Jtam.dvi JOURNAL OF THEORETICAL AND APPLIED MECHANICS 47, 4, pp. 897-921, Warsaw 2009 A FEASIBILITY STUDY ON THE BEHAVIOUR OF A HELICOPTER SMART BLADE AIMED AT BLADE TIP MORPHING Claudio Testa INSEAN – Italian Ship Model Basin, Propulsion and Cavitation Department, Rome, Italy e-mail: c.testa@insean.it Stefania Leone University of Palermo, Transport Engineering Department, Palermo, Italy e-mail: leone@diat.unipa.it Salvatore Ameduri Antonio Concilio CIRA - Italian Aerospace Research Center, Smart Structures Laboratory, Capua, Italy e-mail: s.ameduri@cira.it; a.concilio@cira.it In this paper, the behaviour of ahingeless helicopter bladewith anovel integra- ted smartmorphing actuator is studied. The proposed smart device is aimed at the reduction of BVI noise through transformation of the blade tip shape into an anhedral tip type and is based on the concept of a variable-stiffness blade. In detail, the blade morphing is obtained through joint action of a magneto- rheological-fluid (MRF) device, shape-memory alloy (SMA) tie-rods and a set of concentratedmasses properly distributed spanwise. In this architecture, the MRF system has to provide local bending-stiffness reduction and concentrated masses have to provide inertialmomentswhereas the SMAtie-rods have tomo- uld the blade tip shape. Since the equilibrium configuration of the smart blade deeply depends on the interaction between the aeroelastic response and the actuation loads, in this work a numerical investigation examines potentiality and shortcomings of the proposed integrated smart system tomorph a realistic blade with respect to the baseline configuration. Key words: smart structures, anhedral helicopter blade List of symbols ν – lag displacement w – flap displacement Φ – angle of torsion µ – mass per unit length 898 C. Testa et al. Ω – rotational speed EIz,EIy – bending stiffness (in plane and out of plane, respectively) ϑ – blade pre-twist GJ – torsional stiffness x – spanwise position R – radius of blade βpc – precone angle eA – tension axis offset from elastic axis km1,km2 – principal mass radius of gyration kA – blade cross-section polar radius Lν,Lw – sectional aerodynamic load (in plane and out of plane, re- spectively) MΦ – sectional aerodynamic torsional moment Factw – actuation force MactΦ – actuation moment t – thickness of blade cross section mk – k-th concentrated mass ρ – air density clα – airfoil lift curve slope vi – local induced velocity ed – chordwise offset of aerodynamic centre behind elastic axis σ – blade solidity Nb – number of blade L – anular valve depth h – differencebetween external and internal valve circumferences TMR – contribution to shear stress on valve lateral walls due to fluid activation Rp – piston base radius. 1. Introduction Since the first half of the 90’s the rotorcraft community has devoted considera- ble efforts towards the enhancement of helicopter performances by integrating smart systems intomain rotor blades. Blademorphing is one of the techniques that may be applied to this aim even if the extremely complex environment related to rotating blades affects the capability of it. In fact, high energy levels and significant displacements, forces, moments involved, make unpractical so- me engineering solutions based on smart materials integrated into the rotor system that, in principle, are expected to guarantee light-weight and adapti- A feasibility study on the behaviour of a helicopter... 899 vity. Thus, in spite of the availability of different strategies based on current technologies involved in the reduction of noise and vibration, their practical realisation is currently limited to few approaches. The evaluation of noise ge- nerated by rotating blades is one of the most important analysis related to the helicopter main rotor performance and acoustic certification. The smart architecture examined here is devoted to reduction of aerodynamically gene- rated noise in low-speed descent flight (and sometimes in hovering or fly-over conditions). In this operating condition, the acoustic annoyance is mainly due to the blade-vortex interaction phenomenon (BVI). It occurs when strong tip vortices, dominating the rotor wake, impinge or pass closely to the rotor bla- des resulting in impulsive changes of the blade loads that produce, in turn, high noise and vibration levels. It iswell documented (Johnson, 1980) that the interaction of the shed tip vortex with the following blade induces vibrations, increases pilot workload and reduces component fatigue life increasing main- tenance costs. A possible strategy to alleviate the BVI noise is to diffuse the blade tip vortex or displace it far away from the following blades by increasing the blade vortex miss-distance. Such a solution may be achieved through an anhedral tip shape. Previous research (Prouty, 1993; Tung and Lee, 1994) has shown that typically the tip vortex involved in the blade-vortex impinging is related to a spanwise length of about 10-15% of the blade radius from the tip (controlled zone) and noise is reduced if amean slope variation of 5◦, at least, is achieved. The authors faced the problemof transforming the blade tip region into an anhedral shape in the past (Testa et al., 2005) referring to a simplified struc- tural model and coming to an elementary smart actuation system without inertial effects. Taking advantage from that work, in this paper, an innovative integrated smart stiffness-variable system is examined and a feasibility study is addressed to investigate its potentiality. The basic concept is to achieve the desired blademorphing by exploiting the energy of the centrifugal field in ad- dition to actions providedbyactuators basedonpiezoelectricmaterials (PZT), shape memory alloys (SMA), etc. To this purpose, a magneto-rheological de- vice, located within the controlled zone, has to allow local spanwise reduction of the bending stiffness (against the centrifugal stiffening) when switched-on, whereas the action of SMA elements combined to bending moments induced by eccentric masses (properly distributed inside the blade box) have to bend the rotating blade to obtain an anhedral configuration. In the following, the numerical study is addressed to test the feasibility of the proposed smart con- cept for helicopters; the evaluation of BVI noise and its reduction is, therefore, beyond the aim of this work and is postponed to further studies. 900 C. Testa et al. 2. Actuation strategy Thesmart systemproposed in thiswork isbasedonaquitenewwayof thinking in the framework of actuation systems for rotating blades. Indeed, it combines the advantages of an adaptive stiffness beam with the energy developed by the rotating environment when eccentric masses are properly located into the bladebox. Indetail, the capability tomorph theblade tip is basedonanon/off system composed of amagneto-rheological fluid-based device (MRF), a shape memory alloy-based device (SMA) and a set of concentrated masses properly distributed inside the blade box. The MRF system provides a spanwise local control of the bending stiffness, whereas the SMA tie-rod actuator, combined with the forces induced by the eccentricmasses, bends the structure.When no anhedral configuration is needed, amagnetic field is applied to theMRFdevice so that the fluid viscosity increases and the blade controlled zone is completely locked. In this case, the SMA tie-rod is switched-off and the masses are still located in their rest position on the elastic axis. On the contrary, when the anhedral shape is needed (i.e. descent flight or hovering) the magnetic field is decreased thus reducing the bending stiffness and the concentratedmasses are suitably displaced above the elastic axis and the SMA elements are switched- on. In suchaway, the jointbendingactionof the concentratedmassesandSMA actuator deflects the blade tip region. Once the required anhedral shape is achieved, the SMAactuator is switched-off and themagnetic field is increased until the equilibrium configuration is frozen. Figures 1a and 1b show a sketch of the blade and the lay-out of the smart system, respectively. In Fig.1c a zoom of the controlled zone is shown. 3. An aeroelastic model of the smart blade The evaluation of the performance of the proposed smart architecture in terms of capability to change the blade shape, needs modelling of the coupling be- tween the aeroelastic loads and actuation forces. Thus, in the following, a physically consistent aeroelastic model, including all the actions induced by the actuators embedded into the elastic structure, is briefly outlined. The descent flight condition should be studied; however, in order to derive some guidelines on the behaviour of the smart blade, the attention is focused on the hover condition. The aeroelastic formulation used in this work is obtained by coupling the equations of thebladedynamics introduced inHodges andDowell A feasibility study on the behaviour of a helicopter... 901 Fig. 1. (a) 3D blade; (b) lay-out of the integrated smart system; (c) zoom of the controlled zone (1974) with the aerodynamic loads given by a quasi-steady 2D theory based on the Greenberg theory (Hodges and Ormiston, 1976). Although the aero- dynamic model is quite simple, it is commonly used by helicopter industries for evaluating the blade response at very low frequency analysis. To take into account the 3D trailing vortices effect, the wake-inflow correction is included. Thismodel is an extension of the formulationused inTesta et al. (2005), where only the flapping motion is considered. The hingeless rotor blade is modelled as a long, straight, slender, homogeneous isotropic beam; the theory is inten- ded for moderate displacements, accurate to the second order, and based on the hypothesis that squares of the bending slopes, twist, thickness-radius and chord-radius ratios are small with respect to unity. Radial non-uniformities (mass, stiffness, twist, etc.), chordwise offsets of themass centroid and tension axes from the elastic axis, pre-cone and warping are included; other details, such as blade root feathering flexibility, torque offset, blade sweep and droop are not herein considered. Thus, by assuming that the blade is inextensible 902 C. Testa et al. for bending deformations and neglecting the radial displacement, the blade aeroelastic model may be written as − [ v′ R ∫ x µΩ2x dx ]′ −µΩ2[v+ecos(ϑ+φ)]− [ (e−eA)µΩ 2xcos(ϑ+φ) ]′ + + { [EIz − (EIz −EIy)sin 2(ϑ+φ)]v′′+ 1 2 (EIz −EIy)sin2(ϑ+φ)w ′′ }′′ =Lv − [ w′ R ∫ x µΩ2x dx ]′ − [(e−eA)µΩ 2xsin(ϑ+φ)]′+µΩ2βpcx+ + { [EIy − (EIz −EIy)sin 2(ϑ+φ)]w′′+ 1 2 (EIz −EIy)sin2(ϑ+φ)v ′′ }′′ = =Lw+F act w (3.1) −k2AΩ 2 [ (φ+ϑ)′ R ∫ x µxdx ]′ +µΩ2φ(k2m2−k 2 m1)cos2ϑ+ +(EIz −EIy) [ v′′w′′cos2ϑ+ 1 2 (w′′ 2 −v′′ 2 )sin2ϑ ] + +µeΩ2x(w′ cosϑ−v′ sinϑ)− (GJφ′)′−eA(w ′′cosϑ−v′′ sinϑ) [ R ∫ x µΩ2xdx ] + +µΩ2(k2m2−k 2 m1)cosϑsinϑ+µeΩ 2βpcxcosϑ=Mφ+M act φ where the unknowns are the in-plane (lead-lag, v(x)) and the out-of-plane (flap, w(x)) displacements of the elastic axis, as well as the cross-section tor- sion φ(x) around it. The bending and torsional stiffness are represented by EIy,EIz and GJ, respectively, µ is the blademass for unit length and x the spanwise position. In addition, km1 and km2 are the principal mass radii of gyration, kA is the blade cross-section polar radius of gyration, βpc – pre-cone angle, e – centre of mass offset from the elastic axis and eA – tension axis offset from the elastic axis. The blade pre-twist is assumed to be linear and expressed as ϑ=ϑ75+ϑtw (x R − 3 4 ) (3.2) where ϑ75 is the blade pitch at 75% span (including collective pitch) and ϑtw is the blade linear pre-twist. The forcing terms at the right-hand side of equation (3.1) are the sum of the sectional aerodynamic loads (Lv, Lw, Mφ) and the loads given by the actuation device (Factw and M act φ ). From the description of the smart system A feasibility study on the behaviour of a helicopter... 903 given is Section 2, the actuation loads come from localized bendingmoments exerted by the action of eccentric masses and SMA tie-rods and read (no lagwise action loads arises) Factw =Ω 2t̂ ∑ k [mkδ ′(x−xk)xk]−Fsmab[δ ′(x−xc)−δ ′(x−xd)] (3.3) Mactφ =Ω 2t̂ ∑ k [mkδ(x−xk)xkv ′ k]−Fsmab[δ(x−xc)v ′ c− δ(x−xd)v ′ d] In equations (3.3), mk is the k-th concentrated mass located at the abscissa xk on the elastic axis, t̂ denotes a portion of the cross-section thickness, v ′ k is the lag-bending slope at xk, Fsma is the axial force provided by the SMA actuator, b is the arm with respect to the beam axis, Ω is the rotor angular velocity and δ(x) theDirac delta function.Concerning the aerodynamic loads, the lagwise section load Lv, the flapwise section load Lw, and the sectional pitching moment about the elastic centre Mφ, for a steady-state hovering configuration are given by Hodges and Ormiston (1976) Lv = ρ∞clαc 2 [ v2i −Ω 2x2 cd0 clα −Ωxvi(ϑ+φ) ] Lw = ρ∞clαc 2 · (3.4) · [ −Ωxvi+Ω 2x2 ( ϑ+φ+ x ∫ 0 v′w′′ dx ) +Ω2 xc 2 (βpc+w ′)−Ω2xv(βpc+w ′) ] Mφ =Mac+edLw where ρ denotes air density, c is the local chord, clα – airfoil lift curve slope, ed – chordwise offset of the aerodynamic centre behind the elastic axis and vi – local induced velocity. Thewake behind the rotor disk determines the induced inflow distribution over the disk and plays an important role in the prediction of the aeroelastic behaviour of the main rotor. Hence, accurate modelling of thewake is important for rotor analysis, more so at low flight speedwhere the wake stays close to the disk and deeply affects the blade airloads. There are manywakemodels availablewith varying levels of complexity andaccuracy. In this work, the inflow velocity is supposed steady, uniform along the span and equal to thevalueof non-uniforminflowgivenby theblade elementmomentum theory (BEMT) (Hodges and Ormiston, 1976) at the radial station 0.75R vi = sgn(ϑ+φ75)ΩR πσ 8 ( √ 1+ 12 πσ |ϑ+φ75|−1 ) (3.5) 904 C. Testa et al. where σ =Nbc/(πR) is the blade solidity and φ75 indicates the elastic twist at the radial station 0.75R. As shown in Section 5, the use of the idealized uniform inflow induces rotor behaviour fairly different from that predicted by the blade element mo- mentum theory: the comparative analysis therein performed highlights that the uniform inflow model increases the blade aeroelastic displacements. Al- though the uniform inflow seems to be too coarse with respect to the simple, but more realistic, BEMT model, it allows one to investigate the aeroelastic response of the integrated smart blade in more severe aeroelastic conditions where major bending and torsional loads act. From a numerical standpoint, it allows conservative analysis of the smart rotor. A further refinement of the inflow calculation requires consideration of details of the rotor vortex wake; however, at the beginning of this feasibility study the use of simple andwidely used engineering numerical tools seems to be a good choice with respect to the required accuracy. 4. Steady equilibrium configuration The finite element method (FEM) is used for integration of equations (3.1) that yields the equilibrium configuration of the smart blade. To this aim, the blade is divided into N beam-elements, having three nodes (two boundary and an interior one) and 11 degrees of freedom. Each boundary node, of any element, is characterized by 5 DOFs (v,v′,w,w′,φ), while the internal one is used for taking into account the elastic twist only. Hence, for lag and flap bending deflections, the interpolating polynomial is chosen from the family of Hermite’s polynomials, while Lagrangian polynomials are used for the elastic twist. Fig. 2. Nodal forces andmoments For the i-th beam element, the introduction of thematrix shape functions yields the local field displacement as ue(x)=H(x)qe (4.1) A feasibility study on the behaviour of a helicopter... 905 where thematrix shape functions and the nodal displacements are respectively given by H(x)=    N(x) 0 0 0 N(x) 0 0 0 Nφ(x)    (4.2) q e⊤ = [vi,v ′ i,vj,v ′ j,wi,w ′ i,wj,w ′ j,φi,φk,φj] with N, Nφ being the sub-matrices containing the interpolating polynomials for bending and torsional displacements, respectively. Finally, the application of the FE method transforms equations (3.1) into the following discretized form Kδ=F0+FNL(δ) (4.3) where δ denotes the vector collecting the degrees of freedom of all elements. At the left-hand side, the global aeroelastic stiffness-matrix K is derived from the linear contribution of aerodynamics and structural loads, including the centrifugal stiffening, whereas the global nodal-loads F0 and FNL, at the right-hand side, account for the constant and non-linear terms from the struc- ture, aerodynamics and actuation. The solution to equation (4.3) is obtained iteratively through application of the Newton-Raphson method that, at the k-th iteration, yields ( K− ∂FNL ∂δ ∣ ∣ ∣ k ) δk+1 =Q0− ∂FNL ∂δ ∣ ∣ ∣ k δk (4.4) Note that the blade equilibrium configurationmust satisfy the propulsive trim equation in hovering, that is, the vehicle weight W must be balanced by the rotor thrust T : theelastic displacementsandthecollective angle corresponding to the equilibrium conditions are determined jointly by solving equation (4.4) coupled with the trim equation T −W =0. 5. Numerical results Before showingthe results concerning the smartblade, somenumericalfindings are shown to validate the methodology of Section 4 through which steady responses are obtained. To this aim, the untwisted cantilever beam considered inKwon (1988) has been examined. It has a uniform mass and stiffness distribution, no offsets 906 C. Testa et al. between elastic, mass, tension and aerodynamic axes. Figures 3a, 3b and 3c illustrate the equilibrium tip deflections (flap, lag and torsion) at different precone angles and demonstrate that the agreement with the solution given in Kwon (1988) is very good. Fig. 3. Equilibrium blade tip deflections For the same blade configuration, Fig.4 shows the spanwise distribution of the induced velocity due to the blade element momentum theory, after the steady equilibrium state is reached. The assumption of a steady uniform induced velocity distribution along the span predicts too high downwash at the blade root sections and a too low value in the outer portion of the blade. Coherently, Fig.5 shows that the aerodynamic load Lw associated with the constant induced velocity modelling is lower at the blade root sections and higher in the outer portion of the blade span. The resulting flapwise displacements are shown in Fig.6: the presence of constant downwash induced velocity causes greater flap displacements. For the sake of completeness, lag and torsion displecements are shown in Figs. 7a and 7b, respectively. A feasibility study on the behaviour of a helicopter... 907 Fig. 4. Spanwise distribution of the induced velocity Fig. 5. Spanwise distribution of flapwise load Fig. 6. Flap displacements 908 C. Testa et al. Fig. 7. (a) Lag displacements; (b) torsion Nextwediscuss theapplication of the smartmorphingdevice; its capability to change the shape of the blade tip is investigated through a numerical study performed on a Bo105-type four-bladed rotor having a NACA 0015 cross- section, radius R = 4.9m, local chord c = 0.27m, precone angle βpc = 2.5 ◦ anda rotational speed Ω=44rad/s (Splettstoesser et al., 1993). This analysis is aimed at presenting potentialities and drawbacks of the smart device and to clarify the reason why the coupled action ofmore devices (MRF, SMAand eccentric masses) is necessary to achieve an anhedral shape. Therefore, in the following, the effect induced by the three devices, is studied separately. 5.1. Effect of the MRF device The presence of the MRF system is modelled only within the controlled zone (15% tip blade portion). In particular, a preliminary parametric study (not shown here) indicates that a higher morphing effect of the controlled zone implies a spanwise stiffness reduction localized between 0.87R and 0.9R, corresponding to 13% and 10% of the blade span (starting from the tip), respectively. On the basis of this choice, different bending-stiffness reductions are simulated and the related blade equilibrium configurations are evaluated. Fig. 8. Sketch of the elastic axis with the integratedMFR device A feasibility study on the behaviour of a helicopter... 909 Fig. 9. (a) Out-of-plane displacement; (b) flap rotation As shown inFig.9, the blade shape remains very close to the non-actuated one even for a stiffness reduction ℜ equal to 65% of the initial stiffness. However, by defining a bending slope variation index, conventionally, as ∆ϑ = w′tip −w ′ 2 (w ′ 2 is the flap-bending slope at x2), it results that for ℜ=75%of the initial stiffness a slope variation ∆ϑ=−0.002rad is achieved. The comparison between the non-activated and the activated blade shows that the flap tip displacement remains quite unchanged, wtip ∼=0.1m,whereas ∆ϑ is slightly increased from −0.0017rad to −0.002rad. In order to preserve the necessary robustness, that is, to avoid transforming the controlled zone into a real hinged-beam and experiencing too large displacements, the weakening provided by the MRF device cannot be too large. This is the reason why no further stiffness reductions are considered. Note that the structural stiffness reduction acts in a small region near the blade tip; thus, only slight variations of the natural rotating frequencies appear, as shown in Fig.10, where the first six frequencies are plotted. Fig. 10. Fan diagram: (a) non-activated blade; (b) weakened blade byMRF 910 C. Testa et al. Asamatter of fact, the actuation of theMRFdevice produces only a slight variation of the blade tip shape. 5.2. Effect of the SMA-based device A preliminary investigation has been performed to obtain the spanwise position of the SMAactuator; the outcome of this parametric studywas that, for an efficient use of the SMA device in terms of induced-bending effects, it has to be positioned between 0.87R and 0.92R, corresponding to 13%and 8% of the blade span (starting from the tip), respectively (see Fig.11). For this configuration, the length b of the rigid connection results in the 6% of the local chord (b=0.0162m). Fig. 11. Sketch of the elastic axis with the integrated SMA actuator The investigation on the effects due only to the SMAactuator reveals that the corresponding flap bending moments modify somehow the structure (see Fig.12). As expected, the best configuration is achieved when the maximum allowable number of ribbons (computed with reference to the internal space) is used. For the blade considered in Splettstoesser et al. (1993), 30 the ribbons, providing a 15kN force, produce a slope variation ∆ϑ = −0.0042rad and a tip displacement wtip =0.0982m. Hence, the activation of the SMA actuator produces a greater slope variation than theMRF device. 5.3. Effect of the MRF and SMA devices Coupling the SMAactuatorwith theMRFdevice enhances the advantages of local stiffness reduction. However, in this case, the weakening provided by theMRF cannot be too large because of the coupling between the aeroelastic forces and actuator actions. In particular, numerical investigations show that for a realistic four-bladed rotor, ℜ has to be not greater than 50% of the initial stiffness. Limiting ℜ to 50% of the initial stiffness, the combined action of MRF and SMA yields ∆ϑ=−0.0046rad and wtip =0.096m (see Fig.13). A shortcoming of this actuation strategy is that the blade morphing is achieved when SMA and MRF devices run at the maximum of their own ca- A feasibility study on the behaviour of a helicopter... 911 Fig. 12. Effect of the SMA actuator: (a) flap displacement; (b) rotation Fig. 13. Effect of the SMA/ MRF-based actuation: (a) flap displacement; (b) rotation pability. This problemmay be overcome by incorporating the actions induced by the centrifugal field. Before showing this important result, it is convenient, for the sake of clarity, to summarize the previous investigations. To this pur- pose, Fig.14 depicts the effects induced by the different actuation strategies. 5.4. Inclusion of eccentric masses The smart configuration herein proposed is composed of the MRF and SMA devices with the inclusion of eccentric masses properly located inside the blade box above the elastic axis. Apreliminary investigation aimed at assessing the best lay-out of the smart architecture integrated into the blade has been performed and the outcome of it was that the SMAactuator has to be positioned between 0.87R and 0.92R, theMRFdevice between 0.87R and 0.9R and at least threemasses (properly 912 C. Testa et al. Fig. 14. Comparison among different actuation strategies located spanwise and of suitable amount) are required to achieve the anhedral shape.Making reference to Fig.15, two concentrated masses m1,m2, located just beyond the MRF-SMA device towards the tip and a mass M, placed at the blade tip, are considered. It results that m1 is located at 0.93R whereas m2 is located and 0.97R. Fig. 15. Sketch of the investigated architecture The mass m1 is aimed at improving the effect of the MRF-SMA system, m2 at allowing themoulding of the blade shape, whereas M atmodifying the blade shape for achieving the anhedral configuration. It isworthnoting that in theMRF-SMA-based actuation systemexamined in Section 5.3, the shapememory alloys are called to bend the outer portion of the blade while through the use of concentrated masses, the centrifugal field is devoted to yield the major bending effect with the SMA actuator used to provide a local change in the bending slope in the areawhere theMRFdevice acts (so that the characteristic beak profile is obtained). In details, the numerical analysis shows that by using m1 =m2 =0.25kg, M = 1.5kg (corresponding to the mass increase that is equal to 8% of the blade mass), ℜ = 50% to the initial stiffness, t̂ = b = 0.0162m and using A feasibility study on the behaviour of a helicopter... 913 15 SMA ribbons, the bending slope variation obtained is ∆ϑ=−0.01645rad with a tip deflection wtip = 0.076m (see Fig.16). Note that in this case, the difference between the bending slope at 10% of the span (from the tip) on the basic blade and the slope at the blade tip of the actuated blade yields a bending slope variation equal to −2.2◦, which corresponds to 44% of the requirement (bending slope variation equals to −5◦, see Prouty (1993), Tung and Lee (1994)). Fig. 16. Effect of the concentratedmasses: (a) flap displacement; (b) rotation Anyway, the satisfaction of the requirement iswell beyond the scope of this investigation because the purpose of the presentwork is to address a feasibility studyon a realistic helicoptermain rotor in order to analyse the capabilities of the proposed integrated smart systemand derive useful preliminary guidelines on the rotorcraft blademorphing.Figure 16depicts the comparison amongdif- ferent actuation strategies; starting from the basic blade (line 1) the inclusion of the three masses allow to obtain a different configuration (line 2). The use of aMRFdevice allowsmodifying that deformed shape (line 3). The inclusion of a SMA actuator allows one to reach the characteristic beak profile (line 4), with a tip vertical displacement slightly less than 0.08m. This result could be improved, for instance, by increasing the amount of concentrated masses. However, the presence of eccentric masses must not lead to resonance values next to the rotor harmonics; operatively, any intersection between the rota- ting blade frequencies and the n-per-rev frequencies (nP) should be avoided within the characteristic rotor operating range. For instance, assuming a 15% global mass increase as the maximum allowed, the solution characterised by a 2kg increase appears as a good compromise between the need of achieving the desiderate beakbeam-shape andkeeping away undesired resonanceswithin the operating range. In fact, the blade under investigation has a nominal re- sonance at 40rad/s, when 5P intersects the 2nd lag frequency (Fig.10a); by 914 C. Testa et al. augmenting the global mass by 2kg, this resonance occurs at 50rad/s when 4P intersects the 2nd lag frequency (Fig.17a). By increasing the added mass up to 4kg, the undesired resonance at the nominal speed (44rad/s) occurs (see Fig.17b). Fig. 17. Fan diagram: (a) 8%mass increase; (b) 15%mass increase From this numerical investigation it results that the proposed smart sys- tem integrated into a realistic helicopter blade may be, in principle, effective in morphing the blade tip region so as to get an anhedral shape. However, the goal of blademorphing has to bematched bothwith the aimed BVI noise abatement andwith the requirements concerning the rotor dynamic response. This implies that the amount of additional mass, bending-stiffness reduction and SMA wires strength have to be the result of a compromise between the need of amplifying the bending effect of the centrifugal field and the need of avoiding blade resonances for all flight conditions experienced by the helicop- ter.Other issues, concerning pitch control effectiveness in forwardflight (when blade morphing is not needed) and aeroelastic stability of the non-actuated and actuated rotor affect the final design of the smart blade and should be considered; however they are beyond the aim of the paper. 6. Actuation power In order to estimate the energy supplied to theSMA-MRFsystem, anumerical study is here addressed. The crucial point is the identification of the working condition of the devices. To this aim commercial devices whose properties are provided by the manufacturer, are considered. A feasibility study on the behaviour of a helicopter... 915 6.1. MRF device The MRF device considered in this section (Figs.18 and 19) is composed of two cylinder-piston systems, connected by a wire to the upper and lower part of the virtual hinge. Because of the centrifugal field, to avoid separation of metal particles of the fluid, the magnetic device should be integrated close to the root (around 0.2m far from the rotation axis). In fact in this region, the centrifugal acceleration is estimated to be about 40g, coherent with the maximum value of 80g. Fig. 18. Sketch of theMRF device As shown in Fig.19, each piston base splits the cylinder volume in two parts, filled by the magneto-rheological fluid. A hole allows the fluid to pass through and the piston to slide. If a suitable magnetic field is applied in this passage, fluid viscosity increases up to produce the piston lock; as a consequ- ence, hinge freezing is produced through a wire element connecting the steam to the hinge (see Fig.18). Fig. 19. MRF cylinder-pistonmain features An important aspect concerning the MRF design is the evaluation of the maximum reaction force that the activated fluid is able to provide (locking force). From Srinivasan and McFarland (2001) it results that the maximum allowable pressure ∆Pp is given by ∆Pp =2τMR L h (6.1) 916 C. Testa et al. where L is the annular valve depth, h – difference between external and in- ternal valve circumferences and τMR – contribution to the shear stress on the valve lateral walls due to fluid activation. Once the locking force is known, the above expression yields the minimum value of τMR that the applied ma- gnetic field must provide. Previous numerical results for the fully-actuated blade show that the bending-stiffness reduction produced by the MRF has to be not greater than 50% of the initial stiffness. In order to evaluate the locking force, an iterative procedure may be conveniently used: trial forces to re-establish the equilibrium configuration of the baseline (non-weakened) blade are applied at the top of the rigid connections. For the structure under investigation, it results that 3Nm moment, corresponding to the locking for- ce equal to 185N, is needed. For the sake of safety, the working condition is here performed using a higher locking force value (300N). Making reference to a realisticMRFdevice with internal radius Ri =0.01m, piston base radius Rp =0.01m, annular valve depth L=0.1m and considering a difference be- tween the external and internal valve circumferences equal to h=0.001m,Eq. (6.1) yields τMR ∼=1kPa. A devoted finite element (FE) analysis, performed by FEMMTM code, yields an evaluation of the average value of the magne- tic inductance in the regions of interest that, in turn, allow the evaluation of the required current intensity through the use of specific inductance-shear characteristics for the selected magneto-rheological fluid (released by thema- nufacturer). For the 132 AD magneto-rheological fluid and by considering a device composed of three coils of one hundred copperwire turns, such analysis yields current intensity equal to 1A, voltage drop equal to 0.4V and power supply of 0.4W (note that the piston axial symmetry allows one to model half device only, see Fig.20a). The correspondingmagnetic field is depicted in Fig.20b and 20c. 6.2. SMA actuator The tie-rod device is aimed atmoulding the curvature of 10% blade span extremity. To maximise the bending-stiffness reduction given by the MRF system, the SMA actuator is properly located between 0.87R and 0.92R. From Section 5.4, it results that 15 ribbons, providing 7KN force in the fully-actuated configuration, are used.For theapplicationunder consideration, it is reasonable to assume an activation time not greater than twenty seconds. Within the limits of this assumption, a numerical investigation is addressed to predict the working condition of the actuator (working temperature and A feasibility study on the behaviour of a helicopter... 917 Fig. 20. FEMMTM FEmodel of the cylinder piston: (a) magnetic field distribution; (b) magnetic field detail in the gap zone; (c) zoom of the gap zone wires recovery strain). To this aim, the aeroelastic model of the smart blade and SMA modelling (Liang and Rogers, 1990) are used jointly. Referring to a NiTiCu (10%) SMA wire (see Table 1), trial force values (within the range of 7KN) are applied to the rigid connections of the fully-actuated blade (see Fig.1b) to simulate the SMA bending effect and, in turn, to evaluate the resulting foreshortening of the wire element (Fig.21, black curve). The SMA 918 C. Testa et al. working condition is then evaluated through the knowledge of the SMA force vs. strain curves for different temperatures (Liang andRogers, 1990) (Fig.21, grey curves).Theoutcomeof this analysis is shown inFig.21, yielding theSMA operating temperature equal to 72.6◦Cand recovered strain equal to 0.2%. In theseoperating conditions, apowerof about 30Wis required for theactivation of a single SMAwire (having a length of 0.53m) within a period of 20s (see Ameduri andGianvito, 2008). Hence, for the whole SMAdevice, 225Wmust be supplied for each blade. Table 1.Main features of the SMA actuator Material NiTiCu (10%) Cross-section area 10mm2 Elements number 15 Length 0.25m Austenite activation temperatures:As,Af 30 ◦C, 60◦C Max recovery strain 3.0% Martensite, austenite Young’s moduli 20GPa, 50GPa Resistivity (average value) 200µΩ/cm Fig. 21. SMA force – strain curves A feasibility study on the behaviour of a helicopter... 919 7. Conclusions In this paper, a feasibility study on the behaviour of a smart blade aimed at changing the shape of the blade tip region has been numerically investigated. Themotivation of this study comes fromthe fact that thepractical application of on/off devices integrated into rotating blades and aimed at blademorphing, is nowadays deeply limited by the actuation power involved. Hence, in spite of the need of achieving an anhedral shape in some flight conditions, the lack of suitable actuatorsmake some engineering solutions typically used for reducing noise andvibrationunpractical. For these reasons, thepaperdealswith anovel strategy of actuation based on the bending effect induced by the centrifugal field. To this purpose, the proposed actuator consists of concentrated masses properly located within the controlled zone (10-15% of the tip blade portion) and of suitable amount. To improve the bending action provided by this set of masses, a MRF device designed to decrease the bending-stiffness of the controlled zone, is considered. Finally, in order to mould the blade shape and increase the blade vortex miss-distance, a classical SMA-based actuator is analysed too. Numerical results performed on a realistic Bo-105 type main rotor in ho- vering show the need of using the joint action of the three devices to achieve the anhedral shape. In particular, the spanwise location of the MRF device, SMA actuator and addedmasses as well as the number of SMA elements and themaximum allowable stiffness reduction are the result of a compromise be- tween the need of amplifying the bending effect of the centrifugal field and SMAactuator and the need of assuring aeromechanical behaviour of themain rotor without resonances and aeroelastic instabilities for all flight conditions experienced by the helicopter. Obviously, for a different blade type, the whole smart system should be re-designed. Hence, a tailored design should involve the design of the smart blade as a whole. At the same time, a devoted aeroacoustic study should be performed to evaluate the benefits in terms of noise reduction. In conclusion, the results carried out from this numerical work are preli- minary guidelines for rotorcraft blademorphing. References 1. Ameduri S., Gianvito A., 2008,Risultati Campagna Sperimentale di Carat- terizzazione del Filo di SMA, CIRA-CF-08-1198, Internal report, Capua (CE), September 2008 [in English] 920 C. Testa et al. 2. Hodges D.H., Dowell E.H., 1974,Nonlinear Equation for the Elastic Ben- ding and Torsion of Twisted nonuniform Rotor Blades, NASATND7818 3. Hodges D.H., Ormiston R., 1976, Stability of Elastic Bending and Torsion ofUniformCantileverRotorBlades inHoverwithVariable StructuralCoupling, NASA TND8192 4. Johnson W., 1980,Helicopter Theory, PrincetonUniversity Press 5. Kwon O.J., 1988,A Technique for the Prediction of Aerodynamics and Aero- elasticity of Rotor Blades, Phd Thesis, Georgia Institute of Technology 6. Liang C., Rogers C.A., 1990, One-dimensional thermomechanical consti- tutive relations for shape memory materials, Journal of Intelligent Material Systems and Structures, 1, 207-233 7. Prouty R.W., 1993,Even More Helicopter Aerodynamics, Chapter 29, Phil- lips Pub. Co. 8. Splettstoesser W.R, Niesl G., Cenedese F., Papanikas D.G., 1993, Experimental results of the European HELINOISE aeroacoustic rotor test in theDNW,19thEuropeanRotorcraft ForumProceedings (PaperB8),Cernobbio, Italy 9. SrinivasanA.V.,McFarlandD.M., 2001,Smart Structures – Analysis and Design, Cambridge University Press, pp. 73-96 10. Testa C., Leone S., Ameduri S., Concilio A., 2005, Feasibility study on rotorcraft blademorphing in hovering, 12th SPIE International Symposium on Smart Structures and Materials (SPIE 2005), San Diego-California (USA) 11. Tung C., Lee S., 1994, Evaluation of hover prediction codes, Proceedings of the 50th Annual Forum of Am. Hel. Soc., Washington, DC Studium wykonalności działania „ineligentnej” łopaty helikoptera wyposażonej w układ sterowania kształtem jej końca Streszczenie W pracy przedstawiono analizę właściwości bezprzegubowej łopaty helikoptera, w której zastosowano nowy, zintegrowany i aktywny układ oddziaływania na kształt łopaty. Zadaniem tego układu jest redukcja hałasu generowanego wskutek interak- cji łopaty i wywołanych jej ruchem wirów ośrodka (blade-vortex interaction – BVI) poprzez zmianę kształtu końca łopaty celującegowuzyskanie ujemnegowzniosu.Me- toda wykorzystuję koncepcję łopaty o zmiennej sztywności. W szczególności, kształ- towanie łopaty jest sumarycznymefektemdziałaniamagneto-reologicznegoaktuatora A feasibility study on the behaviour of a helicopter... 921 (MRF), drążkówwykonanych ze stopu z pamięcią kształtu (SMA) i zestawumas sku- pionych odpowiednio rozłożonych wzdłuż łopaty. W takiej architekturze, podzespół MRF wprowadza lokalną redukcję sztywności giętnej, masy skupione wprowadzają dodatkowymoment bezwładności, podczas gdy drążki SMA sterują kształtem końca łopaty. Ponieważ konfiguracja położenia równowagi „inteligentnej” łopaty silnie zale- ży od aerosprężystej odpowiedzi układu oraz sił generowanych przez elementy wyko- nawcze (aktuatory), w pracy skupiono badania na numerycznej symulacji potencjału i ograniczeńwynikających z zastosowania zaproponowanejmetody oddziaływania na kształt rzeczywistej łopaty względem konfiguracji bazowej. Manuscript received November 7, 2008; accepted for print March 25, 2009