Adaptive-Twist Airfoil Based on Electrostatic Stiffness Variation

Adaptive-Twist Airfoil Based on Electrostatic Stiffness

Variation

Wolfram Raither∗

ETH Zurich, Zurich, 8092, Switzerland

Luca De Simoni†

Pilatus Aircraft Ltd., Stans, 6371, Switzerland

Luigi Di Lillo∗


Andrea Bergamini‡

Empa, Dubendorf, 8600, Switzerland

Paolo Ermanni§


Shape-adaptable airfoils with variable shear center location and torsional stiffness rep-resent a promising solution for controlling the aerodynamic loads on a wing by continuousdeformations instead of rigid-body attachments. In the present article, a structural con-cept for an adaptive-twist airfoil based on wing spars with variable mechanical topology isinvestigated. The integration of a smart material system relying on controllable electro-static attraction forces in the spars allows for reversible opening of the wing box and thusfor controlling the airfoil’s twist. While finite element simulations and static testing of anexperimental airfoil demonstrate the concept’s effectiveness, a numerical upscaling to thedimensions of a glider wing evaluates its potential with respect to a realistic application.Under the considered conditions, the upscaled adaptive-twist airfoil permits changes in liftcoefficient by around 20% in such an implementation.

Nomenclature

A Aerodynamic stiffness matrixB Chordwise wing box widthb WidthC Capacityc ChordcL Lift coefficientd DistanceE Young’s modulusG Shear modulusg Gravity accelerationh HeightK Stiffness matrixL Half spanM Mass matrixm Mass

∗Research assistant, Composite Materials and Adaptive Structures Lab, Leonhardstrasse 27.†Engineering trainee, Postfach 992.‡Group leader, Mechanics for Modelling and Simulation, Uberlandstrasse 129.§Full professor, Composite Materials and Adaptive Structures Lab, Leonhardstrasse 27.

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American Institute of Aeronautics and Astronautics

n Number of eigenmodesp Complex eigenvalueQ Shear forcet ThicknessV Voltagev Velocityw Deflection in z-directionx, y, z Coordinate directionsα Angle of attackε0 Vacuum permittivityεr Relative permittivityµ Friction coefficientν Poisson’s ratioρ Densityσ Normal stressτ Shear stressΦ Modal matrixϕ Twist angle about x-axis

I. Introduction

Tracing back to the first engine-powered airplane at all, the Wright Flyer from 1903,1 where it hasbeen applied for flight control, variable elastic wing twist has been proposed again more recently as a shapeadaptation technique for this purpose as well as for replacing conventional high-lift devices, for optimizingthe lift-to-drag ratio or for implementing load alleviation.2

In this context, the application of a semi-active structural concept utilizing aeroelastic amplificationeffects has been identified as a promising approach to vary the lift loads. However, nearly all of the reportedsemi-active strategies rely on conventional mechanisms and actuators attached to the load-carrying structurein order to vary the wing’s shear center location and/or its torsional stiffness, which finally affect the twist ofthe airfoil. Rigid-body kinematics and conventional actuators are observed in concepts based on shiftable3–10

or rotary3–6,11 wing spars as well as in an approach using a clutch-like mechanism and pneumatic jacks foropening and re-closing the wing spars.12,13 As a matter of principle, all these designs suffer not only from thelow degree of integration of the conventional actuators, but also from the general disadvantages of rigid-bodymechanisms, namely from high weight, wear, play and proneness to errors.

Stimulated by the need for research on semi-active structural concepts for variable wing twist withcompliant kinematics and smart materials, recent work has demonstrated the effectivity of adaptive bending-twist coupling by means of variable spar stiffness using a smart material with thermomechanical coupling.14,15

While testing of a scaled experimental airfoil structure and numerical upscaling to the conditions of a gliderwing have shown the great potential of the structural concept, the applied smart material, which exploitsthe glass transition of integrated polymer layers, suffers from high energy demand and long activation times.These issues are addressed by the work on hand by the investigation of an adaptive-twist airfoil based on asimilar structural design, but equipped with a smart material system relying on electromechanical couplingwhich promises advances in energy efficiency and activation speed.

II. Concept of Adaptive-Twist Airfoil with Variable Stiffness

The working principle of the adaptive-twist airfoil discussed in this article is illustrated in figure 1, alongwith the coordinate system that will be referred to in the following discussion. Smart interfaces (1 and 2 infigure 1) are integrated in the wing spars which allow to open and (re-)close the wing box. These changesin topology affect the structure’s chordwise shear centre location and its torsional stiffness, so that they canbe exploited for controlling the twist when the airfoil is subject to a transverse shear load caused by the liftforce.

For the following explanation of the working principle, the lift force is assumed to point in z-direction,which is a good assumption for small angles of attack. In the wing’s initial configuration with both interfaces

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closed (image a) in figure 1), the lift force is further presumed to act in the airfoil’s shear center, so thatno twist occurs. If, for example, interface 1 is opened at first (image b) in figure 1), the shear center movestowards the trailing edge, inducing a nose-up twisting moment, and at the same time the torsional stiffnessis lowered substantially. Accordingly, the airfoil twists in wash-in direction, which raises the lift force.Afterwards, interface 1 can be closed again in order to restore the airfoil’s original load-carrying capability.

1 2 y

a)

b) c)

z

Figure 1. Illustration of the working principle of an adaptive-twist airfoil with variable spar topology. a) both smart inter-faces closed, b) front interface open, c) rear interface open.Arrows represent lift force and twisting moment.

If a reverse twist maneuver is required sub-sequently, interface 2 can be opened (image c)in figure 1). This causes not only the shearcenter to move to the leading edge, but alsothe release of residual stresses “frozen” in thestructure due to the previous closure of inter-face 1. As a consequence, the airfoil twistsback, and interface 2 can be closed again.

The fundamentals of the working princi-ple characterized before determine some gen-eral characteristics of the structural layout anddesign of the adaptive-twist airfoil: First, thewing box has to be placed comparably far up-stream if the airfoil’s shear center has to co-incide with its aerodynamic center in the ini-tial configuration, since the latter is located atabout a quarter of the chord for many commonairfoil shapes. Second, the wing box has a relatively low (chordwise) width for this reason. Third, if the dropin torsional stiffness enabled by opening the wing box shall be fully exploited, also the cells in the airfoil’sfront and back, which remain closed and thus contribute considerably to the overall torsional stiffness, haveto be opened before shape changes are performed. This can be realized either by additional interfaces withvariable topology in the skin or by simple openings. For practical reasons, the latter solution is implementedin the present work. Fourth, as the airfoil’s twist behaviour is dominated by warping in the open state, thewarping stiffness of the remaining structure has to be low in order to allow for a wide twist adaptation range.This fact has an impact on the rib design of the adaptive-twist airfoil, as conventional ribs with plate-likeshape would constrain the warping too much. For the novel airfoil concept, frame-like, open ribs as evidentfrom figures 3 and 4 should be chosen instead, which represent a good compromise between sufficient shearand (local) bending stiffness (according to the ribs’ reinforcing functions) and low warping rigidity.

+

-td

Figure 2. Working principle of electro-bonded laminate (EBL). Dielectric layer(shown in blue) between two electrodes ofdifferent potential attracting each other.Shear forces are transferred by friction atthe electrode-dielectric interface.

As a smart material system putting the desired changes inwing box topology into effect, electro-bonded laminates (EBL)are integrated in the spars. As illustrated in figure 2, the work-ing principle of EBL can be described as the electromechanicalutilization of a plate capacitor. An electric potential betweentwo electrodes separated by a dielectric layer causes an attrac-tion force between the electrodes and, combined with frictionat the electrode-dielectric interface, the possibility to trans-fer shear stresses at this interface. The controllability of thesystem’s shear strength follows directly from the voltage de-pendence of the interlaminar normal stress ensuing from theattraction force, which is referred to as Maxwell stress:16

σ =1

2ε0εr

(V

td

)2

(1)

In equation 1, ε0εr represents the dielectric’s permittivity, V denotes the voltage between the electrodes andtd the thickness of the dielectric layer. The fundamental relations of equation 1 determine the voltage to bein the kV range in usual practical applications of EBL, thicknesses to be of the order of magnitude of 10 µmand relative permittivity values (of commonly applied polymer dielectrics) to range around three.

With respect to a well established bonding at the friction interface, also at least one of the electrodesshould be compliant and thus—in the usual case of a metallic material—also thin in order to allow for anadaptation of the interface, such that potential air gaps can be closed.

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If the shear strength of a single interface is not sufficient for a certain application, or if a symmetricalconfiguration is requested, for example to exclude bending of the interface, several electro-bonded laminatescan be arranged in parallel, which can be expected to be feasible in many applications due to the explainedthin nature of the EBL.

The adjustable shear stress transfer of electro-bonded laminates has been successfully applied underlaboratory conditions for multilayered beams with adaptive bending stiffness17,18 and friction damping19,20

as well as for an active morphing airfoil section with variable-stiffness skin.21 Due to the predominance ofthe capacitive behaviour in its energy balance, the electro-bonded laminate is generally characterized by lowenergy requirements.

III. Numerical Simulation

z

y

x

L

lp

Figure 3. Finite element model of experimental adaptive-twist airfoil (upper skin hidden).

A. Simulation of Experimental Airfoil

In order to generate a suitable design of the experimental airfoil to be investigated by static mechanicaltesting as described in IV, a finite element simulation of this structure has been set up.

A screenshot of the finite element model of the experimental airfoil is shown in figure 3, along with thedefinitions of the coordinate system used for the experimental airfoil and of the airfoil’s spanwise geometricquantities. The general design characteristics of the adaptive-twist airfoil mentioned before can be recognizedin this illustration. Furthermore, a representation of the spanwise linear bearings employed for the wing sparsfor reasons explained in section IV and their protrusion at the wing root are evident from this image. Figure 4presents the geometric parameterization applied to cross sections of adaptive-twist airfoils, and the respectiveparameter values chosen for the experimental airfoil, which has a NACA 0012 shape, are reported in table 1.The dashed lines used in figure 4 for the rib close to the leading edge account for the two different rib shapespresent in the design of the experimental structure: Only every second rib bridges the opening in the skin,which is utilized as an additional degree of freedom in the rib design problem characterized by the trade-offbetween shear and warping stiffness, as introduced before. In figure 5 and table 2 the detailed design of thewing spars featured with double-lap EBL interfaces is reported. Concerning the rib thickness, tr = 0.45mmhas been chosen.

While the skin of the experimental airfoil consists of a carbon-fiber reinforced epoxy, spar plates and ribsare made of glass-fiber reinforced epoxy. The mechanical properties of the respective single plies of thesematerials and the laminate layups of the different components are specified in the appendix. The materialproperties assumed for the aluminium employed for the wing spar bearings can also be found in the appendix.

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c

Bd

hr

ts

br

bo1 b

o2

Figure 4. Geometric parameters of a cross section of an adaptive-twist airfoil.

Table 1. Geometry of experimental airfoil.

Parameter L lp c B d ts hr br bo1 bo2

Value, mm 1’000 200 300 61 47 0.85 5 2 6 6

h

hb

bb

d1

tsi

tso

d2

Spar plates

Dielectrics

Electrodes

Figure 5. Composition and geometric parametersof the front and rear spar with integrated EBLinterfaces.

ANSYS 14.0 is applied for the finite element mod-elling. All structural components except for the linearbearings are thin-walled and thus represented by shell el-ements (SHELL181 ), while the aluminium bearings aremodelled by SOLID185 elements. The structural modelis discretized into finite elements with a characteristic sizeof about 4mm, most of the shell elements being rectan-gular with an approximately square aspect ratio.

A coupled electroelastic numerical modelling of theEBL interfaces goes beyond the scope of this work whichfocuses on the global structural behaviour of the adaptive-twist airfoil instead of the phenomena on the materiallevel. In order to represent the voltage-dependent shearstrength of the electromechanical interfaces in the finiteelement model in a simplified way, the Maxwell stress isdirectly calculated according to equation 1 and applied asa substitute (purely mechanical) stress to the interfaces in the structural model. The friction enabling shearstress transfer at the overlaps of the interfaces is modelled by means of CONTACT173 and TARGET170elements, assuming a friction coefficient of µ = 0.3a. This way, the influence of elastic deformations on theelectric field is neglected, but on the other hand, model size and complexity can be greatly reduced comparedto a coupled-fields simulation.

Corresponding to the experimental setup, the numerical model is clamped at the upper and lower partof the skin inside the wing boxb, and the aerodynamic pressure is replaced by a concentrated shear force atthe wing tip, in the center of pressure, i. e. at y = c/4. This load is introduced in the airfoil’s tip rib forpractical reasons, and therefore the thickness of the tip rib is doubled with respect to the other ribs.

It has to be mentioned that the reported wall design of the experimental adaptive-twist airfoil was notarbitrarily chosen, but is rather the result of a sizing process accounting for the critical requirements for theairfoil. The wing shall be sized for an ultimate shear force of Qmax = 100N, which corresponds to the totallift resultant of the airfoil for a flow velocity of v ∼= 35m/s under standard conditions at sea level.

aUnder similar conditions, experimentally determined values close to µ = 0.3 have been reported.22bExactly, the clamping has a chordwise width of 40mm and is centered with respect to the wing box centroid.

Table 2. Geometry of the wing spars.

Parameter h tsi tso d1 d2 bb hb

Value, mm 12.7 1 0.1 7 2.5 12 6

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First, static strength and stability of the structure have to be ensured for this load. The strength ofthe EBL interfaces, which constitute the structure’s weakest parts, is considered by the aforementionedsimulation of the smart material. Referring to stability, a smallest buckling factor of 3.1 is achieved with thechosen design.c

Second, the adaptive airfoil shall allow for considerable changes in twist. The performance of the chosendesign in this respect is reflected in the results reported in section V.A.

Third, aeroelastic stability has to be ensured for the assumed flight conditions. While divergence of theexperimental airfoil can be directly identified in certain unconverged solutions of the aeroelastic calculationprocedure explained in III.B when applied to the numerical model discussed before, the bending-twist flutterspeed has been determined by a modal flutter calculation (see also III.B). According to these aeroelasticinvestigations, divergence and flutter velocity amount to vdiv = 45m/s and vflut = 100m/s in the respectivecritical state.d

B. Upscaling and Aeroelastic Simulation

With respect to a demonstration of the suitability of the novel wing concept for an application underconditions close to the ones of a realistic airfoil, a numerical upscaling to the dimensions and flight conditionsof a glider plane is performed.

A rectangular wing with a span of 2L = 15m, a chord length of c = 0.6m and a NACA 0012 shape hasbeen assumed for this purpose. Concerning the flight conditions, a flow velocity of v = 40m/s, an airplanemass of m = 300 kg and an operation in standard atmosphere at sea level have been assumed. A stationaryhorizontal flight under these assumptions requires a lift coefficient of

cL =mg

ρv2Lc= 0.33 (2)

if an air density of ρ = 1.225 kg/m3 and a gravitational acceleration of g = 9.81m/s2 are presumed. As thebaseline configuration of the adaptive-twist airfoil in the original state (with both interfaces closed) meetsthis requirement for an angle of attack of α = 3.5◦, this value is used for all aeroelastic calculations. Interms of wing area, aspect ratio, flight speed and surface loading, the assumed conditions are representativeof the ones of a typical 15 m glider plane like the Schleicher ASW 27 .23

The upscaled wing has to meet stability and strength requirements under these operating conditions. Forthis reason, a minimum buckling factor of 1.5 is required for the airfoil designs considered in the upscalinginvestigation. In these simulations, the interface shear stresses are required to stay below τmax

∼= 0.15MPae,which eliminates the need to define interface voltage and specific dielectric properties of the smart material.

In order to solve the coupled aeroelastic problem, the iterative calculation procedure reported in a pre-vious work15 is applied which involves an ANSYS -based structural finite element model as well as—on theaerodynamic side—a code relying on thin-airfoil theory and a lifting line method accounting for spanwiseeffects.

Divergence Analysis

The airfoil’s divergence speed vdiv can be identified in simulations based on the aeroelastic calculation cycleas the smallest flow velocity for which a non-converging solution is observed that shows the characteristicsof torsional divergence.

Flutter Analysis

Modal flutter calculations based on a steady-state aerodynamic operator and a p-method24,25 have beenperformed. For a certain flight speed, the mass matrix M, the stiffness matrix K and the aerodynamicstiffness matrix A can be determined using the aforementioned aeroelastic simulation environment. They

cThis buckling factor is obtained even in the most critical state in which both spar interfaces are open, which is not intendedto be a state of operation of the airfoil.

dConcerning divergence, the critical state is represented by the one with open front interface and closed rear interface. Forflutter, in contrast, the one with open rear spar and closed front spar is most critical. For the aeroelastic simulations, no slidingis assumed to take place in the smart interfaces.

eThis value has been identified as the EBL’s approximate shear strength (including a certain safety) at electric fieldsreasonably below the dielectric’s breakdown strength in preliminary experiments under conditions close to the envisaged ones.

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are then transformed into the according generalized modal matrices M, K and A by means of operationsinvolving the modal matrix Φ extracted from the structural model:

M = ΦTMΦ, K = ΦTKΦ, A = ΦTAΦ (3)

If n eigenmodes are considered for the modal representation of the system, the generalized matrices have thedimension n× n.

The procedure leads to characteristic equations of the form

det(Mp2 +K−A) = 0 (4)

which can be solved for the eigenvalues p.The flutter speed vflut is then given by the smallest flow velocity for which at least one real part of one

of the n eigenvalues exhibits a positive sign. For the calculations reported in the article on hand, the n = 3lowest eigenmodes have been considered.

Concerning the determination of the mass matrix, the mass density values specified in the appendix forthe different materials constituting the airfoil structure have been used.

IV. Experiment

Figure 6. Inner structure of experimentaladaptive-twist airfoil.

Figure 7. Clamping at the root of the exper-imental adaptive-twist airfoil.

Figure 8. Tip of experimental adaptive-twist airfoil.

In order to demonstrate the realizability and effectivity of the proposed structural concept under lab-oratory conditions and to validate the numerical work, an experimental adaptive-twist airfoil has beenmanufactured and subjected to static mechanical tests.

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The main characteristics of the experimental adaptive-twist airfoil have already been mentioned in thecontext of the according numerical simulation, and they are evident from figure 6 which shows a photographof the experimental structure before closing it with the remaining skin parts. The three skin shells have beenmade using the Toho Tenax HTS40/ACG MTM 44-1 unidirectional carbon fibre/epoxy out-of-autoclaveprepreg system. They have been laminated on a positive aluminium mold and—to obtain a smooth outersurface suited for future wind tunnel experiments—a negative GFRP mold. The ribs, on the other hand,consist of wet-laminated GFRP (290 g/m2 Tissa fabric; epoxy resin Hexion L 235 and hardener 235 ), andGFRP plates by Suter Kunststoffe have been employed for the spar parts. In order to integrate the smartEBL interfaces, steel electrodes of 50µm thickness are bonded to the overlap areas of the spar plates usingadhesive tape. As it is obvious from figure 7, a steel block inserted 90mm deep into the structure and bondedby means of epoxy serves as a clamping for the airfoil.

Figure 9. Experimental setup.

To account for the risks of electrical breakdown of the dielectriclayer and other kinds of damage of the electro-bonded laminates,the interfaces are required to be replaceable. This specification hasto be put into practice by designing both spars to be removable bymeans of dovetail bearings milled from aluminium (cf. figure 6).Grooves in the positive dovetail profiles permit to glue in the sparplates, and the negative rails are bonded to the airfoil skin. Dueto the protrusion of spars and bearings at the wing root (see figure7), screw clamps can be applied to constrain the linear motion aftermounting of the spars. Additionally, aluminium end plates at thewing tip allow for screw joints between the respective two parts ofthe linear bearings, as shown in figure 8.

A M5 screw connected to the tip rib by means of a bonded alu-minium part serves for the introduction of controlled transverse shearloads exerted by a Zwick/Roell Z005 tensile tester with 100N loadcell and transmitted by means of a cord. The load application pointat the wing tip, at y = c/4, is also visible in figure 8. The deflec-tions of the loaded airfoil in z-direction are recorded on the upperskin surface, at the chordwise locations of the wing spars, using twoMicro-Epsilon optoNCDT 1700 laser triangulation sensors. Load in-troduction and deflection measurement are visible in the photographof the experimental setup presented in figure 9.

Concerning the application of voltage to the EBL interfaces, two PS350 voltage sources by StanfordResearch Systems are connected to the electrodes, one for each spar. The td = 25µm thick dielectric film3M CM500, which is composed of polycarbonate and poly(methyl methacrylate) layers, is used for the EBLinterfaces. For this material, a relative permittivity of εr = 3.57 has been reported.26

V. Results and Discussion

A. Experimental Airfoil

Figures 10 and 11 present the deflection compliance of the experimental adaptive-twist airfoil recorded atthe two mentioned measurement points for two different system states: In the “back open” state, whoseresults are reported in figure 10, the electro-bonded laminate in the back spar is kept at zero Volts, whilevoltages between 0 and 3000V are applied to the interfaces in the front spar. Accordingly the “front open”state, on which the results of figure 11 are based, is characterized by an electrically grounded front interface,while the EBLs in the back spar are subjected to a positive voltage. Figure 12, on the other hand, showsthe twist compliance derived from these deflections for the same interface states and the same voltage range.Both twist and deflection compliance values are compared in the figures to the according results of the finiteelement simulation discussed before. All results are based on transverse forces Q = 10N.

The electric capacity of one of the integrated double-lap EBL interfaces in the undeformed state istheoretically given by

C = ε0εr2hL

td= 32.1 nF (5)

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while for the interfaces of the experimental structure 9.3 nF (front spar) and 17.4 nF (back spar) havebeen measured at low voltage. The simulations of the experimental structure have thus been conductedusing accordingly corrected dielectric properties for the calculation of the attraction stress of the interfaces,assuming that a lower relative permittivity of the dielectric layer is causative for the reduced capacitance.f

Qualitatively, the deflection results confirm the expectations on the voltage-dependent shear strength ofthe EBL interfaces: Gradually raising the electric potential of the smart material leads to an increasing shearstrength of the wing spars and thus to a decreasing deflection compliance. However, the voltage influence isnot as high in the experimental structure as predicted by the numerical simulation. While at zero voltagethe measured deflections agree with the calculated ones to about 10%, the simulation largely overestimatesthe reductions in deflection by the interface voltage. This indicates that the interfaces in the spars slidemore in the experiment than in the simulation.

There are many potential reasons for the reduced performance of the real EBL interfaces comparedto the theoretical expectations. The presence of air gaps between electrodes and dielectric layers in theexperiment can be assumed as such a reason. Although the manufacturing tolerances have been minimizedas much as possible, these inclusions seem to be unavoidable without taking special countermeasures. Inthe simulation, the according degrading influence has only been considered by a reduced dielectric constant,while the mechanical effect of lost contact at the locations of air gaps, which can be expected to be veryimportant, could not be taken into account. In particular, it can be concluded that the relative reductionin contact area (referring to the contact between electrodes and dielectrics) caused by air inclusions has tobe bigger than the respective relative reduction in capacity, due to the fact that air gaps contribute to thecapacity, but not to the mechanical contact.

Also concerning the twist, the expected influence of the smart interfaces is observed in both experimentaland simulation results: Gradually closing the EBL in the rear spar by application of voltage permits tolower the twist, while activating the front spar raises the twist, allowing for torsional angles of positive sign.Changes in twist compliance by factors of up to about three are possible in both directions.

Surprisingly, the twist angle shows a better agreement between numerical and experimental values athigher voltages, despite being derived from the deflection data. Apparently, the twist is characterized by alimited sensitivity on the influence/-s that caused the deviations of numerical and experimental deflectionvalues. This gives rise to the assumption that the linear bearings of the wing spars—although being clampedat the ends—exhibit a certain play which causes sliding deformations. Such a sliding could not only explainthe high deflection compliance of the experimental structure, but also—due to facilitation of warping of therespective open spar—its relatively high twist angles. These influences might be at the bottom of the higherrelative deviations of the deflection compared to the ones of the twist, which can not be explained only bylocal sliding of the interfaces.

No definite cause was found for the decreasing absolute values of twist deflection for both combinationsof interface activation in the simulation results. The fact that they were not observed when changing thespanwise location or the load indicates that their relevance for the application of the structural concept ingeneral is however low.

B. Upscaling

The lift coefficient of the upscaled adaptive-twist airfoil has been evaluated under variation of two maindesign parameters: the relative chordwise offset d/c of the wing box and the wing aspect ratio L/c. Bothparameter ranges contain the configuration of the glider wing that has been previously introduced as thevirtual example for an application of the adaptive-twist concept. The results are presented in figures 13to 16, showing the capability of the adaptive-twist concept to change the lift loads when integrated in arealistic wing structure. The cL curves are shown for the two system states introduced before, where the“front open” state is set subsequent to an operation of the airfoil in the “rear open” one.

As expected from the relation of shear center and center of pressure, shifting the wing box to the trailingedge generally leads to more pronounced wash-in twist and hence higher lift coefficients. However, theincrements in lift cause the interfaces to slide locally at certain d/c values and thus lead to a twist curvethat does not strictly increase with the wing box offset (in the case shown in figure 13).

Raising the wing aspect ratio results in a convex behaviour, both in terms of the lift coefficient and of thedifference in lift between both states. This is due to the fact that at higher aspect ratios the lower stiffness

fA deeper discussion of this issue is given below.

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0 500 1000 1500 2000 2500 30000.02

0.04

0.06

0.08

0.1

0.12

0.14

Voltage V, V

Def

lect

ion

com

plia

nce

w/Q

, mm

/N

Front spar, experimentRear spar, experimentFront spar, simulationRear spar, simulation

Figure 10. Deflection compliance of the experimentaladaptive-twist airfoil in the two measurement pointswith respect to applied voltage in the “back open”state. Comparison of experimental and numerical re-sults.

0 500 1000 1500 2000 2500 30000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Voltage V, V

Def

lect

ion

com

plia

nce

w/Q

, mm

/N

Front spar, experimentRear spar, experimentFront spar, simulationRear spar, simulation

Figure 11. Deflection compliance of the experimentaladaptive-twist airfoil in the two measurement pointswith respect to applied voltage in the “front open”state. Comparison of experimental and numerical re-sults.

0 500 1000 1500 2000 2500 3000−6

−4

−2

0

2

4

6

8x 10

−3

Voltage V, V

Tw

ist c

ompl

ianc

e φ/

Q, °

/N

Back open, experimentBack open, simulationFront open, experimentFront open, simulation

Figure 12. Twist compliance of the experimental adaptive-twist airfoil with respect to applied voltage in the“back open” and in the “front open” state. Comparison of experimental and numerical results.

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of the airfoil leads to higher twist angles and thus higher lift loads, so that the spar interfaces slide locallyand the shear center shift cannot be maintained anymore by the front interface.

At the present conceptual state of this work, the adaptive capability of the novel airfoil concept shall beevaluated independently from the requirements of specific potential applications. In this sense, the amplitudeof the adaptation range in terms of lift coefficient around the equilibrium value can be used as a performancemeasure here. For the upscaled adaptive-twist airfoil, the amplitude of such lift variations depends on theaspect ratio as well as on the wing box offset. During a wing design process, the former quantity is howevermore likely to be determined by other requirements, so that the latter can be used to adjust the center ofthe lift adaptation range to the equilibrium lift.

Under the assumption of an EBL shear strength of τmax = 0.15MPa (figures 13 and 14), the maximumrelative change in lift that can be achieved between the two operating states of the adaptive-twist airfoil islimited to about 10% in the considered range of parameter values for wing box offset and wing aspect ratio.The presented curves indicate that the performance is mainly compromised by the low shear strength of thesmart interfaces. In order to demonstrate the high dependence of the adaptation capability of the upscaledairfoil on the load-carrying qualities of the spar interfaces, additional calculations assuming a shear strengthof the electro-bonded laminates of τmax = 0.3MPa have been performed. The practical significance of thisdoubled strength value can be given either by an integration of two double-lap interfaces arranged in parallelin each wing spar or by a further development of the EBL technology. The results, which are presented infigures 15 and 16, show considerable increases in the amplitude of the adaptation range, maximum relativechanges in lift ranging around 20%.

0.1 0.12 0.14 0.16 0.180.3

0.32

0.34

0.36

0.38

0.4

0.42

0.44

Normalized wing box offset d/c, −

Lift

coef

ficie

nt c

L, −

Back interface closedFront interface closed

Figure 13. Lift coefficient of upscaled adaptive-twistairfoil with respect to relative wing box offset in the“back open” and in the “front open” state. Aspectratio L/c = 12.5. τmax = 0.15MPa.

5 6 7 8 9 10 11 12 130.31

0.32

0.33

0.34

0.35

0.36

0.37

Aspect ratio L/c, −

Lift

coef

ficie

nt c

L, −


Figure 14. Lift coefficient of upscaled adaptive-twistairfoil with respect to wing aspect ratio in the “backopen” and in the “front open” state. Relative wingbox offset d/c = 0.15. τmax = 0.15MPa.

VI. Conclusion and Outlook

The structural concept of an adaptive-twist airfoil based on spars with controllable topology by integratedelectro-bonded laminates has been shown to be effective by numerical simulation and by experiment. Likein earlier designs relying on variable-stiffness spars, the synergetic interaction of shear center shifting andvariations in torsional stiffness can be exploited for changes in the bending-twist coupling ratio of the airfoilof considerable magnitude. Due to the utilization of aeroelastic coupling, the concept is semi-passive andthus especially promising in terms of energy efficiency and lightweight potential.

Comparing numerical and experimental results for the scaled experimental airfoil reveals that qualita-tively the structure behaves as expected, but the performance of the smart material in its state-of-the-artimplementation falls short of the theoretical expectations for high electric fields. This leads to large quanti-tative deviations between the deflection results of simulations and measurements at higher interface voltages.Moreover, “parasitic” sliding in the linear bearings of the wing spars potentially overlays the desired effects.Nevertheless, the airfoil’s twist behaviour remains predictable by the simulation, and changes in twist com-

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0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.220.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4

Normalized wing box offset d/c, −

Lift

coef

ficie

nt c

L, −


Figure 15. Lift coefficient of upscaled adaptive-twistairfoil with respect to relative wing box offset in the“back open” and in the “front open” state. Aspectratio L/c = 12.5. τmax = 0.3MPa.

4 6 8 10 12 14 16 180.26

0.28

0.3

0.32

0.34

0.36

Aspect ratio L/c, −

Lift

coef

ficie

nt c

L, −


Figure 16. Lift coefficient of upscaled adaptive-twistairfoil with respect to wing aspect ratio in the “backopen” and in the “front open” state. Relative wingbox offset d/c = 0.15. τmax = 0.3MPa.

pliance up to a factor of about three have been observed for the experimental airfoil in both directions oftwist.

It should be mentioned in this context that the concentrated shear loads applied to the experimentalairfoil structure affect the shear strength of the EBL interfaces in an especially negative way, so that highershear strength values can be expected for the realistic case of distributed loading by aerodynamic pressure.

The main problems of the experimental structure, namely the limited performance of the smart interfacesand the presumed play of the linear bearings, are particularly related to the small scale of the experimentalstructure and to the relatively low manufacturing precision under laboratory conditions. For an airfoil ofbigger size produced in an industrial process, these issues would be less pronounced.

Aeroelastic investigations show that the occurrence of divergence and flutter, which represent general lim-itations of the adaptive-twist concept, can be shifted to sufficiently high speeds by an appropriate structuraldesign, so that aeroelastic stability does not constitute the most critical issue for a wide range of operatingconditions of an adaptive twist-airfoil with electrostatic interfaces.

The theoretical upscaling of the concept to the dimensions and operating conditions of a glider plane wingby means of numerical aeroelastic calculations demonstrates the effectiveness of the new structural conceptwhen applied in a realistic design. Furthermore, it shows that an adaptive-twist wing box can in principlebe well integrated in a conventional wing structure. At the same time, the upscaling investigations point outthat, as the maximum twist angles are of the order of few degrees, the resulting achievable changes in liftup to around 20% stay far below the ones of conventional hinged attachments. Due to the low technologyreadiness of the novel airfoil design, this deficit is not surprising. Especially the current implementation ofthe integrated smart material does not provide enough shear strength to virtually close the adaptive sparsunder the conditions assumed for the upscaling. Future work on the proposed structural concept shouldtherefore focus on an extension of the adaptation range of the variably twisting airfoil by improving theelectro-bonded laminates, as well as by structural optimization.

Concerning the very important former point, not only the research on materials combining high per-mittivity with high dielectric strength should continue, but also the failure mechanisms of electro-bondedlaminates should be thoroughly investigated.

At the present state of the technology, the integration of more EBL interfaces in a parallel arrangementin the wing spars represents a viable way to increase the performance of the adaptive-twist airfoil. Providingthat this enhancement of the airfoil design can be implemented, wind tunnel tests on adaptive-twist airfoilswill be carried out.

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Appendix

Material properties

Table 3. Elastic material properties and mass densities used for finiteelement simulations.

E11, GPa E22, GPa G12, GPa ν12, – ρ, kg/m3

CFRP1 100.0 8.0 5.0 0.28 1’550

GFRP2 18.0 = E11 3.5 0.13 1’800

Aluminium 73.1 = E11 = E11

2(1+ν12)0.33 2’780

1Unidirectional reinforcement. E11 and E22 determined by flexural tests.2Bidirectional reinforcement. E11 and E22 determined by flexural tests.

Laminate layups

Table 4. Laminate layups of CFRP and GFRP components.

Component Layup, ◦

Skin [0; 60;−60]sRibs [0/90]

Acknowledgments

RUAG Aviation (Emmen, Switzerland) is acknowledged for component manufacturing.

References

1“The Wright Flyer,” Flight , 11 Dec 1953, pp. 787–788.2Barbarino, S., Bilgen, O., Ajaj, R. M., Friswell, M. I., and Inman, D. J., “A Review of Morphing Aircraft,” Journal of

Intelligent Material Systems and Structures, Vol. 22, No. 9, 2011, pp. 823–877.3Amprikidis, M. and Cooper, J. E., “Experimental Validation of Wing Twist Control using Adaptive Internal Structures,”

45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Palm Springs, 2004.4Cooper, J. E., “Adaptive Stiffness Structures for Air Vehicle Drag Reduction,” Multifunctional Structures/Integration of

Sensors and Antennas. Meeting Proceedings RTO-MP-AVT-141 , Neuilly-sur-Seine, 2006.5Hodigere-Siddaramaiah, V. and Cooper, J. E., “On the Use of Adaptive Internal Structures to Optimise Wing Aero-

dynamic Distribution,” 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference,Newport, 2006.

6Cooper, J. E., “Adaptive Aeroelastic Structures,” Adaptive Structures: Engineering Applications, edited by D. Wagg,I. Bond, P. Weaver, and M. Friswell, John Wiley & Sons, Chichester, 2007, pp. 137–162.

7Ajaj, R. M., Friswell, M. I., Dettmer, W. G., Allegri, G., and Isikveren, A. T., “Conceptual Modeling of an AdaptiveTorsion Wing Structure,” 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference,Denver, 2011.

8Ajaj, R. M., Friswell, M. I., Dettmer, W. G., Allegri, G., and Isikveren, A. T., “Dynamic modelling and actuation of theadaptive torsion wing,” Journal of Intelligent Material Systems and Structures, 2012.

9Ajaj, R. M., Friswell, M. I., Dettmer, W. G., Allegri, G., and Isikveren, A. T., “Performance and control optimisationsusing the adaptive torsion wing,” The Aeronautical Journal , Vol. 116, No. 1184, 2012, pp. 1061–1077.

10Ajaj, R. M., Friswell, M. I., Dettmer, W. G., Isikveren, A. T., and Allegri, G., “Roll control of a MALE UAV using theadaptive torsion wing,” The Aeronautical Journal , Vol. 117, No. 1189, 2013, pp. 299–314.

11Chen, P. C., Sarhaddi, D., Jha, R., Liu, D. D., Griffin, K., and Yurkovich, R., “Variable Stiffness Spar Approach forAircraft Maneuver Enhancement Using ASTROS,” Journal of Aircraft , Vol. 37, No. 5, 2000, pp. 865–871.

12Runge, J.-B., Maıtrise du vrillage de profils aerodynamiques par controle reactif , Ph.D. thesis, Conservatoire Nationaldes Arts et Metiers, Paris, 2010.

13Runge, J.-B., Osmont, D., and Ohayon, R., “Twist control of aerodynamic profiles by a reactive method (experimentalresults),” Journal of Intelligent Material Systems and Structures, Vol. 24, No. 8, 2013, pp. 908–923.

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14Raither, W., Bergamini, A., and Ermanni, P., “Profile beams with adaptive bending-twist coupling by adjustable shearcenter location,” Journal of Intelligent Material Systems and Structures, Vol. 24, No. 3, 2013, pp. 334–346.

15Raither, W., Heymanns, M., Bergamini, A., and Ermanni, P., “Morphing wing structure with controllable twist basedon adaptive bending-twist coupling,” Smart Materials and Structures, Vol. 22, No. 6, 2013, pp. 065017.

16Maxwell, J. C., A Treatise on Electricity and Magnetism, Vol. 1, Clarendon Press, Oxford, 1873.17Bergamini, A., Christen, R., Maag, B., and Motavalli, M., “A sandwich beam with electrostatically tunable bending

stiffness,” Smart Materials and Structures, Vol. 15, 2006, pp. 678–686.18Bergamini, A., Christen, R., and Motavalli, M., “Electrostatically tunable bending stiffness in a GFRP CFRP composite

beam,” Smart materials and structures, Vol. 16, No. 3, June 2007, pp. 575–582.19Bergamini, A., Christen, R., Motavalli, M., and Ermanni, P., “Distributed Damping of Large Structures,” 19th Interna-

tional Conference on Adaptive Structures and Technologies (ICAST), Ascona, 2008.20Bergamini, A., Electrostatic Modification of the Bending Stiffness of Adaptive Structures, Ph.D. thesis, ETH Zurich,

2009.21Raither, W., Furger, E., Zundel, M., Bergamini, A., and Ermanni, P., “Variable-stiffness skin concept for camber-

morphing airfoils,” 24th International Conference on Adaptive Structures Technologies (ICAST), 2013.22Di Lillo, L., Raither, W., Bergamini, A., Zundel, M., and Ermanni, P., “Tuning the mechanical behaviour of structural

elements by electric fields,” Applied physics letters, Vol. 102, No. 22, Jun 2013, pp. 224106.23Type-Certificate. Data Sheet. ASW 27 , EASA, 2008.24Bisplinghoff, R. L. and Ashley, H., Principles of Aeroelasticity, John Wiley & Sons, New York, 1962.25Hodges, D. H. and Pierce., G. A., Introduction to Structural Dynamics and Aeroelasticity, Cambridge University Press,

Cambridge, 2002.26Di Lillo, L., Dielectrics for Variable Stiffness Elements, Ph.D. thesis, ETH Zurich, 2013.

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Adaptive-Twist Airfoil Based on Electrostatic Stiffness Variation