Hssn Phnge,Mohmmd Hossein Abolbshri

aDepartment of Mechanical Engineering,Ferdowsi University of Mashhad,Mashhad 91775-1111,Iran

bDepartment of Mechanical Engineering,Lean Production Engineering Research Center,Ferdowsi University of Mashhad,Mashhad,PO Box 91775-1111,Iran

Mass and performance optimization of an airplane wing leading edge structure against bird strike using Taguchi-based grey relational analysis

Hassan Pahangea,Mohammad Hossein Abolbasharib,*

aDepartment of Mechanical Engineering,Ferdowsi University of Mashhad,Mashhad 91775-1111,Iran

bDepartment of Mechanical Engineering,Lean Production Engineering Research Center,Ferdowsi University of Mashhad,Mashhad,PO Box 91775-1111,Iran

Collisions between birds and aircraft are one of the most dangerous threats to flight safety.In this study,smoothed particles hydrodynamics(SPH)method is used for simulating the bird strike to an airplane wing leading edge structure.In order to verify the model,first,experiment of bird strike to a flat aluminum plate is simulated,and then bird impact on an airplane wing leading edge structure is investigated.After that,considering dimensions of wing internal structural components like ribs,skin and spar as design variables,we try to minimize structural mass and wing skin de formation simultaneously.To do this,bird strike simulations to 18 different wing structures are made based on Taguchi’s L18 factorial design of experiment.Then grey relational analysis is used to minimize structural mass and wing skin de formation due to the bird strike.The analysis of variance(ANOVA)is also applied and it is concluded that the most significant parameter for the performance of wing structure against impact is the skin thickness.Finally,a validation simulation is conducted under the optimal condition to show the improvement of performance of the wing structure.

1.Introduction

Nomenclature A Material B Skin thickness C Rib thickness D Rib distance E Cut out diameter F Spar location Cv Intercept of the Vs-Vpcurve Ds，Ps Constants of Cowper-Symonds law FN Normal force of rivets FNF Critical normal force of rivets FS Shear force of rivets FSF Critical shear force of rivets GRG Grey relational grade i Number of each experiment IE Internal energy density per unit initial volume k Number of responses kt Total number of responses n Total number of experiments P Pressure q Number of design parameters Vp Particle velocity Vs Shock velocity x0i（k） Response values x*0（k） Reference normalized response value x*i（k） Normalized response values yi Response value of the ith experiment α，β Tie break contact constants γe Estimated grey relational grade γi Grey relational grade for ith experiment γm Total average grey relational grade γ0 Gruneisen gamma Δmax Largest value of Δ0i（k）Δmin Smallest value of Δ0i（k）Δ0i（k） Deviation between normalized response and reference values ˙εEquivalent strain rate ζ Distinguishing coefficient μ ρ/ρ0-1 ρ Density ρ0 Initial density ξi（k） Grey relational coefficient σn Dynamic yield stress σy Yield stress

Airplanes and birds occupy the same space during flight and there fore collision between them is inevitable.The damage caused due to these collisions is usually catastrophic.The bird strike to airplanes is not a new problem and has occurred since the early days of aviation history.Thefirst bird strike was recorded by Wright brothers in 1905.According to the Federal Aviation Administration(FAA),in the United States alone,more than 138000 incidents of bird strikes were reported between 1990 and 2013.1The average annual cost of these strikes in the U.S.is at least$187 million.However,this annual cost can be estimated up to$937 million when unreported strikes are considered.Globally,bird and other wildlife strikes killed more than 255 people and destroyed over 243 aircrafts from 1988 to 2013.The number of bird strikes increases every year because of increase in air traffic,bird population and using fewer but more powerful engines per plane.

There fore,the international certification regulations like Federal Aviation Regulations(FAR)require that all forward facing airplane components need to prove a certain level of bird strike tolerance be fore they are allowed for operational use.The acceptance of certification by experimental test is very expensive and time consuming.In addition,achieving a lowweight,bird-proof design requires several experimental tests.Consequently,in order to shorten the design time and reduce cost,numerical simulations are of ten used and are more popular among researchers.In this research,LS-DYNA code has been used to simulate bird strike to the wing leading edge structure.

All forward facing airplane components like engine inlet and fan blades,wing and empennage leading edge,windshield,window frame and radome are subject to bird strike(Fig.1).As can be seen in Fig.1,the most commonly damaged airplane components are engines and wing leading edges.About 31%of all damaging bird strikes involve the wing.2Consequently,many researchers have investigated bird strike to the airplane wing.3–7

Various numerical techniques like Lagrangian approach,arbitrary Lagrangian Eulerian(ALE)method and smoothed particle hydrodynamics(SPH)method are of ten used to model the bird strike phenomena.In Lagrangian approach,the numerical mesh is attached to material points and there fore any material deflection can distort numerical mesh.The major disadvantage of Lagrangian approach is the possibility of inaccurate results in analyzing large deflection problems.ALE technique combines Lagrangian and Eulerian approaches to get better results.In this approach,the numerical mesh does not follow material points exactly.Simulating bird strike by ALE approach is more complicated to per form than the other two methods.The SPH method is the most recent and the most efficient method to analyze bird strike problem because of its high accuracy and high solution speed.The SPH method is a meshless Lagrangian method in which the elements are a set of discrete and mutually interacting nodes.Due to the absence of a mesh connecting individual particles,the SPH method is perfectly suitable for solving problems involving large de formation.

Fig.1 Airplane components struck and damaged by bird worldwide(1999–2008).

Many studies and investigations have been conducted in the past in order to design the aircraft components which can resist in bird strike events.Barber et al.8were thefirst researchers that investigated the experimental behavior of a bird under impact.They conducted a series of bird strike tests on a rigid plate and concluded that the maximum pressure generated at the center of target plate due to bird impact is independent of bird size and is proportional to the square of the impact velocity.On the other hand,many researchers investigated different numerical approaches to simulate bird strike phenomenon.Neiring9used Lagrangian approach to simulate bird strike on enginefan blades.He stated that this method needs to be improved in order to model bird strike accurately.Due to Lagrangian method’s disadvantages in modeling bird strike,some researchers used alternative approaches like ALE and SPH.Langrand et al.10modeled the bird strike against rigid target using both Lagrangian and ALE formulations and compared these approaches.They concluded that both approaches can well predict the experimental pressures,but Lagrangian method needs more time to solve due to decreasing time step.In recent years,a global trend is visible that the SPH approach is preferred compared to the Lagrangian and ALE modeling approaches.Ubels,11McCarthy,12Kavitha,13Zakir14et al.,and many others used the SPH method to investigate the bird strike on an aircraft wing leading edge structure.They showed that the SPH method can well predict the splashing of the bird during the strike.Liu et al.15conducted experiments of bird strike to the sidewall structure of an aircraft nose.They also developed a numerical model using the SPH method to simulate bird strike process and compared dynamic response of structure in numerical model with experimental results.They showed that the SPH method can accurately predict behavior of the bird at high speed impact.Vignjevic et al.16simulated the bird strikes on engine blades with the SPH method.They per formed a number of parametric studies on the bird shape,bird impact location along the length of the blade and impact timing and also compared their results with final de formed shape of the blade recovered from the bird strike test.

A large number of papers have been published on bird strike studies until now,but in the present work,a multiobjective optimization problem is presented.This paper investigates the numerical modeling of bird strike on an aircraft wing leading edge structure and tries to minimize simultaneously structural mass and wing skin de formation.The SPH method is employed to simulate the bird.The modeling procedure is validated first through comparison with an existing test data of a simple experiment.The influence of dimensions of wing internal structural components on the wing’s damage after the collision with a bird is also studied.In this way,a low-weight leading edge structure to resist bird strike incidents is sought.

2.Validation of numerical bird strike modeling

Since the experimental bird strike tests are expensive,time consuming and difficult to per form,explicit numerical simulations are of ten used in order to per form bird strike analysis.Numerical model must be validated with published experimental results be fore it is used for impact simulation on complex aircraft components.Many researchers have compared their bird strike simulation results with the experimental results of bird impact on a rigid flat plate obtained by Wilbeck.17Although Wilbeck’s results are a reliable source of experimental data,but in recent years,some researchers have per formed new bird strike experiments and published more accurate data.One of these researchers was Liu et al.18They carried out numerous bird impact tests against a flat de formable plate.In order to validate our numerical approach,we use their results,too.

2.1.Liu experiment

Liu et al.18conducted a series of bird strike experiments on a flat metallic plate with different striking velocities and measured the dynamic responses of plate.They used killed domestic chicken having a mass of 1.8 kg and velocity of 70,120 and 170 m/s as the projectile.They used two types of common aerospace materials for the target plate.The aluminum alloy(AlCu4Mg1)plates have the thickness of 10 mm and 14 mm and the steel(C45E4)plates have the thickness of 4.5 mm and 8 mm.All of those square plates have dimension of 600 mm×600 mm and all edges are clamped to a fixture.They used laser displacement sensors and strain gauges at different locations on the target plate in order to record the displacements and strains during the test.Fig.2 and Table 1 determine locations of these sensors on the target plate(i.e.,S1,S2,S3,D1,and D2).

In this study,we use the results of experiment number 25 of Liu18to validate our numerical model.In that experiment,the actual impact velocity was 116 m/s and the target was an aluminum plate with the thickness of 10 mm.

2.2.Bird model specifications

In this study,the SPH method is employed to simulate the bird behavior.A real bird body has a complex geometry and it is very demanding to model the bird with a shape exactly the same as the real one.Accordingly,many researchers who investigated appropriate substitute bird geometries have suggested a cylinder with two hemispherical ends and a length to diameter ratio of 2 as a proper shape.16,19–21There fore,in this study,a hemispherical ended cylinder with length to diameter ratio of 2 as bird geometry is employed.Thus by knowing the mass and density of bird,its diameter and length can be computed.

Fig.2 Locations of sensors on target plate.18

Table 1 Exact position of sensors on target plate.18

When a relatively weak projectile,such as a bird,impacts a much stiffer target at high velocity,the projectile material behaves as a hydrodynamic material for which an equation of state(EOS)relating the thermodynamic properties of pressure and density should be adopted.21In this study,the Gruneisen EOS is employed because this kind of equation of state can best predict the behavior of bird in bird strike impacts.22Gruneisen EOS with cubic shock velocity determines pressure for compressed materials as23

and for expanded material as

where Cvis the intercept of the Vs–Vpcurve,Vsthe shock velocity,Vpthe particle velocity;C1,C2and C3are the coefficients of the slope of the Vs–Vpcurve; γ0is the Gruneisen gamma;IEthe internal energy density per unit initial volume;a thefirst order volume correction to γ0;and μ = ρ/ρ0-1 where ρ0and ρ are initial and current material density.The parameters used for Gruneisen EOS are γ0=0,Cv=1480,C1=1.92,C2=C3=0 that are the same as Huertas thesis24for the sake of comparability.

Table 2 summarizes the general parameters used for the SPH bird model.In order to study the mesh sensitivity,analyses are carried out with three different mesh densities(coarse,medium and fine).

2.3.Target model specifications

In this study,the target is a 600 mm×600 mm aluminum plate with the thickness of 10 mm.Since the thickness of the plate is much smaller(about 1/60)compared to its other dimensions,thefinite element mesh of this plate has been created using shell elements.An isotropic elastic plastic model has been used for the target material and also a Cowper–Symonds law has been included to consider the strain rate sensitivity of the yield stress:

Table 2 Specifications of bird model.

where σnis the dynamic yield stress,σythe static yield stress,˙ε the equivalent strain rate of the material,and Dsand Psare both the constants of Cowper–Symonds law.Table 3 shows the properties of aluminum target plate and its finite element model.

2.4.Simulation results

The results of numerical simulation are compared with the experimental measurements reported by Liu et al.18The de formations of the bird model and the target plate at different time instants during impact are shown in Fig.3.

The simulated displacement and strain profiles vs time at the locations of sensors on target plate have been compared to the Liu et al.18experimental results in Fig.4.

As shown in Fig.4,displacement and strain profiles correlate well with Liu et al.18experimental results.Numerical results obtained for three different mesh densities show that discrepancy between graphs is decreased with the mesh refine-ment.The reason for discrepancies may be the simplification of bird geometry and material as well as the idealization of boundary conditions and finally the numerical errors.There fore,it can be concluded that modeling procedure is reliable and can be used for simulating the bird strike on wing leading edge structure.

Table 3 Specifications of target model.

Fig.3 De formation of bird and target plate during impact.

3.Analysis of bird strike on wing leading edge structure

Wing is a significant part of an airplane that generates lift and enables it to fly.Wing leading edge structure is the front part of a wing.The leading edge of an aircraft wing not only has aerodynamic function,but also should be able to protect the inner wing components from foreign object damaging.In this study,the wing has a structural layout consisting of skin,front and rear spars,4 spar caps and 19 ribs.Fig.5 shows these components of the wing structure.These structural parts are made of aluminum alloys and they have been connected to each other by rivets.

In this study we have assumed that initial bird velocity is equal to airplane cruise speed(61 m/s),and the bird impact point is the center of leading edge structure and the impact direction is along the chord line in Fig.6.Displacement boundary condition is applied to the wing root and the wing strut position.

Fig.4 Comparison of numerical and experimental results for displacement and strain on target plate at different locations.

Fig.5 Wing structure components.

Fig.6 Bird and wing structure model.

All contacts between components of the wing structure are modeled with ‘Contact_Automatic_Surface_To_Surface” in LS-DYNA. ‘Contact_Tiebreak_Nodes_To_Surface” is used to define the rivet behavior.In this type of contact,thefailure criterion for rivets can be stated as

where α and β are constants,FNand FNFthe normal force and critical normal force of rivets,respectively,and FSand FSFthe shear force and critical shear force in rivets,respectively.The values of parameters in Eq.(4)to model the rivet failure are shown in Table 4.25

Since all structural components of wing model are thin,they are discretized using four-node shell elements.The constitutive model employed for aluminum parts is an isotropic elastic plastic material model with strain rate sensitivity,as used for the target material in the previous section.A bilinear yield model with isotropic hardening and the Von Mises yield criterion is used to model aluminum behavior.Fig.7 shows a typical bilinear stress–strain curve used in this study.

Also a maximum strain criterion is used to define material failure,and it means when the equivalent strain in an elementreaches thefailure strain,that element no longer carries any load and will be deleted.The material properties for two aluminum alloys that are used here are represented in Table 5.26

Table 4 Rivet failure parameters.25

Fig.7 Bilinear stress–strain curve.

Designing of an optimum impact resistant wing leading edge structure is a challenge and requires extensive experimental testing.The present work aims at numerically predicting the response of a certain wing leading edge against bird strike,determining the effect of wing internal components on wing’s damage and mass,and designing an optimum wing structure using Taguchi method with grey relational analysis.Taguchi method can obtain optimum condition with the lowest cost and minimum number of experiments.Design of experiment process will be explained in Section 3.1.

3.1.Design of experiments

Taguchi’s design of experiments(DoE)is a statistical technique which uses an orthogonal array to study the entire parametric space with a minimal number of experiments.This work is conducted with 6 control factors;one of them has 2 levels and 5 other parameters vary at three levels.The wing’s 6 structural dimensions(control factors)considered in this study are wing skin thickness,wing rib thickness,wing rib distance,wing rib cut out(lightening hole)diameter,main spar location in chord direction relative to wing leading edge,and component material.All of these control factors and their levels are depicted in Table 6.

The levels of each parameter were considered on the basis of one level above and one level below to the primary design values,which had been obtained be fore.It should be noted that magnitudes shown in Table 6 are standard values.

Considering number of control variables and their levels,486 runs are needed,but modeling and running of this number of experiments are time consuming and exhausting,so in order to overcome this problem,we use Taguchi method.The degrees of freedom required for this study is 11 and Taguchi’s L18(2135)orthogonal array with 17 degrees of freedom is used to define the 18 trial conditions.Table 7 shows the experimental plan according to the selected orthogonal array.

The response variables chosen for the present work are wing structural mass and maximum displacement of wing skinafter the impact.These factors are highly significant and play an important role in the performance of a wing structure.

Table 5 Aluminum alloys’properties.26

Table 6 Control variables and their levels.

Table 7 Taguchi L18(2135)orthogonal array.

3.2.Signal-to-noise ratio(S/N)analysis

In the Taguchi method,a statistical parameter(the ratio of the mean to the standard deviation)called signal-to-noise ratio(S/N)is used to represent a performance characteristic.A larger S/N corresponds to a better quality.Since lower mass and skin displacement are desirable characteristics,in this study,the smaller-the-better quality characteristic has been used for calculating S/N of the responses.S/N can be calculated using the following equation:

where n is total number of experiments,i the No.of each experiment,and yithe response value of the ith experiment.Results of all 18 experiments and corresponding S/N are shown in Table 8.

The average of S/N for each level of a control variable is called the mean S/N and the maximum mean S/N of each parameter shows the optimal level of that parameter.Table 9 and Fig.8 show the mean S/N for wing structural mass.The last column of Table 9 shows that skin thickness and spar location have the most and the least effect on the wing’s mass,respectively.

As can be seen in Fig.8,the best combination of structural dimensions for minimizing the wing mass is A2B1C1D3E3F2,namely,material of Al 7075,skin thickness of 0.6350 mm,rib thickness of 1.016 mm,rib distance of 300 mm,cut out diameter of 76.2 mm,and spar location of 25%.

Table 10 and Fig.9 show the mean S/N for maximum skin displacement.

The last column of Table 10 shows that skin thickness and cut out diameter have the most and the least effect on the maximum displacement,respectively.As can be seen in Fig.9,the best combination of structural dimensions for minimizing the maximum displacement is A2B3C3D1E3F3,namely,materialof Al 7075,skin thickness of 1.0160 mm,rib thickness of 1.600 mm,rib distance of 200 mm,cut out diameter of 76.2 mm,and spar location of 30%.

Table 8 Experiment and S/N results.

Table 9 Mean S/N for mass.

Fig.8 Mass S/N graphs.

Table 10 Mean S/N for maximum displacement.

3.3.Grey relational analysis(GRA)

This study aims at minimizing the structural mass and wing skin deformation simultaneously.Although the Taguchi method cannot solve multi-objective optimization problem,this kind of problem can be converted into a single response one with grey relational analysis(GRA).

In GRA,experimental data are first normalized and transferred in the range from zero to one,afterward the grey relational coefficients are calculated,and then grey relational grades(GRG)are calculated by averaging the grey relational coefficients for the respective responses.So the multi response optimization problem is converted to a mono response problem.These steps are given as follows.

Fig.9 Displacement S/N graphs.

3.3.1.Grey relational generation

In this paper,minimizations of both structural mass and maximum displacement are desirable.There fore,the experimental data should be normalized as follows27:

The normalized values of structural mass and maximum displacement are shown in Table 11.As can be seen,the normalized values range between zero and one.

3.3.2.Grey relational coefficient and grey relational grade

Grey relational coefficients denote the relationship between the ideal and actual experimental results.Grey relational coefficient can be calculated as27

where Δ0i（k）is the deviation sequence of reference sequence x*0（k）and comparability sequence x*i（k）, Δminthe smallest value of the difference between x*0（k）and x*i（k）,Δmaxthe largest value of the difference between x*0（k）and x*i（k）,and ζ the distinguishing coefficient in the range between zero and one.In this study,ζ=0.5 is chosen.27

Grey relational grade is the mean of grey relational coefficients corresponding to each response and can be calculated using Eq.(11)

Table 11 Normalized experimental results.

where γiis the grey relational grade for the ith experiment and ktthe total number of responses(in this study,ktis 2).The grey relational coefficients and grey relational grades are calculated by Eqs.(7)and(11),respectively and presented in Table 12.

The higher the grey relational grade is,the better the multiple performance characteristics are.There fore,the higher grey relational grade indicates that the corresponding structural dimension combination is closer to the optimal point.Table 13 shows the mean of the grey relational grade for each level of the parameters and the values are represented graphically in Fig.10.

From the grey relational grade graph,the best combination of structural dimensions for minimizing the maximum displacement and structural mass simultaneously is A2B3C1D3E3F2,i.e.,material of Al 7075,skin thickness of 1.016 mm,rib thicknessof 1.016 mm,rib distanceof 300 mm,cut out diameter of 76.2 mm,and spar location of 25%.

3.3.3.Analysis of variance(ANOVA) for grey relational grade ANOVA is a statistical technique for analyzing the effect of design variables on a response.ANOVA was carried out on the grey relational grade values and the results are presented in Table 14.

Table 12 Grey relational coefficients and grades.

Table 13 Response table for grey relational grade.

Fig.10 Grey relational grade graph.

Table 14 ANOVA for grey relational grade.

The percentage contribution of each parameter is shown in the last column of Table 14.The results of the ANOVA indicate that material,skin thickness,rib thickness,rib distance,cut out diameter,and spar location influenced the grey relational grade values with 29.47%,45.30%,3.49%,2.40%,5.76%,and 1.39%,respectively.There fore,skin thickness and material are the two parameters significantly affecting the grey relational grade values and the spar location has no significant effect on the grey relational grade values.

3.3.4.Confirmation test

In the final step of Taguchi based GRA,once the optimum levels of the structural dimensions were selected,a confirmation test at the optimal levels was conducted to confirm and validate optimization results and also determine the improvement of responses.The grey relational grade at the optimal level of the design parameters can be estimated as28

Table 15 Results of confirmation experiment.

where γeis the estimated grey relational grade, γmthe total average grey relational grade,γithe average grey relational grade at the optimal level,and q the number of design parameters.Here q is equal to 6.

The estimated grey relational grade and experimental value which are obtained from the simulation at optimum point are indicated in Table 15.

Table 15 determines that there is a good agreement between the predicted and experimental results.It also shows that the grey relational grade at the optimal parameter combination has improved 50.3%compared to that at the initial parameter combination.

4.Conclusions

In this study,first,the experiment of bird strike to a flat aluminum plate has been simulated and the results have been verified by comparing with the experimental results.Then,the bird impact on an airplane wing leading edge structure is investigated.By considering dimensions of wing internal structural components,namely,skin thickness,rib thickness,rib distance,cut out diameter,spar location,and material,as design variables,the structural mass and wing skin de formation are simultaneously minimized using Taguchi based grey relational analysis.The following conclusions can be drawn from the present study:

(1)The bird strike simulation results agree well with experimental data and the model can be reliably employed for optimizing the structure.

(2)The signal-to-noise ratio analysis results give the optimal values for minimizing the wing mass and skin displacement when a single objective optimization is conducted.

(3)Multi-objective optimization results obtained using grey relational analysis give the recommended levels of structural dimensions when both the wing mass and the maximum skin displacement are simultaneously considered.

(4)Based on the analysis of variance for the grey relational grades,the skin thickness with the contribution of 45.3%is the most significant design variable on wing mass and maximum skin displacement.

(5)The grey relational gradefrom initial to optimal parameter combination has improved by 50.3%,which shows the improvement of performance of wing structure.

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4 June 2015;revised 18 September 2015;accepted 7 April 2016

Available online 22 June 2016

Bird strike;

Grey relational analysis;

Multi-objective optimiza

tion;

Smooth particle hydrodynamics(SPH);

Wing leading edge structure

?2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.Thisisan open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author.Tel.:+98 51 38805004.

E-mail addresses:h.pahange@yahoo.com(H.Pahange),abolbash@um.ac.ir(M.H.Abolbashari).

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http://dx.doi.org/10.1016/j.cja.2016.06.008

1000-9361?2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.

This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).