 60deg the bladesuffers more than twice the magnitude of effective plasticstrain compared with that of attitude angle 0deg and the plastic

1898e ndash 01

1705e ndash 01

1512e ndash 01

1319e ndash 01

1125e ndash 01

9323e ndash 02

7392e ndash 02

5460e ndash 02

3529e ndash 02

1598e ndash 02

ndash3332e ndash 032

3 4

(a)

3294e ndash 01

2960e ndash 01

2627e ndash 01

2294e ndash 01

1960e ndash 01

1627e ndash 01

1294e ndash 01

9605e ndash 02

6272e ndash 02

2939e ndash 02

ndash3947e ndash 033

(b)

2032e ndash 01

1825e ndash 01

1617e ndash 01

1410e ndash 01

1202e ndash 01

9950e ndash 02

7876e ndash 02

5803e ndash 02

3729e ndash 02

1655e ndash 02

ndash4189e ndash 033

(c)

Figure 16 Effective plastic strain contours at time t 10ms (a) 0deg (b) α minus 45deg (c) β minus 60deg

Complexity 11

deformation at the root of the leading edge is more sig-nificant which would increase the risk of a fan blade releaseevent

Moreover it is invaluable to ensure the safety of com-mercial airlines and engine manufacture by adopting therealistic bird model with the dangerous attitude angle in thecertification of engine designs for resistance to bird strikeswhich will provide sufficient resistance in actual bird-strikeevents However attitude angles of the bird were set upbased on the assumption in this paper If the bird attitudecould be determined through experiments or control al-gorithms [38ndash42] it is of great significance to investigate theeffect of bird attitude on soft impact damage as well as thedistribution of flocking bird

Data Availability

All data included in this study are available from the cor-responding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is research was supported by the National Key Researchand Development Program of China (Grant no2016YFB0201800) and the National Natural Science Foun-dation of China (Grant no 11772192)

References

[1] R H Mao S A Meguid and T Y Ng ldquoTransient threedimensional finite element analysis of a bird striking a fanbladerdquo International Journal of Mechanics and Materials inDesign vol 4 no 1 pp 79ndash96 2008

[2] S Heimbs ldquoComputational methods for bird strike simula-tions a reviewrdquo Computers amp Structures vol 89 no 23-24pp 2093ndash2112 2011

[3] J S Wilbeck Impact Behavior of Low Strength Projectiles AirForce Materials Lab Ohio AFFDL-TR-75-5 1978

[4] J S Wilbeck and J L Rand ldquo+e development of a substitutebird modelrdquo Journal of Engineering for Power vol 103 no 4pp 725ndash730 1981

[5] A Airoldi and B Cacchione ldquoModelling of impact forces andpressures in Lagrangian bird strike analysesrdquo InternationalJournal of Impact Engineering vol 32 no 10 pp 1651ndash16772006

[6] M A Lavoie A Gakwaya M N Ensan D G Zimcik andD Nandlall ldquoldquoBirdrsquos substitute test results and evaluation ofavailable numerical methodsrdquo International Journal of ImpactEngineering vol 36 no 10-11 pp 1276ndash1287 2009

[7] M Guida F Marulo M Meo and M Riccio ldquoEvaluation andvalidation of multi-physics FE methods to simulate bird strikeon a wing leading edgerdquo in Proceedings of the 13th EuropeanConference on Composite Materials (ECCM) StockholmSweden June 2008

[8] M A Lavoie A Gakwaya M N Ensan and D G ZimcikldquoReview of existing numerical methods and validation pro-cedure available for bird strike modellingrdquo International

Journal of Applied Mathematics and Computer Science vol 2no 4 pp 111ndash118 2007

[9] M A Lavoie A Gakwaya M Nejad Ensan and D G ZimcikldquoValidation of available approaches for numerical bird strikemodeling toolsrdquo International Review of Mechanical Engi-neering vol 1 no 4 pp 380ndash389 2007

[10] M A McCarthy J R Xiao C T McCarthy et al ldquoModellingof bird strike on an aircraft wing leading edge made from fibremetal laminates-part 2 modelling of impact with SPH birdmodelrdquo Applied Composite Materials vol 11 no 5pp 317ndash340 2004

[11] L Nizampatnam and W Horn ldquoInvestigation of equation ofstate models for predicting bird impact loadsrdquo in Proceedingsof the 46th AIAA Aerospace Sciences Meeting and Exhibitpp 7ndash10 2013

[12] R Hedayati M Sadighi and M Mohammadi-Aghdam ldquoOnthe difference of pressure readings from the numerical ex-perimental and theoretical results in different bird strikestudiesrdquo Aerospace Science and Technology vol 32 no 1pp 260ndash266 2014

[13] L S Nizampatnam Models and Methods for Bird Strike LoadPredictions Wichita State University Wichita Kansas 2007

[14] S McCallum H Shoji and H Akiyama ldquoDevelopment of anadvanced multi-material bird-strike model using thesmoothed particle Hydrodynamics methodrdquo InternationalJournal of Crashworthiness vol 18 no 6 pp 579ndash597 2013

[15] R Hedayati and S Ziaei-Rad ldquoA new bird model and theeffect of bird geometry in impacts from various orientationsrdquoAerospace Science and Technology vol 28 no 1 pp 9ndash202013

[16] A Serge ldquoSoft impacts on aerospace structuresrdquo Progress inAerospace Sciences vol 81 pp 1ndash17 2016

[17] J Kou F Xu S Ji and X Zhang ldquoInfluence of bird yawpitchorientation on bird-strike resistance of aircraft structuresrdquoExplosion and Shock Waves vol 37 no 5 pp 937ndash944 2017

[18] Z Zhang L Li and D Zhang ldquoEffect of arbitrary yawpitchangle in bird strike numerical simulation using SPHmethodrdquoAerospace Science and Technology vol 81 pp 284ndash293 2018

[19] D Zhang and Q Fei ldquoEffect of bird geometry and impactorientation in bird striking on a rotary jet-engine fan analysisusing SPH methodrdquo Aerospace Science and Technologyvol 54 pp 320ndash329 2016

[20] R H Mao S A Meguid and T Y Ng ldquoEffects of incidenceangle in bird strike on integrity of aero-engine fan bladerdquoInternational Journal of Crashworthiness vol 14 no 4pp 295ndash308 2009

[21] C Yang C Chen N Wang et al ldquoBiologically inspiredmotion modeling and neural control for robot learning fromdemonstrationsrdquo IEEE Transactions on Cognitive and De-velopmental Systems vol 11 no 2 pp 281ndash291 2019

[22] C Yang C Chen W He R Cui and Z Li ldquoRobot learningsystem based on adaptive neural control and dynamicmovement primitivesrdquo IEEE Transactions on Neural Networksand Learning Systems vol 30 no 3 pp 777ndash787 2019

[23] C Yang D Huang W He and L Cheng ldquoNeural control ofrobot manipulators with trajectory tracking constraints andinput saturationrdquo IEEE Transactions on Neural Networks andLearning Systems pp 1ndash12 2020

[24] H Huang T Zhang C Yang and C L P Chen ldquoMotorlearning and generalization using broad learning adaptiveneural controlrdquo IEEE Transactions on Industrial Electronicsvol 67 no 10 pp 8608ndash8617 2020

12 Complexity

[25] H Huang C Yang and C L P Chen ldquoOptimal robot-envi-ronment interaction under broad fuzzy neural adaptive controlrdquoIEEE Transactions on Cybernetics pp 1ndash12 2020

[26] F Allaeys G Luyckx W Van Paepegem and J DegrieckldquoNumerical and experimental investigation of the shock andsteady state pressures in the bird material during bird strikerdquoInternational Journal of Impact Engineering vol 107pp 12ndash22 2017

[27] M Kim A Zammit A Siddens and J Bayandor ldquoAn ex-tensive crashworthiness methodology for advanced pro-pulsion systems part I soft impact damage assessment ofcomposite fan stage assembliesrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting Including the New HorizonsForum and Aerospace Exposition Orlando Florida January2011

[28] R Hedayati and M Sadighi Bird Strike An Experimental+eoretical and Numerical Investigation Woodhead Pub-lishing in Mechanical Engineering Elsevier AmsterdamNetherlands 978-0-08-100093-9 2016

[29] S K Sinha K E Turner and N Jain ldquoDynamic loading onturbofan blades due to bird-strikerdquo Journal of Engineering forGas Turbines and Power vol 133 no 12 Article ID 1225042011

[30] Federal Aviation Administration ldquoElectronic code of federalRegulationsrdquo Title 14 Aeronautics and Space National Ar-chives and Records Administration Washington DC USAChapter I Subchapter C Part 33-Airworthiness StandardsAircraft Engines Section 3376 2020

[31] Federal Aviation Administration ldquoBird ingestion certificationstandardsrdquo Advisory Circular Federal Aviation Administra-tion Wasington DC USA 3376-1A 2009

[32] R A Dolbeer S E Wright J R Weller and M J BegierWildlife Strikes to Civil Aircraft in the United States 1990-2017National Wildlife Strike Database Washington DC USA2018

[33] C J Shepherd G J Appleby-+omas P J Hazell andD F Allsop ldquo+e dynamic behaviour of ballistic gelatinrdquo AIPConference Proceedings vol 1195 pp 1399ndash1402 2009

[34] J O Hallquist LS-DYNA+eory Manual Livermore SoftwareTechnology Corporation Livermore CA USA 2007

[35] R Vignjevic M Orłowski T De Vuyst and J C CampbellldquoA parametric study of bird strike on engine bladesrdquo Inter-national Journal of Impact Engineering vol 60 pp 44ndash572013

[36] G R Johnson and W H Cook ldquoFracture characteristics ofthree metals subjected to various strains strain rates tem-peratures and pressuresrdquo Engineering Fracture Mechanicsvol 21 no 1 pp 31ndash48 1985

[37] D Leseur Experimental Investigations of Material Models forTi-6A1-4V and 2024-T3 Lawrence Livermore National LabLivermore CA USA UCRL-ID-134691 1999

[38] C Yang Y Jiang W He J Na Z Li and B Xu ldquoAdaptiveparameter estimation and control design for robot manipu-lators with finite-time convergencerdquo IEEE Transactions onIndustrial Electronics vol 65 no 10 pp 8112ndash8123 2018

[39] C Yang G Peng L Cheng J Na and Z Li ldquoForce sensorlessadmittance control for teleoperation of uncertain robotmanipulator using neural networksrdquo IEEE Transactions onSystems Man and Cybernetics Systems pp 1ndash11 2019

[40] G Peng C Yang W He and C L P Chen ldquoForce sensorlessadmittance control with neural learning for robots with ac-tuator saturationrdquo IEEE Transactions on Industrial Elec-tronics vol 67 no 4 pp 3138ndash3148 2020

[41] C Yang H Wu Z Li W He N Wang and C-Y Su ldquoMindcontrol of a robotic arm with visual fusion technologyrdquo IEEETransactions on Industrial Informatics vol 14 no 9pp 3822ndash3830 2018

[42] H Lin T Zhang Z Chen H Song and C Yang ldquoAdaptivefuzzy Gaussian mixture models for shape approximation inrobot graspingrdquo International Journal of Fuzzy Systemsvol 21 no 4 pp 1026ndash1037 2019

Complexity 13

accounting for 28 of the total specified species +erefore themallard (a typical species of waterfowl) is represented as ageneral realistic bird model Since a real bird consists of severalinternal cavities bone structures etc with complex geometrythe presented bird model can reflect the bird shape to someextent not exactly the same as the real one+emain geometriccharacteristics are given as follows (1) Wilbeck [3] found thatbone effect of a bird can be assumed negligible and thus auniform density of the real bird model is used (2) the head issimplified to be an ellipsoid and the neck was considered as acircular-conical-frustum [19] (3) geometric parameters of thebird torso were modelled considering the geometry of a realmallard bird in Ref [12] (4) the mass of bird wings accountedfor 19 of the total mass in accordance with Ref [14] +einterparticular distance is 2mm and the amount of SPHparticles is 153621 as shown in Figure 4

33 Bird Material Constitutive Model With a general ma-terial model for both solids and fluids to describe the fluidicbehavior of the bird material the Cauchy stress tensor isdivided into a hydrostatic part and a deviatoric part [16]

σij minus Pδij + sij (7)

in which the hydrostatic pressure P is written as

P minusσkk

3

minus σ11 + σ22 + σ33( 1113857

3 (8)

where σij represents stress tensor and sij represents devia-toric stress tensor Variable δij represents Kronecker deltasymbol

Since the compression of bird material during impactinduces a change in the bird density [27] theMiendashGruneisen equation of state (EOS) was used to reflectthe relationship between the pressure and the density [15]

P ρ0C

2μ 1 + 1 minus c02( 1113857( 1113857μ minus (a2)μ21113960 1113961

1 minus S1 minus 1( 1113857μ minus S2 μ2μ + 11113872 1113873 minus S3 μ3(μ + 1)2

1113872 11138731113960 11139612

+ c0 + aμ( 1113857E

(9)

A linear EOS is adopted for the bird material model [26]and equation (9) can be written as

P ρ0C

2μ1 minus S1 minus 1( 1113857μ1113858 1113859

2 (10)

where C S1 S2 and S3 are coefficients of the relationshipbetween the shock and particle velocities and c0 representsMiendashGruneisen gamma a is the first-order volume cor-rection to c0 μ represents the relative change in density

Porcine gelatinewith 10porosity is used instead of the birdmaterial [26] Parameters of porcine gelatine can be obtainedfrom Ref [33] +us for the developed bird model parametersare given as follows ρ0 954kgm3 C 1447ms S1 177

34 Attitude Angle Description In this research work birdattitude was defined based on the TaitndashBryan angles +eTaitndashBryan angles are three angles named as yaw angle αpitch angle β and roll angle c +ey were introduced todescribe the orientation of a bird As shown in Figure 5 aright-handed Cartesian coordinate system was defined in thecenter of bird gravity and any bird attitude can be pa-rameterized by three TaitndashBryan angles α β and c

In a field event of the bird strike it is difficult andcomplicated to record the TaitndashBryan angles of bird in-gestion Attitude angles of the real bird are assumed in a widerange from 0deg to 60deg and the orientation of bird based on anindividual TaitndashBryan angle was studied at a time Con-sidering the weight of wings accounting for about 19 birdmass [14] the effect of the roll angle on the slicing action of abird is relatively small +erefore bird attitude based on theroll angle was neglected Yaw angle α and pitch angle β wereselected as plusmn15deg plusmn30deg plusmn45degand plusmn60deg respectively Figure 6shows the attitude angles of a realistic bird where the at-titude angle is represented as the angle between the roll axisand the impact velocity

4 Numerical Model of a Fan Assembly

41 Fan Assembly Model +e fan assembly consists of 24equally spaced (15deg) wide-chord blades and a fan disc +efan assembly was modelled with 8-noded solid elementsBending is the basic mode of load carrying capacity forblades during impact With a single-point integration atthe element centroid solid elements can carry membranestresses only [34] +us blades were assigned 3 layers ofsolid elements through the thickness A tied-contact re-lationship was assumed to represent the attachment be-tween the blade and the fan hub Fixed boundaryconstraints of z-displacement direction were defined onthe side of the hub component To restrict nonphysicaldeformations relevant to zero energy modes stiffnesshourglass control with exact volume integration [34] wasapplied to the simulation model Figure 7 shows the finiteelement model of the fan assembly +e fan assemblyconsists of 165200 solid elements with a total of 222912nodes +e minimum element size of the fan assemblymodel was 042mm at the tip of the blade leading edgeand the corresponding time step for explicit dynamicsimulation was 406E-8 s In addition Figure 7 givesnumbers to fan blades during slicing a bird so that it canidentify the blade damage in the simulation of the impacton a fully bladed fan rotor

42 Blade Material Constitutive Model Bird strike eventscan be described as high strains and high strain rates in shortduration with considerable intensity [35] +erefore theempirical JohnsonndashCook relation was selected [36]

σy A + Bεn( 1113857 1 + C ln _εlowast( 1113857 1 minus T

lowastm( 1113857 (11)

in which

4 Complexity

Tlowast

T minus Troom( 1113857 Tmelt minus Troom( 1113857 (12)

where σy represents the equivalent von Mises stress εrepresents the equivalent plastic strain and _εlowast represents thenormalized equivalent plastic strain rate +e parameters AB C m and n are material constants T Tmelt and Troomrepresent the metal temperature melting temperature androom temperature respectively

Material fracture is determined by a cumulative damagelaw a function of mean stress strain rate and temperature[36]

D 1113944Δεεf

(13)

in which Figure 5 Definition of the TaitndashBryan angles

426 mm

(a)

340 m

m

(b)

86 mm

86 m

m

(c)

(d)

Figure 4 A realistic birdmodel by the SPHmethod (a) Left view (b) Front view (c) Bottom view (d) A real mallard compared to the SPHmodel

Complexity 5

εf D1 + D2 exp D3σlowast

( 11138571113858 1113859 1 + D4 ln _εlowast1113858 1113859 1 + D5Tlowast

1113858 1113859

(14)

where ∆ε is the increment of equivalent plastic strain and σlowastis the mean normalized by the equivalent stress D1 D2 D3D4 and D5 are damage constants Failures are assumed tooccur when D 1

+e fan assembly is made of titanium alloy Ti-6Al-4Vand material parameters are derived from Ref [37] as listedin Table 1 In addition the MiendashGruneisen EOS (equation(3)) was defined in conjunction with the material consti-tutive model and parameters for Ti-6Al-4V are as followsC 513times103ms S1 1028 c0 123 and a 017 [35]

43 Stress Initialization +e rotating fan assembly un-dergoes a constant centrifugal force resulting in significantdeformation and initial stresses prior to impact It is nec-essary to evaluate the prestress of the rotating componentsespecially for blades [16] +us a preload analysis procedurewas conducted by assigning rotational velocity of 542 radsin an implicit solution+e initial stress of blades assembly isshown in Figure 8

5 Results and Discussion

51 Bird Model Calibration +e effect of the high-intensityshock wave on the blade damage can be ignored for the

z

x

v0α

(a)

z

x

v0α

(b)

z

y

v0β

(c)

z

y

v0β

(d)

Figure 6 Schematic of yaw and pitch angles (a) Positive yaw angle α (b) Negative yaw angle α (c) Positive pitch angle β (d) Negative pitchangle β

Tip on the leadingedge of fan blade

v0

EnlargedBird

Axis of rotary

Fan assembly

Back view

Mos

t crit

ical

loca

tion

Bottom view

1

2

3

4

56

XX

Y

ZZ

Y

ω = 542 rads

Figure 7 FE model of a fan assembly subjected to a bird

6 Complexity

reason that the initial bird loading area is almost like a pointloading [29] +e focus of blade damage analysis needs to beon accurately capturing the steady stagnation pressure phaseof impact [27] +us the stagnation pressure is representedas a criterion to calibrate bird models Numerical simulationof a normal impact on a rigid plate was established in ac-cordance with the experimental setup in Ref [26] A seg-ment sensor was assigned at the center of the plate to extractthe impact pressure +e stagnation pressures were esti-mated by averaging the pressure between T03 and 2T03[26] where T0 denotes the duration of the bird strike event+e theoretical curve of the stagnation pressure was de-termined by equation (3) and test data was derived fromRef [26] as shown in Figure 9+e numerical results were ina range between theoretical and experimental values +estagnation pressures captured by simulation of the real birdwere in closer agreement with the test data than those in thecase of the hemispherical-ended cylinder

52MostCritical IngestionParameters +e critical ingestionparameters are required to be identified for the specified birdingestion [30] In this section simulations of a full fan as-sembly subjected to a real bird were performed to determinethe critical location and ingestion speed under FARsect3376(c) (1) and FAR sect3376(c) (3)

521 Most Critical Ingestion Speed Complying with FARsect3376(c)(1) the critical ingestion speed is required to reflectthe most severe situation within the range of speeds used fornormal flight operations up to 460m (1500 feet) but not lessthan V1 minimum for airplanes [30] +erefore simulationsof the bird ingested at different speeds were performedaimed at the fan blade height of 80 Figure 10(a) shows theeffect of ingestion speed on impact loading history +e peakvalues of impact force generated by a real bird targeted atspeeds of 60ms 65ms 70ms 80ms 105ms and 130ms are 18335KN at 395ms 18253KN at 397ms 19891 KNat 348ms 21096KN at 348ms 21216KN at 299ms and17095KN at 250ms respectively As the speed increasesthe impact duration becomes shorter It is also found that thehigher the impact speed is the earlier the peak force occursAs the normalized sum of effective plastic strains shown inFigure 10(b) the ingestion speed of 65ms caused the mostsevere plastic strain+erefore 65ms was represented as themost critical speed

522 Most Critical Exposed Location To find out the mostcritical location under FAR sect3376(c)(1) the real bird aimedat different target points on the leading edge of blades wasevaluated at a speed of 65ms Figure 11(a) shows the effectof target location on the time histories of impact force +epeak values of impact force generated by a real bird aimed at

the fan blade height of 50 70 75 80 85 and 90are 16379KN at 384ms 16825KN at 430ms 17730KN at392ms 18253KN at 397ms 15592KN at 439ms and17169KN at 485ms respectively It can be observed thatthe impact location of 80 blade height reaches the max-imum value of peak impact force As the blade damageindicated in Figure 11(b) with the single medium birdtargeted at the fan blade height of 80 it occurs to the most

Table 1 Material properties of Ti-6Al-4V

Material ρ (kgm3) A (MPa) B (MPa) C m n D1 D2 D3 D4 D5

Ti-6Al-4V 44times103 1098 1092 0014 11 093 -009 025 -05 014 387

Effective stress (v ndash m)

6529e + 02

5804e + 02

5080e + 02

4355e + 02

3631e + 02

2906e + 02

2182e + 02

1457e + 02

7330e + 01

8491e ndash 01

7253e + 02

Figure 8 von Mises stress (MPa) of the fan assembly

Stag

natio

n pr

essu

re (M

Pa)

Theoretical pressure(z = 01)Hemispherical endedcylinderReal bird (mallard)

Experiment (pigeons)Experiment (porousgelatine)

0

2

4

6

8

10

12

110 120 130 140 150100Impact velocity (ms)

Figure 9 Calibration of stagnation pressures

Complexity 7

severe blade plastic strain As a result the most criticallocation for a middle-sized bird should be aimed at 80 ofthe fan blade height

53 Effect of Attitude Angles on Soft-Impact DamageFigure 12 shows the deformation of bird oriented along theengine axis As expected it can be clearly observed that priorto the impact of the bird torso the real bird was sliced intomore pieces +e orientation of bird has a direct effect on

slicing action of fan blades With respect to different atti-tudes the contact area and duration of bird strikes changeresulting in a significant impact on the effect of the birdstrike on rotatory blades and the possibility of blade failures

Figure 13 shows the effect of the yaw angle on impactloading history As shown in Figure 13(a) peak values ofimpact force generated by a real bird with respect to yawangle of 15deg 30deg 45deg and 60deg are 20153KN at 397ms17052KN at 431ms 17634KN at 433ms and 18697 KNat 428ms respectively As shown in Figure 13(b) the peak

Impa

ct fo

rce (

KN)

2 4 6 8 100Time (ms)

0

50

100

150

200

250

60 ms65 ms70 ms

80 ms105 ms130 ms

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

60 ms65 ms70 ms

80 ms105 ms130 ms

(b)

Figure 10 Effect of ingestion speed on the impact loading history and blade damage (a)+e impact loading history (b) Normalized sum ofeffective plastic strains

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

507075

808590

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

507075

808590

(b)

Figure 11 Effect of target location on the impact loading history and blade damage (a) +e impact loading history (b) Normalized sum ofeffective plastic strains

8 Complexity

values of impact force derived from a real bird with yawangle of minus 15deg minus 30deg minus 45deg and minus 60deg are 15732KN at 522ms13799KN at 433ms 20647KN at 370ms and 24666KNat 485ms respectively It can be concluded that a yaw angleof the bird would generate a variation in the impact loadinghistory and a negative yaw angle has a more significant effecton the impact loading history

Figure 14 shows the effect of pitch angle on the timehistories of impact loads As shown in Figure 14(a) withrespect to pitch angles of 15deg 30deg 45deg and 60deg the peakimpact loads are 20515KN at 435ms 22720 KN at 391ms26147 KN at 433ms and 26940 KN at 392ms respectivelyObviously the peak impact force increases as the positivepitch angle increases As shown in Figure 14(b) peak valuesof impact loading obtained from a real bird model with pitchangles of minus 15deg minus 30deg minus 45deg and minus 60deg are 16073KN at 393ms

16828KN at 390ms 18485KN at 386ms and 22406 KNat 385ms respectively It is observed that a negative yawangle would result in a variation in the impact loadinghistory

Figure 15 shows effective plastic strains of a single bladewhich undergoes the most severe plastic deformation duringimpact Obviously with the change of the bird attitude anglethe blade undergoes more severe plastic deformation Es-pecially as subjected to a real bird with a yaw angle of minus 45deg ora pitch angle of minus 60deg the blade suffers more than twice themagnitude of effective plastic strain compared with a realbird oriented along the engine centerline It can be con-cluded that attitude angles would increase the possibility offan blade failure Moreover the yaw angle of bird ingestionhas a significant effect on the location of the blade with themost severe plastic deformation

9972e + 02 1244e + 03 1255e + 031129e + 031004e + 038782e + 027527e + 026273e + 025018e + 023764e + 022509e + 021255e + 020000e + 00

1335e + 031314e + 031293e + 031163e + 031034e + 039049e + 027756e + 026463e + 025171e + 023878e + 022585e + 021293e + 020000e + 00

1182e + 031051e + 039197e + 027883e + 026569e + 025255e + 023942e + 022628e + 021314e + 020000e + 00

1202e + 031069e + 039351e + 028017e + 026683e + 025349e + 024015e + 022681e + 021347e + 021243e + 00

1120e + 039951e + 028707e + 027464e + 026220e + 024976e + 023732e + 022488e + 021244e + 020000e + 00

8975e + 027977e + 026980e + 025983e + 024986e + 023989e + 022992e + 021994e + 029972e + 010000e + 00

t = 10 ms t = 20 ms t = 25 ms

t = 45 mst = 35 mst = 30 ms

z

x

(a)

Figure 12 Bird deformation during the slicing action

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 13 Yaw angle effect on impact loading history (a) Positive yaw angle α (b) Negative yaw angle α

Complexity 9

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

300

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)Im

pact

forc

e (KN

)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 14 Pitch angle effect on impact loading history (a) Positive pitch angle β (b) Negative pitch angle β

Effec

tive p

lasti

c str

ains

0deg15deg on 3 blade30deg on 4 blade45deg on 4 blade60deg on 4 blade

ndash15deg on 6 bladendash30deg on 5 bladendash45deg on 3 bladendash60deg on 5 blade

2 4 6 8 10Time (ms)

00

12

24

36

48

60

(a)

Effec

tive p

lasti

c str

ains

of t

he b

lade

3

12

24

36

48

60

4 6 8 10Time (ms)

0deg15deg30deg45deg60deg

ndash15degndash30degndash45degndash60deg

00

2

(b)

Figure 15 Attitude angle effect on blade damage (a) Yaw angle α (b) Pitch angle β

10 Complexity

Figure 16 shows the effective plastic strains of the fanassembly It can be seen that a ldquocusprdquo plastic deformationoccurs at the leading edge and the maximum plastic strainoccurred to the impact location Compared with the plasticdeformation of a fan assembly during a normal impact (seeFigure 16(a)) subjected to a bird with an attitude angle ofα minus 45deg and β minus 60deg fan blade failure occurs at the impactlocation and the plastic deformation at the root of the fanblade leading edge is more significant which would increasethe risk of a fan blade release event

6 Conclusions

Considering a geometric shape similar to what has alreadybeen published as a real mallard [12] a real bird model wasdeveloped +en this paper discusses the effect of attitudeangles of the realistic bird model on the soft impact damageof a full fan assembly Besides the stagnation pressure isrepresented as a criterion to calibrate the developed bird

model Results show a good correlation with available testdata [26]

In accordance with certification requirements the mostcritical ingestion parameters for the new bird model wereinvestigated It is found that the real bird aimed at the fanblade height of 80 with an ingestion speed of 65msproduces the most severe damage to the full fan assembly

Complying with the critical ingestion parameters of thebird simulations of a full fan assembly subjected to a realbird with respect to various attitude angles reveal that bothyaw and pitch angles of the bird have a significant effect onthe impact loading history +e blade that undergoes thehighest magnitude of effective plastic strain would beconfronted with a more plastic deformation than that in thecase of a normal impact (attitude angle 0deg) even though theimpact loading decreases Especially as subjected to a realbird with yaw angle of minus 45deg or pitch angle of minus 60deg the bladesuffers more than twice the magnitude of effective plasticstrain compared with that of attitude angle 0deg and the plastic

1898e ndash 01

1705e ndash 01

1512e ndash 01

1319e ndash 01

1125e ndash 01

9323e ndash 02

7392e ndash 02

5460e ndash 02

3529e ndash 02

1598e ndash 02

ndash3332e ndash 032

3 4

(a)

3294e ndash 01

2960e ndash 01

2627e ndash 01

2294e ndash 01

1960e ndash 01

1627e ndash 01

1294e ndash 01

9605e ndash 02

6272e ndash 02

2939e ndash 02

ndash3947e ndash 033

(b)

2032e ndash 01

1825e ndash 01

1617e ndash 01

1410e ndash 01

1202e ndash 01

9950e ndash 02

7876e ndash 02

5803e ndash 02

3729e ndash 02

1655e ndash 02

ndash4189e ndash 033

(c)

Figure 16 Effective plastic strain contours at time t 10ms (a) 0deg (b) α minus 45deg (c) β minus 60deg

Complexity 11

deformation at the root of the leading edge is more sig-nificant which would increase the risk of a fan blade releaseevent

Moreover it is invaluable to ensure the safety of com-mercial airlines and engine manufacture by adopting therealistic bird model with the dangerous attitude angle in thecertification of engine designs for resistance to bird strikeswhich will provide sufficient resistance in actual bird-strikeevents However attitude angles of the bird were set upbased on the assumption in this paper If the bird attitudecould be determined through experiments or control al-gorithms [38ndash42] it is of great significance to investigate theeffect of bird attitude on soft impact damage as well as thedistribution of flocking bird

Data Availability

All data included in this study are available from the cor-responding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is research was supported by the National Key Researchand Development Program of China (Grant no2016YFB0201800) and the National Natural Science Foun-dation of China (Grant no 11772192)

References

[1] R H Mao S A Meguid and T Y Ng ldquoTransient threedimensional finite element analysis of a bird striking a fanbladerdquo International Journal of Mechanics and Materials inDesign vol 4 no 1 pp 79ndash96 2008

[2] S Heimbs ldquoComputational methods for bird strike simula-tions a reviewrdquo Computers amp Structures vol 89 no 23-24pp 2093ndash2112 2011

[3] J S Wilbeck Impact Behavior of Low Strength Projectiles AirForce Materials Lab Ohio AFFDL-TR-75-5 1978

[4] J S Wilbeck and J L Rand ldquo+e development of a substitutebird modelrdquo Journal of Engineering for Power vol 103 no 4pp 725ndash730 1981

[5] A Airoldi and B Cacchione ldquoModelling of impact forces andpressures in Lagrangian bird strike analysesrdquo InternationalJournal of Impact Engineering vol 32 no 10 pp 1651ndash16772006

[6] M A Lavoie A Gakwaya M N Ensan D G Zimcik andD Nandlall ldquoldquoBirdrsquos substitute test results and evaluation ofavailable numerical methodsrdquo International Journal of ImpactEngineering vol 36 no 10-11 pp 1276ndash1287 2009

[7] M Guida F Marulo M Meo and M Riccio ldquoEvaluation andvalidation of multi-physics FE methods to simulate bird strikeon a wing leading edgerdquo in Proceedings of the 13th EuropeanConference on Composite Materials (ECCM) StockholmSweden June 2008

[8] M A Lavoie A Gakwaya M N Ensan and D G ZimcikldquoReview of existing numerical methods and validation pro-cedure available for bird strike modellingrdquo International

Journal of Applied Mathematics and Computer Science vol 2no 4 pp 111ndash118 2007

[9] M A Lavoie A Gakwaya M Nejad Ensan and D G ZimcikldquoValidation of available approaches for numerical bird strikemodeling toolsrdquo International Review of Mechanical Engi-neering vol 1 no 4 pp 380ndash389 2007

[10] M A McCarthy J R Xiao C T McCarthy et al ldquoModellingof bird strike on an aircraft wing leading edge made from fibremetal laminates-part 2 modelling of impact with SPH birdmodelrdquo Applied Composite Materials vol 11 no 5pp 317ndash340 2004

[11] L Nizampatnam and W Horn ldquoInvestigation of equation ofstate models for predicting bird impact loadsrdquo in Proceedingsof the 46th AIAA Aerospace Sciences Meeting and Exhibitpp 7ndash10 2013

[12] R Hedayati M Sadighi and M Mohammadi-Aghdam ldquoOnthe difference of pressure readings from the numerical ex-perimental and theoretical results in different bird strikestudiesrdquo Aerospace Science and Technology vol 32 no 1pp 260ndash266 2014

[13] L S Nizampatnam Models and Methods for Bird Strike LoadPredictions Wichita State University Wichita Kansas 2007

[14] S McCallum H Shoji and H Akiyama ldquoDevelopment of anadvanced multi-material bird-strike model using thesmoothed particle Hydrodynamics methodrdquo InternationalJournal of Crashworthiness vol 18 no 6 pp 579ndash597 2013

[15] R Hedayati and S Ziaei-Rad ldquoA new bird model and theeffect of bird geometry in impacts from various orientationsrdquoAerospace Science and Technology vol 28 no 1 pp 9ndash202013

[16] A Serge ldquoSoft impacts on aerospace structuresrdquo Progress inAerospace Sciences vol 81 pp 1ndash17 2016

[17] J Kou F Xu S Ji and X Zhang ldquoInfluence of bird yawpitchorientation on bird-strike resistance of aircraft structuresrdquoExplosion and Shock Waves vol 37 no 5 pp 937ndash944 2017

[18] Z Zhang L Li and D Zhang ldquoEffect of arbitrary yawpitchangle in bird strike numerical simulation using SPHmethodrdquoAerospace Science and Technology vol 81 pp 284ndash293 2018

[19] D Zhang and Q Fei ldquoEffect of bird geometry and impactorientation in bird striking on a rotary jet-engine fan analysisusing SPH methodrdquo Aerospace Science and Technologyvol 54 pp 320ndash329 2016

[20] R H Mao S A Meguid and T Y Ng ldquoEffects of incidenceangle in bird strike on integrity of aero-engine fan bladerdquoInternational Journal of Crashworthiness vol 14 no 4pp 295ndash308 2009

[21] C Yang C Chen N Wang et al ldquoBiologically inspiredmotion modeling and neural control for robot learning fromdemonstrationsrdquo IEEE Transactions on Cognitive and De-velopmental Systems vol 11 no 2 pp 281ndash291 2019

[22] C Yang C Chen W He R Cui and Z Li ldquoRobot learningsystem based on adaptive neural control and dynamicmovement primitivesrdquo IEEE Transactions on Neural Networksand Learning Systems vol 30 no 3 pp 777ndash787 2019

[23] C Yang D Huang W He and L Cheng ldquoNeural control ofrobot manipulators with trajectory tracking constraints andinput saturationrdquo IEEE Transactions on Neural Networks andLearning Systems pp 1ndash12 2020

[24] H Huang T Zhang C Yang and C L P Chen ldquoMotorlearning and generalization using broad learning adaptiveneural controlrdquo IEEE Transactions on Industrial Electronicsvol 67 no 10 pp 8608ndash8617 2020

12 Complexity

[25] H Huang C Yang and C L P Chen ldquoOptimal robot-envi-ronment interaction under broad fuzzy neural adaptive controlrdquoIEEE Transactions on Cybernetics pp 1ndash12 2020

[26] F Allaeys G Luyckx W Van Paepegem and J DegrieckldquoNumerical and experimental investigation of the shock andsteady state pressures in the bird material during bird strikerdquoInternational Journal of Impact Engineering vol 107pp 12ndash22 2017

[27] M Kim A Zammit A Siddens and J Bayandor ldquoAn ex-tensive crashworthiness methodology for advanced pro-pulsion systems part I soft impact damage assessment ofcomposite fan stage assembliesrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting Including the New HorizonsForum and Aerospace Exposition Orlando Florida January2011

[28] R Hedayati and M Sadighi Bird Strike An Experimental+eoretical and Numerical Investigation Woodhead Pub-lishing in Mechanical Engineering Elsevier AmsterdamNetherlands 978-0-08-100093-9 2016

[29] S K Sinha K E Turner and N Jain ldquoDynamic loading onturbofan blades due to bird-strikerdquo Journal of Engineering forGas Turbines and Power vol 133 no 12 Article ID 1225042011

[30] Federal Aviation Administration ldquoElectronic code of federalRegulationsrdquo Title 14 Aeronautics and Space National Ar-chives and Records Administration Washington DC USAChapter I Subchapter C Part 33-Airworthiness StandardsAircraft Engines Section 3376 2020

[31] Federal Aviation Administration ldquoBird ingestion certificationstandardsrdquo Advisory Circular Federal Aviation Administra-tion Wasington DC USA 3376-1A 2009

[32] R A Dolbeer S E Wright J R Weller and M J BegierWildlife Strikes to Civil Aircraft in the United States 1990-2017National Wildlife Strike Database Washington DC USA2018

[33] C J Shepherd G J Appleby-+omas P J Hazell andD F Allsop ldquo+e dynamic behaviour of ballistic gelatinrdquo AIPConference Proceedings vol 1195 pp 1399ndash1402 2009

[34] J O Hallquist LS-DYNA+eory Manual Livermore SoftwareTechnology Corporation Livermore CA USA 2007

[35] R Vignjevic M Orłowski T De Vuyst and J C CampbellldquoA parametric study of bird strike on engine bladesrdquo Inter-national Journal of Impact Engineering vol 60 pp 44ndash572013

[36] G R Johnson and W H Cook ldquoFracture characteristics ofthree metals subjected to various strains strain rates tem-peratures and pressuresrdquo Engineering Fracture Mechanicsvol 21 no 1 pp 31ndash48 1985

[37] D Leseur Experimental Investigations of Material Models forTi-6A1-4V and 2024-T3 Lawrence Livermore National LabLivermore CA USA UCRL-ID-134691 1999

[38] C Yang Y Jiang W He J Na Z Li and B Xu ldquoAdaptiveparameter estimation and control design for robot manipu-lators with finite-time convergencerdquo IEEE Transactions onIndustrial Electronics vol 65 no 10 pp 8112ndash8123 2018

[39] C Yang G Peng L Cheng J Na and Z Li ldquoForce sensorlessadmittance control for teleoperation of uncertain robotmanipulator using neural networksrdquo IEEE Transactions onSystems Man and Cybernetics Systems pp 1ndash11 2019

[40] G Peng C Yang W He and C L P Chen ldquoForce sensorlessadmittance control with neural learning for robots with ac-tuator saturationrdquo IEEE Transactions on Industrial Elec-tronics vol 67 no 4 pp 3138ndash3148 2020

[41] C Yang H Wu Z Li W He N Wang and C-Y Su ldquoMindcontrol of a robotic arm with visual fusion technologyrdquo IEEETransactions on Industrial Informatics vol 14 no 9pp 3822ndash3830 2018

[42] H Lin T Zhang Z Chen H Song and C Yang ldquoAdaptivefuzzy Gaussian mixture models for shape approximation inrobot graspingrdquo International Journal of Fuzzy Systemsvol 21 no 4 pp 1026ndash1037 2019

Complexity 13

Tlowast

T minus Troom( 1113857 Tmelt minus Troom( 1113857 (12)

where σy represents the equivalent von Mises stress εrepresents the equivalent plastic strain and _εlowast represents thenormalized equivalent plastic strain rate +e parameters AB C m and n are material constants T Tmelt and Troomrepresent the metal temperature melting temperature androom temperature respectively

Material fracture is determined by a cumulative damagelaw a function of mean stress strain rate and temperature[36]

D 1113944Δεεf

(13)

in which Figure 5 Definition of the TaitndashBryan angles

426 mm

(a)

340 m

m

(b)

86 mm

86 m

m

(c)

(d)

Figure 4 A realistic birdmodel by the SPHmethod (a) Left view (b) Front view (c) Bottom view (d) A real mallard compared to the SPHmodel

Complexity 5

εf D1 + D2 exp D3σlowast

( 11138571113858 1113859 1 + D4 ln _εlowast1113858 1113859 1 + D5Tlowast

1113858 1113859

(14)

where ∆ε is the increment of equivalent plastic strain and σlowastis the mean normalized by the equivalent stress D1 D2 D3D4 and D5 are damage constants Failures are assumed tooccur when D 1

+e fan assembly is made of titanium alloy Ti-6Al-4Vand material parameters are derived from Ref [37] as listedin Table 1 In addition the MiendashGruneisen EOS (equation(3)) was defined in conjunction with the material consti-tutive model and parameters for Ti-6Al-4V are as followsC 513times103ms S1 1028 c0 123 and a 017 [35]

43 Stress Initialization +e rotating fan assembly un-dergoes a constant centrifugal force resulting in significantdeformation and initial stresses prior to impact It is nec-essary to evaluate the prestress of the rotating componentsespecially for blades [16] +us a preload analysis procedurewas conducted by assigning rotational velocity of 542 radsin an implicit solution+e initial stress of blades assembly isshown in Figure 8

5 Results and Discussion

51 Bird Model Calibration +e effect of the high-intensityshock wave on the blade damage can be ignored for the

z

x

v0α

(a)

z

x

v0α

(b)

z

y

v0β

(c)

z

y

v0β

(d)

Figure 6 Schematic of yaw and pitch angles (a) Positive yaw angle α (b) Negative yaw angle α (c) Positive pitch angle β (d) Negative pitchangle β

Tip on the leadingedge of fan blade

v0

EnlargedBird

Axis of rotary

Fan assembly

Back view

Mos

t crit

ical

loca

tion

Bottom view

1

2

3

4

56

XX

Y

ZZ

Y

ω = 542 rads

Figure 7 FE model of a fan assembly subjected to a bird

6 Complexity

reason that the initial bird loading area is almost like a pointloading [29] +e focus of blade damage analysis needs to beon accurately capturing the steady stagnation pressure phaseof impact [27] +us the stagnation pressure is representedas a criterion to calibrate bird models Numerical simulationof a normal impact on a rigid plate was established in ac-cordance with the experimental setup in Ref [26] A seg-ment sensor was assigned at the center of the plate to extractthe impact pressure +e stagnation pressures were esti-mated by averaging the pressure between T03 and 2T03[26] where T0 denotes the duration of the bird strike event+e theoretical curve of the stagnation pressure was de-termined by equation (3) and test data was derived fromRef [26] as shown in Figure 9+e numerical results were ina range between theoretical and experimental values +estagnation pressures captured by simulation of the real birdwere in closer agreement with the test data than those in thecase of the hemispherical-ended cylinder

52MostCritical IngestionParameters +e critical ingestionparameters are required to be identified for the specified birdingestion [30] In this section simulations of a full fan as-sembly subjected to a real bird were performed to determinethe critical location and ingestion speed under FARsect3376(c) (1) and FAR sect3376(c) (3)

521 Most Critical Ingestion Speed Complying with FARsect3376(c)(1) the critical ingestion speed is required to reflectthe most severe situation within the range of speeds used fornormal flight operations up to 460m (1500 feet) but not lessthan V1 minimum for airplanes [30] +erefore simulationsof the bird ingested at different speeds were performedaimed at the fan blade height of 80 Figure 10(a) shows theeffect of ingestion speed on impact loading history +e peakvalues of impact force generated by a real bird targeted atspeeds of 60ms 65ms 70ms 80ms 105ms and 130ms are 18335KN at 395ms 18253KN at 397ms 19891 KNat 348ms 21096KN at 348ms 21216KN at 299ms and17095KN at 250ms respectively As the speed increasesthe impact duration becomes shorter It is also found that thehigher the impact speed is the earlier the peak force occursAs the normalized sum of effective plastic strains shown inFigure 10(b) the ingestion speed of 65ms caused the mostsevere plastic strain+erefore 65ms was represented as themost critical speed

522 Most Critical Exposed Location To find out the mostcritical location under FAR sect3376(c)(1) the real bird aimedat different target points on the leading edge of blades wasevaluated at a speed of 65ms Figure 11(a) shows the effectof target location on the time histories of impact force +epeak values of impact force generated by a real bird aimed at

the fan blade height of 50 70 75 80 85 and 90are 16379KN at 384ms 16825KN at 430ms 17730KN at392ms 18253KN at 397ms 15592KN at 439ms and17169KN at 485ms respectively It can be observed thatthe impact location of 80 blade height reaches the max-imum value of peak impact force As the blade damageindicated in Figure 11(b) with the single medium birdtargeted at the fan blade height of 80 it occurs to the most

Table 1 Material properties of Ti-6Al-4V

Material ρ (kgm3) A (MPa) B (MPa) C m n D1 D2 D3 D4 D5

Ti-6Al-4V 44times103 1098 1092 0014 11 093 -009 025 -05 014 387

Effective stress (v ndash m)

6529e + 02

5804e + 02

5080e + 02

4355e + 02

3631e + 02

2906e + 02

2182e + 02

1457e + 02

7330e + 01

8491e ndash 01

7253e + 02

Figure 8 von Mises stress (MPa) of the fan assembly

Stag

natio

n pr

essu

re (M

Pa)

Theoretical pressure(z = 01)Hemispherical endedcylinderReal bird (mallard)

Experiment (pigeons)Experiment (porousgelatine)

0

2

4

6

8

10

12

110 120 130 140 150100Impact velocity (ms)

Figure 9 Calibration of stagnation pressures

Complexity 7

severe blade plastic strain As a result the most criticallocation for a middle-sized bird should be aimed at 80 ofthe fan blade height

53 Effect of Attitude Angles on Soft-Impact DamageFigure 12 shows the deformation of bird oriented along theengine axis As expected it can be clearly observed that priorto the impact of the bird torso the real bird was sliced intomore pieces +e orientation of bird has a direct effect on

slicing action of fan blades With respect to different atti-tudes the contact area and duration of bird strikes changeresulting in a significant impact on the effect of the birdstrike on rotatory blades and the possibility of blade failures

Figure 13 shows the effect of the yaw angle on impactloading history As shown in Figure 13(a) peak values ofimpact force generated by a real bird with respect to yawangle of 15deg 30deg 45deg and 60deg are 20153KN at 397ms17052KN at 431ms 17634KN at 433ms and 18697 KNat 428ms respectively As shown in Figure 13(b) the peak

Impa

ct fo

rce (

KN)

2 4 6 8 100Time (ms)

0

50

100

150

200

250

60 ms65 ms70 ms

80 ms105 ms130 ms

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

60 ms65 ms70 ms

80 ms105 ms130 ms

(b)

Figure 10 Effect of ingestion speed on the impact loading history and blade damage (a)+e impact loading history (b) Normalized sum ofeffective plastic strains

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

507075

808590

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

507075

808590

(b)

Figure 11 Effect of target location on the impact loading history and blade damage (a) +e impact loading history (b) Normalized sum ofeffective plastic strains

8 Complexity

values of impact force derived from a real bird with yawangle of minus 15deg minus 30deg minus 45deg and minus 60deg are 15732KN at 522ms13799KN at 433ms 20647KN at 370ms and 24666KNat 485ms respectively It can be concluded that a yaw angleof the bird would generate a variation in the impact loadinghistory and a negative yaw angle has a more significant effecton the impact loading history

Figure 14 shows the effect of pitch angle on the timehistories of impact loads As shown in Figure 14(a) withrespect to pitch angles of 15deg 30deg 45deg and 60deg the peakimpact loads are 20515KN at 435ms 22720 KN at 391ms26147 KN at 433ms and 26940 KN at 392ms respectivelyObviously the peak impact force increases as the positivepitch angle increases As shown in Figure 14(b) peak valuesof impact loading obtained from a real bird model with pitchangles of minus 15deg minus 30deg minus 45deg and minus 60deg are 16073KN at 393ms

16828KN at 390ms 18485KN at 386ms and 22406 KNat 385ms respectively It is observed that a negative yawangle would result in a variation in the impact loadinghistory

Figure 15 shows effective plastic strains of a single bladewhich undergoes the most severe plastic deformation duringimpact Obviously with the change of the bird attitude anglethe blade undergoes more severe plastic deformation Es-pecially as subjected to a real bird with a yaw angle of minus 45deg ora pitch angle of minus 60deg the blade suffers more than twice themagnitude of effective plastic strain compared with a realbird oriented along the engine centerline It can be con-cluded that attitude angles would increase the possibility offan blade failure Moreover the yaw angle of bird ingestionhas a significant effect on the location of the blade with themost severe plastic deformation

9972e + 02 1244e + 03 1255e + 031129e + 031004e + 038782e + 027527e + 026273e + 025018e + 023764e + 022509e + 021255e + 020000e + 00

1335e + 031314e + 031293e + 031163e + 031034e + 039049e + 027756e + 026463e + 025171e + 023878e + 022585e + 021293e + 020000e + 00

1182e + 031051e + 039197e + 027883e + 026569e + 025255e + 023942e + 022628e + 021314e + 020000e + 00

1202e + 031069e + 039351e + 028017e + 026683e + 025349e + 024015e + 022681e + 021347e + 021243e + 00

1120e + 039951e + 028707e + 027464e + 026220e + 024976e + 023732e + 022488e + 021244e + 020000e + 00

8975e + 027977e + 026980e + 025983e + 024986e + 023989e + 022992e + 021994e + 029972e + 010000e + 00

t = 10 ms t = 20 ms t = 25 ms

t = 45 mst = 35 mst = 30 ms

z

x

(a)

Figure 12 Bird deformation during the slicing action

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 13 Yaw angle effect on impact loading history (a) Positive yaw angle α (b) Negative yaw angle α

Complexity 9

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

300

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)Im

pact

forc

e (KN

)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 14 Pitch angle effect on impact loading history (a) Positive pitch angle β (b) Negative pitch angle β

Effec

tive p

lasti

c str

ains

0deg15deg on 3 blade30deg on 4 blade45deg on 4 blade60deg on 4 blade

ndash15deg on 6 bladendash30deg on 5 bladendash45deg on 3 bladendash60deg on 5 blade

2 4 6 8 10Time (ms)

00

12

24

36

48

60

(a)

Effec

tive p

lasti

c str

ains

of t

he b

lade

3

12

24

36

48

60

4 6 8 10Time (ms)

0deg15deg30deg45deg60deg

ndash15degndash30degndash45degndash60deg

00

2

(b)

Figure 15 Attitude angle effect on blade damage (a) Yaw angle α (b) Pitch angle β

10 Complexity

Figure 16 shows the effective plastic strains of the fanassembly It can be seen that a ldquocusprdquo plastic deformationoccurs at the leading edge and the maximum plastic strainoccurred to the impact location Compared with the plasticdeformation of a fan assembly during a normal impact (seeFigure 16(a)) subjected to a bird with an attitude angle ofα minus 45deg and β minus 60deg fan blade failure occurs at the impactlocation and the plastic deformation at the root of the fanblade leading edge is more significant which would increasethe risk of a fan blade release event

6 Conclusions

Considering a geometric shape similar to what has alreadybeen published as a real mallard [12] a real bird model wasdeveloped +en this paper discusses the effect of attitudeangles of the realistic bird model on the soft impact damageof a full fan assembly Besides the stagnation pressure isrepresented as a criterion to calibrate the developed bird

model Results show a good correlation with available testdata [26]

In accordance with certification requirements the mostcritical ingestion parameters for the new bird model wereinvestigated It is found that the real bird aimed at the fanblade height of 80 with an ingestion speed of 65msproduces the most severe damage to the full fan assembly

Complying with the critical ingestion parameters of thebird simulations of a full fan assembly subjected to a realbird with respect to various attitude angles reveal that bothyaw and pitch angles of the bird have a significant effect onthe impact loading history +e blade that undergoes thehighest magnitude of effective plastic strain would beconfronted with a more plastic deformation than that in thecase of a normal impact (attitude angle 0deg) even though theimpact loading decreases Especially as subjected to a realbird with yaw angle of minus 45deg or pitch angle of minus 60deg the bladesuffers more than twice the magnitude of effective plasticstrain compared with that of attitude angle 0deg and the plastic

1898e ndash 01

1705e ndash 01

1512e ndash 01

1319e ndash 01

1125e ndash 01

9323e ndash 02

7392e ndash 02

5460e ndash 02

3529e ndash 02

1598e ndash 02

ndash3332e ndash 032

3 4

(a)

3294e ndash 01

2960e ndash 01

2627e ndash 01

2294e ndash 01

1960e ndash 01

1627e ndash 01

1294e ndash 01

9605e ndash 02

6272e ndash 02

2939e ndash 02

ndash3947e ndash 033

(b)

2032e ndash 01

1825e ndash 01

1617e ndash 01

1410e ndash 01

1202e ndash 01

9950e ndash 02

7876e ndash 02

5803e ndash 02

3729e ndash 02

1655e ndash 02

ndash4189e ndash 033

(c)

Figure 16 Effective plastic strain contours at time t 10ms (a) 0deg (b) α minus 45deg (c) β minus 60deg

Complexity 11

deformation at the root of the leading edge is more sig-nificant which would increase the risk of a fan blade releaseevent

Moreover it is invaluable to ensure the safety of com-mercial airlines and engine manufacture by adopting therealistic bird model with the dangerous attitude angle in thecertification of engine designs for resistance to bird strikeswhich will provide sufficient resistance in actual bird-strikeevents However attitude angles of the bird were set upbased on the assumption in this paper If the bird attitudecould be determined through experiments or control al-gorithms [38ndash42] it is of great significance to investigate theeffect of bird attitude on soft impact damage as well as thedistribution of flocking bird

Data Availability

All data included in this study are available from the cor-responding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is research was supported by the National Key Researchand Development Program of China (Grant no2016YFB0201800) and the National Natural Science Foun-dation of China (Grant no 11772192)

References

[1] R H Mao S A Meguid and T Y Ng ldquoTransient threedimensional finite element analysis of a bird striking a fanbladerdquo International Journal of Mechanics and Materials inDesign vol 4 no 1 pp 79ndash96 2008

[2] S Heimbs ldquoComputational methods for bird strike simula-tions a reviewrdquo Computers amp Structures vol 89 no 23-24pp 2093ndash2112 2011

[3] J S Wilbeck Impact Behavior of Low Strength Projectiles AirForce Materials Lab Ohio AFFDL-TR-75-5 1978

[4] J S Wilbeck and J L Rand ldquo+e development of a substitutebird modelrdquo Journal of Engineering for Power vol 103 no 4pp 725ndash730 1981

[5] A Airoldi and B Cacchione ldquoModelling of impact forces andpressures in Lagrangian bird strike analysesrdquo InternationalJournal of Impact Engineering vol 32 no 10 pp 1651ndash16772006

[6] M A Lavoie A Gakwaya M N Ensan D G Zimcik andD Nandlall ldquoldquoBirdrsquos substitute test results and evaluation ofavailable numerical methodsrdquo International Journal of ImpactEngineering vol 36 no 10-11 pp 1276ndash1287 2009

[7] M Guida F Marulo M Meo and M Riccio ldquoEvaluation andvalidation of multi-physics FE methods to simulate bird strikeon a wing leading edgerdquo in Proceedings of the 13th EuropeanConference on Composite Materials (ECCM) StockholmSweden June 2008

[8] M A Lavoie A Gakwaya M N Ensan and D G ZimcikldquoReview of existing numerical methods and validation pro-cedure available for bird strike modellingrdquo International

Journal of Applied Mathematics and Computer Science vol 2no 4 pp 111ndash118 2007

[9] M A Lavoie A Gakwaya M Nejad Ensan and D G ZimcikldquoValidation of available approaches for numerical bird strikemodeling toolsrdquo International Review of Mechanical Engi-neering vol 1 no 4 pp 380ndash389 2007

[10] M A McCarthy J R Xiao C T McCarthy et al ldquoModellingof bird strike on an aircraft wing leading edge made from fibremetal laminates-part 2 modelling of impact with SPH birdmodelrdquo Applied Composite Materials vol 11 no 5pp 317ndash340 2004

[11] L Nizampatnam and W Horn ldquoInvestigation of equation ofstate models for predicting bird impact loadsrdquo in Proceedingsof the 46th AIAA Aerospace Sciences Meeting and Exhibitpp 7ndash10 2013

[12] R Hedayati M Sadighi and M Mohammadi-Aghdam ldquoOnthe difference of pressure readings from the numerical ex-perimental and theoretical results in different bird strikestudiesrdquo Aerospace Science and Technology vol 32 no 1pp 260ndash266 2014

[13] L S Nizampatnam Models and Methods for Bird Strike LoadPredictions Wichita State University Wichita Kansas 2007

[14] S McCallum H Shoji and H Akiyama ldquoDevelopment of anadvanced multi-material bird-strike model using thesmoothed particle Hydrodynamics methodrdquo InternationalJournal of Crashworthiness vol 18 no 6 pp 579ndash597 2013

[15] R Hedayati and S Ziaei-Rad ldquoA new bird model and theeffect of bird geometry in impacts from various orientationsrdquoAerospace Science and Technology vol 28 no 1 pp 9ndash202013

[16] A Serge ldquoSoft impacts on aerospace structuresrdquo Progress inAerospace Sciences vol 81 pp 1ndash17 2016

[17] J Kou F Xu S Ji and X Zhang ldquoInfluence of bird yawpitchorientation on bird-strike resistance of aircraft structuresrdquoExplosion and Shock Waves vol 37 no 5 pp 937ndash944 2017

[18] Z Zhang L Li and D Zhang ldquoEffect of arbitrary yawpitchangle in bird strike numerical simulation using SPHmethodrdquoAerospace Science and Technology vol 81 pp 284ndash293 2018

[19] D Zhang and Q Fei ldquoEffect of bird geometry and impactorientation in bird striking on a rotary jet-engine fan analysisusing SPH methodrdquo Aerospace Science and Technologyvol 54 pp 320ndash329 2016

[20] R H Mao S A Meguid and T Y Ng ldquoEffects of incidenceangle in bird strike on integrity of aero-engine fan bladerdquoInternational Journal of Crashworthiness vol 14 no 4pp 295ndash308 2009

[21] C Yang C Chen N Wang et al ldquoBiologically inspiredmotion modeling and neural control for robot learning fromdemonstrationsrdquo IEEE Transactions on Cognitive and De-velopmental Systems vol 11 no 2 pp 281ndash291 2019

[22] C Yang C Chen W He R Cui and Z Li ldquoRobot learningsystem based on adaptive neural control and dynamicmovement primitivesrdquo IEEE Transactions on Neural Networksand Learning Systems vol 30 no 3 pp 777ndash787 2019

[23] C Yang D Huang W He and L Cheng ldquoNeural control ofrobot manipulators with trajectory tracking constraints andinput saturationrdquo IEEE Transactions on Neural Networks andLearning Systems pp 1ndash12 2020

[24] H Huang T Zhang C Yang and C L P Chen ldquoMotorlearning and generalization using broad learning adaptiveneural controlrdquo IEEE Transactions on Industrial Electronicsvol 67 no 10 pp 8608ndash8617 2020

12 Complexity

[25] H Huang C Yang and C L P Chen ldquoOptimal robot-envi-ronment interaction under broad fuzzy neural adaptive controlrdquoIEEE Transactions on Cybernetics pp 1ndash12 2020

[26] F Allaeys G Luyckx W Van Paepegem and J DegrieckldquoNumerical and experimental investigation of the shock andsteady state pressures in the bird material during bird strikerdquoInternational Journal of Impact Engineering vol 107pp 12ndash22 2017

[27] M Kim A Zammit A Siddens and J Bayandor ldquoAn ex-tensive crashworthiness methodology for advanced pro-pulsion systems part I soft impact damage assessment ofcomposite fan stage assembliesrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting Including the New HorizonsForum and Aerospace Exposition Orlando Florida January2011

[28] R Hedayati and M Sadighi Bird Strike An Experimental+eoretical and Numerical Investigation Woodhead Pub-lishing in Mechanical Engineering Elsevier AmsterdamNetherlands 978-0-08-100093-9 2016

[29] S K Sinha K E Turner and N Jain ldquoDynamic loading onturbofan blades due to bird-strikerdquo Journal of Engineering forGas Turbines and Power vol 133 no 12 Article ID 1225042011

[30] Federal Aviation Administration ldquoElectronic code of federalRegulationsrdquo Title 14 Aeronautics and Space National Ar-chives and Records Administration Washington DC USAChapter I Subchapter C Part 33-Airworthiness StandardsAircraft Engines Section 3376 2020

[31] Federal Aviation Administration ldquoBird ingestion certificationstandardsrdquo Advisory Circular Federal Aviation Administra-tion Wasington DC USA 3376-1A 2009

[32] R A Dolbeer S E Wright J R Weller and M J BegierWildlife Strikes to Civil Aircraft in the United States 1990-2017National Wildlife Strike Database Washington DC USA2018

[33] C J Shepherd G J Appleby-+omas P J Hazell andD F Allsop ldquo+e dynamic behaviour of ballistic gelatinrdquo AIPConference Proceedings vol 1195 pp 1399ndash1402 2009

[34] J O Hallquist LS-DYNA+eory Manual Livermore SoftwareTechnology Corporation Livermore CA USA 2007

[35] R Vignjevic M Orłowski T De Vuyst and J C CampbellldquoA parametric study of bird strike on engine bladesrdquo Inter-national Journal of Impact Engineering vol 60 pp 44ndash572013

[36] G R Johnson and W H Cook ldquoFracture characteristics ofthree metals subjected to various strains strain rates tem-peratures and pressuresrdquo Engineering Fracture Mechanicsvol 21 no 1 pp 31ndash48 1985

[37] D Leseur Experimental Investigations of Material Models forTi-6A1-4V and 2024-T3 Lawrence Livermore National LabLivermore CA USA UCRL-ID-134691 1999

[38] C Yang Y Jiang W He J Na Z Li and B Xu ldquoAdaptiveparameter estimation and control design for robot manipu-lators with finite-time convergencerdquo IEEE Transactions onIndustrial Electronics vol 65 no 10 pp 8112ndash8123 2018

[39] C Yang G Peng L Cheng J Na and Z Li ldquoForce sensorlessadmittance control for teleoperation of uncertain robotmanipulator using neural networksrdquo IEEE Transactions onSystems Man and Cybernetics Systems pp 1ndash11 2019

[40] G Peng C Yang W He and C L P Chen ldquoForce sensorlessadmittance control with neural learning for robots with ac-tuator saturationrdquo IEEE Transactions on Industrial Elec-tronics vol 67 no 4 pp 3138ndash3148 2020

[41] C Yang H Wu Z Li W He N Wang and C-Y Su ldquoMindcontrol of a robotic arm with visual fusion technologyrdquo IEEETransactions on Industrial Informatics vol 14 no 9pp 3822ndash3830 2018

[42] H Lin T Zhang Z Chen H Song and C Yang ldquoAdaptivefuzzy Gaussian mixture models for shape approximation inrobot graspingrdquo International Journal of Fuzzy Systemsvol 21 no 4 pp 1026ndash1037 2019

Complexity 13

εf D1 + D2 exp D3σlowast

( 11138571113858 1113859 1 + D4 ln _εlowast1113858 1113859 1 + D5Tlowast

1113858 1113859

(14)

where ∆ε is the increment of equivalent plastic strain and σlowastis the mean normalized by the equivalent stress D1 D2 D3D4 and D5 are damage constants Failures are assumed tooccur when D 1

+e fan assembly is made of titanium alloy Ti-6Al-4Vand material parameters are derived from Ref [37] as listedin Table 1 In addition the MiendashGruneisen EOS (equation(3)) was defined in conjunction with the material consti-tutive model and parameters for Ti-6Al-4V are as followsC 513times103ms S1 1028 c0 123 and a 017 [35]

43 Stress Initialization +e rotating fan assembly un-dergoes a constant centrifugal force resulting in significantdeformation and initial stresses prior to impact It is nec-essary to evaluate the prestress of the rotating componentsespecially for blades [16] +us a preload analysis procedurewas conducted by assigning rotational velocity of 542 radsin an implicit solution+e initial stress of blades assembly isshown in Figure 8

5 Results and Discussion

51 Bird Model Calibration +e effect of the high-intensityshock wave on the blade damage can be ignored for the

z

x

v0α

(a)

z

x

v0α

(b)

z

y

v0β

(c)

z

y

v0β

(d)

Figure 6 Schematic of yaw and pitch angles (a) Positive yaw angle α (b) Negative yaw angle α (c) Positive pitch angle β (d) Negative pitchangle β

Tip on the leadingedge of fan blade

v0

EnlargedBird

Axis of rotary

Fan assembly

Back view

Mos

t crit

ical

loca

tion

Bottom view

1

2

3

4

56

XX

Y

ZZ

Y

ω = 542 rads

Figure 7 FE model of a fan assembly subjected to a bird

6 Complexity

reason that the initial bird loading area is almost like a pointloading [29] +e focus of blade damage analysis needs to beon accurately capturing the steady stagnation pressure phaseof impact [27] +us the stagnation pressure is representedas a criterion to calibrate bird models Numerical simulationof a normal impact on a rigid plate was established in ac-cordance with the experimental setup in Ref [26] A seg-ment sensor was assigned at the center of the plate to extractthe impact pressure +e stagnation pressures were esti-mated by averaging the pressure between T03 and 2T03[26] where T0 denotes the duration of the bird strike event+e theoretical curve of the stagnation pressure was de-termined by equation (3) and test data was derived fromRef [26] as shown in Figure 9+e numerical results were ina range between theoretical and experimental values +estagnation pressures captured by simulation of the real birdwere in closer agreement with the test data than those in thecase of the hemispherical-ended cylinder

52MostCritical IngestionParameters +e critical ingestionparameters are required to be identified for the specified birdingestion [30] In this section simulations of a full fan as-sembly subjected to a real bird were performed to determinethe critical location and ingestion speed under FARsect3376(c) (1) and FAR sect3376(c) (3)

521 Most Critical Ingestion Speed Complying with FARsect3376(c)(1) the critical ingestion speed is required to reflectthe most severe situation within the range of speeds used fornormal flight operations up to 460m (1500 feet) but not lessthan V1 minimum for airplanes [30] +erefore simulationsof the bird ingested at different speeds were performedaimed at the fan blade height of 80 Figure 10(a) shows theeffect of ingestion speed on impact loading history +e peakvalues of impact force generated by a real bird targeted atspeeds of 60ms 65ms 70ms 80ms 105ms and 130ms are 18335KN at 395ms 18253KN at 397ms 19891 KNat 348ms 21096KN at 348ms 21216KN at 299ms and17095KN at 250ms respectively As the speed increasesthe impact duration becomes shorter It is also found that thehigher the impact speed is the earlier the peak force occursAs the normalized sum of effective plastic strains shown inFigure 10(b) the ingestion speed of 65ms caused the mostsevere plastic strain+erefore 65ms was represented as themost critical speed

522 Most Critical Exposed Location To find out the mostcritical location under FAR sect3376(c)(1) the real bird aimedat different target points on the leading edge of blades wasevaluated at a speed of 65ms Figure 11(a) shows the effectof target location on the time histories of impact force +epeak values of impact force generated by a real bird aimed at

the fan blade height of 50 70 75 80 85 and 90are 16379KN at 384ms 16825KN at 430ms 17730KN at392ms 18253KN at 397ms 15592KN at 439ms and17169KN at 485ms respectively It can be observed thatthe impact location of 80 blade height reaches the max-imum value of peak impact force As the blade damageindicated in Figure 11(b) with the single medium birdtargeted at the fan blade height of 80 it occurs to the most

Table 1 Material properties of Ti-6Al-4V

Material ρ (kgm3) A (MPa) B (MPa) C m n D1 D2 D3 D4 D5

Ti-6Al-4V 44times103 1098 1092 0014 11 093 -009 025 -05 014 387

Effective stress (v ndash m)

6529e + 02

5804e + 02

5080e + 02

4355e + 02

3631e + 02

2906e + 02

2182e + 02

1457e + 02

7330e + 01

8491e ndash 01

7253e + 02

Figure 8 von Mises stress (MPa) of the fan assembly

Stag

natio

n pr

essu

re (M

Pa)

Theoretical pressure(z = 01)Hemispherical endedcylinderReal bird (mallard)

Experiment (pigeons)Experiment (porousgelatine)

0

2

4

6

8

10

12

110 120 130 140 150100Impact velocity (ms)

Figure 9 Calibration of stagnation pressures

Complexity 7

severe blade plastic strain As a result the most criticallocation for a middle-sized bird should be aimed at 80 ofthe fan blade height

53 Effect of Attitude Angles on Soft-Impact DamageFigure 12 shows the deformation of bird oriented along theengine axis As expected it can be clearly observed that priorto the impact of the bird torso the real bird was sliced intomore pieces +e orientation of bird has a direct effect on

slicing action of fan blades With respect to different atti-tudes the contact area and duration of bird strikes changeresulting in a significant impact on the effect of the birdstrike on rotatory blades and the possibility of blade failures

Figure 13 shows the effect of the yaw angle on impactloading history As shown in Figure 13(a) peak values ofimpact force generated by a real bird with respect to yawangle of 15deg 30deg 45deg and 60deg are 20153KN at 397ms17052KN at 431ms 17634KN at 433ms and 18697 KNat 428ms respectively As shown in Figure 13(b) the peak

Impa

ct fo

rce (

KN)

2 4 6 8 100Time (ms)

0

50

100

150

200

250

60 ms65 ms70 ms

80 ms105 ms130 ms

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

60 ms65 ms70 ms

80 ms105 ms130 ms

(b)

Figure 10 Effect of ingestion speed on the impact loading history and blade damage (a)+e impact loading history (b) Normalized sum ofeffective plastic strains

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

507075

808590

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

507075

808590

(b)

Figure 11 Effect of target location on the impact loading history and blade damage (a) +e impact loading history (b) Normalized sum ofeffective plastic strains

8 Complexity

values of impact force derived from a real bird with yawangle of minus 15deg minus 30deg minus 45deg and minus 60deg are 15732KN at 522ms13799KN at 433ms 20647KN at 370ms and 24666KNat 485ms respectively It can be concluded that a yaw angleof the bird would generate a variation in the impact loadinghistory and a negative yaw angle has a more significant effecton the impact loading history

Figure 14 shows the effect of pitch angle on the timehistories of impact loads As shown in Figure 14(a) withrespect to pitch angles of 15deg 30deg 45deg and 60deg the peakimpact loads are 20515KN at 435ms 22720 KN at 391ms26147 KN at 433ms and 26940 KN at 392ms respectivelyObviously the peak impact force increases as the positivepitch angle increases As shown in Figure 14(b) peak valuesof impact loading obtained from a real bird model with pitchangles of minus 15deg minus 30deg minus 45deg and minus 60deg are 16073KN at 393ms

16828KN at 390ms 18485KN at 386ms and 22406 KNat 385ms respectively It is observed that a negative yawangle would result in a variation in the impact loadinghistory

Figure 15 shows effective plastic strains of a single bladewhich undergoes the most severe plastic deformation duringimpact Obviously with the change of the bird attitude anglethe blade undergoes more severe plastic deformation Es-pecially as subjected to a real bird with a yaw angle of minus 45deg ora pitch angle of minus 60deg the blade suffers more than twice themagnitude of effective plastic strain compared with a realbird oriented along the engine centerline It can be con-cluded that attitude angles would increase the possibility offan blade failure Moreover the yaw angle of bird ingestionhas a significant effect on the location of the blade with themost severe plastic deformation

9972e + 02 1244e + 03 1255e + 031129e + 031004e + 038782e + 027527e + 026273e + 025018e + 023764e + 022509e + 021255e + 020000e + 00

1335e + 031314e + 031293e + 031163e + 031034e + 039049e + 027756e + 026463e + 025171e + 023878e + 022585e + 021293e + 020000e + 00

1182e + 031051e + 039197e + 027883e + 026569e + 025255e + 023942e + 022628e + 021314e + 020000e + 00

1202e + 031069e + 039351e + 028017e + 026683e + 025349e + 024015e + 022681e + 021347e + 021243e + 00

1120e + 039951e + 028707e + 027464e + 026220e + 024976e + 023732e + 022488e + 021244e + 020000e + 00

8975e + 027977e + 026980e + 025983e + 024986e + 023989e + 022992e + 021994e + 029972e + 010000e + 00

t = 10 ms t = 20 ms t = 25 ms

t = 45 mst = 35 mst = 30 ms

z

x

(a)

Figure 12 Bird deformation during the slicing action

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 13 Yaw angle effect on impact loading history (a) Positive yaw angle α (b) Negative yaw angle α

Complexity 9

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

300

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)Im

pact

forc

e (KN

)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 14 Pitch angle effect on impact loading history (a) Positive pitch angle β (b) Negative pitch angle β

Effec

tive p

lasti

c str

ains

0deg15deg on 3 blade30deg on 4 blade45deg on 4 blade60deg on 4 blade

ndash15deg on 6 bladendash30deg on 5 bladendash45deg on 3 bladendash60deg on 5 blade

2 4 6 8 10Time (ms)

00

12

24

36

48

60

(a)

Effec

tive p

lasti

c str

ains

of t

he b

lade

3

12

24

36

48

60

4 6 8 10Time (ms)

0deg15deg30deg45deg60deg

ndash15degndash30degndash45degndash60deg

00

2

(b)

Figure 15 Attitude angle effect on blade damage (a) Yaw angle α (b) Pitch angle β

10 Complexity

Figure 16 shows the effective plastic strains of the fanassembly It can be seen that a ldquocusprdquo plastic deformationoccurs at the leading edge and the maximum plastic strainoccurred to the impact location Compared with the plasticdeformation of a fan assembly during a normal impact (seeFigure 16(a)) subjected to a bird with an attitude angle ofα minus 45deg and β minus 60deg fan blade failure occurs at the impactlocation and the plastic deformation at the root of the fanblade leading edge is more significant which would increasethe risk of a fan blade release event

6 Conclusions

Considering a geometric shape similar to what has alreadybeen published as a real mallard [12] a real bird model wasdeveloped +en this paper discusses the effect of attitudeangles of the realistic bird model on the soft impact damageof a full fan assembly Besides the stagnation pressure isrepresented as a criterion to calibrate the developed bird

model Results show a good correlation with available testdata [26]

In accordance with certification requirements the mostcritical ingestion parameters for the new bird model wereinvestigated It is found that the real bird aimed at the fanblade height of 80 with an ingestion speed of 65msproduces the most severe damage to the full fan assembly

Complying with the critical ingestion parameters of thebird simulations of a full fan assembly subjected to a realbird with respect to various attitude angles reveal that bothyaw and pitch angles of the bird have a significant effect onthe impact loading history +e blade that undergoes thehighest magnitude of effective plastic strain would beconfronted with a more plastic deformation than that in thecase of a normal impact (attitude angle 0deg) even though theimpact loading decreases Especially as subjected to a realbird with yaw angle of minus 45deg or pitch angle of minus 60deg the bladesuffers more than twice the magnitude of effective plasticstrain compared with that of attitude angle 0deg and the plastic

1898e ndash 01

1705e ndash 01

1512e ndash 01

1319e ndash 01

1125e ndash 01

9323e ndash 02

7392e ndash 02

5460e ndash 02

3529e ndash 02

1598e ndash 02

ndash3332e ndash 032

3 4

(a)

3294e ndash 01

2960e ndash 01

2627e ndash 01

2294e ndash 01

1960e ndash 01

1627e ndash 01

1294e ndash 01

9605e ndash 02

6272e ndash 02

2939e ndash 02

ndash3947e ndash 033

(b)

2032e ndash 01

1825e ndash 01

1617e ndash 01

1410e ndash 01

1202e ndash 01

9950e ndash 02

7876e ndash 02

5803e ndash 02

3729e ndash 02

1655e ndash 02

ndash4189e ndash 033

(c)

Figure 16 Effective plastic strain contours at time t 10ms (a) 0deg (b) α minus 45deg (c) β minus 60deg

Complexity 11

deformation at the root of the leading edge is more sig-nificant which would increase the risk of a fan blade releaseevent

Moreover it is invaluable to ensure the safety of com-mercial airlines and engine manufacture by adopting therealistic bird model with the dangerous attitude angle in thecertification of engine designs for resistance to bird strikeswhich will provide sufficient resistance in actual bird-strikeevents However attitude angles of the bird were set upbased on the assumption in this paper If the bird attitudecould be determined through experiments or control al-gorithms [38ndash42] it is of great significance to investigate theeffect of bird attitude on soft impact damage as well as thedistribution of flocking bird

Data Availability

All data included in this study are available from the cor-responding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is research was supported by the National Key Researchand Development Program of China (Grant no2016YFB0201800) and the National Natural Science Foun-dation of China (Grant no 11772192)

References

[1] R H Mao S A Meguid and T Y Ng ldquoTransient threedimensional finite element analysis of a bird striking a fanbladerdquo International Journal of Mechanics and Materials inDesign vol 4 no 1 pp 79ndash96 2008

[2] S Heimbs ldquoComputational methods for bird strike simula-tions a reviewrdquo Computers amp Structures vol 89 no 23-24pp 2093ndash2112 2011

[3] J S Wilbeck Impact Behavior of Low Strength Projectiles AirForce Materials Lab Ohio AFFDL-TR-75-5 1978

[4] J S Wilbeck and J L Rand ldquo+e development of a substitutebird modelrdquo Journal of Engineering for Power vol 103 no 4pp 725ndash730 1981

[5] A Airoldi and B Cacchione ldquoModelling of impact forces andpressures in Lagrangian bird strike analysesrdquo InternationalJournal of Impact Engineering vol 32 no 10 pp 1651ndash16772006

[6] M A Lavoie A Gakwaya M N Ensan D G Zimcik andD Nandlall ldquoldquoBirdrsquos substitute test results and evaluation ofavailable numerical methodsrdquo International Journal of ImpactEngineering vol 36 no 10-11 pp 1276ndash1287 2009

[7] M Guida F Marulo M Meo and M Riccio ldquoEvaluation andvalidation of multi-physics FE methods to simulate bird strikeon a wing leading edgerdquo in Proceedings of the 13th EuropeanConference on Composite Materials (ECCM) StockholmSweden June 2008

[8] M A Lavoie A Gakwaya M N Ensan and D G ZimcikldquoReview of existing numerical methods and validation pro-cedure available for bird strike modellingrdquo International

Journal of Applied Mathematics and Computer Science vol 2no 4 pp 111ndash118 2007

[9] M A Lavoie A Gakwaya M Nejad Ensan and D G ZimcikldquoValidation of available approaches for numerical bird strikemodeling toolsrdquo International Review of Mechanical Engi-neering vol 1 no 4 pp 380ndash389 2007

[10] M A McCarthy J R Xiao C T McCarthy et al ldquoModellingof bird strike on an aircraft wing leading edge made from fibremetal laminates-part 2 modelling of impact with SPH birdmodelrdquo Applied Composite Materials vol 11 no 5pp 317ndash340 2004

[11] L Nizampatnam and W Horn ldquoInvestigation of equation ofstate models for predicting bird impact loadsrdquo in Proceedingsof the 46th AIAA Aerospace Sciences Meeting and Exhibitpp 7ndash10 2013

[12] R Hedayati M Sadighi and M Mohammadi-Aghdam ldquoOnthe difference of pressure readings from the numerical ex-perimental and theoretical results in different bird strikestudiesrdquo Aerospace Science and Technology vol 32 no 1pp 260ndash266 2014

[13] L S Nizampatnam Models and Methods for Bird Strike LoadPredictions Wichita State University Wichita Kansas 2007

[14] S McCallum H Shoji and H Akiyama ldquoDevelopment of anadvanced multi-material bird-strike model using thesmoothed particle Hydrodynamics methodrdquo InternationalJournal of Crashworthiness vol 18 no 6 pp 579ndash597 2013

[15] R Hedayati and S Ziaei-Rad ldquoA new bird model and theeffect of bird geometry in impacts from various orientationsrdquoAerospace Science and Technology vol 28 no 1 pp 9ndash202013

[16] A Serge ldquoSoft impacts on aerospace structuresrdquo Progress inAerospace Sciences vol 81 pp 1ndash17 2016

[17] J Kou F Xu S Ji and X Zhang ldquoInfluence of bird yawpitchorientation on bird-strike resistance of aircraft structuresrdquoExplosion and Shock Waves vol 37 no 5 pp 937ndash944 2017

[18] Z Zhang L Li and D Zhang ldquoEffect of arbitrary yawpitchangle in bird strike numerical simulation using SPHmethodrdquoAerospace Science and Technology vol 81 pp 284ndash293 2018

[19] D Zhang and Q Fei ldquoEffect of bird geometry and impactorientation in bird striking on a rotary jet-engine fan analysisusing SPH methodrdquo Aerospace Science and Technologyvol 54 pp 320ndash329 2016

[20] R H Mao S A Meguid and T Y Ng ldquoEffects of incidenceangle in bird strike on integrity of aero-engine fan bladerdquoInternational Journal of Crashworthiness vol 14 no 4pp 295ndash308 2009

[21] C Yang C Chen N Wang et al ldquoBiologically inspiredmotion modeling and neural control for robot learning fromdemonstrationsrdquo IEEE Transactions on Cognitive and De-velopmental Systems vol 11 no 2 pp 281ndash291 2019

[22] C Yang C Chen W He R Cui and Z Li ldquoRobot learningsystem based on adaptive neural control and dynamicmovement primitivesrdquo IEEE Transactions on Neural Networksand Learning Systems vol 30 no 3 pp 777ndash787 2019

[23] C Yang D Huang W He and L Cheng ldquoNeural control ofrobot manipulators with trajectory tracking constraints andinput saturationrdquo IEEE Transactions on Neural Networks andLearning Systems pp 1ndash12 2020

[24] H Huang T Zhang C Yang and C L P Chen ldquoMotorlearning and generalization using broad learning adaptiveneural controlrdquo IEEE Transactions on Industrial Electronicsvol 67 no 10 pp 8608ndash8617 2020

12 Complexity

[25] H Huang C Yang and C L P Chen ldquoOptimal robot-envi-ronment interaction under broad fuzzy neural adaptive controlrdquoIEEE Transactions on Cybernetics pp 1ndash12 2020

[26] F Allaeys G Luyckx W Van Paepegem and J DegrieckldquoNumerical and experimental investigation of the shock andsteady state pressures in the bird material during bird strikerdquoInternational Journal of Impact Engineering vol 107pp 12ndash22 2017

[27] M Kim A Zammit A Siddens and J Bayandor ldquoAn ex-tensive crashworthiness methodology for advanced pro-pulsion systems part I soft impact damage assessment ofcomposite fan stage assembliesrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting Including the New HorizonsForum and Aerospace Exposition Orlando Florida January2011

[28] R Hedayati and M Sadighi Bird Strike An Experimental+eoretical and Numerical Investigation Woodhead Pub-lishing in Mechanical Engineering Elsevier AmsterdamNetherlands 978-0-08-100093-9 2016

[29] S K Sinha K E Turner and N Jain ldquoDynamic loading onturbofan blades due to bird-strikerdquo Journal of Engineering forGas Turbines and Power vol 133 no 12 Article ID 1225042011

[30] Federal Aviation Administration ldquoElectronic code of federalRegulationsrdquo Title 14 Aeronautics and Space National Ar-chives and Records Administration Washington DC USAChapter I Subchapter C Part 33-Airworthiness StandardsAircraft Engines Section 3376 2020

[31] Federal Aviation Administration ldquoBird ingestion certificationstandardsrdquo Advisory Circular Federal Aviation Administra-tion Wasington DC USA 3376-1A 2009

[32] R A Dolbeer S E Wright J R Weller and M J BegierWildlife Strikes to Civil Aircraft in the United States 1990-2017National Wildlife Strike Database Washington DC USA2018

[33] C J Shepherd G J Appleby-+omas P J Hazell andD F Allsop ldquo+e dynamic behaviour of ballistic gelatinrdquo AIPConference Proceedings vol 1195 pp 1399ndash1402 2009

[34] J O Hallquist LS-DYNA+eory Manual Livermore SoftwareTechnology Corporation Livermore CA USA 2007

[35] R Vignjevic M Orłowski T De Vuyst and J C CampbellldquoA parametric study of bird strike on engine bladesrdquo Inter-national Journal of Impact Engineering vol 60 pp 44ndash572013

[36] G R Johnson and W H Cook ldquoFracture characteristics ofthree metals subjected to various strains strain rates tem-peratures and pressuresrdquo Engineering Fracture Mechanicsvol 21 no 1 pp 31ndash48 1985

[37] D Leseur Experimental Investigations of Material Models forTi-6A1-4V and 2024-T3 Lawrence Livermore National LabLivermore CA USA UCRL-ID-134691 1999

[38] C Yang Y Jiang W He J Na Z Li and B Xu ldquoAdaptiveparameter estimation and control design for robot manipu-lators with finite-time convergencerdquo IEEE Transactions onIndustrial Electronics vol 65 no 10 pp 8112ndash8123 2018

[39] C Yang G Peng L Cheng J Na and Z Li ldquoForce sensorlessadmittance control for teleoperation of uncertain robotmanipulator using neural networksrdquo IEEE Transactions onSystems Man and Cybernetics Systems pp 1ndash11 2019

[40] G Peng C Yang W He and C L P Chen ldquoForce sensorlessadmittance control with neural learning for robots with ac-tuator saturationrdquo IEEE Transactions on Industrial Elec-tronics vol 67 no 4 pp 3138ndash3148 2020

[41] C Yang H Wu Z Li W He N Wang and C-Y Su ldquoMindcontrol of a robotic arm with visual fusion technologyrdquo IEEETransactions on Industrial Informatics vol 14 no 9pp 3822ndash3830 2018

[42] H Lin T Zhang Z Chen H Song and C Yang ldquoAdaptivefuzzy Gaussian mixture models for shape approximation inrobot graspingrdquo International Journal of Fuzzy Systemsvol 21 no 4 pp 1026ndash1037 2019

Complexity 13

reason that the initial bird loading area is almost like a pointloading [29] +e focus of blade damage analysis needs to beon accurately capturing the steady stagnation pressure phaseof impact [27] +us the stagnation pressure is representedas a criterion to calibrate bird models Numerical simulationof a normal impact on a rigid plate was established in ac-cordance with the experimental setup in Ref [26] A seg-ment sensor was assigned at the center of the plate to extractthe impact pressure +e stagnation pressures were esti-mated by averaging the pressure between T03 and 2T03[26] where T0 denotes the duration of the bird strike event+e theoretical curve of the stagnation pressure was de-termined by equation (3) and test data was derived fromRef [26] as shown in Figure 9+e numerical results were ina range between theoretical and experimental values +estagnation pressures captured by simulation of the real birdwere in closer agreement with the test data than those in thecase of the hemispherical-ended cylinder

52MostCritical IngestionParameters +e critical ingestionparameters are required to be identified for the specified birdingestion [30] In this section simulations of a full fan as-sembly subjected to a real bird were performed to determinethe critical location and ingestion speed under FARsect3376(c) (1) and FAR sect3376(c) (3)

521 Most Critical Ingestion Speed Complying with FARsect3376(c)(1) the critical ingestion speed is required to reflectthe most severe situation within the range of speeds used fornormal flight operations up to 460m (1500 feet) but not lessthan V1 minimum for airplanes [30] +erefore simulationsof the bird ingested at different speeds were performedaimed at the fan blade height of 80 Figure 10(a) shows theeffect of ingestion speed on impact loading history +e peakvalues of impact force generated by a real bird targeted atspeeds of 60ms 65ms 70ms 80ms 105ms and 130ms are 18335KN at 395ms 18253KN at 397ms 19891 KNat 348ms 21096KN at 348ms 21216KN at 299ms and17095KN at 250ms respectively As the speed increasesthe impact duration becomes shorter It is also found that thehigher the impact speed is the earlier the peak force occursAs the normalized sum of effective plastic strains shown inFigure 10(b) the ingestion speed of 65ms caused the mostsevere plastic strain+erefore 65ms was represented as themost critical speed

522 Most Critical Exposed Location To find out the mostcritical location under FAR sect3376(c)(1) the real bird aimedat different target points on the leading edge of blades wasevaluated at a speed of 65ms Figure 11(a) shows the effectof target location on the time histories of impact force +epeak values of impact force generated by a real bird aimed at

the fan blade height of 50 70 75 80 85 and 90are 16379KN at 384ms 16825KN at 430ms 17730KN at392ms 18253KN at 397ms 15592KN at 439ms and17169KN at 485ms respectively It can be observed thatthe impact location of 80 blade height reaches the max-imum value of peak impact force As the blade damageindicated in Figure 11(b) with the single medium birdtargeted at the fan blade height of 80 it occurs to the most

Table 1 Material properties of Ti-6Al-4V

Material ρ (kgm3) A (MPa) B (MPa) C m n D1 D2 D3 D4 D5

Ti-6Al-4V 44times103 1098 1092 0014 11 093 -009 025 -05 014 387

Effective stress (v ndash m)

6529e + 02

5804e + 02

5080e + 02

4355e + 02

3631e + 02

2906e + 02

2182e + 02

1457e + 02

7330e + 01

8491e ndash 01

7253e + 02

Figure 8 von Mises stress (MPa) of the fan assembly

Stag

natio

n pr

essu

re (M

Pa)

Theoretical pressure(z = 01)Hemispherical endedcylinderReal bird (mallard)

Experiment (pigeons)Experiment (porousgelatine)

0

2

4

6

8

10

12

110 120 130 140 150100Impact velocity (ms)

Figure 9 Calibration of stagnation pressures

Complexity 7

severe blade plastic strain As a result the most criticallocation for a middle-sized bird should be aimed at 80 ofthe fan blade height

53 Effect of Attitude Angles on Soft-Impact DamageFigure 12 shows the deformation of bird oriented along theengine axis As expected it can be clearly observed that priorto the impact of the bird torso the real bird was sliced intomore pieces +e orientation of bird has a direct effect on

slicing action of fan blades With respect to different atti-tudes the contact area and duration of bird strikes changeresulting in a significant impact on the effect of the birdstrike on rotatory blades and the possibility of blade failures

Figure 13 shows the effect of the yaw angle on impactloading history As shown in Figure 13(a) peak values ofimpact force generated by a real bird with respect to yawangle of 15deg 30deg 45deg and 60deg are 20153KN at 397ms17052KN at 431ms 17634KN at 433ms and 18697 KNat 428ms respectively As shown in Figure 13(b) the peak

Impa

ct fo

rce (

KN)

2 4 6 8 100Time (ms)

0

50

100

150

200

250

60 ms65 ms70 ms

80 ms105 ms130 ms

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

60 ms65 ms70 ms

80 ms105 ms130 ms

(b)

Figure 10 Effect of ingestion speed on the impact loading history and blade damage (a)+e impact loading history (b) Normalized sum ofeffective plastic strains

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

507075

808590

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

507075

808590

(b)

Figure 11 Effect of target location on the impact loading history and blade damage (a) +e impact loading history (b) Normalized sum ofeffective plastic strains

8 Complexity

values of impact force derived from a real bird with yawangle of minus 15deg minus 30deg minus 45deg and minus 60deg are 15732KN at 522ms13799KN at 433ms 20647KN at 370ms and 24666KNat 485ms respectively It can be concluded that a yaw angleof the bird would generate a variation in the impact loadinghistory and a negative yaw angle has a more significant effecton the impact loading history

Figure 14 shows the effect of pitch angle on the timehistories of impact loads As shown in Figure 14(a) withrespect to pitch angles of 15deg 30deg 45deg and 60deg the peakimpact loads are 20515KN at 435ms 22720 KN at 391ms26147 KN at 433ms and 26940 KN at 392ms respectivelyObviously the peak impact force increases as the positivepitch angle increases As shown in Figure 14(b) peak valuesof impact loading obtained from a real bird model with pitchangles of minus 15deg minus 30deg minus 45deg and minus 60deg are 16073KN at 393ms

16828KN at 390ms 18485KN at 386ms and 22406 KNat 385ms respectively It is observed that a negative yawangle would result in a variation in the impact loadinghistory

Figure 15 shows effective plastic strains of a single bladewhich undergoes the most severe plastic deformation duringimpact Obviously with the change of the bird attitude anglethe blade undergoes more severe plastic deformation Es-pecially as subjected to a real bird with a yaw angle of minus 45deg ora pitch angle of minus 60deg the blade suffers more than twice themagnitude of effective plastic strain compared with a realbird oriented along the engine centerline It can be con-cluded that attitude angles would increase the possibility offan blade failure Moreover the yaw angle of bird ingestionhas a significant effect on the location of the blade with themost severe plastic deformation

9972e + 02 1244e + 03 1255e + 031129e + 031004e + 038782e + 027527e + 026273e + 025018e + 023764e + 022509e + 021255e + 020000e + 00

1335e + 031314e + 031293e + 031163e + 031034e + 039049e + 027756e + 026463e + 025171e + 023878e + 022585e + 021293e + 020000e + 00

1182e + 031051e + 039197e + 027883e + 026569e + 025255e + 023942e + 022628e + 021314e + 020000e + 00

1202e + 031069e + 039351e + 028017e + 026683e + 025349e + 024015e + 022681e + 021347e + 021243e + 00

1120e + 039951e + 028707e + 027464e + 026220e + 024976e + 023732e + 022488e + 021244e + 020000e + 00

8975e + 027977e + 026980e + 025983e + 024986e + 023989e + 022992e + 021994e + 029972e + 010000e + 00

t = 10 ms t = 20 ms t = 25 ms

t = 45 mst = 35 mst = 30 ms

z

x

(a)

Figure 12 Bird deformation during the slicing action

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 13 Yaw angle effect on impact loading history (a) Positive yaw angle α (b) Negative yaw angle α

Complexity 9

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

300

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)Im

pact

forc

e (KN

)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 14 Pitch angle effect on impact loading history (a) Positive pitch angle β (b) Negative pitch angle β

Effec

tive p

lasti

c str

ains

0deg15deg on 3 blade30deg on 4 blade45deg on 4 blade60deg on 4 blade

ndash15deg on 6 bladendash30deg on 5 bladendash45deg on 3 bladendash60deg on 5 blade

2 4 6 8 10Time (ms)

00

12

24

36

48

60

(a)

Effec

tive p

lasti

c str

ains

of t

he b

lade

3

12

24

36

48

60

4 6 8 10Time (ms)

0deg15deg30deg45deg60deg

ndash15degndash30degndash45degndash60deg

00

2

(b)

Figure 15 Attitude angle effect on blade damage (a) Yaw angle α (b) Pitch angle β

10 Complexity

Figure 16 shows the effective plastic strains of the fanassembly It can be seen that a ldquocusprdquo plastic deformationoccurs at the leading edge and the maximum plastic strainoccurred to the impact location Compared with the plasticdeformation of a fan assembly during a normal impact (seeFigure 16(a)) subjected to a bird with an attitude angle ofα minus 45deg and β minus 60deg fan blade failure occurs at the impactlocation and the plastic deformation at the root of the fanblade leading edge is more significant which would increasethe risk of a fan blade release event

6 Conclusions

Considering a geometric shape similar to what has alreadybeen published as a real mallard [12] a real bird model wasdeveloped +en this paper discusses the effect of attitudeangles of the realistic bird model on the soft impact damageof a full fan assembly Besides the stagnation pressure isrepresented as a criterion to calibrate the developed bird

model Results show a good correlation with available testdata [26]

In accordance with certification requirements the mostcritical ingestion parameters for the new bird model wereinvestigated It is found that the real bird aimed at the fanblade height of 80 with an ingestion speed of 65msproduces the most severe damage to the full fan assembly

Complying with the critical ingestion parameters of thebird simulations of a full fan assembly subjected to a realbird with respect to various attitude angles reveal that bothyaw and pitch angles of the bird have a significant effect onthe impact loading history +e blade that undergoes thehighest magnitude of effective plastic strain would beconfronted with a more plastic deformation than that in thecase of a normal impact (attitude angle 0deg) even though theimpact loading decreases Especially as subjected to a realbird with yaw angle of minus 45deg or pitch angle of minus 60deg the bladesuffers more than twice the magnitude of effective plasticstrain compared with that of attitude angle 0deg and the plastic

1898e ndash 01

1705e ndash 01

1512e ndash 01

1319e ndash 01

1125e ndash 01

9323e ndash 02

7392e ndash 02

5460e ndash 02

3529e ndash 02

1598e ndash 02

ndash3332e ndash 032

3 4

(a)

3294e ndash 01

2960e ndash 01

2627e ndash 01

2294e ndash 01

1960e ndash 01

1627e ndash 01

1294e ndash 01

9605e ndash 02

6272e ndash 02

2939e ndash 02

ndash3947e ndash 033

(b)

2032e ndash 01

1825e ndash 01

1617e ndash 01

1410e ndash 01

1202e ndash 01

9950e ndash 02

7876e ndash 02

5803e ndash 02

3729e ndash 02

1655e ndash 02

ndash4189e ndash 033

(c)

Figure 16 Effective plastic strain contours at time t 10ms (a) 0deg (b) α minus 45deg (c) β minus 60deg

Complexity 11

deformation at the root of the leading edge is more sig-nificant which would increase the risk of a fan blade releaseevent

Moreover it is invaluable to ensure the safety of com-mercial airlines and engine manufacture by adopting therealistic bird model with the dangerous attitude angle in thecertification of engine designs for resistance to bird strikeswhich will provide sufficient resistance in actual bird-strikeevents However attitude angles of the bird were set upbased on the assumption in this paper If the bird attitudecould be determined through experiments or control al-gorithms [38ndash42] it is of great significance to investigate theeffect of bird attitude on soft impact damage as well as thedistribution of flocking bird

Data Availability

All data included in this study are available from the cor-responding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is research was supported by the National Key Researchand Development Program of China (Grant no2016YFB0201800) and the National Natural Science Foun-dation of China (Grant no 11772192)

References

[1] R H Mao S A Meguid and T Y Ng ldquoTransient threedimensional finite element analysis of a bird striking a fanbladerdquo International Journal of Mechanics and Materials inDesign vol 4 no 1 pp 79ndash96 2008

[2] S Heimbs ldquoComputational methods for bird strike simula-tions a reviewrdquo Computers amp Structures vol 89 no 23-24pp 2093ndash2112 2011

[3] J S Wilbeck Impact Behavior of Low Strength Projectiles AirForce Materials Lab Ohio AFFDL-TR-75-5 1978

[4] J S Wilbeck and J L Rand ldquo+e development of a substitutebird modelrdquo Journal of Engineering for Power vol 103 no 4pp 725ndash730 1981

[5] A Airoldi and B Cacchione ldquoModelling of impact forces andpressures in Lagrangian bird strike analysesrdquo InternationalJournal of Impact Engineering vol 32 no 10 pp 1651ndash16772006

[6] M A Lavoie A Gakwaya M N Ensan D G Zimcik andD Nandlall ldquoldquoBirdrsquos substitute test results and evaluation ofavailable numerical methodsrdquo International Journal of ImpactEngineering vol 36 no 10-11 pp 1276ndash1287 2009

[7] M Guida F Marulo M Meo and M Riccio ldquoEvaluation andvalidation of multi-physics FE methods to simulate bird strikeon a wing leading edgerdquo in Proceedings of the 13th EuropeanConference on Composite Materials (ECCM) StockholmSweden June 2008

[8] M A Lavoie A Gakwaya M N Ensan and D G ZimcikldquoReview of existing numerical methods and validation pro-cedure available for bird strike modellingrdquo International

Journal of Applied Mathematics and Computer Science vol 2no 4 pp 111ndash118 2007

[9] M A Lavoie A Gakwaya M Nejad Ensan and D G ZimcikldquoValidation of available approaches for numerical bird strikemodeling toolsrdquo International Review of Mechanical Engi-neering vol 1 no 4 pp 380ndash389 2007

[10] M A McCarthy J R Xiao C T McCarthy et al ldquoModellingof bird strike on an aircraft wing leading edge made from fibremetal laminates-part 2 modelling of impact with SPH birdmodelrdquo Applied Composite Materials vol 11 no 5pp 317ndash340 2004

[11] L Nizampatnam and W Horn ldquoInvestigation of equation ofstate models for predicting bird impact loadsrdquo in Proceedingsof the 46th AIAA Aerospace Sciences Meeting and Exhibitpp 7ndash10 2013

[12] R Hedayati M Sadighi and M Mohammadi-Aghdam ldquoOnthe difference of pressure readings from the numerical ex-perimental and theoretical results in different bird strikestudiesrdquo Aerospace Science and Technology vol 32 no 1pp 260ndash266 2014

[13] L S Nizampatnam Models and Methods for Bird Strike LoadPredictions Wichita State University Wichita Kansas 2007

[14] S McCallum H Shoji and H Akiyama ldquoDevelopment of anadvanced multi-material bird-strike model using thesmoothed particle Hydrodynamics methodrdquo InternationalJournal of Crashworthiness vol 18 no 6 pp 579ndash597 2013

[15] R Hedayati and S Ziaei-Rad ldquoA new bird model and theeffect of bird geometry in impacts from various orientationsrdquoAerospace Science and Technology vol 28 no 1 pp 9ndash202013

[16] A Serge ldquoSoft impacts on aerospace structuresrdquo Progress inAerospace Sciences vol 81 pp 1ndash17 2016

[17] J Kou F Xu S Ji and X Zhang ldquoInfluence of bird yawpitchorientation on bird-strike resistance of aircraft structuresrdquoExplosion and Shock Waves vol 37 no 5 pp 937ndash944 2017

[18] Z Zhang L Li and D Zhang ldquoEffect of arbitrary yawpitchangle in bird strike numerical simulation using SPHmethodrdquoAerospace Science and Technology vol 81 pp 284ndash293 2018

[19] D Zhang and Q Fei ldquoEffect of bird geometry and impactorientation in bird striking on a rotary jet-engine fan analysisusing SPH methodrdquo Aerospace Science and Technologyvol 54 pp 320ndash329 2016

[20] R H Mao S A Meguid and T Y Ng ldquoEffects of incidenceangle in bird strike on integrity of aero-engine fan bladerdquoInternational Journal of Crashworthiness vol 14 no 4pp 295ndash308 2009

[21] C Yang C Chen N Wang et al ldquoBiologically inspiredmotion modeling and neural control for robot learning fromdemonstrationsrdquo IEEE Transactions on Cognitive and De-velopmental Systems vol 11 no 2 pp 281ndash291 2019

[22] C Yang C Chen W He R Cui and Z Li ldquoRobot learningsystem based on adaptive neural control and dynamicmovement primitivesrdquo IEEE Transactions on Neural Networksand Learning Systems vol 30 no 3 pp 777ndash787 2019

[23] C Yang D Huang W He and L Cheng ldquoNeural control ofrobot manipulators with trajectory tracking constraints andinput saturationrdquo IEEE Transactions on Neural Networks andLearning Systems pp 1ndash12 2020

[24] H Huang T Zhang C Yang and C L P Chen ldquoMotorlearning and generalization using broad learning adaptiveneural controlrdquo IEEE Transactions on Industrial Electronicsvol 67 no 10 pp 8608ndash8617 2020

12 Complexity

[25] H Huang C Yang and C L P Chen ldquoOptimal robot-envi-ronment interaction under broad fuzzy neural adaptive controlrdquoIEEE Transactions on Cybernetics pp 1ndash12 2020

[26] F Allaeys G Luyckx W Van Paepegem and J DegrieckldquoNumerical and experimental investigation of the shock andsteady state pressures in the bird material during bird strikerdquoInternational Journal of Impact Engineering vol 107pp 12ndash22 2017

[27] M Kim A Zammit A Siddens and J Bayandor ldquoAn ex-tensive crashworthiness methodology for advanced pro-pulsion systems part I soft impact damage assessment ofcomposite fan stage assembliesrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting Including the New HorizonsForum and Aerospace Exposition Orlando Florida January2011

[28] R Hedayati and M Sadighi Bird Strike An Experimental+eoretical and Numerical Investigation Woodhead Pub-lishing in Mechanical Engineering Elsevier AmsterdamNetherlands 978-0-08-100093-9 2016

[29] S K Sinha K E Turner and N Jain ldquoDynamic loading onturbofan blades due to bird-strikerdquo Journal of Engineering forGas Turbines and Power vol 133 no 12 Article ID 1225042011

[30] Federal Aviation Administration ldquoElectronic code of federalRegulationsrdquo Title 14 Aeronautics and Space National Ar-chives and Records Administration Washington DC USAChapter I Subchapter C Part 33-Airworthiness StandardsAircraft Engines Section 3376 2020

[31] Federal Aviation Administration ldquoBird ingestion certificationstandardsrdquo Advisory Circular Federal Aviation Administra-tion Wasington DC USA 3376-1A 2009

[32] R A Dolbeer S E Wright J R Weller and M J BegierWildlife Strikes to Civil Aircraft in the United States 1990-2017National Wildlife Strike Database Washington DC USA2018

[33] C J Shepherd G J Appleby-+omas P J Hazell andD F Allsop ldquo+e dynamic behaviour of ballistic gelatinrdquo AIPConference Proceedings vol 1195 pp 1399ndash1402 2009

[34] J O Hallquist LS-DYNA+eory Manual Livermore SoftwareTechnology Corporation Livermore CA USA 2007

[35] R Vignjevic M Orłowski T De Vuyst and J C CampbellldquoA parametric study of bird strike on engine bladesrdquo Inter-national Journal of Impact Engineering vol 60 pp 44ndash572013

[36] G R Johnson and W H Cook ldquoFracture characteristics ofthree metals subjected to various strains strain rates tem-peratures and pressuresrdquo Engineering Fracture Mechanicsvol 21 no 1 pp 31ndash48 1985

[37] D Leseur Experimental Investigations of Material Models forTi-6A1-4V and 2024-T3 Lawrence Livermore National LabLivermore CA USA UCRL-ID-134691 1999

[38] C Yang Y Jiang W He J Na Z Li and B Xu ldquoAdaptiveparameter estimation and control design for robot manipu-lators with finite-time convergencerdquo IEEE Transactions onIndustrial Electronics vol 65 no 10 pp 8112ndash8123 2018

[39] C Yang G Peng L Cheng J Na and Z Li ldquoForce sensorlessadmittance control for teleoperation of uncertain robotmanipulator using neural networksrdquo IEEE Transactions onSystems Man and Cybernetics Systems pp 1ndash11 2019

[40] G Peng C Yang W He and C L P Chen ldquoForce sensorlessadmittance control with neural learning for robots with ac-tuator saturationrdquo IEEE Transactions on Industrial Elec-tronics vol 67 no 4 pp 3138ndash3148 2020

[41] C Yang H Wu Z Li W He N Wang and C-Y Su ldquoMindcontrol of a robotic arm with visual fusion technologyrdquo IEEETransactions on Industrial Informatics vol 14 no 9pp 3822ndash3830 2018

[42] H Lin T Zhang Z Chen H Song and C Yang ldquoAdaptivefuzzy Gaussian mixture models for shape approximation inrobot graspingrdquo International Journal of Fuzzy Systemsvol 21 no 4 pp 1026ndash1037 2019

Complexity 13

severe blade plastic strain As a result the most criticallocation for a middle-sized bird should be aimed at 80 ofthe fan blade height

53 Effect of Attitude Angles on Soft-Impact DamageFigure 12 shows the deformation of bird oriented along theengine axis As expected it can be clearly observed that priorto the impact of the bird torso the real bird was sliced intomore pieces +e orientation of bird has a direct effect on

slicing action of fan blades With respect to different atti-tudes the contact area and duration of bird strikes changeresulting in a significant impact on the effect of the birdstrike on rotatory blades and the possibility of blade failures

Figure 13 shows the effect of the yaw angle on impactloading history As shown in Figure 13(a) peak values ofimpact force generated by a real bird with respect to yawangle of 15deg 30deg 45deg and 60deg are 20153KN at 397ms17052KN at 431ms 17634KN at 433ms and 18697 KNat 428ms respectively As shown in Figure 13(b) the peak

Impa

ct fo

rce (

KN)

2 4 6 8 100Time (ms)

0

50

100

150

200

250

60 ms65 ms70 ms

80 ms105 ms130 ms

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

60 ms65 ms70 ms

80 ms105 ms130 ms

(b)

Figure 10 Effect of ingestion speed on the impact loading history and blade damage (a)+e impact loading history (b) Normalized sum ofeffective plastic strains

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

507075

808590

(a)

Nor

mal

ized

sum

of e

ffect

ive p

lasti

c str

ains

00

02

04

06

08

10

2 4 6 8 100Time (ms)

507075

808590

(b)

Figure 11 Effect of target location on the impact loading history and blade damage (a) +e impact loading history (b) Normalized sum ofeffective plastic strains

8 Complexity

values of impact force derived from a real bird with yawangle of minus 15deg minus 30deg minus 45deg and minus 60deg are 15732KN at 522ms13799KN at 433ms 20647KN at 370ms and 24666KNat 485ms respectively It can be concluded that a yaw angleof the bird would generate a variation in the impact loadinghistory and a negative yaw angle has a more significant effecton the impact loading history

Figure 14 shows the effect of pitch angle on the timehistories of impact loads As shown in Figure 14(a) withrespect to pitch angles of 15deg 30deg 45deg and 60deg the peakimpact loads are 20515KN at 435ms 22720 KN at 391ms26147 KN at 433ms and 26940 KN at 392ms respectivelyObviously the peak impact force increases as the positivepitch angle increases As shown in Figure 14(b) peak valuesof impact loading obtained from a real bird model with pitchangles of minus 15deg minus 30deg minus 45deg and minus 60deg are 16073KN at 393ms

16828KN at 390ms 18485KN at 386ms and 22406 KNat 385ms respectively It is observed that a negative yawangle would result in a variation in the impact loadinghistory

Figure 15 shows effective plastic strains of a single bladewhich undergoes the most severe plastic deformation duringimpact Obviously with the change of the bird attitude anglethe blade undergoes more severe plastic deformation Es-pecially as subjected to a real bird with a yaw angle of minus 45deg ora pitch angle of minus 60deg the blade suffers more than twice themagnitude of effective plastic strain compared with a realbird oriented along the engine centerline It can be con-cluded that attitude angles would increase the possibility offan blade failure Moreover the yaw angle of bird ingestionhas a significant effect on the location of the blade with themost severe plastic deformation

9972e + 02 1244e + 03 1255e + 031129e + 031004e + 038782e + 027527e + 026273e + 025018e + 023764e + 022509e + 021255e + 020000e + 00

1335e + 031314e + 031293e + 031163e + 031034e + 039049e + 027756e + 026463e + 025171e + 023878e + 022585e + 021293e + 020000e + 00

1182e + 031051e + 039197e + 027883e + 026569e + 025255e + 023942e + 022628e + 021314e + 020000e + 00

1202e + 031069e + 039351e + 028017e + 026683e + 025349e + 024015e + 022681e + 021347e + 021243e + 00

1120e + 039951e + 028707e + 027464e + 026220e + 024976e + 023732e + 022488e + 021244e + 020000e + 00

8975e + 027977e + 026980e + 025983e + 024986e + 023989e + 022992e + 021994e + 029972e + 010000e + 00

t = 10 ms t = 20 ms t = 25 ms

t = 45 mst = 35 mst = 30 ms

z

x

(a)

Figure 12 Bird deformation during the slicing action

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 13 Yaw angle effect on impact loading history (a) Positive yaw angle α (b) Negative yaw angle α

Complexity 9

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

300

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)Im

pact

forc

e (KN

)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 14 Pitch angle effect on impact loading history (a) Positive pitch angle β (b) Negative pitch angle β

Effec

tive p

lasti

c str

ains

0deg15deg on 3 blade30deg on 4 blade45deg on 4 blade60deg on 4 blade

ndash15deg on 6 bladendash30deg on 5 bladendash45deg on 3 bladendash60deg on 5 blade

2 4 6 8 10Time (ms)

00

12

24

36

48

60

(a)

Effec

tive p

lasti

c str

ains

of t

he b

lade

3

12

24

36

48

60

4 6 8 10Time (ms)

0deg15deg30deg45deg60deg

ndash15degndash30degndash45degndash60deg

00

2

(b)

Figure 15 Attitude angle effect on blade damage (a) Yaw angle α (b) Pitch angle β

10 Complexity

Figure 16 shows the effective plastic strains of the fanassembly It can be seen that a ldquocusprdquo plastic deformationoccurs at the leading edge and the maximum plastic strainoccurred to the impact location Compared with the plasticdeformation of a fan assembly during a normal impact (seeFigure 16(a)) subjected to a bird with an attitude angle ofα minus 45deg and β minus 60deg fan blade failure occurs at the impactlocation and the plastic deformation at the root of the fanblade leading edge is more significant which would increasethe risk of a fan blade release event

6 Conclusions

Considering a geometric shape similar to what has alreadybeen published as a real mallard [12] a real bird model wasdeveloped +en this paper discusses the effect of attitudeangles of the realistic bird model on the soft impact damageof a full fan assembly Besides the stagnation pressure isrepresented as a criterion to calibrate the developed bird

model Results show a good correlation with available testdata [26]

In accordance with certification requirements the mostcritical ingestion parameters for the new bird model wereinvestigated It is found that the real bird aimed at the fanblade height of 80 with an ingestion speed of 65msproduces the most severe damage to the full fan assembly

Complying with the critical ingestion parameters of thebird simulations of a full fan assembly subjected to a realbird with respect to various attitude angles reveal that bothyaw and pitch angles of the bird have a significant effect onthe impact loading history +e blade that undergoes thehighest magnitude of effective plastic strain would beconfronted with a more plastic deformation than that in thecase of a normal impact (attitude angle 0deg) even though theimpact loading decreases Especially as subjected to a realbird with yaw angle of minus 45deg or pitch angle of minus 60deg the bladesuffers more than twice the magnitude of effective plasticstrain compared with that of attitude angle 0deg and the plastic

1898e ndash 01

1705e ndash 01

1512e ndash 01

1319e ndash 01

1125e ndash 01

9323e ndash 02

7392e ndash 02

5460e ndash 02

3529e ndash 02

1598e ndash 02

ndash3332e ndash 032

3 4

(a)

3294e ndash 01

2960e ndash 01

2627e ndash 01

2294e ndash 01

1960e ndash 01

1627e ndash 01

1294e ndash 01

9605e ndash 02

6272e ndash 02

2939e ndash 02

ndash3947e ndash 033

(b)

2032e ndash 01

1825e ndash 01

1617e ndash 01

1410e ndash 01

1202e ndash 01

9950e ndash 02

7876e ndash 02

5803e ndash 02

3729e ndash 02

1655e ndash 02

ndash4189e ndash 033

(c)

Figure 16 Effective plastic strain contours at time t 10ms (a) 0deg (b) α minus 45deg (c) β minus 60deg

Complexity 11

deformation at the root of the leading edge is more sig-nificant which would increase the risk of a fan blade releaseevent

Moreover it is invaluable to ensure the safety of com-mercial airlines and engine manufacture by adopting therealistic bird model with the dangerous attitude angle in thecertification of engine designs for resistance to bird strikeswhich will provide sufficient resistance in actual bird-strikeevents However attitude angles of the bird were set upbased on the assumption in this paper If the bird attitudecould be determined through experiments or control al-gorithms [38ndash42] it is of great significance to investigate theeffect of bird attitude on soft impact damage as well as thedistribution of flocking bird

Data Availability

All data included in this study are available from the cor-responding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is research was supported by the National Key Researchand Development Program of China (Grant no2016YFB0201800) and the National Natural Science Foun-dation of China (Grant no 11772192)

References

[1] R H Mao S A Meguid and T Y Ng ldquoTransient threedimensional finite element analysis of a bird striking a fanbladerdquo International Journal of Mechanics and Materials inDesign vol 4 no 1 pp 79ndash96 2008

[2] S Heimbs ldquoComputational methods for bird strike simula-tions a reviewrdquo Computers amp Structures vol 89 no 23-24pp 2093ndash2112 2011

[3] J S Wilbeck Impact Behavior of Low Strength Projectiles AirForce Materials Lab Ohio AFFDL-TR-75-5 1978

[4] J S Wilbeck and J L Rand ldquo+e development of a substitutebird modelrdquo Journal of Engineering for Power vol 103 no 4pp 725ndash730 1981

[5] A Airoldi and B Cacchione ldquoModelling of impact forces andpressures in Lagrangian bird strike analysesrdquo InternationalJournal of Impact Engineering vol 32 no 10 pp 1651ndash16772006

[6] M A Lavoie A Gakwaya M N Ensan D G Zimcik andD Nandlall ldquoldquoBirdrsquos substitute test results and evaluation ofavailable numerical methodsrdquo International Journal of ImpactEngineering vol 36 no 10-11 pp 1276ndash1287 2009

[7] M Guida F Marulo M Meo and M Riccio ldquoEvaluation andvalidation of multi-physics FE methods to simulate bird strikeon a wing leading edgerdquo in Proceedings of the 13th EuropeanConference on Composite Materials (ECCM) StockholmSweden June 2008

[8] M A Lavoie A Gakwaya M N Ensan and D G ZimcikldquoReview of existing numerical methods and validation pro-cedure available for bird strike modellingrdquo International

Journal of Applied Mathematics and Computer Science vol 2no 4 pp 111ndash118 2007

[9] M A Lavoie A Gakwaya M Nejad Ensan and D G ZimcikldquoValidation of available approaches for numerical bird strikemodeling toolsrdquo International Review of Mechanical Engi-neering vol 1 no 4 pp 380ndash389 2007

[10] M A McCarthy J R Xiao C T McCarthy et al ldquoModellingof bird strike on an aircraft wing leading edge made from fibremetal laminates-part 2 modelling of impact with SPH birdmodelrdquo Applied Composite Materials vol 11 no 5pp 317ndash340 2004

[11] L Nizampatnam and W Horn ldquoInvestigation of equation ofstate models for predicting bird impact loadsrdquo in Proceedingsof the 46th AIAA Aerospace Sciences Meeting and Exhibitpp 7ndash10 2013

[12] R Hedayati M Sadighi and M Mohammadi-Aghdam ldquoOnthe difference of pressure readings from the numerical ex-perimental and theoretical results in different bird strikestudiesrdquo Aerospace Science and Technology vol 32 no 1pp 260ndash266 2014

[13] L S Nizampatnam Models and Methods for Bird Strike LoadPredictions Wichita State University Wichita Kansas 2007

[14] S McCallum H Shoji and H Akiyama ldquoDevelopment of anadvanced multi-material bird-strike model using thesmoothed particle Hydrodynamics methodrdquo InternationalJournal of Crashworthiness vol 18 no 6 pp 579ndash597 2013

[15] R Hedayati and S Ziaei-Rad ldquoA new bird model and theeffect of bird geometry in impacts from various orientationsrdquoAerospace Science and Technology vol 28 no 1 pp 9ndash202013

[16] A Serge ldquoSoft impacts on aerospace structuresrdquo Progress inAerospace Sciences vol 81 pp 1ndash17 2016

[17] J Kou F Xu S Ji and X Zhang ldquoInfluence of bird yawpitchorientation on bird-strike resistance of aircraft structuresrdquoExplosion and Shock Waves vol 37 no 5 pp 937ndash944 2017

[18] Z Zhang L Li and D Zhang ldquoEffect of arbitrary yawpitchangle in bird strike numerical simulation using SPHmethodrdquoAerospace Science and Technology vol 81 pp 284ndash293 2018

[19] D Zhang and Q Fei ldquoEffect of bird geometry and impactorientation in bird striking on a rotary jet-engine fan analysisusing SPH methodrdquo Aerospace Science and Technologyvol 54 pp 320ndash329 2016

[20] R H Mao S A Meguid and T Y Ng ldquoEffects of incidenceangle in bird strike on integrity of aero-engine fan bladerdquoInternational Journal of Crashworthiness vol 14 no 4pp 295ndash308 2009

[21] C Yang C Chen N Wang et al ldquoBiologically inspiredmotion modeling and neural control for robot learning fromdemonstrationsrdquo IEEE Transactions on Cognitive and De-velopmental Systems vol 11 no 2 pp 281ndash291 2019

[22] C Yang C Chen W He R Cui and Z Li ldquoRobot learningsystem based on adaptive neural control and dynamicmovement primitivesrdquo IEEE Transactions on Neural Networksand Learning Systems vol 30 no 3 pp 777ndash787 2019

[23] C Yang D Huang W He and L Cheng ldquoNeural control ofrobot manipulators with trajectory tracking constraints andinput saturationrdquo IEEE Transactions on Neural Networks andLearning Systems pp 1ndash12 2020

[24] H Huang T Zhang C Yang and C L P Chen ldquoMotorlearning and generalization using broad learning adaptiveneural controlrdquo IEEE Transactions on Industrial Electronicsvol 67 no 10 pp 8608ndash8617 2020

12 Complexity

[25] H Huang C Yang and C L P Chen ldquoOptimal robot-envi-ronment interaction under broad fuzzy neural adaptive controlrdquoIEEE Transactions on Cybernetics pp 1ndash12 2020

[26] F Allaeys G Luyckx W Van Paepegem and J DegrieckldquoNumerical and experimental investigation of the shock andsteady state pressures in the bird material during bird strikerdquoInternational Journal of Impact Engineering vol 107pp 12ndash22 2017

[27] M Kim A Zammit A Siddens and J Bayandor ldquoAn ex-tensive crashworthiness methodology for advanced pro-pulsion systems part I soft impact damage assessment ofcomposite fan stage assembliesrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting Including the New HorizonsForum and Aerospace Exposition Orlando Florida January2011

[28] R Hedayati and M Sadighi Bird Strike An Experimental+eoretical and Numerical Investigation Woodhead Pub-lishing in Mechanical Engineering Elsevier AmsterdamNetherlands 978-0-08-100093-9 2016

[29] S K Sinha K E Turner and N Jain ldquoDynamic loading onturbofan blades due to bird-strikerdquo Journal of Engineering forGas Turbines and Power vol 133 no 12 Article ID 1225042011

[30] Federal Aviation Administration ldquoElectronic code of federalRegulationsrdquo Title 14 Aeronautics and Space National Ar-chives and Records Administration Washington DC USAChapter I Subchapter C Part 33-Airworthiness StandardsAircraft Engines Section 3376 2020

[31] Federal Aviation Administration ldquoBird ingestion certificationstandardsrdquo Advisory Circular Federal Aviation Administra-tion Wasington DC USA 3376-1A 2009

[32] R A Dolbeer S E Wright J R Weller and M J BegierWildlife Strikes to Civil Aircraft in the United States 1990-2017National Wildlife Strike Database Washington DC USA2018

[33] C J Shepherd G J Appleby-+omas P J Hazell andD F Allsop ldquo+e dynamic behaviour of ballistic gelatinrdquo AIPConference Proceedings vol 1195 pp 1399ndash1402 2009

[34] J O Hallquist LS-DYNA+eory Manual Livermore SoftwareTechnology Corporation Livermore CA USA 2007

[35] R Vignjevic M Orłowski T De Vuyst and J C CampbellldquoA parametric study of bird strike on engine bladesrdquo Inter-national Journal of Impact Engineering vol 60 pp 44ndash572013

[36] G R Johnson and W H Cook ldquoFracture characteristics ofthree metals subjected to various strains strain rates tem-peratures and pressuresrdquo Engineering Fracture Mechanicsvol 21 no 1 pp 31ndash48 1985

[37] D Leseur Experimental Investigations of Material Models forTi-6A1-4V and 2024-T3 Lawrence Livermore National LabLivermore CA USA UCRL-ID-134691 1999

[38] C Yang Y Jiang W He J Na Z Li and B Xu ldquoAdaptiveparameter estimation and control design for robot manipu-lators with finite-time convergencerdquo IEEE Transactions onIndustrial Electronics vol 65 no 10 pp 8112ndash8123 2018

[39] C Yang G Peng L Cheng J Na and Z Li ldquoForce sensorlessadmittance control for teleoperation of uncertain robotmanipulator using neural networksrdquo IEEE Transactions onSystems Man and Cybernetics Systems pp 1ndash11 2019

[40] G Peng C Yang W He and C L P Chen ldquoForce sensorlessadmittance control with neural learning for robots with ac-tuator saturationrdquo IEEE Transactions on Industrial Elec-tronics vol 67 no 4 pp 3138ndash3148 2020

[41] C Yang H Wu Z Li W He N Wang and C-Y Su ldquoMindcontrol of a robotic arm with visual fusion technologyrdquo IEEETransactions on Industrial Informatics vol 14 no 9pp 3822ndash3830 2018

[42] H Lin T Zhang Z Chen H Song and C Yang ldquoAdaptivefuzzy Gaussian mixture models for shape approximation inrobot graspingrdquo International Journal of Fuzzy Systemsvol 21 no 4 pp 1026ndash1037 2019

Complexity 13

values of impact force derived from a real bird with yawangle of minus 15deg minus 30deg minus 45deg and minus 60deg are 15732KN at 522ms13799KN at 433ms 20647KN at 370ms and 24666KNat 485ms respectively It can be concluded that a yaw angleof the bird would generate a variation in the impact loadinghistory and a negative yaw angle has a more significant effecton the impact loading history

Figure 14 shows the effect of pitch angle on the timehistories of impact loads As shown in Figure 14(a) withrespect to pitch angles of 15deg 30deg 45deg and 60deg the peakimpact loads are 20515KN at 435ms 22720 KN at 391ms26147 KN at 433ms and 26940 KN at 392ms respectivelyObviously the peak impact force increases as the positivepitch angle increases As shown in Figure 14(b) peak valuesof impact loading obtained from a real bird model with pitchangles of minus 15deg minus 30deg minus 45deg and minus 60deg are 16073KN at 393ms

16828KN at 390ms 18485KN at 386ms and 22406 KNat 385ms respectively It is observed that a negative yawangle would result in a variation in the impact loadinghistory

Figure 15 shows effective plastic strains of a single bladewhich undergoes the most severe plastic deformation duringimpact Obviously with the change of the bird attitude anglethe blade undergoes more severe plastic deformation Es-pecially as subjected to a real bird with a yaw angle of minus 45deg ora pitch angle of minus 60deg the blade suffers more than twice themagnitude of effective plastic strain compared with a realbird oriented along the engine centerline It can be con-cluded that attitude angles would increase the possibility offan blade failure Moreover the yaw angle of bird ingestionhas a significant effect on the location of the blade with themost severe plastic deformation

9972e + 02 1244e + 03 1255e + 031129e + 031004e + 038782e + 027527e + 026273e + 025018e + 023764e + 022509e + 021255e + 020000e + 00

1335e + 031314e + 031293e + 031163e + 031034e + 039049e + 027756e + 026463e + 025171e + 023878e + 022585e + 021293e + 020000e + 00

1182e + 031051e + 039197e + 027883e + 026569e + 025255e + 023942e + 022628e + 021314e + 020000e + 00

1202e + 031069e + 039351e + 028017e + 026683e + 025349e + 024015e + 022681e + 021347e + 021243e + 00

1120e + 039951e + 028707e + 027464e + 026220e + 024976e + 023732e + 022488e + 021244e + 020000e + 00

8975e + 027977e + 026980e + 025983e + 024986e + 023989e + 022992e + 021994e + 029972e + 010000e + 00

t = 10 ms t = 20 ms t = 25 ms

t = 45 mst = 35 mst = 30 ms

z

x

(a)

Figure 12 Bird deformation during the slicing action

Impa

ct fo

rce (

KN)

0

40

80

120

160

200

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 13 Yaw angle effect on impact loading history (a) Positive yaw angle α (b) Negative yaw angle α

Complexity 9

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

300

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)Im

pact

forc

e (KN

)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 14 Pitch angle effect on impact loading history (a) Positive pitch angle β (b) Negative pitch angle β

Effec

tive p

lasti

c str

ains

0deg15deg on 3 blade30deg on 4 blade45deg on 4 blade60deg on 4 blade

ndash15deg on 6 bladendash30deg on 5 bladendash45deg on 3 bladendash60deg on 5 blade

2 4 6 8 10Time (ms)

00

12

24

36

48

60

(a)

Effec

tive p

lasti

c str

ains

of t

he b

lade

3

12

24

36

48

60

4 6 8 10Time (ms)

0deg15deg30deg45deg60deg

ndash15degndash30degndash45degndash60deg

00

2

(b)

Figure 15 Attitude angle effect on blade damage (a) Yaw angle α (b) Pitch angle β

10 Complexity

Figure 16 shows the effective plastic strains of the fanassembly It can be seen that a ldquocusprdquo plastic deformationoccurs at the leading edge and the maximum plastic strainoccurred to the impact location Compared with the plasticdeformation of a fan assembly during a normal impact (seeFigure 16(a)) subjected to a bird with an attitude angle ofα minus 45deg and β minus 60deg fan blade failure occurs at the impactlocation and the plastic deformation at the root of the fanblade leading edge is more significant which would increasethe risk of a fan blade release event

6 Conclusions

Considering a geometric shape similar to what has alreadybeen published as a real mallard [12] a real bird model wasdeveloped +en this paper discusses the effect of attitudeangles of the realistic bird model on the soft impact damageof a full fan assembly Besides the stagnation pressure isrepresented as a criterion to calibrate the developed bird

model Results show a good correlation with available testdata [26]

In accordance with certification requirements the mostcritical ingestion parameters for the new bird model wereinvestigated It is found that the real bird aimed at the fanblade height of 80 with an ingestion speed of 65msproduces the most severe damage to the full fan assembly

Complying with the critical ingestion parameters of thebird simulations of a full fan assembly subjected to a realbird with respect to various attitude angles reveal that bothyaw and pitch angles of the bird have a significant effect onthe impact loading history +e blade that undergoes thehighest magnitude of effective plastic strain would beconfronted with a more plastic deformation than that in thecase of a normal impact (attitude angle 0deg) even though theimpact loading decreases Especially as subjected to a realbird with yaw angle of minus 45deg or pitch angle of minus 60deg the bladesuffers more than twice the magnitude of effective plasticstrain compared with that of attitude angle 0deg and the plastic

1898e ndash 01

1705e ndash 01

1512e ndash 01

1319e ndash 01

1125e ndash 01

9323e ndash 02

7392e ndash 02

5460e ndash 02

3529e ndash 02

1598e ndash 02

ndash3332e ndash 032

3 4

(a)

3294e ndash 01

2960e ndash 01

2627e ndash 01

2294e ndash 01

1960e ndash 01

1627e ndash 01

1294e ndash 01

9605e ndash 02

6272e ndash 02

2939e ndash 02

ndash3947e ndash 033

(b)

2032e ndash 01

1825e ndash 01

1617e ndash 01

1410e ndash 01

1202e ndash 01

9950e ndash 02

7876e ndash 02

5803e ndash 02

3729e ndash 02

1655e ndash 02

ndash4189e ndash 033

(c)

Figure 16 Effective plastic strain contours at time t 10ms (a) 0deg (b) α minus 45deg (c) β minus 60deg

Complexity 11

deformation at the root of the leading edge is more sig-nificant which would increase the risk of a fan blade releaseevent

Moreover it is invaluable to ensure the safety of com-mercial airlines and engine manufacture by adopting therealistic bird model with the dangerous attitude angle in thecertification of engine designs for resistance to bird strikeswhich will provide sufficient resistance in actual bird-strikeevents However attitude angles of the bird were set upbased on the assumption in this paper If the bird attitudecould be determined through experiments or control al-gorithms [38ndash42] it is of great significance to investigate theeffect of bird attitude on soft impact damage as well as thedistribution of flocking bird

Data Availability

All data included in this study are available from the cor-responding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is research was supported by the National Key Researchand Development Program of China (Grant no2016YFB0201800) and the National Natural Science Foun-dation of China (Grant no 11772192)

References

[1] R H Mao S A Meguid and T Y Ng ldquoTransient threedimensional finite element analysis of a bird striking a fanbladerdquo International Journal of Mechanics and Materials inDesign vol 4 no 1 pp 79ndash96 2008

[2] S Heimbs ldquoComputational methods for bird strike simula-tions a reviewrdquo Computers amp Structures vol 89 no 23-24pp 2093ndash2112 2011

[3] J S Wilbeck Impact Behavior of Low Strength Projectiles AirForce Materials Lab Ohio AFFDL-TR-75-5 1978

[4] J S Wilbeck and J L Rand ldquo+e development of a substitutebird modelrdquo Journal of Engineering for Power vol 103 no 4pp 725ndash730 1981

[5] A Airoldi and B Cacchione ldquoModelling of impact forces andpressures in Lagrangian bird strike analysesrdquo InternationalJournal of Impact Engineering vol 32 no 10 pp 1651ndash16772006

[6] M A Lavoie A Gakwaya M N Ensan D G Zimcik andD Nandlall ldquoldquoBirdrsquos substitute test results and evaluation ofavailable numerical methodsrdquo International Journal of ImpactEngineering vol 36 no 10-11 pp 1276ndash1287 2009

[7] M Guida F Marulo M Meo and M Riccio ldquoEvaluation andvalidation of multi-physics FE methods to simulate bird strikeon a wing leading edgerdquo in Proceedings of the 13th EuropeanConference on Composite Materials (ECCM) StockholmSweden June 2008

[8] M A Lavoie A Gakwaya M N Ensan and D G ZimcikldquoReview of existing numerical methods and validation pro-cedure available for bird strike modellingrdquo International

Journal of Applied Mathematics and Computer Science vol 2no 4 pp 111ndash118 2007

[9] M A Lavoie A Gakwaya M Nejad Ensan and D G ZimcikldquoValidation of available approaches for numerical bird strikemodeling toolsrdquo International Review of Mechanical Engi-neering vol 1 no 4 pp 380ndash389 2007

[10] M A McCarthy J R Xiao C T McCarthy et al ldquoModellingof bird strike on an aircraft wing leading edge made from fibremetal laminates-part 2 modelling of impact with SPH birdmodelrdquo Applied Composite Materials vol 11 no 5pp 317ndash340 2004

[11] L Nizampatnam and W Horn ldquoInvestigation of equation ofstate models for predicting bird impact loadsrdquo in Proceedingsof the 46th AIAA Aerospace Sciences Meeting and Exhibitpp 7ndash10 2013

[12] R Hedayati M Sadighi and M Mohammadi-Aghdam ldquoOnthe difference of pressure readings from the numerical ex-perimental and theoretical results in different bird strikestudiesrdquo Aerospace Science and Technology vol 32 no 1pp 260ndash266 2014

[13] L S Nizampatnam Models and Methods for Bird Strike LoadPredictions Wichita State University Wichita Kansas 2007

[14] S McCallum H Shoji and H Akiyama ldquoDevelopment of anadvanced multi-material bird-strike model using thesmoothed particle Hydrodynamics methodrdquo InternationalJournal of Crashworthiness vol 18 no 6 pp 579ndash597 2013

[15] R Hedayati and S Ziaei-Rad ldquoA new bird model and theeffect of bird geometry in impacts from various orientationsrdquoAerospace Science and Technology vol 28 no 1 pp 9ndash202013

[16] A Serge ldquoSoft impacts on aerospace structuresrdquo Progress inAerospace Sciences vol 81 pp 1ndash17 2016

[17] J Kou F Xu S Ji and X Zhang ldquoInfluence of bird yawpitchorientation on bird-strike resistance of aircraft structuresrdquoExplosion and Shock Waves vol 37 no 5 pp 937ndash944 2017

[18] Z Zhang L Li and D Zhang ldquoEffect of arbitrary yawpitchangle in bird strike numerical simulation using SPHmethodrdquoAerospace Science and Technology vol 81 pp 284ndash293 2018

[19] D Zhang and Q Fei ldquoEffect of bird geometry and impactorientation in bird striking on a rotary jet-engine fan analysisusing SPH methodrdquo Aerospace Science and Technologyvol 54 pp 320ndash329 2016

[20] R H Mao S A Meguid and T Y Ng ldquoEffects of incidenceangle in bird strike on integrity of aero-engine fan bladerdquoInternational Journal of Crashworthiness vol 14 no 4pp 295ndash308 2009

[21] C Yang C Chen N Wang et al ldquoBiologically inspiredmotion modeling and neural control for robot learning fromdemonstrationsrdquo IEEE Transactions on Cognitive and De-velopmental Systems vol 11 no 2 pp 281ndash291 2019

[22] C Yang C Chen W He R Cui and Z Li ldquoRobot learningsystem based on adaptive neural control and dynamicmovement primitivesrdquo IEEE Transactions on Neural Networksand Learning Systems vol 30 no 3 pp 777ndash787 2019

[23] C Yang D Huang W He and L Cheng ldquoNeural control ofrobot manipulators with trajectory tracking constraints andinput saturationrdquo IEEE Transactions on Neural Networks andLearning Systems pp 1ndash12 2020

[24] H Huang T Zhang C Yang and C L P Chen ldquoMotorlearning and generalization using broad learning adaptiveneural controlrdquo IEEE Transactions on Industrial Electronicsvol 67 no 10 pp 8608ndash8617 2020

12 Complexity

[25] H Huang C Yang and C L P Chen ldquoOptimal robot-envi-ronment interaction under broad fuzzy neural adaptive controlrdquoIEEE Transactions on Cybernetics pp 1ndash12 2020

[26] F Allaeys G Luyckx W Van Paepegem and J DegrieckldquoNumerical and experimental investigation of the shock andsteady state pressures in the bird material during bird strikerdquoInternational Journal of Impact Engineering vol 107pp 12ndash22 2017

[27] M Kim A Zammit A Siddens and J Bayandor ldquoAn ex-tensive crashworthiness methodology for advanced pro-pulsion systems part I soft impact damage assessment ofcomposite fan stage assembliesrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting Including the New HorizonsForum and Aerospace Exposition Orlando Florida January2011

[28] R Hedayati and M Sadighi Bird Strike An Experimental+eoretical and Numerical Investigation Woodhead Pub-lishing in Mechanical Engineering Elsevier AmsterdamNetherlands 978-0-08-100093-9 2016

[29] S K Sinha K E Turner and N Jain ldquoDynamic loading onturbofan blades due to bird-strikerdquo Journal of Engineering forGas Turbines and Power vol 133 no 12 Article ID 1225042011

[30] Federal Aviation Administration ldquoElectronic code of federalRegulationsrdquo Title 14 Aeronautics and Space National Ar-chives and Records Administration Washington DC USAChapter I Subchapter C Part 33-Airworthiness StandardsAircraft Engines Section 3376 2020

[31] Federal Aviation Administration ldquoBird ingestion certificationstandardsrdquo Advisory Circular Federal Aviation Administra-tion Wasington DC USA 3376-1A 2009

[32] R A Dolbeer S E Wright J R Weller and M J BegierWildlife Strikes to Civil Aircraft in the United States 1990-2017National Wildlife Strike Database Washington DC USA2018

[33] C J Shepherd G J Appleby-+omas P J Hazell andD F Allsop ldquo+e dynamic behaviour of ballistic gelatinrdquo AIPConference Proceedings vol 1195 pp 1399ndash1402 2009

[34] J O Hallquist LS-DYNA+eory Manual Livermore SoftwareTechnology Corporation Livermore CA USA 2007

[35] R Vignjevic M Orłowski T De Vuyst and J C CampbellldquoA parametric study of bird strike on engine bladesrdquo Inter-national Journal of Impact Engineering vol 60 pp 44ndash572013

[36] G R Johnson and W H Cook ldquoFracture characteristics ofthree metals subjected to various strains strain rates tem-peratures and pressuresrdquo Engineering Fracture Mechanicsvol 21 no 1 pp 31ndash48 1985

[37] D Leseur Experimental Investigations of Material Models forTi-6A1-4V and 2024-T3 Lawrence Livermore National LabLivermore CA USA UCRL-ID-134691 1999

[38] C Yang Y Jiang W He J Na Z Li and B Xu ldquoAdaptiveparameter estimation and control design for robot manipu-lators with finite-time convergencerdquo IEEE Transactions onIndustrial Electronics vol 65 no 10 pp 8112ndash8123 2018

[39] C Yang G Peng L Cheng J Na and Z Li ldquoForce sensorlessadmittance control for teleoperation of uncertain robotmanipulator using neural networksrdquo IEEE Transactions onSystems Man and Cybernetics Systems pp 1ndash11 2019

[40] G Peng C Yang W He and C L P Chen ldquoForce sensorlessadmittance control with neural learning for robots with ac-tuator saturationrdquo IEEE Transactions on Industrial Elec-tronics vol 67 no 4 pp 3138ndash3148 2020

[41] C Yang H Wu Z Li W He N Wang and C-Y Su ldquoMindcontrol of a robotic arm with visual fusion technologyrdquo IEEETransactions on Industrial Informatics vol 14 no 9pp 3822ndash3830 2018

[42] H Lin T Zhang Z Chen H Song and C Yang ldquoAdaptivefuzzy Gaussian mixture models for shape approximation inrobot graspingrdquo International Journal of Fuzzy Systemsvol 21 no 4 pp 1026ndash1037 2019

Complexity 13

Impa

ct fo

rce (

KN)

0

50

100

150

200

250

300

2 4 6 8 100Time (ms)

0deg15deg30deg

45deg60deg

(a)Im

pact

forc

e (KN

)

0

50

100

150

200

250

2 4 6 8 100Time (ms)

0degndash15degndash30deg

ndash45degndash60deg

(b)

Figure 14 Pitch angle effect on impact loading history (a) Positive pitch angle β (b) Negative pitch angle β

Effec

tive p

lasti

c str

ains

0deg15deg on 3 blade30deg on 4 blade45deg on 4 blade60deg on 4 blade

ndash15deg on 6 bladendash30deg on 5 bladendash45deg on 3 bladendash60deg on 5 blade

2 4 6 8 10Time (ms)

00

12

24

36

48

60

(a)

Effec

tive p

lasti

c str

ains

of t

he b

lade

3

12

24

36

48

60

4 6 8 10Time (ms)

0deg15deg30deg45deg60deg

ndash15degndash30degndash45degndash60deg

00

2

(b)

Figure 15 Attitude angle effect on blade damage (a) Yaw angle α (b) Pitch angle β

10 Complexity

Figure 16 shows the effective plastic strains of the fanassembly It can be seen that a ldquocusprdquo plastic deformationoccurs at the leading edge and the maximum plastic strainoccurred to the impact location Compared with the plasticdeformation of a fan assembly during a normal impact (seeFigure 16(a)) subjected to a bird with an attitude angle ofα minus 45deg and β minus 60deg fan blade failure occurs at the impactlocation and the plastic deformation at the root of the fanblade leading edge is more significant which would increasethe risk of a fan blade release event

6 Conclusions

Considering a geometric shape similar to what has alreadybeen published as a real mallard [12] a real bird model wasdeveloped +en this paper discusses the effect of attitudeangles of the realistic bird model on the soft impact damageof a full fan assembly Besides the stagnation pressure isrepresented as a criterion to calibrate the developed bird

model Results show a good correlation with available testdata [26]

In accordance with certification requirements the mostcritical ingestion parameters for the new bird model wereinvestigated It is found that the real bird aimed at the fanblade height of 80 with an ingestion speed of 65msproduces the most severe damage to the full fan assembly

Complying with the critical ingestion parameters of thebird simulations of a full fan assembly subjected to a realbird with respect to various attitude angles reveal that bothyaw and pitch angles of the bird have a significant effect onthe impact loading history +e blade that undergoes thehighest magnitude of effective plastic strain would beconfronted with a more plastic deformation than that in thecase of a normal impact (attitude angle 0deg) even though theimpact loading decreases Especially as subjected to a realbird with yaw angle of minus 45deg or pitch angle of minus 60deg the bladesuffers more than twice the magnitude of effective plasticstrain compared with that of attitude angle 0deg and the plastic

1898e ndash 01

1705e ndash 01

1512e ndash 01

1319e ndash 01

1125e ndash 01

9323e ndash 02

7392e ndash 02

5460e ndash 02

3529e ndash 02

1598e ndash 02

ndash3332e ndash 032

3 4

(a)

3294e ndash 01

2960e ndash 01

2627e ndash 01

2294e ndash 01

1960e ndash 01

1627e ndash 01

1294e ndash 01

9605e ndash 02

6272e ndash 02

2939e ndash 02

ndash3947e ndash 033

(b)

2032e ndash 01

1825e ndash 01

1617e ndash 01

1410e ndash 01

1202e ndash 01

9950e ndash 02

7876e ndash 02

5803e ndash 02

3729e ndash 02

1655e ndash 02

ndash4189e ndash 033

(c)

Figure 16 Effective plastic strain contours at time t 10ms (a) 0deg (b) α minus 45deg (c) β minus 60deg

Complexity 11

deformation at the root of the leading edge is more sig-nificant which would increase the risk of a fan blade releaseevent

Moreover it is invaluable to ensure the safety of com-mercial airlines and engine manufacture by adopting therealistic bird model with the dangerous attitude angle in thecertification of engine designs for resistance to bird strikeswhich will provide sufficient resistance in actual bird-strikeevents However attitude angles of the bird were set upbased on the assumption in this paper If the bird attitudecould be determined through experiments or control al-gorithms [38ndash42] it is of great significance to investigate theeffect of bird attitude on soft impact damage as well as thedistribution of flocking bird

Data Availability

All data included in this study are available from the cor-responding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is research was supported by the National Key Researchand Development Program of China (Grant no2016YFB0201800) and the National Natural Science Foun-dation of China (Grant no 11772192)

References

[1] R H Mao S A Meguid and T Y Ng ldquoTransient threedimensional finite element analysis of a bird striking a fanbladerdquo International Journal of Mechanics and Materials inDesign vol 4 no 1 pp 79ndash96 2008

[2] S Heimbs ldquoComputational methods for bird strike simula-tions a reviewrdquo Computers amp Structures vol 89 no 23-24pp 2093ndash2112 2011

[3] J S Wilbeck Impact Behavior of Low Strength Projectiles AirForce Materials Lab Ohio AFFDL-TR-75-5 1978

[4] J S Wilbeck and J L Rand ldquo+e development of a substitutebird modelrdquo Journal of Engineering for Power vol 103 no 4pp 725ndash730 1981

[5] A Airoldi and B Cacchione ldquoModelling of impact forces andpressures in Lagrangian bird strike analysesrdquo InternationalJournal of Impact Engineering vol 32 no 10 pp 1651ndash16772006

[6] M A Lavoie A Gakwaya M N Ensan D G Zimcik andD Nandlall ldquoldquoBirdrsquos substitute test results and evaluation ofavailable numerical methodsrdquo International Journal of ImpactEngineering vol 36 no 10-11 pp 1276ndash1287 2009

[7] M Guida F Marulo M Meo and M Riccio ldquoEvaluation andvalidation of multi-physics FE methods to simulate bird strikeon a wing leading edgerdquo in Proceedings of the 13th EuropeanConference on Composite Materials (ECCM) StockholmSweden June 2008

[8] M A Lavoie A Gakwaya M N Ensan and D G ZimcikldquoReview of existing numerical methods and validation pro-cedure available for bird strike modellingrdquo International

Journal of Applied Mathematics and Computer Science vol 2no 4 pp 111ndash118 2007

[9] M A Lavoie A Gakwaya M Nejad Ensan and D G ZimcikldquoValidation of available approaches for numerical bird strikemodeling toolsrdquo International Review of Mechanical Engi-neering vol 1 no 4 pp 380ndash389 2007

[10] M A McCarthy J R Xiao C T McCarthy et al ldquoModellingof bird strike on an aircraft wing leading edge made from fibremetal laminates-part 2 modelling of impact with SPH birdmodelrdquo Applied Composite Materials vol 11 no 5pp 317ndash340 2004

[11] L Nizampatnam and W Horn ldquoInvestigation of equation ofstate models for predicting bird impact loadsrdquo in Proceedingsof the 46th AIAA Aerospace Sciences Meeting and Exhibitpp 7ndash10 2013

[12] R Hedayati M Sadighi and M Mohammadi-Aghdam ldquoOnthe difference of pressure readings from the numerical ex-perimental and theoretical results in different bird strikestudiesrdquo Aerospace Science and Technology vol 32 no 1pp 260ndash266 2014

[13] L S Nizampatnam Models and Methods for Bird Strike LoadPredictions Wichita State University Wichita Kansas 2007

[14] S McCallum H Shoji and H Akiyama ldquoDevelopment of anadvanced multi-material bird-strike model using thesmoothed particle Hydrodynamics methodrdquo InternationalJournal of Crashworthiness vol 18 no 6 pp 579ndash597 2013

[15] R Hedayati and S Ziaei-Rad ldquoA new bird model and theeffect of bird geometry in impacts from various orientationsrdquoAerospace Science and Technology vol 28 no 1 pp 9ndash202013

[16] A Serge ldquoSoft impacts on aerospace structuresrdquo Progress inAerospace Sciences vol 81 pp 1ndash17 2016

[17] J Kou F Xu S Ji and X Zhang ldquoInfluence of bird yawpitchorientation on bird-strike resistance of aircraft structuresrdquoExplosion and Shock Waves vol 37 no 5 pp 937ndash944 2017

[18] Z Zhang L Li and D Zhang ldquoEffect of arbitrary yawpitchangle in bird strike numerical simulation using SPHmethodrdquoAerospace Science and Technology vol 81 pp 284ndash293 2018

[19] D Zhang and Q Fei ldquoEffect of bird geometry and impactorientation in bird striking on a rotary jet-engine fan analysisusing SPH methodrdquo Aerospace Science and Technologyvol 54 pp 320ndash329 2016

[20] R H Mao S A Meguid and T Y Ng ldquoEffects of incidenceangle in bird strike on integrity of aero-engine fan bladerdquoInternational Journal of Crashworthiness vol 14 no 4pp 295ndash308 2009

[21] C Yang C Chen N Wang et al ldquoBiologically inspiredmotion modeling and neural control for robot learning fromdemonstrationsrdquo IEEE Transactions on Cognitive and De-velopmental Systems vol 11 no 2 pp 281ndash291 2019

[22] C Yang C Chen W He R Cui and Z Li ldquoRobot learningsystem based on adaptive neural control and dynamicmovement primitivesrdquo IEEE Transactions on Neural Networksand Learning Systems vol 30 no 3 pp 777ndash787 2019

[23] C Yang D Huang W He and L Cheng ldquoNeural control ofrobot manipulators with trajectory tracking constraints andinput saturationrdquo IEEE Transactions on Neural Networks andLearning Systems pp 1ndash12 2020

[24] H Huang T Zhang C Yang and C L P Chen ldquoMotorlearning and generalization using broad learning adaptiveneural controlrdquo IEEE Transactions on Industrial Electronicsvol 67 no 10 pp 8608ndash8617 2020

12 Complexity

[25] H Huang C Yang and C L P Chen ldquoOptimal robot-envi-ronment interaction under broad fuzzy neural adaptive controlrdquoIEEE Transactions on Cybernetics pp 1ndash12 2020

[26] F Allaeys G Luyckx W Van Paepegem and J DegrieckldquoNumerical and experimental investigation of the shock andsteady state pressures in the bird material during bird strikerdquoInternational Journal of Impact Engineering vol 107pp 12ndash22 2017

[27] M Kim A Zammit A Siddens and J Bayandor ldquoAn ex-tensive crashworthiness methodology for advanced pro-pulsion systems part I soft impact damage assessment ofcomposite fan stage assembliesrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting Including the New HorizonsForum and Aerospace Exposition Orlando Florida January2011

[28] R Hedayati and M Sadighi Bird Strike An Experimental+eoretical and Numerical Investigation Woodhead Pub-lishing in Mechanical Engineering Elsevier AmsterdamNetherlands 978-0-08-100093-9 2016

[29] S K Sinha K E Turner and N Jain ldquoDynamic loading onturbofan blades due to bird-strikerdquo Journal of Engineering forGas Turbines and Power vol 133 no 12 Article ID 1225042011

[30] Federal Aviation Administration ldquoElectronic code of federalRegulationsrdquo Title 14 Aeronautics and Space National Ar-chives and Records Administration Washington DC USAChapter I Subchapter C Part 33-Airworthiness StandardsAircraft Engines Section 3376 2020

[31] Federal Aviation Administration ldquoBird ingestion certificationstandardsrdquo Advisory Circular Federal Aviation Administra-tion Wasington DC USA 3376-1A 2009

[32] R A Dolbeer S E Wright J R Weller and M J BegierWildlife Strikes to Civil Aircraft in the United States 1990-2017National Wildlife Strike Database Washington DC USA2018

[33] C J Shepherd G J Appleby-+omas P J Hazell andD F Allsop ldquo+e dynamic behaviour of ballistic gelatinrdquo AIPConference Proceedings vol 1195 pp 1399ndash1402 2009

[34] J O Hallquist LS-DYNA+eory Manual Livermore SoftwareTechnology Corporation Livermore CA USA 2007

[35] R Vignjevic M Orłowski T De Vuyst and J C CampbellldquoA parametric study of bird strike on engine bladesrdquo Inter-national Journal of Impact Engineering vol 60 pp 44ndash572013

[36] G R Johnson and W H Cook ldquoFracture characteristics ofthree metals subjected to various strains strain rates tem-peratures and pressuresrdquo Engineering Fracture Mechanicsvol 21 no 1 pp 31ndash48 1985

[37] D Leseur Experimental Investigations of Material Models forTi-6A1-4V and 2024-T3 Lawrence Livermore National LabLivermore CA USA UCRL-ID-134691 1999

[38] C Yang Y Jiang W He J Na Z Li and B Xu ldquoAdaptiveparameter estimation and control design for robot manipu-lators with finite-time convergencerdquo IEEE Transactions onIndustrial Electronics vol 65 no 10 pp 8112ndash8123 2018

[39] C Yang G Peng L Cheng J Na and Z Li ldquoForce sensorlessadmittance control for teleoperation of uncertain robotmanipulator using neural networksrdquo IEEE Transactions onSystems Man and Cybernetics Systems pp 1ndash11 2019

[40] G Peng C Yang W He and C L P Chen ldquoForce sensorlessadmittance control with neural learning for robots with ac-tuator saturationrdquo IEEE Transactions on Industrial Elec-tronics vol 67 no 4 pp 3138ndash3148 2020

[41] C Yang H Wu Z Li W He N Wang and C-Y Su ldquoMindcontrol of a robotic arm with visual fusion technologyrdquo IEEETransactions on Industrial Informatics vol 14 no 9pp 3822ndash3830 2018

[42] H Lin T Zhang Z Chen H Song and C Yang ldquoAdaptivefuzzy Gaussian mixture models for shape approximation inrobot graspingrdquo International Journal of Fuzzy Systemsvol 21 no 4 pp 1026ndash1037 2019

Complexity 13

Figure 16 shows the effective plastic strains of the fanassembly It can be seen that a ldquocusprdquo plastic deformationoccurs at the leading edge and the maximum plastic strainoccurred to the impact location Compared with the plasticdeformation of a fan assembly during a normal impact (seeFigure 16(a)) subjected to a bird with an attitude angle ofα minus 45deg and β minus 60deg fan blade failure occurs at the impactlocation and the plastic deformation at the root of the fanblade leading edge is more significant which would increasethe risk of a fan blade release event

6 Conclusions

Considering a geometric shape similar to what has alreadybeen published as a real mallard [12] a real bird model wasdeveloped +en this paper discusses the effect of attitudeangles of the realistic bird model on the soft impact damageof a full fan assembly Besides the stagnation pressure isrepresented as a criterion to calibrate the developed bird

model Results show a good correlation with available testdata [26]

In accordance with certification requirements the mostcritical ingestion parameters for the new bird model wereinvestigated It is found that the real bird aimed at the fanblade height of 80 with an ingestion speed of 65msproduces the most severe damage to the full fan assembly

Complying with the critical ingestion parameters of thebird simulations of a full fan assembly subjected to a realbird with respect to various attitude angles reveal that bothyaw and pitch angles of the bird have a significant effect onthe impact loading history +e blade that undergoes thehighest magnitude of effective plastic strain would beconfronted with a more plastic deformation than that in thecase of a normal impact (attitude angle 0deg) even though theimpact loading decreases Especially as subjected to a realbird with yaw angle of minus 45deg or pitch angle of minus 60deg the bladesuffers more than twice the magnitude of effective plasticstrain compared with that of attitude angle 0deg and the plastic

1898e ndash 01

1705e ndash 01

1512e ndash 01

1319e ndash 01

1125e ndash 01

9323e ndash 02

7392e ndash 02

5460e ndash 02

3529e ndash 02

1598e ndash 02

ndash3332e ndash 032

3 4

(a)

3294e ndash 01

2960e ndash 01

2627e ndash 01

2294e ndash 01

1960e ndash 01

1627e ndash 01

1294e ndash 01

9605e ndash 02

6272e ndash 02

2939e ndash 02

ndash3947e ndash 033

(b)

2032e ndash 01

1825e ndash 01

1617e ndash 01

1410e ndash 01

1202e ndash 01

9950e ndash 02

7876e ndash 02

5803e ndash 02

3729e ndash 02

1655e ndash 02

ndash4189e ndash 033

(c)

Figure 16 Effective plastic strain contours at time t 10ms (a) 0deg (b) α minus 45deg (c) β minus 60deg

Complexity 11

deformation at the root of the leading edge is more sig-nificant which would increase the risk of a fan blade releaseevent

Moreover it is invaluable to ensure the safety of com-mercial airlines and engine manufacture by adopting therealistic bird model with the dangerous attitude angle in thecertification of engine designs for resistance to bird strikeswhich will provide sufficient resistance in actual bird-strikeevents However attitude angles of the bird were set upbased on the assumption in this paper If the bird attitudecould be determined through experiments or control al-gorithms [38ndash42] it is of great significance to investigate theeffect of bird attitude on soft impact damage as well as thedistribution of flocking bird

Data Availability

All data included in this study are available from the cor-responding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is research was supported by the National Key Researchand Development Program of China (Grant no2016YFB0201800) and the National Natural Science Foun-dation of China (Grant no 11772192)

References

[1] R H Mao S A Meguid and T Y Ng ldquoTransient threedimensional finite element analysis of a bird striking a fanbladerdquo International Journal of Mechanics and Materials inDesign vol 4 no 1 pp 79ndash96 2008

[2] S Heimbs ldquoComputational methods for bird strike simula-tions a reviewrdquo Computers amp Structures vol 89 no 23-24pp 2093ndash2112 2011

[3] J S Wilbeck Impact Behavior of Low Strength Projectiles AirForce Materials Lab Ohio AFFDL-TR-75-5 1978

[4] J S Wilbeck and J L Rand ldquo+e development of a substitutebird modelrdquo Journal of Engineering for Power vol 103 no 4pp 725ndash730 1981

[5] A Airoldi and B Cacchione ldquoModelling of impact forces andpressures in Lagrangian bird strike analysesrdquo InternationalJournal of Impact Engineering vol 32 no 10 pp 1651ndash16772006

[6] M A Lavoie A Gakwaya M N Ensan D G Zimcik andD Nandlall ldquoldquoBirdrsquos substitute test results and evaluation ofavailable numerical methodsrdquo International Journal of ImpactEngineering vol 36 no 10-11 pp 1276ndash1287 2009

[7] M Guida F Marulo M Meo and M Riccio ldquoEvaluation andvalidation of multi-physics FE methods to simulate bird strikeon a wing leading edgerdquo in Proceedings of the 13th EuropeanConference on Composite Materials (ECCM) StockholmSweden June 2008

[8] M A Lavoie A Gakwaya M N Ensan and D G ZimcikldquoReview of existing numerical methods and validation pro-cedure available for bird strike modellingrdquo International

Journal of Applied Mathematics and Computer Science vol 2no 4 pp 111ndash118 2007

[9] M A Lavoie A Gakwaya M Nejad Ensan and D G ZimcikldquoValidation of available approaches for numerical bird strikemodeling toolsrdquo International Review of Mechanical Engi-neering vol 1 no 4 pp 380ndash389 2007

[10] M A McCarthy J R Xiao C T McCarthy et al ldquoModellingof bird strike on an aircraft wing leading edge made from fibremetal laminates-part 2 modelling of impact with SPH birdmodelrdquo Applied Composite Materials vol 11 no 5pp 317ndash340 2004

[11] L Nizampatnam and W Horn ldquoInvestigation of equation ofstate models for predicting bird impact loadsrdquo in Proceedingsof the 46th AIAA Aerospace Sciences Meeting and Exhibitpp 7ndash10 2013

[12] R Hedayati M Sadighi and M Mohammadi-Aghdam ldquoOnthe difference of pressure readings from the numerical ex-perimental and theoretical results in different bird strikestudiesrdquo Aerospace Science and Technology vol 32 no 1pp 260ndash266 2014

[13] L S Nizampatnam Models and Methods for Bird Strike LoadPredictions Wichita State University Wichita Kansas 2007

[14] S McCallum H Shoji and H Akiyama ldquoDevelopment of anadvanced multi-material bird-strike model using thesmoothed particle Hydrodynamics methodrdquo InternationalJournal of Crashworthiness vol 18 no 6 pp 579ndash597 2013

[15] R Hedayati and S Ziaei-Rad ldquoA new bird model and theeffect of bird geometry in impacts from various orientationsrdquoAerospace Science and Technology vol 28 no 1 pp 9ndash202013

[16] A Serge ldquoSoft impacts on aerospace structuresrdquo Progress inAerospace Sciences vol 81 pp 1ndash17 2016

[17] J Kou F Xu S Ji and X Zhang ldquoInfluence of bird yawpitchorientation on bird-strike resistance of aircraft structuresrdquoExplosion and Shock Waves vol 37 no 5 pp 937ndash944 2017

[18] Z Zhang L Li and D Zhang ldquoEffect of arbitrary yawpitchangle in bird strike numerical simulation using SPHmethodrdquoAerospace Science and Technology vol 81 pp 284ndash293 2018

[19] D Zhang and Q Fei ldquoEffect of bird geometry and impactorientation in bird striking on a rotary jet-engine fan analysisusing SPH methodrdquo Aerospace Science and Technologyvol 54 pp 320ndash329 2016

[20] R H Mao S A Meguid and T Y Ng ldquoEffects of incidenceangle in bird strike on integrity of aero-engine fan bladerdquoInternational Journal of Crashworthiness vol 14 no 4pp 295ndash308 2009

[21] C Yang C Chen N Wang et al ldquoBiologically inspiredmotion modeling and neural control for robot learning fromdemonstrationsrdquo IEEE Transactions on Cognitive and De-velopmental Systems vol 11 no 2 pp 281ndash291 2019

[22] C Yang C Chen W He R Cui and Z Li ldquoRobot learningsystem based on adaptive neural control and dynamicmovement primitivesrdquo IEEE Transactions on Neural Networksand Learning Systems vol 30 no 3 pp 777ndash787 2019

[23] C Yang D Huang W He and L Cheng ldquoNeural control ofrobot manipulators with trajectory tracking constraints andinput saturationrdquo IEEE Transactions on Neural Networks andLearning Systems pp 1ndash12 2020

[24] H Huang T Zhang C Yang and C L P Chen ldquoMotorlearning and generalization using broad learning adaptiveneural controlrdquo IEEE Transactions on Industrial Electronicsvol 67 no 10 pp 8608ndash8617 2020

12 Complexity

[25] H Huang C Yang and C L P Chen ldquoOptimal robot-envi-ronment interaction under broad fuzzy neural adaptive controlrdquoIEEE Transactions on Cybernetics pp 1ndash12 2020

[26] F Allaeys G Luyckx W Van Paepegem and J DegrieckldquoNumerical and experimental investigation of the shock andsteady state pressures in the bird material during bird strikerdquoInternational Journal of Impact Engineering vol 107pp 12ndash22 2017

[27] M Kim A Zammit A Siddens and J Bayandor ldquoAn ex-tensive crashworthiness methodology for advanced pro-pulsion systems part I soft impact damage assessment ofcomposite fan stage assembliesrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting Including the New HorizonsForum and Aerospace Exposition Orlando Florida January2011

[28] R Hedayati and M Sadighi Bird Strike An Experimental+eoretical and Numerical Investigation Woodhead Pub-lishing in Mechanical Engineering Elsevier AmsterdamNetherlands 978-0-08-100093-9 2016

[29] S K Sinha K E Turner and N Jain ldquoDynamic loading onturbofan blades due to bird-strikerdquo Journal of Engineering forGas Turbines and Power vol 133 no 12 Article ID 1225042011

[30] Federal Aviation Administration ldquoElectronic code of federalRegulationsrdquo Title 14 Aeronautics and Space National Ar-chives and Records Administration Washington DC USAChapter I Subchapter C Part 33-Airworthiness StandardsAircraft Engines Section 3376 2020

[31] Federal Aviation Administration ldquoBird ingestion certificationstandardsrdquo Advisory Circular Federal Aviation Administra-tion Wasington DC USA 3376-1A 2009

[32] R A Dolbeer S E Wright J R Weller and M J BegierWildlife Strikes to Civil Aircraft in the United States 1990-2017National Wildlife Strike Database Washington DC USA2018

[33] C J Shepherd G J Appleby-+omas P J Hazell andD F Allsop ldquo+e dynamic behaviour of ballistic gelatinrdquo AIPConference Proceedings vol 1195 pp 1399ndash1402 2009

[34] J O Hallquist LS-DYNA+eory Manual Livermore SoftwareTechnology Corporation Livermore CA USA 2007

[35] R Vignjevic M Orłowski T De Vuyst and J C CampbellldquoA parametric study of bird strike on engine bladesrdquo Inter-national Journal of Impact Engineering vol 60 pp 44ndash572013

[36] G R Johnson and W H Cook ldquoFracture characteristics ofthree metals subjected to various strains strain rates tem-peratures and pressuresrdquo Engineering Fracture Mechanicsvol 21 no 1 pp 31ndash48 1985

[37] D Leseur Experimental Investigations of Material Models forTi-6A1-4V and 2024-T3 Lawrence Livermore National LabLivermore CA USA UCRL-ID-134691 1999

[38] C Yang Y Jiang W He J Na Z Li and B Xu ldquoAdaptiveparameter estimation and control design for robot manipu-lators with finite-time convergencerdquo IEEE Transactions onIndustrial Electronics vol 65 no 10 pp 8112ndash8123 2018

[39] C Yang G Peng L Cheng J Na and Z Li ldquoForce sensorlessadmittance control for teleoperation of uncertain robotmanipulator using neural networksrdquo IEEE Transactions onSystems Man and Cybernetics Systems pp 1ndash11 2019

[40] G Peng C Yang W He and C L P Chen ldquoForce sensorlessadmittance control with neural learning for robots with ac-tuator saturationrdquo IEEE Transactions on Industrial Elec-tronics vol 67 no 4 pp 3138ndash3148 2020

[41] C Yang H Wu Z Li W He N Wang and C-Y Su ldquoMindcontrol of a robotic arm with visual fusion technologyrdquo IEEETransactions on Industrial Informatics vol 14 no 9pp 3822ndash3830 2018

[42] H Lin T Zhang Z Chen H Song and C Yang ldquoAdaptivefuzzy Gaussian mixture models for shape approximation inrobot graspingrdquo International Journal of Fuzzy Systemsvol 21 no 4 pp 1026ndash1037 2019

Complexity 13

deformation at the root of the leading edge is more sig-nificant which would increase the risk of a fan blade releaseevent

Moreover it is invaluable to ensure the safety of com-mercial airlines and engine manufacture by adopting therealistic bird model with the dangerous attitude angle in thecertification of engine designs for resistance to bird strikeswhich will provide sufficient resistance in actual bird-strikeevents However attitude angles of the bird were set upbased on the assumption in this paper If the bird attitudecould be determined through experiments or control al-gorithms [38ndash42] it is of great significance to investigate theeffect of bird attitude on soft impact damage as well as thedistribution of flocking bird

Data Availability

All data included in this study are available from the cor-responding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+is research was supported by the National Key Researchand Development Program of China (Grant no2016YFB0201800) and the National Natural Science Foun-dation of China (Grant no 11772192)

References

[1] R H Mao S A Meguid and T Y Ng ldquoTransient threedimensional finite element analysis of a bird striking a fanbladerdquo International Journal of Mechanics and Materials inDesign vol 4 no 1 pp 79ndash96 2008

[2] S Heimbs ldquoComputational methods for bird strike simula-tions a reviewrdquo Computers amp Structures vol 89 no 23-24pp 2093ndash2112 2011

[3] J S Wilbeck Impact Behavior of Low Strength Projectiles AirForce Materials Lab Ohio AFFDL-TR-75-5 1978

[4] J S Wilbeck and J L Rand ldquo+e development of a substitutebird modelrdquo Journal of Engineering for Power vol 103 no 4pp 725ndash730 1981

[5] A Airoldi and B Cacchione ldquoModelling of impact forces andpressures in Lagrangian bird strike analysesrdquo InternationalJournal of Impact Engineering vol 32 no 10 pp 1651ndash16772006

[6] M A Lavoie A Gakwaya M N Ensan D G Zimcik andD Nandlall ldquoldquoBirdrsquos substitute test results and evaluation ofavailable numerical methodsrdquo International Journal of ImpactEngineering vol 36 no 10-11 pp 1276ndash1287 2009

[7] M Guida F Marulo M Meo and M Riccio ldquoEvaluation andvalidation of multi-physics FE methods to simulate bird strikeon a wing leading edgerdquo in Proceedings of the 13th EuropeanConference on Composite Materials (ECCM) StockholmSweden June 2008

[8] M A Lavoie A Gakwaya M N Ensan and D G ZimcikldquoReview of existing numerical methods and validation pro-cedure available for bird strike modellingrdquo International

Journal of Applied Mathematics and Computer Science vol 2no 4 pp 111ndash118 2007

[9] M A Lavoie A Gakwaya M Nejad Ensan and D G ZimcikldquoValidation of available approaches for numerical bird strikemodeling toolsrdquo International Review of Mechanical Engi-neering vol 1 no 4 pp 380ndash389 2007

[10] M A McCarthy J R Xiao C T McCarthy et al ldquoModellingof bird strike on an aircraft wing leading edge made from fibremetal laminates-part 2 modelling of impact with SPH birdmodelrdquo Applied Composite Materials vol 11 no 5pp 317ndash340 2004

[11] L Nizampatnam and W Horn ldquoInvestigation of equation ofstate models for predicting bird impact loadsrdquo in Proceedingsof the 46th AIAA Aerospace Sciences Meeting and Exhibitpp 7ndash10 2013

[12] R Hedayati M Sadighi and M Mohammadi-Aghdam ldquoOnthe difference of pressure readings from the numerical ex-perimental and theoretical results in different bird strikestudiesrdquo Aerospace Science and Technology vol 32 no 1pp 260ndash266 2014

[13] L S Nizampatnam Models and Methods for Bird Strike LoadPredictions Wichita State University Wichita Kansas 2007

[14] S McCallum H Shoji and H Akiyama ldquoDevelopment of anadvanced multi-material bird-strike model using thesmoothed particle Hydrodynamics methodrdquo InternationalJournal of Crashworthiness vol 18 no 6 pp 579ndash597 2013

[15] R Hedayati and S Ziaei-Rad ldquoA new bird model and theeffect of bird geometry in impacts from various orientationsrdquoAerospace Science and Technology vol 28 no 1 pp 9ndash202013

[16] A Serge ldquoSoft impacts on aerospace structuresrdquo Progress inAerospace Sciences vol 81 pp 1ndash17 2016

[17] J Kou F Xu S Ji and X Zhang ldquoInfluence of bird yawpitchorientation on bird-strike resistance of aircraft structuresrdquoExplosion and Shock Waves vol 37 no 5 pp 937ndash944 2017

[18] Z Zhang L Li and D Zhang ldquoEffect of arbitrary yawpitchangle in bird strike numerical simulation using SPHmethodrdquoAerospace Science and Technology vol 81 pp 284ndash293 2018

[19] D Zhang and Q Fei ldquoEffect of bird geometry and impactorientation in bird striking on a rotary jet-engine fan analysisusing SPH methodrdquo Aerospace Science and Technologyvol 54 pp 320ndash329 2016

[20] R H Mao S A Meguid and T Y Ng ldquoEffects of incidenceangle in bird strike on integrity of aero-engine fan bladerdquoInternational Journal of Crashworthiness vol 14 no 4pp 295ndash308 2009

[21] C Yang C Chen N Wang et al ldquoBiologically inspiredmotion modeling and neural control for robot learning fromdemonstrationsrdquo IEEE Transactions on Cognitive and De-velopmental Systems vol 11 no 2 pp 281ndash291 2019

[22] C Yang C Chen W He R Cui and Z Li ldquoRobot learningsystem based on adaptive neural control and dynamicmovement primitivesrdquo IEEE Transactions on Neural Networksand Learning Systems vol 30 no 3 pp 777ndash787 2019

[23] C Yang D Huang W He and L Cheng ldquoNeural control ofrobot manipulators with trajectory tracking constraints andinput saturationrdquo IEEE Transactions on Neural Networks andLearning Systems pp 1ndash12 2020

[24] H Huang T Zhang C Yang and C L P Chen ldquoMotorlearning and generalization using broad learning adaptiveneural controlrdquo IEEE Transactions on Industrial Electronicsvol 67 no 10 pp 8608ndash8617 2020

12 Complexity

[25] H Huang C Yang and C L P Chen ldquoOptimal robot-envi-ronment interaction under broad fuzzy neural adaptive controlrdquoIEEE Transactions on Cybernetics pp 1ndash12 2020

[26] F Allaeys G Luyckx W Van Paepegem and J DegrieckldquoNumerical and experimental investigation of the shock andsteady state pressures in the bird material during bird strikerdquoInternational Journal of Impact Engineering vol 107pp 12ndash22 2017

[27] M Kim A Zammit A Siddens and J Bayandor ldquoAn ex-tensive crashworthiness methodology for advanced pro-pulsion systems part I soft impact damage assessment ofcomposite fan stage assembliesrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting Including the New HorizonsForum and Aerospace Exposition Orlando Florida January2011

[28] R Hedayati and M Sadighi Bird Strike An Experimental+eoretical and Numerical Investigation Woodhead Pub-lishing in Mechanical Engineering Elsevier AmsterdamNetherlands 978-0-08-100093-9 2016

[29] S K Sinha K E Turner and N Jain ldquoDynamic loading onturbofan blades due to bird-strikerdquo Journal of Engineering forGas Turbines and Power vol 133 no 12 Article ID 1225042011

[30] Federal Aviation Administration ldquoElectronic code of federalRegulationsrdquo Title 14 Aeronautics and Space National Ar-chives and Records Administration Washington DC USAChapter I Subchapter C Part 33-Airworthiness StandardsAircraft Engines Section 3376 2020

[31] Federal Aviation Administration ldquoBird ingestion certificationstandardsrdquo Advisory Circular Federal Aviation Administra-tion Wasington DC USA 3376-1A 2009

[32] R A Dolbeer S E Wright J R Weller and M J BegierWildlife Strikes to Civil Aircraft in the United States 1990-2017National Wildlife Strike Database Washington DC USA2018

[33] C J Shepherd G J Appleby-+omas P J Hazell andD F Allsop ldquo+e dynamic behaviour of ballistic gelatinrdquo AIPConference Proceedings vol 1195 pp 1399ndash1402 2009

[34] J O Hallquist LS-DYNA+eory Manual Livermore SoftwareTechnology Corporation Livermore CA USA 2007

[35] R Vignjevic M Orłowski T De Vuyst and J C CampbellldquoA parametric study of bird strike on engine bladesrdquo Inter-national Journal of Impact Engineering vol 60 pp 44ndash572013

[36] G R Johnson and W H Cook ldquoFracture characteristics ofthree metals subjected to various strains strain rates tem-peratures and pressuresrdquo Engineering Fracture Mechanicsvol 21 no 1 pp 31ndash48 1985

[37] D Leseur Experimental Investigations of Material Models forTi-6A1-4V and 2024-T3 Lawrence Livermore National LabLivermore CA USA UCRL-ID-134691 1999

[38] C Yang Y Jiang W He J Na Z Li and B Xu ldquoAdaptiveparameter estimation and control design for robot manipu-lators with finite-time convergencerdquo IEEE Transactions onIndustrial Electronics vol 65 no 10 pp 8112ndash8123 2018

[39] C Yang G Peng L Cheng J Na and Z Li ldquoForce sensorlessadmittance control for teleoperation of uncertain robotmanipulator using neural networksrdquo IEEE Transactions onSystems Man and Cybernetics Systems pp 1ndash11 2019

[40] G Peng C Yang W He and C L P Chen ldquoForce sensorlessadmittance control with neural learning for robots with ac-tuator saturationrdquo IEEE Transactions on Industrial Elec-tronics vol 67 no 4 pp 3138ndash3148 2020

[41] C Yang H Wu Z Li W He N Wang and C-Y Su ldquoMindcontrol of a robotic arm with visual fusion technologyrdquo IEEETransactions on Industrial Informatics vol 14 no 9pp 3822ndash3830 2018

[42] H Lin T Zhang Z Chen H Song and C Yang ldquoAdaptivefuzzy Gaussian mixture models for shape approximation inrobot graspingrdquo International Journal of Fuzzy Systemsvol 21 no 4 pp 1026ndash1037 2019

Complexity 13

[25] H Huang C Yang and C L P Chen ldquoOptimal robot-envi-ronment interaction under broad fuzzy neural adaptive controlrdquoIEEE Transactions on Cybernetics pp 1ndash12 2020

[26] F Allaeys G Luyckx W Van Paepegem and J DegrieckldquoNumerical and experimental investigation of the shock andsteady state pressures in the bird material during bird strikerdquoInternational Journal of Impact Engineering vol 107pp 12ndash22 2017

[27] M Kim A Zammit A Siddens and J Bayandor ldquoAn ex-tensive crashworthiness methodology for advanced pro-pulsion systems part I soft impact damage assessment ofcomposite fan stage assembliesrdquo in Proceedings of the 49thAIAA Aerospace Sciences Meeting Including the New HorizonsForum and Aerospace Exposition Orlando Florida January2011

[28] R Hedayati and M Sadighi Bird Strike An Experimental+eoretical and Numerical Investigation Woodhead Pub-lishing in Mechanical Engineering Elsevier AmsterdamNetherlands 978-0-08-100093-9 2016

[29] S K Sinha K E Turner and N Jain ldquoDynamic loading onturbofan blades due to bird-strikerdquo Journal of Engineering forGas Turbines and Power vol 133 no 12 Article ID 1225042011

[30] Federal Aviation Administration ldquoElectronic code of federalRegulationsrdquo Title 14 Aeronautics and Space National Ar-chives and Records Administration Washington DC USAChapter I Subchapter C Part 33-Airworthiness StandardsAircraft Engines Section 3376 2020

[31] Federal Aviation Administration ldquoBird ingestion certificationstandardsrdquo Advisory Circular Federal Aviation Administra-tion Wasington DC USA 3376-1A 2009

[32] R A Dolbeer S E Wright J R Weller and M J BegierWildlife Strikes to Civil Aircraft in the United States 1990-2017National Wildlife Strike Database Washington DC USA2018

[33] C J Shepherd G J Appleby-+omas P J Hazell andD F Allsop ldquo+e dynamic behaviour of ballistic gelatinrdquo AIPConference Proceedings vol 1195 pp 1399ndash1402 2009

[34] J O Hallquist LS-DYNA+eory Manual Livermore SoftwareTechnology Corporation Livermore CA USA 2007

[35] R Vignjevic M Orłowski T De Vuyst and J C CampbellldquoA parametric study of bird strike on engine bladesrdquo Inter-national Journal of Impact Engineering vol 60 pp 44ndash572013

[36] G R Johnson and W H Cook ldquoFracture characteristics ofthree metals subjected to various strains strain rates tem-peratures and pressuresrdquo Engineering Fracture Mechanicsvol 21 no 1 pp 31ndash48 1985

[37] D Leseur Experimental Investigations of Material Models forTi-6A1-4V and 2024-T3 Lawrence Livermore National LabLivermore CA USA UCRL-ID-134691 1999

[38] C Yang Y Jiang W He J Na Z Li and B Xu ldquoAdaptiveparameter estimation and control design for robot manipu-lators with finite-time convergencerdquo IEEE Transactions onIndustrial Electronics vol 65 no 10 pp 8112ndash8123 2018

[39] C Yang G Peng L Cheng J Na and Z Li ldquoForce sensorlessadmittance control for teleoperation of uncertain robotmanipulator using neural networksrdquo IEEE Transactions onSystems Man and Cybernetics Systems pp 1ndash11 2019

[40] G Peng C Yang W He and C L P Chen ldquoForce sensorlessadmittance control with neural learning for robots with ac-tuator saturationrdquo IEEE Transactions on Industrial Elec-tronics vol 67 no 4 pp 3138ndash3148 2020

[41] C Yang H Wu Z Li W He N Wang and C-Y Su ldquoMindcontrol of a robotic arm with visual fusion technologyrdquo IEEETransactions on Industrial Informatics vol 14 no 9pp 3822ndash3830 2018

[42] H Lin T Zhang Z Chen H Song and C Yang ldquoAdaptivefuzzy Gaussian mixture models for shape approximation inrobot graspingrdquo International Journal of Fuzzy Systemsvol 21 no 4 pp 1026ndash1037 2019

Complexity 13