rotory-wing aeroelasticity - current status and future … of rotary-wing aeroelastic stability and...

c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

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AIAA 2001-0427

Rotary-Wing Aeroelasticity -Current Status and Future Trends

Peretz P. FriedmannFrangois-Xavier Bagnoud ProfessorDepartment of Aerospace EngineeringThe University of MichiganAnn Arbor, Ml 48109-2140, USA

39th AIAA Aerospace SciencesMeeting & Exhibit

8-11 January 2001 / Reno, NVFor permission to copy or republish, contact the American Institute of Aeronautics and Astronautics1801 Alexander Bell Drive, Suite 500, Reston, VA 20191


2001-0427

Rotary-Wing Aeroelasticity -Current Status and Future Trends

Peretz P. Friedmann*Frangois-Xavier Bagnoud Professor

Department of Aerospace EngineeringThe University of Michigan

Ann Arbor, MI 48109-2140, USA

AbstractThis paper is a sequel to an earlier survey pa-per on the same subject and it reviews the state-of-the-art in rotary-wing aeroelasticity by provid-ing a fairly detailed examination of the researchactivity carried out during the last decade. Theprincipal topics considered are: modeling of com-posite rotor blades; modeling the characteristicsof elastomeric lag dampers; aeroelasticity of swepttip rotors; comprehensive helicopter analysis codes;aeroelastic characteristics of hingeless and bearing-less rotors; modeling of unsteady aerodynamics anddynamic stall; aeroelastic and aeromechanical stabi-lization using active controls; and vibration reduc-tion using active controls.

1 Introduction andBackground

1.1 Concise Perspective andPrevious Surveys

When reviewing research in rotary-wing aeroelastic-ity (RWA), it is important to mention a few his-torical facts. The Wright brothers flew in 1903, andSikorsky built and started flying the first operationalhelicopter, the R-4 or (VS-316) in 1942. The R-4was a three bladed helicopter with a rotor diame-ter of 11.6 m and was powered by a 185-hp engine.Thus, the initial gap between fixed-wing and rotary-wing technologies is approximately 39 years. There-fore, it is not surprising that certain rotary wingproblems, particularly those pertaining to unsteady

* Fellow AIAA.Copyright © 2001 by P.P. Friedmann. Published by theAmerican Institute of Aeronautics and Astronautics, Inc. bypermission.

aerodynamics, are still not well understood. Thisis also compounded by the complexity of the vehi-cle when compared to fixed-wing aircraft. RWA hasbeen the most active area in aeroelasticity duringthe last three decades. This vigorous research activ-ity has generated a considerable number of reviewpapers and several books on this topic have beenpublished during this period.

These review papers are described in chrono-logical order so as to provide a historical perspec-tive on this evolving field [16, 22, 28, 29, 30, 31,32, 33, 47, 48, 61, 79, 82]. One of the first signifi-cant reviews of rotary-wing dynamic and aeroelas-tic problems was provided by Loewy [61], where awide range of dynamic problems was reviewed inconsiderable detail. A more limited survey empha-sizing the role of unsteady aerodynamics and vibra-tion problems in forward flight was presented byDat [22]. Two comprehensive reviews of rotary-wingaeroelasticity were presented by Friedmann [28, 29].In Ref. [28], a detailed chronological discussion ofthe flap-lag and coupled flap-lag-torsion problems inhover and forward flight was presented, emphasiz-ing the inherently nonlinear nature of the hingelessblade aeroelastic stability problem. The nonlineari-ties considered were geometrical nonlinearities dueto moderate blade deflections. In Ref. [29], therole of unsteady aerodynamics, including dynamicstall, was examined, together with the treatment ofnonlinear aeroelastic problems in forward flight. Fi-nite element solutions to RWA problems were alsoconsidered, together with the treatment of coupledrotor-fuselage problems. Another detailed survey byOrmiston [79] discussed the aeroelasticity of hinge-less and bearingless rotors, in hover, from an exper-imental and theoretical point of view.

It is important to mention that whileaeroelastic stability plays an important role in thedesign of rotor systems, the aeroelastic response

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problem as represented by the rotorcraft vibrationand dynamic loads prediction, plays an even morecritical role. Thus, two other surveys have dealtexclusively with vibration and its control in rotor-craft [62, 92]. These papers focus on the vibrationscaused by the aeroelastic response of the rotor, andthe study of various passive, semi-active and activedevices for controlling such vibrations.

Johnson [47, 48] has published a comprehen-sive review paper addressing both aeroelastic sta-bility and vibration problems for advanced rotorsystems. In a sequel [30] to his previous reviewpapers, Priedmann discussed the principal develop-ments which have taken place between 1983-87, em-phasizing new methods for formulating aeroelasticproblems, advances in treatment of the aeroelas-tic problem in forward flight, coupled rotor-fuselageanalyses, structural blade modeling, structural opti-mization, and the use of active control for vibrationreduction and stability augmentation.

A comprehensive report [82] which containsa detailed review of the theoretical and experimen-tal development in the aeroelastic and aeromechan-ical stability of helicopters and tilt-rotor aircraft,carried out under Army/NASA sponsorship dur-ing the period 1967-87 was prepared by Ormiston,Warmbrodt, Hodges and Peters. Somewhat later,key ideas and developments in four specific areas:(a) role of geometric nonlinearities in RWA, (b)structural modeling of composite blades, (c) coupledrotor-fuselage aeromechanical problems and their ac-tive control, and (d) higher harmonic control (HHC)for vibration reduction in rotorcraft, were consideredby Priedmann [31]. At the same time, Chopra[16]surveyed the state-of-the-art in aeromechanical sta-bility of helicopters, including pitch-flap, flap-lag,coupled flap-lag-torsion, air and ground resonance.Advances in aeromechanical analysis of bearingless,circulation controlled and composite rotors were alsotreated in this detailed paper. Perhaps the mostcomprehensive paper on RWA was written by Fried-mann and Hodges [33]. This paper contains closeto 350 references and dwells on all the important as-pects of rotary-wing aeroelastic stability and respon-sive problems. The treatment is broad and compre-hensive, and is current up to 1991. A partial reviewof some recent developments can also be found inRef. [32].

In addition to the numerous papers dealingwith the subject of this review, it should be alsonoted that this topic is also described in a number ofbooks. Among these, the most notable one is John-son's [46] monumental treatise on helicopter theorywhich contains extensive, detailed and useful ma-

terial on aerodynamic, dynamic and mathematicalaspects of rotary-wing aerodynamics, dynamics andaeroelasticity. A more recent book [8] treats severalaeroelastic and structural dynamic problems in ro-torcraft. Quite recently, Leishman [57] has writtenan excellent book on helicopter aerodynamics, whichcontains good treatments of unsteady aerodynamics,rotor wake model, and dynamic stall.

1.2 Fundamental DifferencesBetween Rotary-Wing andFixed-Wing Aeroelasticity

The basic problem in fixed wing aeroelasticity isthe coupled bending-torsion problem which is essen-tially a linear problem. The basic problem in rotary-wing aeroelasticity is the coupled flap-lag-torsion(CFLT) of an isolated blade. CFLT is inherentlynonlinear because of the geometric nonlinearities as-sociated with moderate (or large) blade deflections,that must be incorporated into the structural, in-ertia, and aerodynamic terms associated with thisaeroelastic problem. A typical hingeless blade withan advanced geometry tip is shown in Fig. 1. Thegeometry associated with the basic CFLT problemis depicted in Fig. 2. It is important to note thatfor the RWA problem, coupling between bendingout of the plane of rotation (flap), bending in theplane of rotation (lag) and torsion is critical, andneglect of one of these degrees of freedom may pro-duce inaccurate and misleading results. Figure 2shows the undeformed and deformed geometry, andcross-sectional positions.

Rotary-wing aeroelastic problems can be sep-arated in two regimes: hover and forward flight.In hover, the equations of motion have constantcoefficients, whereas in forward flight, the equa-tions have periodic coefficients. The fundamen-tally nonlinear nature of RWA requires coupling be-tween the aeroelastic problem and the flight con-dition of the entire helicopter as represented by itstrim state. Two types of trim procedures, propulsivetrim and wind-tunnel trim, have been used. The firsttrim procedure stimulates straight and level forward-flight conditions, as shown in Fig. 3, and the secondtrim procedure corresponds to the conditions expe-rienced when testing the rotor on a support in thewind tunnel [29]. Aeroelastic stability boundariescan be obtained by linearizing equations of motionabout the equilibrium position determined from acoupled trim-aeroelastic analysis. In hover, lineareigenanalysis is used to obtain the aeroelastic sta-bility boundaries, and in forward flight, aeroelasticstability is usually determined from Floquet theory



[33].The lead-lag degree of freedom, with its low

aerodynamic and structural damping, is a criticaldegree of freedom in most rotary-wing aeroelasticproblems. Another important class of problems iscoupled rotor-fuselage aeroelastic problems, denotedaeromechanical problems. This problem involvescoupling of the fuselage rigid body degrees of free-dom (primarily pitch and roll) with the blade degreesof freedom (primarily lead-lag). The geometry de-picting a typical coupled rotor-fuselage of a systemis shown in Fig. 4. On the ground, the aerome-chanical instability is called ground-resonance, andin flight it is known as air-resonance. It is inter-esting to note that while active flutter suppressionhas not been an area of concern in RWA, active sup-pression of aeromechanical instabilities has receivedconsiderable attention.

The aeroelastic response problem that mani-fests itself as blade loads, hub loads, or fuselage vi-brations, plays a key role for rotary-wing vehicles,and, therefore, vibration prediction and its controlhas been an area of intense activity. Modeling un-steady aerodynamic loads on the blade and the rotoris a major challenge. The combination of blade ad-vancing and rotational speed is a source of complex-ity. At large advance rations, many different flowregimes coexist: transonic flow with shock waveson the advancing blade, and flow reversal and low-speed unsteady stall on the retreating blade. Time-varying unsteady wake geometry, which is an impor-tant source of unsteady loads, vibration, and noise,is excruciatingly complex. Computation of the un-steady free wake has been a major challenge, andit is essential for correct computation of vibrationsand noise. Figure 5, taken from Ref. [Ill], depictsthree free-wake calculations based upon three differ-ent free-wake models. Rotor-fuselage interactionalaerodynamics is another difficult problem.

1.3 Objectives of this paperThis paper describes developments in RWA thathave taken place during the last decade, thus it isintended to be a sequel to Ref. [33]. The paperwill focus on both aeroelastic stability problems aswell as the aeroelastic response problem by describ-ing the principal research activities on the subjectslisted below:

• Recent developments in the modeling of com-posite rotor blades undergoing moderate andlarge deformation and their incorporation ina variety of aeroelastic stability and responsestudies.

• Modeling of nonlinear elastomeric lag dampersand their influence on aeromechanical andaeroelastic stability problems.

• Aeroelastic behavior of swept tip rotors and cor-relation with experiments.

• Development and validation of comprehensivehelicopter analysis codes, and the incorporationof multibody techniques in such codes.

• Relative aeroelastic characteristics of hingelessand bearingless rotors.

• Development of improved unsteady aerody-namic models, modeling of dynamic stall, andtheir incorporation in aeroelastic stability andresponse studies.

• Active control of aeroelastic stability and re-sponse (i.e. vibration) in rotorcraft.

It should be emphasized that not all the top-ics listed above are treated with the same level ofdetail. The scope of the treatment of any particulartopic depends on the amount of research available aswell as overall space allocations within this survey.

2 Composite Blade Modelsand Their Application

Structural dynamic and aeroelastic modeling of com-posite blades undergoing moderate or large deflec-tions and their application to the study of hinge-less, bearingless, and tilt-rotor blade aeroelasticityas well as coupled rotor-fuselage problems has beena particularly active area of research. Due to itsimportance, this research has also been addressed inseveral survey papers [33, 41, 52]. The principal con-clusions from this body of research are summarizednext. The most important requirements for mod-eling composite helicopter blades are the capabil-ity to represent transverse shear deformation, cross-sectional warping, and elastic coupling due to mate-rial anisotropy, in addition to an adequate represen-tation of geometric nonlinearities. A most effectiveapproach to modeling this complex beam problemis to split the basic three dimensional, geometricallynonlinear elasticity problem into two separate prob-lems: (1) a geometrically nonlinear, one-dimensionalproblem of a beam in the spanwise direction, and(2) a two-dimensional linear elastic problem fromwhich the warping and the cross-sectional propertiesat any spanwise station are determined. This twostage approach was intuitively used by Kosmatka



and Priedmann [55]. A rigorous foundation for thisapproach was established by Atilgan and Hodges [2]using an asymptotic analysis. Later this approachwas further refined by Cesnik, Sutyrin and Hodges[14, 15]. Finally, this approach was generalized, lead-ing to a general cross-sectional modeling technique[12], which is linked by a variational formulation tothe one-dimensional beam theory. The authors de-note this approach by the term, "dimensional reduc-tion".

The composite blade theories that are cur-rently available can be separated into three groups:

(a) Theories that are based on dimensional reduc-tion of the basic three dimensional elasticityproblem using a variational asymptotic method.In these theories, the spanwise beam problemis capable of handling large deformations andsmall strains. A separate finite element analysisis used to obtain the cross-sectional propertiesand the appropriate warping representation.The finite element cross-sectional analysis is ca-pable of representing arbitrary cross-sections,with anisotropic material properties, and a va-riety of wall thicknesses [2, 12, 14, 15, 43].

(b) Theories based on ad-hoc decoupling betweenthe geometrically nonlinear, spanwise one di-mensional beam theory, combined with a fi-nite element cross-sectional analysis to deter-mine the cross-sectional constants and warp-ing. In these theories, the assumption of mod-erate blade deflections, based on an orderingscheme, is often used to simplify the span-wise one-dimensional beam model. The cross-sectional analysis is still capable of modelinganisotropic, arbitrary cross-sections, with mul-ticell construction and various wall thicknesses.This cross-sectional analysis is usually linear[45, 55, 121, 122, 124].

(c) Theories combining assumptions on thin walled,single cell or two-cell, composite cross-sections,with a moderate deflection type of one-dimensional beam theory. In these theories,shear is included and different types of warp-ing functions can also be included. These theo-ries usually provide useful and good approxima-tions, however, they do not have the accuracy,generality, and logical appeal of either (a) or (b)type of theories [91, 99, 100, 101, 102, 114].

The composite blade models discussed abovehave been used for a variety of applications. A rep-resentative, but incomplete, list of such applicationsis provided next:

(1) Determination of composite coupling coeffi-cients, twist and deformation for compositebeams or blades, for which experimental datais available [12, 26, 42, 43, 100].

(2) Free vibration analysis of rotating compositeblades [26, 43, 121].

(3) Aeroelastic behavior of composite hingeless andbearingless rotor blades in hover and forwardflight [36, 37, 99, 114, 121, 122, 123, 124].

(4) Air and ground resonance of helicopters withelastically tailored composite blades [101].

(5) Tilt-rotor aeroelastic stability and responsewith elastically-coupled composite rotor blades[4, 78, 104, 105].

Some results taken from [124] are shown hereto illustrate the effect of composite blade construc-tion on the aeroelastic stability of a typical com-posite hingeless helicopter blade in hover and for-ward flight. The fundamental, coupled rotating nat-ural frequencies of the blade in lag, flap and tor-sion, respectively are ULI = 0.765; UFI — 1.096;and LJTI — 3.356, when the ply orientation is zero.The four bladed hingeless rotor operates at a averageweight coefficient Cw — 0.005, and a Lock numberof 7 = 5.0, with solidity a = 0.076.

The undeformed element coordinate systemfor the swept-tip composite blade is shown in Fig.6. The blade model belongs to category (b) de-scribed earlier in this section. The finite elementnodal degrees of freedom for the spanwise, moder-ate deflection beam model are shown in Fig. 7. Thetwo cell composite cross-section which is analyzedby a separate finite element cross-sectional analysisis depicted in Fig. 8. Stability of the lag degreeof freedom is illustrated in Fig. 9. Usually this isthe degree of freedom which tends to become un-stable in hover. The effect of the composite con-struction is illustrated for a straight blade where theply angle A.v in the middle vertical and the innerhalf of the rear vertical wall are changed between—90 < Av < 90. As evident from the real part ofthis root locus plot, the change in ply angle can in-fluence blade stability (i.e. damping) substantiallyin both a beneficial and detrimental manner. How-ever, it is insufficient to destabilize the blade. Theimaginary part of the plot shows the changes in thefrequency of the aeroelastic lag mode as a result ofchanges in ply orientation. Numerous results can befound in Ref. [124] where it is shown that combi-nation of ply orientation and tip-sweep can slightlydestabilize the blade in hover. Figure 10 shows the



effect of ply orientation on hingeless blade stabilityin forward flight, at an advance ratio of // = 0.30.For forward flight stability, information is extractedfrom the linearized perturbation equations about thecoupled trim-aeroelastic response in forward flight,using Floquet theory [29]. The real part of the char-acteristic exponent, is an indicator of the dampingin the lag degree of freedom. Again, the ply an-gle Av is varied between — 90 < A.v < 90. Whiledamping levels change substantially, ply orientationis not sufficient to destabilize the blade for this par-ticular case. Other results from Ref. [124] indicatethat blade response and loads can be changed sig-nificantly by changing ply orientation.

These results, and similar results obtained inthe various studies mentioned in this section clearlyindicate that composite blade construction has con-siderable potential for aeroelastic tailoring leading toenhanced blade stability and reduced vibratory load-ing in the rotor. However, this remarkable potentialhas not been exploited by the helicopter manufactur-ers. While most modern helicopter blades are builtof composites, the primary reason for the compositeconstruction of these blades is their excellent fatiguecharacteristics, which result in unlimited blade life.Thus, composite blades have a large advantage overthe older metal blades, that had to be replaced aftera few thousand hours of operation.

3 Modeling of ElastomericLag Dampers and their

Incorporation in AeroelasticAnalyses

The effect of lag dampers on aeroelastic and aero-mechanical stability of hingeless and bearinglessrotored helicopters has always been an importantarea of endeavor. During the last decade, impor-tant advances in this area have been made. Themost important recent developments have focusedon the analytical and experimental modeling ofthe nonlinear properties of elastomeric lag dampers[9, 38, 39, 56, 81, 97, 98].

The body of research in this area consistsof two different approaches. Gandhi and Chopra[38, 39] have developed a nonlinear elastomericdamper model, based on a combination of linearand nonlinear springs and dashpots. The damperis characterized by a nonlinear constitutive differen-tial equation. This approach is capable of capturing,partially, the viscoelastic, hysteretic, energy dissi-pating properties of elastomeric lag dampers, as well

as dependence on operating conditions and steady-state lag angles. The damper model is incorporatedin the ground resonance problem of an articulatedrotor, and in the air resonance problem of a hin-geless rotor, in hover. The blades have only flapand lag degrees of freedom, the fuselage has pitchand roll, and the damper states are appended to theequations of motion. The results show that model-ing of the dampers is important for stability predic-tion. However, the paper [38] makes no attempt toconnect the damper model with any real elastomericdamper, that is in actual use. Subsequently, in [39],a slightly improved model of the damper was incor-porated in an aeroelastic and aeromechanical analy-sis of a three bladed bearingless rotor in forwardflight. Both shaft fixed and shaft free aeroelasticbehavior is examined, and the role of the damper isfound to be important. However, the damper and itsbehavior is not associated with any real elastomericdamper used in rot or craft.

A much more fundamental and comprehen-sive approach to the modeling of nonlinear lagdampers is presented in Refs. [9, 97, 98]. In thefirst of these two studies, a nonlinear anelastic dis-placement field (ADF) damper model, based on ac-curate three-dimensional material modeling and ir-reversible thermodynamics, was developed from ba-sic principles. Material nonlinearities are introducedby nonlinear functions that describe the dependenceof the unrelaxed and relaxed material moduli andthe anelastic strain rate, on the instantaneous totaland anelastic strains. The parameters that char-acterize the nonlinear material behavior are identi-fied through harmonic strain controlled experimen-tal tests. Nonlinear finite element equations are ob-tained in terms of the resulting ADF parameters.

In the second paper [97] for a simplified case,corresponding to pure shear behavior, two coupledpartial differential equations are obtained: one de-scribes motion and the second governs creep evo-lution in time. The parameters required for themodel implementation are obtained from suitablematerial characterization tests. Damper behavioris modeled by a finite element method, and com-bined with a three degree of freedom offset hinged,spring restrained blade model, as shown in Fig. 11.Nonlinear lag damper equations are coupled withthe blade equations and are solved simultaneously.Nonlinear equations are linearized about the steadystate response solution. Blade stability in forwardflight is obtained from Floquet theory. The siliconrubber damper was modeled with a single finite el-ement. The nonlinear behavior of the elastomericdamper has a significant effect on lag mode stabil-



ity in hover and forward flight. Damper response inforward flight depends on blade loading and advanceratio. A good indicator of the success of this modelto predict the hysteretic behavior of lag dampersis illustrated by Fig. 12. This figure shows thenondimensional lag damper force versus lag anglefor several advance ratios, p, = 0; 0.05; 0.20 and0.40, for fixed blade loading. The static lag angledecreases initially from hover to a minimum at anadvance ratio of 0.20, and subsequently it increases.Dynamic amplitudes increase steadily with advanceratio. Note that the ADF damper model predictssubstantial variations in the area and aspect ratioof damper hysteresis loops with advance ratio. TheIJL = 0.40 loop displays the characteristic asymme-try shown by elastomeric materials undergoing har-monic excitation with a static bias.

In a more recent sequel to this study [9], themodel was extended to include friction type ele-ments. These elements consist of friction-dampingand linear-spring elements which are added in par-allel to the original ADF model. The new modelrepresents a substantial improvement over the ba-sic ADF model, described previously in this section.Thus, the peak error between predicted and exper-imentally determined material complex moduli wasreduced from 72% to 18% for the storage modulus,and from 90% to 10% for the loss modulus. Thismodel clearly represents a very substantial improve-ment over its predecessor, and it is the best modelof its kind available.

4 Aeroelastic Behavior ofSwept Tip Rotors

Rotor blades with swept tips, which imply bothsweep and anhedral of the blade tip region, shownin Fig. 1, experience bending-torsion and bending-axial coupling effects due to sweep and anhedral.Swept tips influence blade dynamics because theyare located at regions of high dynamic pressure andrelatively large elastic displacements. Swept tips en-hance rotor performance, and are effective for reduc-ing aerodynamic noise and blade vibrations. Mostmodern helicopter blades have swept tips, whichsometimes are also denoted by the term advancedgeometry tips. Therefore the study of aeroelastic be-havior of rotor blades with advanced geometry tipshas received considerable attention during the pastdecade [26, 54, 63, 64, 113, 121, 122, 123, 124]. InRef. [54], isotropic swept tip rotors with advancedgeometry tips have been treated. Moderate deflec-tion beam theory is coupled with unsteady transonic

small disturbance theory (TSD) to calculate the un-steady transonic flow, three dimensional effects andshock waves on the advancing blade tips. The timehistory of the angle of attack distributions, obtainedfrom the rotor dynamic code, is used as input to thefinite difference TSD code. The non uniform inflowdistribution over the rotor disk is calculated using afree wake model. The coupling between the variousanalyses is carried out in a somewhat ad-hoc man-ner, which causes the results to be suitable primar-ily for response calculations, and thus blade stabilitywas not considered.

The aeroelastic behavior of swept tip com-posite blades was considered in a number of detailedstudies [121, 122, 123, 124]. The principal objectiveof these studies was the development of a practical,efficient structural dynamic model for swept tip ro-tor blades undergoing moderate deflections. Subse-quently, the model was used to determine the effectof tip sweep and composite blade construction onthe aerodynamic stability of swept tip rotor bladesin hover and forward flight. Aeroelastic blade re-sponse and blade loads, in forward flight were alsoconsidered in these studies. The principal goal ofthese studies was the examination of the structuralcoupling effects. Therefore, the aerodynamic loadsused were based upon quasisteady Greenberg the-ory combined with uniform inflow. Unsteady loadswere formulated using a general implicit formula-tion [11] which permitted the replacement of theseloads by compressible unsteady loads combined witha free-wake analysis in studies which were conductedlater [23, 24]. Results obtained in these studies[121, 122, 123, 124] show that combinations of tipsweep and composite constructions can substantiallyaffect both blade stability, response and loads.

The aeroelastic stability of straight and swepttip rotor blades in hover and forward flight wasstudied both experimentally and analytically in tworecent comprehensive papers [63, 64]. Two Mach-scaled rotors, with a diameter of 7.5 ft, having bothstraight and swept tip blades, were tested in hoverand forward flight. The purpose of the tests was toprovide hover and forward flight data for compari-son with analytical models. Data from the tests wascompared with calculations from a comprehensiverotor code, CAMRAD II [50, 51]. Correlations be-tween test and calculations for regressing lag modedamping are shown in Fig. 13 of Ref. [64]. Thecorrelation between theory and experiment is verygood. The aerodynamic loads were calculated withthree different inflow models: no dynamic inflow,Pit Peters dynamic inflow, and momentum theorydynamic inflow. The differences due to these inflow

6American Institute of Aeronautics and Astronuatics


models are small.For forward flight, the correlation between

the test results for regressing lag mode damping andthe experimental data is not as good as in hover asevident from Fig. 14, taken from Ref. [64]. The ad-dition of dynamic inflow increases the damping, thusthe results without dynamic inflow are closer to theexperimental data. Subsequently in Ref. [63], sensi-tivity studies, using parameter variations in aerody-namic center, center of gravity, blade mass, torqueoffsets, etc. were conducted. With these parame-ter variations, modest improvements between theoryand test results for the swept tip rotors in forwardflight were obtained.

The studies considered in this section indicatethat the accurate modeling of aeroelastic stabilityand response of swept tip rotors still represents achallenge, and good correlations with experimentaldata are not easily achieved.

5 Development and Validationof Comprehensive

Helicopter Analysis Codes

The development and validation of comprehen-sive helicopter analysis codes such as CAMRADII [50, 51], 2GCHAS [1, 59, 60, 68, 81, 93, 108],RDYNE [103], COPTER [20], UMARC [18] andCAMRAD/JA [49] has been another topic that hasreceived considerable attention. Among these codes,the two most advanced, CAMRAD II and 2GCHAS,have taken advantage of multibody dynamics thatfacilitate the effective treatment of complex config-urations [7, 44, 94].

Among the various comprehensive helicopteranalysis codes, CAMRAD II is perhaps the mostwidely used, both in the U.S. as well as Europe andJapan. The code has been more successful than itscompetitors in correlating with experimental data.The 2GCHAS code has also undergone considerablevalidation during the last five years and overall thecorrelations indicate generally satisfactory predic-tive capability for a fairly wide range of rotorcraftproblems. It is expected that in the near future, ver-sions of this code that are capable of running on aPC will become available.

The UMARC code developed at the Univer-sity of Maryland has also enjoyed considerable suc-cess, as students who graduated have taken the codewith them and started using it in an industrial set-ting.

6 Aeroelastic Characteristicsof Hingeless and Bearingless

Rotors

During the last three decades, the helicopter indus-try in the U.S. and abroad has invested a very sub-stantial amount of resources in the development ofproduction hingeless and bearingless rotor systems.Hingeless rotored helicopters, such as the MBB BO-105, and the Westland Lynx have been in productionfor almost 25 years. However, successful bearing-less rotored helicopters have gone into productiononly during the last decade. Typical examples arethe MD-900 Explorer [96], the Comanche bearing-less main rotor (BMR) [83], the Eurocopter EC135[53], it is also interesting to note that the MD900and the Comanche have five bladed rotors, whilethe EC 135 is four bladed. This is an indication thatBMR technology has matured in the last decade, andsubstantial gains in the understanding of aeroelasticand aeromechanical aspects of these rotors have beenmade. It is also fair to say that the improved under-standing of hingeless rotor behavior has made signif-icant contributions toward improved understandingof BMR's. This section highlights research carriedout during the last decade that has contributed to-wards the fundamental understanding of hingelessand bearingless rotor aeroelastic behavior.

A number of theoretical studies dealing withthe physical coupling mechanism present in hinge-less rotored helicopters air and ground resonance inhover [80] and forward flight [67] have clarified thecoupling mechanism between body and blade modes,and the effect of forward flight on air resonance.An aeroelastic analysis methodology for BMR heli-copters in hover and forward flight was developed byGandhi and Chopra [40]. The approach correlatedreasonably well with shaft-fixed hover stability dataobtained in tests, and then it was used to predictshaft-free stability in forward flight. These theoret-ical studies were useful, however work done by thehelicopter industry, which is discussed next, revealsin a more comprehensive manner, the advances madein the dynamic design of hingeless and bearinglessrotor systems.

An insightful study by Weller [117] providesa comparison of the aeromechanical stability char-acteristics, in hover, for two models of convention-ally designed soft-in-plane main rotors. One modelis a bearingless configuration, simulating the Bellhelicopter M680 main rotor. The second model isa hingeless rotor similar to the MBB BO-105 mainrotor. The purpose of the paper was to compare



the test data obtained from the two models, identifytheir respective aeromechanical stability character-istics, and determine the design features that havea primary effect on the air and ground resonancebehavior in hover.

To understand better the relative aeroelasticcharacteristics of hingeless versus BMR's, illustra-tions describing their operation are relevant. Thegeometry of a typical hingeless rotor was depictedin Fig. 1. The bearingless rotor with an elastomericdamper is more complicated, and is shown in Fig.15, taken from Ref. [83]. In a bearingless rotor, eachblade is connected to the hub center by a flexuralarm called a flexbeam, which bends in lag, flap andtwists by undergoing torsional deformation. Theflexbeam usually has an inboard portion that estab-lishes a virtual lap hinge, while the outboard por-tion is shaped so as to yield a torsionally soft regionfor relatively large control inputs. A structurallystiff external cuff encloses the flexbeam and trans-mits control inputs to the blade that are applied bythe pitch link. The cuff is bolted to the blade andthe flexbeam at its outboard end, as shown in Fig.15. At the inboard end of the cuff, a shear-restraintmechanism, called a snubber, connects the cuff tothe flexbeam. The shear restraint transmits bothflapwise and lagwise shears from the cuff to the flex-ure. The snubber housing contains elastomeric shearpads that are used to augment structural damping inthe lead-lag or inplane direction, and thus this com-bination is called an elastomeric lag damper, alsoshown in Fig. 15. To further clarify the operation ofthe bearingless hub and damper combination, con-sider Fig. 16 taken from Ref. [53]. The top portionof Fig. 16 is the view of the blade from the top, andthe bottom part is a section through the flexbeam,damper and control (right part) as well as a sectionthrough the damper (left side).

The mechanism whereby the inplane bendingof the flexbeam in lead-lag, produces displacementand damping is illustrated by Fig. 17, also fromRef. [53]. Figure 17 shows the displacement be-tween the cuff and flexbeam at the location of thedamper due to inplane bending as well as the lead-lag damping that is produced. It is also important tonote that the shear stiffness of the damper dependson material and geometrical properties, environmen-tal conditions (temperature), axial loads, as well asdisplacement amplitudes. Finally it should be men-tioned that the cuff flexbeam combination representsa structural element with a redundant load path,that has to be modeled carefully [6].

In Ref. [117], two Froude-scaled models, onehingeless and one bearingless were tested. While the

paper does not explicitly state the scale used, a com-parison of the model radius with the MBB BO-105blade radius, reveals that it is a 1:4 scale versionof the production rotor, and it is reasonable to as-sume that the bearingless rotor was scaled in thesame manner. The rotors were tested on the Ad-vanced Rotorcraft Experimental Dynamics (ARED)system, which can provide body pitch and roll de-grees of freedom. The rotors were extensively testedin both low and high thrust condition. The resultsobtained indicate that the hingeless rotor conceptoffers better stability margins at moderate to highthrust conditions due to its aeroelastic characteris-tics, thus the hingeless rotor is more stable at Igthrust and above. For low thrust conditions, how-ever, the bearingless rotor is better because of itslarger structural damping due to the elastomeric lagdamper. In these comparisons, it is also importantto keep in mind that the hingeless rotor had nolag damper, and its damping was from its inherentstructural damping.

In a sequel [118] to this study [117] Wellerconducted a very careful experimental examinationof a somewhat larger model BMR with a diameterof 9.37 ft. The BMR used in [117] had a diameterof 7.95 ft. This was also a four-bladed rotor, withan elastomeric lag damper similar to that consideredearlier [117]. The following parameters were changedduring the test: fundamental flap frequency, bladebuilt in cone and sweep angles, pitch link inclina-tion, flexbeam prepitch and shear restraint to flexureattachment. The extensive results show, that mod-est changes in these parameters provided only veryminor improvements in the aeromechanical stabilitymargins. The two studies mentioned [117, 118] con-tain a large amount of valuable experimental data,but almost no correlation with analytical models isprovided.

An outstanding study is Ref. [83] which de-scribes in detail the aeroelastic stability wind tun-nel testing of the Comanche BMR and the corre-lations with an analytical model. This BMR con-figuration is depicted in Fig. 15. A series of windtunnel tests were performed on a 1/6 Froude-scaledmodel of the RAH-66 Comanche BMR at the BoeingV/STOL wind tunnel. The tests had two objectives:(a) establish the aeromechanical stability character-istics of the coupled rotor-fuselage system, and (b)correlate the experimental data with analytical sta-bility predictions so that the methodology can beused with confidence for the full-scale aircraft. Aninitial test of the rotor with elastomeric dampers,shown in Fig. 15, uncovered a limit cycle instability.This instability manifested itself for the minimum



flight weight configuration. Figure 18, taken fromRef. [83], depicts the frequency and damping of thecoupled rotor-body system with elastomeric snub-ber/dampers. The presence of the body degrees offreedom and their coupling with the blade degrees offreedom modifies significantly the dynamic charac-teristics compared to the isolated rotor case. A fre-quency coalescence between the lag regressing andthe flap regressing-body roll mode now exists. Nearthis coalescence, the damping is low, and a limit cy-cle oscillation occurs at the regressing lag frequency.Closer examination of this nonlinear problem, pre-sented in the paper [83] revealed that this problemmay also be present when flying with the proto-type flight weight. A decision was made to replacethe elastomeric snubber/damper by a Fluidlastic®snubber/damper, that is also shown in Fig. 15. TheFluidlastic® snubber/damper is similar to the elas-tomeric dampers except that it includes a chamberwithin the flat elements which is filled with siliconefluid to provide the blade lead-lag damping. As theelastomeric elements that constitute the wall of thechamber flex in shear, the fluid is forced to flowaround a rigid diverter protruding into the fluid,thereby generating a damping force.

Further study revealed that nonlinearities inthe stiffness and loss factor of the elastomeric snub-ber/dampers were the cause of this limit cycle be-havior. As shown in Ref. [83], the stiffness ofthe Fluidlastic® damper is nearly linear, and us-ing it eliminates the limit cycle instability. Figure19 shows the hover air response characteristics ofthe prototype flight weight configuration with theFluidlastic® dampers at 9 degree collective. Thetest data for both frequency and damping are alsocompared with analytical results obtained from theUMARC/B code, which is a Boeing modified ver-sion of UMARC [18]. The correlations between theresults for the code in both hover and forward flightare quite good.

The aeromechanical design aspects of anotherproduction BMR that is flying on the EuropeanEC 135 are described in Ref. [53]. The feature of thisBMR equipped with an elastomeric lag damper areshown in Fig. 16. This rotor has excellent dampingmargins throughout its operation envelope. Modaldamping for this rotor in level flight, is shown in Fig.20. The dots are from the flight test and the solidline is the result of a calculation performed by C AM-RAD II. The agreement between theory and test aregood. The damping amounts to approximately 2.5%in the rotating system.

It is remarkable that all three productionBMR systems have been developed during the last

decade. This clearly indicates that the state-of-the-art of BMR aeroelastic design has made substantialadvances in this period.

7 Improved UnsteadyAerodynamic Models and

Modeling of Dynamic StallThe accurate representation of the unsteady aero-dynamic loading environment on rotorcraft plays acritical role in the prediction of aeroelastic stabil-ity and response. The representation of the nonlin-ear structural portion as well as the inertial load-ing for the rotary-wing aeroelastic problem can bedone accurately by using finite elements and multi-body techniques. However, the prediction of the un-steady aerodynamic environment, presents a majorchallenge, and in some cases large errors in the calcu-lation of the unsteady aerodynamic loads cannot beavoided. When dealing with the unsteady aerody-namic loads, it is convenient to distinguish betweentwo separate cases: approximate unsteady aerody-namic models for attached flow and dynamic stallmodels. These topics together with their applicationto the rotary-wing aeroelastic problem are discussednext.

7.1 Approximate UnsteadyAerodynamic Models and Their

Application to AeroelasticProblems

An useful unsteady aerodynamic model that pro-vides approximate unsteady aerodynamic loads inthe time domain was developed by Peters and his as-sociates [86, 87]. The finite state inflow model is anapproximate theory that provides global rotor-diskdownwash under unsteady flight conditions, and itis different from airfoil theory which produces localdownwash. The finite state inflow theory is an exactrepresentation of the three dimensional incompress-ible potential flow equations of the wake. The wakeis assumed to be a cylinder in hover and a skewedcylinder in forward flight. However, the model alsoincorporates the most important effect of wake con-traction. Detailed descriptions of this theory canalso be found in Refs. [84, 85]. This theory has beenemployed in several aeroelastic stability studies inhover and forward flight.

A typical application of this theory to theaeroelastic stability of composite rotor blades inhover can be found in Ref. [95] which integrates



geometrically-exact nonlinear beam theory and thegeneralized dynamic wake theory within a finite el-ement framework. The theory is applied to severalexamples, including limited correlation with experi-mental data.

In another study [77], the three dimensionalfinite-state wake model [84] is applied to hingeless-rotor aeromechanical stability in hover and forwardflight. A very interesting aspect of this study is thecorrelation with experimental data for an aerome-chanical stability problem in which the regressinglag mode, couples with fuselage roll to produce aninstability. Figure 21, taken from Ref. [77], showsthe regressing-lag mode damping as a function ofrotor speed (RPM). The dots are the experimen-tal data, the solid line is for M — 1, which rep-resents an earlier version of this theory [90], andthe dashed line corresponds to the three-dimensionalfinite-state wake model with 9 harmonic wake com-ponents (M = 9). Clearly, for this particular case,there is practically no difference between the finite-state wake model and dynamic inflow. It is alsoimportant to note that the good correlation betweenthe theory and the experimental data evident for theregressing lag mode, is not replicated by the othermodes, as can be seen by examining the other resultsin this study. However, in all the cases considered,there is practically no difference between the resultsbased on dynamic inflow and those based on finite-state wake theory with 9 harmonics.

Another, related, interesting study conductedrecently [110] attempts to enhance the efficiency ofthe finite state wake model by using aerodynamiceigenmodes to develop reduced order models for ro-torcraft. This technique, pioneered by Dowell, hasproven itself quite effective for fixed wing and tur-bomachinery flows. The study concluded that thefinite-state wake model is very compact, and its ef-fectiveness can not be enhanced by reduced ordermodeling.

One of the shortcomings of the finite statewake model is its inability to model blade vortexinteraction (BVI) which is an important source ofrotor vibratory loads at lower advance ratios. Tomodel BVI effects, free wake models, similar to thosedepicted in Fig. 5 are required. An efficient rotorfree-wake model was developed by Bagai and Leish-man [3]. This wake model has been incorporatedinto the UMARC code and has been used in numer-ous studies since then.

Another new and useful approximate un-steady aerodynamic theory that was developed tomodel two-dimensional, compressible loads for anairfoil/flap combination in unsteady free-stream is

presented in Refs. [74, 76]. Aerodynamic loads areobtained in the frequency domain for an airfoil/flapcombination using the doublet-lattice method. Sub-sequently, the loads are approximated in the fre-quency domain as rational functions of the Laplacevariable using a least squares fit to the unsteadyaerodynamic loads. Transformation to the time do-main yields a state space model for the unsteadyaerodynamic loads. An important feature of this ap-proximate unsteady aerodynamic model is its abilityto model the hinge moment on actively controlledflaps used for vibration reduction, which are dis-cussed later in this paper.

7.2 Dynamic Stall and ItsIncorporation into Aeroelastic

AnalysesDynamic stall is a strongly nonlinear unsteady aero-dynamic effect which plays a major role in aeroelas-tic stability and response calculations. This topic isreviewed in detail in a new book by Leishman [57],in Chapter 9. Dynamic stall is associated with theretreating blade and borders on the reversed flowregion, as shown in Fig. 22. For such conditions,the angle of attack of the blade cross-section can bevery large. Although the torsional response of theblade is relatively low under normal conditions, atthe flight envelope boundary, where dynamic stalleffects are pronounced, large transient-torsional ex-cursion may be excited, accompanied by low neg-ative damping in pitch. This, in turn, generatedexcessive control and blade vibratory loads, whichimpose speed and load limitations on the rotor asa whole. It can also cause stall flutter. Due to itsimportance, dynamic stall has been the subject ofa large number of studies which have led to an im-proved understanding of this complex aerodynamiceffect [29, 30, 33]. Dynamic stall is usually incorpo-rated in rotary-wing aeroelastic analysis using semi-empirical models. These models have a number ofcommon features. They are intended to incorporatetwo-dimensional, nonlinear, airfoil unsteady aerody-namic effects in analytical studies in the time do-main, and they are suitable for stepwise numericalintegration in time. The semi-empirical nature ofthe model is due to a number of free parameters thatare determined by fitting the theoretical expressionsto the experimental data, obtained from oscillatingairfoil tests.

During the last two decades, two primarysemi-empirical dynamic stall models have emerged.

(1) The ONER A dynamic stall model, which de-



scribes the unsteady airfoil behavior in both at-tached flow and during dynamic stall using a setof nonlinear differential equations. Since its ini-tial derivation in 1984, the model has undergonerevisions and improvement. The most recentversion of this model was documented by Petot[88]. The coefficients in the equations of thismodel are determined by parameter identifica-tion from experimental measurements on oscil-lating airfoils. The model requires 22 empiricalcoefficients. Figure 23 shows typical hystereticlift and moment coefficients computed with theONERA dynamic stall model, for a NACA 0012airfoil, at M = 0.379, k = 0.075, and timevarying angle of attack a = 10.3 -f 8.1sina;t.A more recent version of this model was im-proved by Truong [115]. The improvement con-tains a Hopf bifurcation model and some three-dimensional corrections, it requires 18 coeffi-cients, however, it has some oscillatory prob-lems, and has been used less than the previousversions.

(2) The Leishman-Beddoes model [58] is capableof representing the unsteady lift, pitching mo-ment, and drag characteristics of an airfoil un-dergoing dynamic stall. This model consists ofthree distinct components: (a) an attached flowmodel for the unsteady linear airloads, (b) aseparated flow model for the nonlinear airloads,and (c) a dynamic stall model for the leading-edge vortex induced airloads. The model con-tains a rigorous representation of compressibil-ity in the attached flow part of the model, usingcompressible indicial response functions. Thetreatment of nonlinear aerodynamic effects as-sociated with separated flows are derived fromthe Kirchoff-Helmholtz model to define an ef-fective separation point that can be generalizedempirically. The model uses relatively few em-pirical constants, with all but four derived fromstatic airfoil data [57]. This model is also un-dergoing continuous improvement. The mostrecent one was introduced in Ref. [116]. Thisdynamic stall model has been embedded in the2GCHAS [93] as well as the UMARC [18] codes.

The dynamic stall models described brieflyabove have been used in a number of aeroelastic sta-bility and response studies. The ONERA dynamicstall model has been employed in several aeroelasticstability studies. In Ref. [5], the effect of dynamicstall on isolated blade flap-lag stability is considered.The nonlinear equations of blade motion of a hinge-less rotor modeled as the offset hinged spring re-

strained blade model, with coupled flap-lag dynam-ics for each blade, is combined with the dynamic stallmodel. The nonlinear equations of blade motion areperturbed about a periodic forced response, and thedamping is evaluated by Floquet eigenanalysis. Thedamping is correlated with experimental data, andthe correlation is not very satisfactory. The rea-son for this discrepancy is probably due to the factthat perturbation of the equations in the presenceof dynamic stall is a questionable approach. A moreeffective approach would have been to integrate theequations of motion in the time domain, and extractthe damping information from the response curvesfor the appropriate rotor degrees of freedom. In asequel to this study, presented in Ref. [19], the au-thors consider a hingeless rotor with fully coupledflap-lag-torsional dynamics (2 mode representationfor each degree of freedom) and the aerodynamicloads are obtained by a combining the ONERA dy-namic stall model with a finite state wake model.The correlation between analysis and test is fair.Figure 24, taken from this study, depicts the in-fluence of different levels of aerodynamic modeling:(a) blade element theory with quasisteady stall, (b)the same theory but with dynamic stall, and (c) dy-namic stall and finite state wake theory. The figureshows the lag damping for a three bladed hingelessrotor at two shaft angles a5, over the advance ratiorange 0 < IJL < 0.60, and a collective pitch settingof OQ = 3. Figure 24(a) shows the rotor operat-ing at low thrust, all three models are reasonablyclose to experimental data. Figure 24 (b) depicts alarge negative shaft angle as = —16, and dampingdecreases with advance ratio. This is a low-thrustcase and dynamic stall and static stall theories areclose. Dynamic stall and the wake model improvethe agreement at low /x (JJL < 0.20), however, thesetheories fail to predict the loss of damping at thehigher advance ratio. It appears that the reason forthis discrepancy is similar to that mentioned for theearlier study.

Aeroelastic stability studies involving theLeishman dynamic stall model were conducted byTorok and Chopra [112]. It was noted that the ef-fect of flow separation and dynamic stall on rotor-lagdamping in high speed flight is quite significant.

Finally it should be mentioned that recently aEuropean study group has completed a monumentalreport which compares several up-to-date dynamicstall models, in their ability to predict rotor behaviorin the presence of dynamic stall [89]. Seven differentstall models were compared in this study, and thepredictions were compared with detailed measure-ments conducted on a model rotor in a wind tunnel.



The study has identified three-dimensional phenom-ena as being significant. Clearly, this effect is beyondthe reach of present two-dimensional semi-empiricalmodels. This effect produces an unexpected increasein lift and moment at 0.7R blade span. The au-thors speculate that progress in computational aero-dynamics, as applied to rotors, might lead to a qual-itative explanation of these phenomena.

8 Active Control ofAeroelastic Stability and

Response (i.e. Vibration) inRotorcraft

The desire to develop rotorcraft having a "jetsmooth" ride has shifted the emphasis in the areaof vibration alleviation (i.e. reduction of aeroelas-tic response) from traditional passive means of vi-bration reduction such as vibration absorbers andisolators to active control strategies [34]. Stringentrequirements on vibration levels strive for verticalaccelerations below 0.05g at most fuselage locations.These requirements imply that helicopter manufac-turers may be willing to tolerate the expense asso-ciated with an active control system that operatesin the rotating frame, i.e. the rotor. Once sucha control system is present, it can also be used foradditional objectives such as noise reduction, perfor-mance enhancements and stabilization of aeroelasticphenomena. This section summarizes and highlightsrecent accomplishments in two areas, stabilization ofaeroelastic and aeromechanical phenomena and vi-bration reduction in rotorcraft using active controls.

8.1 Stabilization of Aeromechanicaland Aeroelastic Phenomena by

Active ControlsSome of the previous research in this area has beenreviewed and discussed in Ref. [33]. One of the mostcomprehensive studies on air resonance suppression,in hover and forward flight, using blade pitch controlwas carried out by Takahashi and Priedmann [109].The model consisted of a coupled rotor-fuselage sys-tem representing a four bladed hingeless rotor at-tached to a rigid fuselage, as depicted in Fig. 4, withpitch and roll degrees of freedom. The controlleroperated through a conventional swash plate thatintroduced the same pitch input to all the blades.The controller design was based on an optimal stateestimator combined with optimal feedback gains.Optimal loop shapes were designed using the loop

transfer recovery approach. The outcome of this de-sign process resulted in a simple controller that useda single roll rate measurement in the body (non-rotating frame), and suppressed air resonance by us-ing a sine and a cosine swashplate input. The con-troller was shown to stabilize the system throughouta wide range of loading conditions and forward flightspeeds, with pitch inputs of 3 or less.

More recently, Weller [119] conducted an ex-perimental program to demonstrate the benefitsof applying active rotor control techniques to im-prove the aeromechanical stability characteristics ofa bearingless main rotor (BMR) model. This modelof the BMR was identical to that tested earlier[118]. Apparently the author was unaware of theanalytical work done earlier in this field [109]. Healso seemed reluctant to use modern control tech-niques, and much of this work was done either ex-perimentally or by using an electrohydraulic sim-ulator. Pitch and roll velocities and accelerationswere measured and transformed into pylon positionand velocity information which was fed back using afixed-gain relationship to produce cyclic swash platecommands 9C and Os so as to increase the dampingof the aeromechanical problem. Results indicate thepylon position feedback could increase damping by1%, at most. However, destabilizing trends at highthrust were present. Pylon velocity feedback wassuperior to position feedback, and the destabilizingtrends were reduced. This result is entirely consis-tent with the findings of Ref. [109]. Thus, it illus-trates that experimental trial and error approachesto active control, without analytical simulation andthe physical understanding it produces lead to lessthan effective research.

Finally, it is important to note that air res-onance, which is an aeromechanical instability, is amild instability as opposed to flutter which is an ex-plosive instability. Stabilizing flutter in rotorcraftusing active control has not been considered seri-ously because it may be impractical.

Recently, Celi [10] has written an interestingpaper on stabilization of a blade with a severed pitchlink, using a trailing edge flap. This paper is on theboundary between aeroelasticity and reconfigurablecontrols. This problem is shown in Fig. 25, thefailure of the pitch link causes the blade to be freefloating and uncontrollable. It is shown in the paper,that the trailing edge flap is capable of correctingthe catastrophic consequences of the pitch link fail-ure by trimming the blade, through an optimizationbased trim procedure. Unfortunately, flap deflectionof 18-22 degrees are required, and actuation powerrequirements were not considered in the paper.



8.2 Vibration Reduction inRotorcraft

As mentioned earlier, vibration reduction in rotor-craft is essentially the control of the aeroelastic re-sponse problem. Active control approaches to ro-torcraft vibration reduction are perceived to be arequirement so that rotorcraft can experience vi-bration levels comparable to fixed-wing transportaircraft. During the last 25 years, several ap-proaches to active vibration control in rotorcrafthave emerged [34]. The first approach developed washigher harmonic control (HHC). The controller ap-plies pitch inputs through a conventional swashplate.All blades experience the same inputs, and the vibra-tory aerodynamic loads are modified at their source,before they propagate into the fuselage. An alter-native is individual blade control (IBC), where timevarying pitch is introduced directly in the rotatingreference frame. The IBC can be implemented usingseveral approaches. One can oscillate each blade inpitch by actuating it at the root, this approach wasused initially, in this approach the entire blade is os-cillated. Alternatively, a small partial span trailingedge flap, shown in Fig. 26, can be actuated on theblade, this approach is sometimes called the activelycontrolled flap (ACF). Another approach twists theentire blade by embedding piezoelectric fibers, thisapproach is known as the active twist rotor (ATR),and the blade structure is shown schematically inFig. 27. All the approaches mentioned control vibra-tions in the rotating frame. An alternative approachsometimes known as active control of structural re-sponse (ACSR) controls vibrations in the fuselage,or the fixed frame, as illustrated in Fig. 28. In thisapproach, stiff actuators introduce small amplitudeexcitation between the rotor and the fuselage, suchthat the sum of the response of the airframe at spec-ified locations, due to rotor loads and the excitationdue to controls, is reduced to a minimum.

It is important to note that among theseapproaches, only the ACSR system is actually in-stalled on a production helicopter, the EH101, builtby a European partnership between Westland andAgusta. All the other systems have been tested inwind tunnels. The HHC approach and IBC schemewith root actuation have been flight tested [34],while the ACF will be flight tested at the end ofthis year (2001) on a MD-900 Explorer.

The strong interest in active vibration controlin rotorcraft has resulted in a large number of pa-pers on this topic during the last decade, and to dojustice to this topic would require a separate surveypaper. Thus, only a limited number of papers will

be described in this section.Among the various active control approaches,

IBC implemented by the actively controlled flap ap-pears to be the most promising concept. Further-more, the ACF has also considerable potential fornoise reduction and performance enhancement. Anumber of recent studies have established the re-markable potential of the ACF for vibration reduc-tion using a flexible blade model, similar to thatshown in Fig. 26, with coupled flap-lag-1orsionaldynamics and modified Theodorsen aerodynamicswhich include the effect of time-varying free stream[69, 70, 71, 72]. Milgram and Chopra [66] have de-veloped an analytical simulation incorporating anunsteady compressible aerodynamic model. Theaeroelastic model was developed using the compre-hensive analysis code UMARC. Experimental resultsfrom wind tunnel tests of the ACF were also pre-sented [106].

The need for an improved aeroelastic simula-tion model for the flap-blade combination led to thedevelopment of a new and improved model based ona compressible time domain unsteady aerodynamicmodel. This simulation capability could accommo-date three different flap configurations, and also dualflaps. Detailed vibration reduction studies from thismodel were presented in Refs. [73, 74, 75].

Subsequently, this model was improved byadding a free-wake model to the time domain un-steady compressible theory [23, 24]. The resultingcomprehensive simulation model facilitated the ex-amination of two distinctly different flight regimes inwhich vibrations are reduced using the ACF. A highspeed flight, where advance ratio effects are domi-nant and the influence of the free wake is limited,and low and moderate advance ratio regimes whereblade vortex interactions (BVI) are important.

It is also important to mention that in thistime period, very valuable experimental results onthe practical implementation of the ACF and itsapplication to fundamental vibration reduction inthe open loop mode, on a Mach scaled two bladedrotor, were reported by Fulton and Ormiston [35].The availability of these results permitted a com-parison between the comprehensive simulation de-veloped [24] and the experimental data obtained byFulton and Ormiston [35]. To illustrate the vibra-tion reduction capability of the actively controlledflap and the reliability of the simulation model, sometypical results obtained in Ref. [24, 25] are presentednext.

The results are presented for a four bladedhingeless rotor. Figure 29 shows the baseline andcontrolled vibratory hub shears and moments, with



compressible unsteady aerodynamics (referred to asRFA aerodynamics) and a free wake model, at anadvance ratio // = 0.15 where BVI is important.Figure 30 depicts similar results at a higher advanceratio // = 0.30. Two important observations are rele-vant: (1) the vibratory loads in the presence of BVIare approximately four times higher than those atIJL — 0.30, and (2) while the actively controlled flapis quite effective in reducing vibrations at both ad-vance ratios, its performance in the presence of BVIis not as good as in the higher advance ratio regime.

Figure 31 depicts the flap deflections requiredfor vibration reduction at these two advance ratios,the maximum flap deflection required for the allevi-ation of BVI effects can exceed 15 degrees. Thus,BVI vibration alleviation is more demanding thanvibrations at high speed.

All the results presented were for a flap op-erating in the closed loop mode using a control lawdescribed in Ref. [24, 25].

The simulation capability used here was alsovalidated by comparing with experimental data ob-tained by [35] for the open-loop operation of the flap,and the correlation in most cases is quite good.

Numerous other studies on vibration reduc-tion using actively controlled flaps were carried outrecently [17, 65, 107]. In many cases, the imple-mentation of the ACF is accomplished using ac-tuators built from active materials, such as piezo-electric materials or magnetostrictive materials [17].Such materials are limited in their force and strokeproducing capability. Therefore, there is consider-able concern whether such materials are adequatefor implementing the ACF for full scale configura-tions. Fortunately, an electromagnetic actuator forindividual blade control has been recently developed[27]. The electromagnetic actuator is combined with

TMa trailing-edge control surface, called the Heliflap ,which is suitable for active rotor control applica-tions. The device is rugged, compact with no ex-ternal linkages and no moving parts except the flapitself, and has excellent force, deflection, frequencycharacteristics, and good power and thermal dissipa-tion characteristics. The amplitude and frequencyare controlled by modulation of the electrical cur-rent to the actuators. It was bench tested and whirltested on a full-scale OH-58 rotor at 81% operatingRPM and low collective. Flap deflections of ±6 de-grees at frequencies of 4.4/rev were achieved. Thisdevice appears to be quite promising, its force andstroke producing capability is much higher than thatprovided by active materials based actuation. Ifthe electromagnetic actuator performs as planned,it could replace adaptive materials based actuation

for helicopter rotor control applications.Another successful combination between in-

dividual blade control and adaptive materials basedactuation is the ATR shown in Fig. 27, which wasdeveloped jointly by MIT, the Army and NASA Lan-gley Research Center [13, 120]. The first of thesestudies describes the aeroelastic modeling of theATR using a simple flap-torsion model of the activetwist blade, which is intended for approximate stud-ies, and is implemented in a code called PETRA.The results are compared with results from CAM-RAD II. The vibration results based on CAMRAD IIpredicted large vibrations in the 4/rev vertical hubshear, for less than 2 degrees maximum thrust. Thesecond paper describes the correlation between thestructural dynamic model developed for the ATRblade, bench tests, and rotating tests. The predic-tion of the blade torsional load in hover is within20%.

There was also considerable activity in vi-bration reduction in the fixed system, namely thefuselage, using active control. A very comprehen-sive study of vibration reduction using ACSR, em-ploying a sophisticated simulation model was com-pleted by Cribbs and Friedmann [21]. This studywas the first to use rotor fuselage interactional aero-dynamics, combined with a free wake model, and athree dimensional finite element model of the fuse-lage. Several control algorithms were tested, andexcellent vibration reduction was demonstrated inthe simulations.

9 Concluding Remarks andFuture Trends

9.1 Concluding RemarksThe research activity in RWA during the last decadehas been vigorous and innovative, and it is the mostactive research area in aeroelasticity. This is quiteimpressive when one realizes that rotary wing vehi-cles represent 4-6% of the total aerospace business.While some of the problems in rotorcraft aeroelas-ticity and aeromechanics have existed for a consider-able amount of time, good fundamental understand-ing and reliable solutions are often obtained slowlyand with considerable difficulty. The most impor-tant milestones during this period have been:

• The development of three new helicopters withbearingless main rotors, two in production(EC135, MD-900) and one (Comanche) on theverge of production.



• Development of methods based on first princi-ples, for characterizing elastomeric lag dampers.

• Development of reliable techniques for modelingof composite main rotor blades with advancedgeometry tips.

• Development of effective active control meth-ods for vibration reduction in rotorcraft, and inparticular, the approach based on the activelycontrolled trailing edge flap.

9.2 Future TrendsDespite the perception that exists in some circlesthat RWA is mature, and new areas whose descrip-tion is characterized by fashionable collections ofcurrent buzzwords are more important, the authorpredicts that RWA and aeromechanics will continueto prosper because a number of fundamental prob-lems are still not understood and are not amenableto reliable computer simulations. The need to buildbetter rotorcraft with low vibration levels, low noiseand enhanced performance will continue to motivateresearchers in RWA and aeromechanics to developinnovative approaches for the solution of these prob-lems.

An area that is critical for both RWA as wellas for the design of better rotorcraft is developmentof good coupling methods between finite elementbased structural dynamic models of blades and com-putational fluid mechanics for rotors. This relativelynew field known as computational aeroelasticity [32]is in its infancy for fixed wing vehicles, and has re-ceived very little attention in RWA. Development ofthis field can have major payoffs in the prediction ofrotor loading, which has been a weakness in rotor-craft design. Much work has been done on rotorcraftvibration reduction using adaptive materials basedactuation. However, if the electromagneticalry actu-ated flap [27] lives up to its potential, it will supplantthe adaptive materials based actuation as the bestapproach for actuating the ACF. This will facilitatethe development of active rotors, with dual trailingedge flaps, that may be used for vibration reduction,noise alleviation and performance enhancement.

Persistent research on the simulation of dy-namic stall by direct solution of the Navier-Stokesequations, has the potential for replacing semi-empirical two-dimensional dynamic stall models, bythree-dimensional models based on basic principles.Such a simulation capability will also lay the ground-work for developing active methods for controllingdynamic stall. However, achieving some of these ob-jectives may take 5-10 years, since solution of these

problems in a short time frame is not feasible.Development of new configurations, of small

unmanned rotorcraft could provide the impetus forinnovative designs and concepts. Scaling issues inthe design of such vehicles could also be very impor-tant.

References[1] Anon., 2GCHAS Theory Manual, U.S.

Aeroflightdynamics Directorate, ATCOM,TM 93-A-004, 1993.

[2] Atilgan, A.R and Hodges, D.H., "Uni-fied Nonlinear Analysis for Nonhomoge-neous Anisotropic Beams with Closed Cross-Section," AIAA Journal, Vol. 29, No. 11, No-vember 1991, pp. 1990 - 1999.

[3] Bagai, A., and Leishman, J.G., "RotorFree-Wake Modeling Using a Pseudo-ImplicitTechnique-Including Comparisons with Ex-perimental Data," Journal of the AmericanHelicopter Society, Vol. 40, No. 3, July 1995,pp. 29-41.

[4] Barkai, S.M., and Rand, O., "The Influenceof Composite Induced Couplings on Tiltro-tor Whirl Flutter Stability," Journal of TheAmerican Helicopter Society, Vol. 43, No. 2,April 1998, pp. 133 - 145.

[5] Barwey, D., Gaonkar, G.H., and Ormis-ton, R.A., "Investigation of Dynamic StallEffects on Isolated Rotor Flap-Lag Stabil-ity with Experimental Correlation," Journalof the American Helicopter Society, Vol. 36,No. 4, October 1991, pp. 12 - 24.

[6] Bauchau, O.A., and Chiang, W., "DynamicAnalysis of Rotor Flexbeams Based on Nonlin-ear Anisotropic Shell Models," Journal of TheAmerican Helicopter Society, Vol. 38, No. 1,January 1993, pp. 55-61.

[7] Bauchau, O.A., and Rang, N.K., "A Multi-body Formulation for Helicopter StructuralDynamic Analysis," Journal of the AmericanHelicopter Society, Vol. 38, No. 2, April 1993,pp. 3 - 14.

[8] Bielawa, R.L., Rotary-Wing Aeroelasticity andStructural Dynamics, AIAA Education Series,AIAA, 1992.



[9] Brackbill, C.R., Lesieutre, G.A., Smith, E.G.,and Ruhl, L.E., "Characterization and Mod-eling of Low Strain Amplitude and FrequencyDependent Behavior of Elastomeric DamperMaterials," Journal of The American Heli-copter Society, Vol. 45, No. 1, January 2000,pp. 34-42.

[10] Celi, R., "Stabilization of a Blade with a Sev-ered Pitch Link Using a Trailing Edge Flap,"Paper G.18, Proceedings of the 25th EuropeanRotorcraft Forum, Rome, Italy, September 14-16 1999.

[11] Celi, R. and Friedmann, P.P., "Rotor BladeAeroelasticity in Forward Flight With anImplicit Aerodynamic Formulation," AIAAJournal, Vol. 26, No. 5, May 1988, pp. 1425- 1433.

[12] Cesnik, C.E.S., and Hodges, D.H., "VABS:A New Concept for Composite Rotor BladeCross-Sectional Modeling," Journal of theAmerican Helicopter Society, Vol. 42, No. 1,January 1997, pp. 27 - 38.

[13] Cesnik, C.E.S., Shin, S., Wilbur, M.L., andWilkie, W.K., "Design and Testing of theNASA/Army/MIT Active Twist PrototypeBlade," Proceedings of the 26th European Ro-torcraft Forum, The Hague, The Netherlands,September 26-29 2000, pp. 17.1 - 17.11.

[14] Cesnik, C.E.S., Sutyrin, V.G., andHodges, D.H., "Refined Theory of Twistedand Curved Composite Beams: The Roleof Short-Wavelength Extrapolation," Inter-national Journal of Solids and Structures,Vol. 33, No. 10, No. 10, 1996, pp. 1387-1408.

[15] Cesnik, C.E.S., Sutyrin, Y.G., andHodges, D.H., "A Refined CompositeBeam Theory Based on the Variational-Asymptotical Method," AIAA Paper 93-1616,34th AIAA/ASME/ASCE/AHS/ASC Struc-tures, Structural Dynamics, and MaterialsConference, April 19-22 1993, pp. 2710 -2720, La Jolla, CA.

[16] Chopra, I., "Perspectives in Aeromechani-cal Stability of Helicopter Rotors," Vertica,Vol. 14, No. 4, No. 4, 1990, pp. 457 - 508.

[17] Chopra, I., "Status of Application of SmartStructures Technology to Rotorcraft Sys-tems," Journal of The American HelicopterSociety, Vol. 45, No. 4, October 2000, pp. 228-252.

[18] Chopra, I., and Bir, G., "University of Mary-land Advanced Rotor Code:UMARC," Pro-ceedings of AHS Aeromechanics SpecialistsConference on Aerodynamics, Acoustics andDynamics, San Francisco, CA, Jan. 19-211994.

[19] Chunduru, S.J., Subramanian, S., andGaonkar, G.H., "Dynamic Stall and WakeEffects on Trim and Stability of HingelessRotors With Experimental Correlation,"Journal of The American Helicopter Society,Vol. 42, No. 4, October 1997, pp. 370 - 382.

[20] Corrigan, J.J., "Computational of Loads Dur-ing Maneuvering Flight Using a Comprehen-sive Rotorcraft Code," Proceedings of 2nd In-ternational Aeromechanics Specialists7 Con-ference, Bridgeport, CT, October 11-13 1995,pp. 2.44 - 2.64.

[21] Cribbs, R. and Friedmann, P.P., "Vi-bration Reduction in Rotorcraft Usingan Enhanced ACSR Model," AIAA Pa-per No. 2000-1687, Proceedings of theAIAA/ASME/ASCE/AHS/ASC 41st Struc-tures, Structural Dynamics and MaterialsConference, Atlanta, GA, April 3-6 2000.

[22] Dat, R., Aeroelasticity of Rotary Wing Air-craft in Helicopter Aerodynamics and Dynam-ics, Vol. 63, Agard Lecture Series, 1973, Ch. 4.

[23] de Terlizzi, M. and Friedmann, P.P.,"Aeroelastic Response of Swept-Tip RotorsIncluding the Effects of BVI," Proceedingsof the 54th Annual Form of the AmericanHelicopter Society, Washington, DC, May1998. pp. 644 - 663.

[24] de Terlizzi, M. and Friedmann, P.P., "ActiveControl of BVI Induced Vibrations Using aRefined Aerodynamic Model and Experimen-tal Correlation," Proceedings of the 55th An-nual Forum of the American Helicopter So-ciety, Montreal, Quebec, Canada, May 25-271999.

[25] de Terlizzi, M. and Friedmann, P.P., "ActiveControl of Vibrations due to BVI and Exper-imental Correlation," Proceedings of the 25thEuropean Rotorcraft Forum, Rome, Italy, Sep-tember 14-16 1999, pp. G6.1 - G6.16.

[26] Epps, J.J., and Chandra, R., "The Nat-ural Frequencies of Rotating Beams with TipSweep," Journal of The American Helicopter



Society, Vol. 41, No. 1, January 1996, pp. 29 -36.

[27] Fink, D.A, Hawkey, T.J., Gadreau, P.J., Well-man, B., and Ormiston, R.A., "An Electro-magnetic Actuator for Individual Blade Con-trol," Proceedings of the 56th Annual Forumof the American Helicopter Society, VirginiaBeach, VA, May 2-4 2000.

[28] Friedmann, P.P., "Recent Development inRotary-Wing Aeroelasticity," Journal of Air-craft, Vol. 14, No. 11, No. 11, 1977, pp. 1027- 1041.

[29] Friedmann, P.P., "Formulation and Solutionof Rotary-Wing Aeroelastic Stability and Re-sponse Problems," Vertica, Vol. 7, No. 2,No. 2, 1983, pp. 101 - 141.

[30] Friedmann, P.P., "Recent Trends in Rotary-Wing Aeroelasticity," Vertica, Vol. 11,No. 1/2, No. 1/2, 1987, pp. 139-170.

[31] Friedmann, P.P., "Helicopter Rotor Dynamicsand Aeroelasticity: Some Key Ideas and In-sights," Vertica, Vol. 14, No. 1, No. 1, 1990,pp. 101 - 121.

[32] Friedmann, P.P, "Renaissance of Aeroelas-ticity and Its Future," Journal of Aircraft,Vol. 36, No. 1, January-February 1999, pp. 105-121.

[33] Friedmann, P.P., and Hodges, D.A., "Rotary-Wing Aeroelasticity with Application toVTOL Vehicles," Flight Vehicles, Materi-als, Structures, and Dynamics-Assessmentand Future Directions, Noor, A.K. and Ven-neri, S.L., Eds., Vol. 5, New York, ASME,1993, Ch. 6, pp. 299 - 391.

[34] Friedmann, P.P., and Millott, T.A., "Vi-bration Reduction in Rotorcraft Using Ac-tive Control: A Comparison of Various Ap-proaches," AIAA Journal of Guidance, Con-trol and Dynamics, Vol. 18, No. 4, July-August1995, pp. 664 - 673.

[35] Fulton, M. and Ormiston, R.A., "Small-ScaleRotor Experiments with On-Blade Elevens toReduce Blade Vibratory Loads in ForwardFlight," Proceedings of the 54th Annual Forumof the American Helicopter Society, Washing-ton, DC, May 20-22 1998, pp. 433 - 451.

[36] Fulton, M.V., and Hodges, D.H., "AeroelasticStability of Composite Hingeless Rotor Bladesin Hover: Part I: Theory," Mathematical andComputer Modeling, Vol. 18, No. 3/4, August1993, pp. 1 - 18.

[37] Fulton, M.V., and Hodges, D.H., "AeroelasticStability of Composite Hingeless Rotor Bladesin Hover: Part I: Results," Mathematical andComputer Modeling, Vol. 18, No. 3/4, August1993, pp. 19 - 36.

[38] Gandhi, F., and Chopra, I., "An Analyti-cal Model for a Nonlinear Elastomeric LagDamper and Its Effect on Aeromechanical Sta-bility in Hover," Journal of the American He-licopter Society, Vol. 39, No. 4, October 1994,pp. 59 - 69.

[39] Gandhi, F., and Chopra, I., "Analysis of Bear-ingless Main Rotor Aeroelasticity Using an Im-proved Time Domain Nonlinear ElastomericDamper Model," Journal of the American He-licopter Society, Vol. 41, No. 3, July 1996,pp. 267 - 277.

[40] Gandhi, F., and Chopra, I., "An Aeroelas-tic Analysis Methodology for Bearingless MainRotor Helicopters," Journal of The AmericanHelicopter Society, VoL 43, No. 1, January1998, pp. 66 - 75.

[41] Hodges, D.H., "A Review of Composite Ro-tor Blade Modeling," AIAA Journal, Vol. 28,No. 3, No. 3, 1990, pp. 561 - 565.

[42] Hodges, D.H., Atilgan, A.R., Fulton, M.V.,and Rehfield, L.W., "Free-Vibration Analysisof Composite Beams," Journal of The Amer-ican Helicopter Society, VoL 36, No. 3, July1991, pp. 36 - 47.

[43] Hodges, D.H, Shang, X, and Cesnik, C.E.S.,"Finite Element Solution of Nonlinear Intrin-sic Equations for Curved Composite Beams,"Journal of the American Helicopter Society,VoL 41, No. 4, October 1996, pp. 313 - 321.

[44] Hopkins, S.A., Ruzicka, G.C., and Ormis-ton, R.A., "Analytical Investigations of Cou-pled Rotorcraft/Engine/Drive Train Dynam-ics," Proceedings of 2nd International Aerome-chanics Specialists' Conference, Bridgeport,CT, October 11-13 1995, pp. 2.1 - 2.23.

[45] le, C.A. and Kosmatka, J.B., "Formulation ofa Nonlinear Theory for Spinning Anisotropic



Beams," Recent Advances in Structural Dy-namic Modeling of Composite Rotor Bladesand Thick Composites, Vol. AD-Vol. 30,Winter Annual Meeting of ASME, (Fried-mann, P.P. and Kosmatka, J.B., Editors),Anaheim, CA, November 8-13 1992, pp. 41 -57.

[46] Johnson, W., Helicopter Theory, PrincetonUniversity Press, 1980.

[47] Johnson, W., "Recent Developments in Dy-namics of Advanced Rotor Systems - Part I,"Vertica, Vol. 10, No. 1, No. 1, 1986, pp. 73 -107.

[48] Johnson, W., "Recent Developments in Dy-namics of Advanced Rotor Systems - Part II,"Vertica, Vol. 10, No. 2, No. 2, 1986, pp. 109 -150.

[49] Johnson, W., A Comprehensive AnalyticalModel of Rotorcraft Aerodynamics and Dy-namics, Vol. I: Theory Manual, Johnson Aero-nautics, Palo Alto, CA, 1988.

[50] Johnson, W., CAMR AD II, ComprehensiveAnalytical Model of Rotorcraft Aerodynam-ics and Dynamics, Johnson Aeronautics, PaloAlto, CA, 1992-1997.

[51] Johnson, W., "Technology Drivers in the De-velopment of CAMRAD II," Presented atAHS Aeromechanics Specialists Conference onAerodynamics, Acoustics and Dynamics, SanFrancisco, CA, Jan. 19-21 1994.

[52] Jung, S.N., Nagaraj, V.T., and Chopra, L,"Assessment of Composite Rotor Blade Mod-eling Techniques," Journal of The AmericanHelicopter Society, Vol. 44, No. 3, July 1999,pp. 188 - 205.

[53] Kampa, K., Enenkl, B., Polz, G., andRoth, G., "Aeromechanic Aspects in the De-sign of the EC135," Journal of The AmericanHelicopter Society, Vol. 44, No. 2, April 1999,pp. 83 - 93.

[54] Kim, K., and Chopra, L, "Aeroelastic Analysisof Swept, Anhedral, and Tapered Tip RotorBlades," Journal of the American HelicopterSociety, Vol. 37, No. 1, Jan. 1992, pp. 15 - 30.

[55] Kosmatka, J.B. and Friedmann, P.P., "Vibra-tion Analysis of Composite TurbopropellersUsing a Nonlinear Beam-Type Finite ElementApproach," AIAA Journal, Vol. 27, No. 11,November 1989, pp. 1606 - 1614.

[56] Kunz, D.L., "Influence of Elastomeric LagDamper Modeling on the Predicted DynamicResponse of Helicopter Rotor Systems," AIAAPaper 96-1219-CP, AIAA Dynamics Special-ists' Conference, Salt Lake City, UT, April 18-19 1996, pp. 154 - 164.

[57] Leishman, J.G., Principles of Helicopter Aero-dynamics, Cambridge University Press, 2000.

[58] Leishman, J.G. and Beddoes, T.S., "A Gen-eralized Model for Unsteady AerodynamicBehavior and Dynamic Stall Using IndicialMethod," Journal of The American HelicopterSociety, Vol. 34, No. 3, July 1989, pp. 3 - 17.

[59] Lim, J.W., and Anastassiades, T., "Correla-tion of 2GCHAS Analysis with ExperimentalData," Journal of the American Helicopter So-ciety, Vol. 40, No. 4, October 1995, pp. 18 -33.

[60] Lim, J.W., Panda, B., Sopher, R., Cas-sarino, S.J., and Lee, C.S., "Current Status ofU.S. Army Comprehensive Helicopter AnalysisSystem," Proceedings of the 56th Annual Fo-rum of the American Helicopter Society, Vir-ginia Beach, VA, May 2-4 2000.

[61] Loewy, R.G., "Review of Rotary-WingV/STOL Dynamic and Aeroelastic Prob-lems," Journal of The American HelicopterSociety, Vol. 14, No. 3, July 1969, pp. 3 - 23.

[62] Loewy, R.G., "Helicopter Vibrations: A Tech-nological Perspective," Journal of The Ameri-can Helicopter Society, Vol. 29, No. 4, October1984, pp. 4 - 30.

[63] Maier, H.T. and Abrego, A.L., "AnalyticalModel Sensitivity Study for Aeroelastic Stabil-ity of Straight and Swept-Tip Rotor Blades,"Proceedings of the 26th European RotorcraftForum, The Hague, The Netherlands, Septem-ber 26-29 2000.

[64] Maier, T.H., Sharpe, D.L., and Abrego, A.L.,"Aeroelastic Stability for Straight and Swept-Tip Rotor Blades in Hover and ForwardFlight," Proceedings of the 55th Annual Forumof the American Helicopter Society, Montreal,Quebec, Canada, May 25-27 1999.

[65] Milgram, J., and Chopra, L, "A ParametricDesign Study for Actively Controlled TrailingEdge Flaps," Journal of The American He-licopter Society, Vol. 43, No. 2, April 1998,pp. 110 - 119.



[66] Milgram, J., Chopra, L, and Straub, F.K., "AComprehensive Rotorcraft Aeroelastic Analy-sis with Trailing Edge Flap Model: Valida-tion with Experimental Data," 52nd Annu-ual Forum of the American Helicopter Society,Washington, DC, June 4-6 1996, pp. 715 - 725.

[67] Milgram, J.H., and Chopra, L, "Air Resonanceof Hingeless Rotor Helicopters in TrimmedForward Flight," Journal of The AmericanHelicopter Society, Vol. 39, No. 4, October1994, pp. 46 - 58.

[68] Millot, T.A., Friedmann, P.P., and Yuan, K.,"Correlation Studies for Hingeless Rotors inForward Flight Using 2GCHAS," Journal ofThe American Helicopter Society, Vol. 43,No. 3, July 1998, pp. 257 - 262.

[69] Millott, T., and Friedmann, P.P., "The Practi-cal Implementation of an Actively ControlledFlap to Reduce Vibrations in Helicopter Ro-tors," Proceedings of the 49th Annual Forumof the American Helicopter Society, St. Louis,MO, may 1993, pp. 1079 - 1092.

[70] Millott, T.A., and Friedmann, P.P., "Vibra-tion Reduction in Helicopter Rotors Usingan Active Control Surface Located on theBlade," AIAA Paper 92-2451, Proceedings of33rd Structures, Structural Dynamics, andMaterials Conference, Dallas, TX, April 1992,pp. 1974 - 1988.

[71] Millott, T.A., and Friedmann, P.P., "Vibra-tion and Reduction in Hingeless Rotor Us-ing an Actively Controlled Trailing Edge Flap:Implementation and Time Domain Simula-tion," AIAA Paper 94-1306, Proceedings of35th AIAA/ASME/ASCE/AHS/ASC Struc-tures, Structual Dynamics and Materials Con-ference, Hilton Head, SC, April 18-20 1994,pp. 9 - 22.

[72] Millott, T.A., and Friedmann, P.P., "Vibra-tion Reduction in Helicopter Rotors Usingan Actively Controlled Partial Span TrailingEdge Flap Located on the Blade," NASA, CR4611, June 1994.

[73] Myrtle, T.F., "Development of an ImprovedAeroelastic Model for the Investigation of Vi-bration Reduction in Helicopter Rotors Us-ing Trailing Edge Flaps," Ph.D. Dissertation,Mechanical and Aerospace Engineering Dept.,University of California, Los Angeles, CA,June 1998.

[74] Myrtle, T.F., and Friedmann, P.P., "Un-steady Compressible Aerodynamics of aFlapped Airfoil with Application to He-licopter Vibration Reduction," AIAA Pa-per 97-1083-CP, Proceedings of the 38thAIAA/ASME/ASCE/AHS Structures, Struc-tural Dynamics and Materials Conference,Kissimmee, FL, April, 7-10 1997, pp. 224 -240.

[75] Myrtle, T.F., and Friedmann, P.P., "VibrationReduction in Rotorcraft Using the ActivelyControlled Trailing Edge Flap and Issues Re-lated to Practical Implementation," Proceed-ings of the 54th Annual Forum of the Ameri-can Helicopter Society, Washington, DC, May,20-22 1998.

[76] Myrtle, T.R. and Friedmann, P.P., "Appli-cation of a New Compressible Time DomainAerodynamic Model to Vibration Reductionin Helicopters Using An Actively ControlledFlap," Journal of The American HelicopterSociety, Vol. 46, No. 1, January 2001.

[77] Nagabhushanam, J., and Gaonkar, G.H.,"Hingeless-Rotor Aeromechanical Stability inAxial and Forward Flight With Wake Dynam-ics," Journal of The American Helicopter So-ciety, Vol. 44, No. 3, July 1999, pp. 222 - 233.

[78] Nixon, M.W., "Aeroelastic Response and Sta-bility of Tiltrotors with Elastically- CoupledComposite Rotor Blades," Ph.D. Dissertation,Dept. of Aerospace Engineering, University ofMaryland, 1993.

[79] Ormiston, R.A., "Investigation of HingelessRotor Stability," Vertica, Vol. 7, No. 2, No. 2,1983, pp. 143 - 181.

[80] Ormiston, R.A., "Rotor-Fuselage Dynamicsof Helicopter Air and Ground Resonance,"Journal of The American Helicopter Society,Vol. 36, No. 2, April 1991, pp. 3 - 20.

[81] Ormiston, R.A., Saberi, H., and Anastani-ades, T., "Application of 2 GCHAS to theInvestigation of Aeromechanical Stability ofHingeless and Bearingless Rotor Helicopters,"51st Annual Forum of the American Heli-copter Society, Fort Worth, TX, May 9-111995, pp. 1132 - 1155.

[82] Ormiston, R.A., Warmbrodt, W.G.,Hodges, D.H., and Peters, D.A., "Survey



of Army/NASA Rotorcraft Aeroelastic Sta-bility Research," NASA, TM 101026, October1971.

[83] Panda, B., and Mychalowycz, E., "AeroelasticStability Wind Tunnel Testing with AnalyticalCorrelation of the Comanche Bearingless MainRotor," Journal of The American HelicopterSociety, Vol. 42, No. 3, July 1997, pp. 207 -217.

[84] Peters, D.A., Boyd, D.D., and He, C.J.,"Finite-State Induced-Flow Model for Rotorsin Hover and Forward Flight," Journal of TheAmerican Helicopter Society, Vol. 34, No. 4,October 1989.

[85] Peters, D.A. and He, C.H., "A Closed-FormUnsteady Aerodynamic Theory for Lifting Ro-tors in Hover and Forward Flight," Proceed-ings of the 43rd Annual Forum of the Amer-ican Helicopter Society, St. Louis, MO, May18-20 1987.

[86] Peters, D.A., and He, C.J., "Finite StateInduced Flow Models Part II: Three Di-mensional Rotor Disk," Journal of Aircraft,Vol. 32, No. 2, March-April 1995, pp. 323 -333.

[87] Peters, D.A., Karunamoorthy, S., andCao, W., "Finite State Induced Flow ModelsPart I: Two Dimensional Thin Airfoil," Jour-nal of Aircraft, Vol. 32, No. 2, March-April1995, pp. 313 - 322.

[88] Petot, D., "Differential Equation Modelingof Dynamic Stall," La Reserche Aerospatiale,Vol. 5, 1989, pp. 59 - 71.

[89] Petot, D., Arnaud, G., Harrison, R.,Stevens, J., Dieterich, O., van der Wall, B.C.,Young, C., and Szechenyi, E., "Stall Effectsand Blade Torsion - An Evaluation of Pre-dictive Tools," Journal of The AmericanHelicopter Society, Vol. 44, No. 4, October1999, pp. 320 - 331.

[90] Pitt, D.M. and Peters, D.A., "Theoretical Pre-diction of Dynamic Inflow Derivatives," Ver-tica, Vol. 5, No. 1, No. 1, 1981, pp. 21 - 34.

[91] Rand, O., "Periodic Response of Thin-WalledComposite Helicopter Rotor Blades," Journalof The American Helicopter Society, Vol. 36,No. 4, October 1991, pp. 3 - 11.

[92] Reichert, G., "Helicopter Vibration Control -A Survey," Vertica, Vol. 5, No. 1, No. 1, 1981,pp. 1 - 20.

[93] Rutkowski, M.J. et al, "Comprehensive Aero-mechanics Analysis of Complex Rotorcraft Us-ing 2GCHAS," Journal of the American Heli-copter Society, Vol. 40, No. 4, October 1995,pp. 3 - 17.

[94] Saberi, H., Jung, Y.C., and Anastassiades, T.,"Finite Element and Modal Method in Multi-body Dynamic Code," Proceedings of 2nd In-ternational Aeromechanics Specialists' Con-ference, Bridgeport, CT, October 11-13 1995,pp. 8.1 - 8.16.

[95] Shang, X., Hodges, D.H., and Peters, D.A.,"Aeroelastic Stability of Composite HingelessRotors in Hover with Finite-State UnsteadyAerodynamics," Journal of The American He-licopter Society, Vol. 44, No. 3, July 1999,pp. 206 - 221.

[96] Silverthorn, L.J., Anand, V.R., and Lau-zon, D.M., "FAA Certification of the MD900 Dynamic Systems," Presented at the 6thInternational Workshop on Dynamics andAeroelastic Stability Modeling of RotorcraftSystems, University of California, Los Ange-les, November 1995.

[97] Smith, E. et al, "Aeroelastic Response andStability of Helicopters with Elastomeric LagDampers," Journal of the American HelicopterSociety, Vol. 41, No. 3, July 1996, pp. 257 -266.

[98] Smith, E. et al, "Formulation, Validation andApplication of a Finite Element Model forElastomeric Lag Dampers," Journal of theAmerican Helicopter Society, Vol. 41, No. 3,July 1996, pp. 247 - 256.

[99] Smith, E.G., "Aeroelastic Response and Aero-mechanical Stability of Helicopters with Elas-ticity Coupled Composite Rotor Blades,"Ph.D. Dissertation, Dept. of Aerospace Engi-neering, University of Maryland, July 1992.

[100] Smith, E.G., and Chopra, I., "Formulation andEvaluation of an Analytical Model for Com-posite Box-Beams," Journal of The AmericanHelicopter Society, Vol. 36, No. 3, July 1991,pp. 23 - 35.



[101] Smith, E.G. and Chopra, L, "Air and GroundResonance With Elastically Tailored Compos-ite Rotor Blades," Journal of The AmericanHelicopter Society, Vol. 38, No. 4, October1993. pp. 50 - 61.

[102] Song, O., and Librescu, L., "Structural Mod-eling and Free Vibration Analysis of Rotat-ing Composite Thin-Walled Beams," Journalof The American Helicopter Society, Vol. 42,No. 4, October 1997, pp. 358 - 369.

[103] Sopher, R. and Hallock, D., "Time HistoryAnalysis of Rotorcraft Dynamics Based on aComponent Approach," Journal of The Amer-ican Helicopter Society, Vol. 31, No. 1, Janu-ary 1986, pp. 43-51.

[104] Srinivas, V., and Chopra, L, "Validationof a Comprehensive Aeroelastic Analysis forTiltrotor Aircraft," Journal of The AmericanHelicopter Society, Vol. 43, No. 3, July 1998.

[105] Srinivas, V., Chopra, L, and Nixon, M.W.,"Aeroelastic Analysis of Advanced GeometryTiltrotor Aircraft," Journal of The AmericanHelicopter Society, Vol. 43, No. 3, July 1998,pp. 212 - 221.

[106] Straub, F.K., "Active Flap Control for Vi-bration Reduction and Performance Improve-ment," Proceedings of the 51st American Heli-copter Society Forum, Fort Worth, TX, 1995,pp. 381 - 392.

[107] Straub, F.K. and Charles, B.D., "Comprehen-sive Modeling of Rotors with Trailing EdgeFlaps," Proceedings of the 55th Annual Forumof the American Helicopter Society, Montreal,Canada, May 25-27 1999.

[108] Straub, F.K., Sangha, K.B., and Panda, B.,"Advanced Finite Element Modeling of RotorBlade Aeroelasticity," Journal of the Ameri-can Helicopter Society, Vol. 39, No. 2, April1994. pp. 56 - 68.

[109] Takahashi, M.D., and Friedmann, P.P., "Heli-copter Air Resonance Modeling and Suppres-sion Using Active Control," Journal of Guid-ance, Control and Dynamics, Vol. 14, No. 6,Nov./Dec. 1991, pp. 1294 - 1300.

[110] Tang, D., Dowell, E.H., and Peters, D.A.,"Reduced Order Aerodynamic Models BasedUpon Inflow Eigenmodes," Journal of TheAmerican Helicopter Society, Vol. 43, No. 4,October 1998, pp. 342 - 351.

[Ill] Torok, M.S., and Berezin, C.R., "Aerody-namic and Wake Methodology EvaluationUsing Model UH-60A Experimental Data,"Journal of the American Helicopter Society,Vol. 39, No. 2, April 1994, pp. 21 - 29.

[112] Torok, M.S., and Chopra, L, "Hingeless Ro-tor Aeroelastic Stability Analysis with Re-fined Aerodynamic Modeling," Journal of theAmerican Helicopter Society, Vol. 36, No. 4,October 1991, pp. 48 - 56.

[113] Toulmay, F., Arnaud, G., Falchero, D., andVillat, V., "Analytical Prediction of RotorDynamics for Advanced Geometry Blades,"52nd Annuual Forum of the American He-licopter Society, Washington, DC, June 4-61996, pp. 685 - 703.

[114] Tracy, A.L., and Chopra, L, "AeroelasticAnalysis of a Composite Bearingless Rotor inForward Flight Using an Improved WarpingModel," Journal of the American HelicopterSociety, Vol. 40, No. 3, July 1995, pp. 80 - 91.

[115] Truong, V.K., "Prediction of Helicopter Ro-tor Airloads Based on Physical Modeling of3-D Unsteady Aerodynamics," Paper No. 96,Proceedings 22nd European Rotorcraft Forum,Brighton, UK, September 17-19 1996, pp. 96.1- 96.14.

[116] Tyler, J.C., and Leishman, J.G., "Analysis ofPitch and Plunge Effects on Unsteady Air-foil Behavior," Journal of The American Heli-copter Society, Vol. 37, No. 3, July 1992, pp. 69-82.

[117] Weller, W.H., "Relative Aeromechanical Sta-bility Characteristics for Hingeless and Bear-ingless Rotors," Journal of The American He-licopter Society, Vol. 35, No. 3, July 1990,pp. 68-77.

[118] Weller, W.H., "Variation in Hover Aerome-chanical Stability Trends with BearinglessMain Rotor Design," Journal of The Ameri-can Helicopter Society, Vol. 39, No. 1, January1994, pp. 70 - 80.

[119] Weller, W.H., "Fuselage State Feedback forAeromechanical Stability Augmentation of aBearingless Main Rotor," Journal of TheAmerican Helicopter Society, Vol. 41, No. 2,April 1996, pp. 85 - 93.


c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)1 Sponsoring Organization.

[120] Wilkie, W.K., Wilbur, W.M, Mirick, P.H.,Cesnik, C.E.S., and Shin, S., "AeroelasticAnalysis of the NASA/Army/MIT ActiveTwist Rotor," Proceedings of the 55th An-nual Forum of the American Helicopter Soci-ety, Montreal, Canada, May 25-27 1999.

[121] Yuan, K., Friedmann, P.P., and Venkate-san, C., "Aeroelastic Behavior of CompositeRotor Blades with Swept Tips," Proceedingsof the 48th Annual Forum of American Heli-copter Society, Washington, DC, June 1992,pp. 1039 - 1059.

[122] Yuan, K., Friedmann, P.P., and Venkate-san, C., "A New Aeroelastic Model forComposite Rotor Blades with Straight andSwept Tips," AIAA Paper 92-2259, 33rdAIAA/ASME/AHS/ASC Structures, Struc-tural Dynamics and Materials Conference,Dallas, TX, April 13-15 1992, pp. 1371 - 1390.

[123] Yuan, K., Friedmann, PP., and Venkate-san, C., "Aeroelastic Stability, Responseand Loads of Swept Tip Composite Ro-tor Blades in Forward Flight," Proceedings35th AIAA/ASME/ASCE/AHS/ASC Struc-tures, Structural Dynamics and MaterialsConference, Hilton Head, SC, April 18-201994, pp. 23-42.

[124] Yuan, K.A., and Friedmann, P.P., "Aeroelas-ticity and Structural Optimization of Compos-ite Helicopter Rotor Blades with Swept Tips,"NASA, CR 4665, May 1995.

Inboard segment -Pitch change bearing-

Outboard segment -

Swept tip

Rotor hub

Swash plate Pitch link

Figure 1: Typical hingeless blade with advancedgeometry tip.

Featheringaxis

Front view

Aerodynamic center A.C.Tension center T.C.

MassoanterC.a^MVU_/ \ ^-Posifionof

EfcsHccenterEaOKkl.. \ "A'SSSSSf

Position ofblade cross sectionbefore deformation

Note: Blade cross section after deformation is not in the plane of the paper

Figure 2: Undeformed and deformed blade configu-rations shown at the top, and cross-sectional loca-tions shown at the bottom, illustrating the geomet-rically nonlinear aspects of the basic coupled flap-lag-torsional problem.



Shaft Axis

Figure 3: Schematic description of the helicopterin forward flight used for coupled trim/aeroelasticanalysis (propulsive trim).

Tail rotor -Torsion

RollFuselage

Figure 4: Coupled rotor-fuselage dynamic system,with active control flaps shown on the blades.

BLADE-ROOT

Figure 6: Undeformed blade coordinate system,showing typical elements of the blade span.

(a)

(b)

(c)

l,x

Figure 5: Qualitative features of three differentfree-wake models at an advance ratio of // = 0.1.Wake geometry (a) FREEWARE model, (b) John-son (modified Scully) model, and (c) RotorCRAFTmodel.

a,

02,x

"

Figure 7: Finite element nodal degrees of freedom.



: -0.010-

fc-0.020-

-90

TWO-CELL COMPOSITE BLADEAEROELASTIC STABILITY (MU=0.3)

unstablestable

|— log mode [

-60 -30 0 30 60VERTICAL WALL PLY ORIENTATION (DEC)

90

Figure 10: Characteristic exponent for the funda-mental lag mode at an advance ratio of // = 0.30.

Figure 8: Two cell composite cross-section, includ-ing ply orientations, A^ and A^ in the vertical andhorizontal walls, respectively.

0.770-1

0.760-

50.750-

: 0.740-

10.730-

0.720-

0.710-

45

i

-.0300 -.0250 -.0200 -4)150 -.0100 -.0050 .0000REAL PART (DAMPING)

Figure 9: Root locus for the first lag mode.

.-Fixed hub„ Lag damper (undeformed)

-Lag damper (deformed)Hub springsLag hinge

Pitch bearinglocation

Figure 11: Offset hinged spring restrained hinge-less blade model, coupled with an elastomeric lagdamper model.

O.l

& 0.04

II 0.02

Hover

[1=0.2

0 L_0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Lag angle (degrees)

Figure 12: Hysteretic characteristics of damper forcevs. lag angle for ADF damper model.



1•0Sa

Test- No Dynamic Inflow- Pitt & Peters D.L- Momentum Theory D.I.

= 2°

- 1 2 - 6 0 6Collective Pitch (deg)

12

Figure 13: Comparison of CAMRAD II calculationswith three inflow models and measured hover re-gressing mode damping versus collective pitch angle,swept tip blade with 2 degree precone hub, sweep 30degrees aft.

h

Figure 15: Description of the Comanche bearing-less main rotor, including both elastomeric andFluidlastic® damper configuration.

2.0

1.5 -

a8u?

4 0.5 -

0.0

• Test— - - - - No Dynamic Inflow———— Dynamic Inflow, Reg.— - - Dynamic Inflow, Adv.— - - - - Dynamic Inflow, Coll.— — - Dynamic Inflow, React.

0.1 0.2 0.3Advance Ratio,

Lead LagDamper Flexbeam

0.5Control Cuff

Figure 14: Comparison with swept tip rotor of mea-sured forward flight regressing lag mode damping,CAMRAD II periodic solution without dynamic in-flow and with dynamic inflow, 0-degree shaft angle,6-degree collective pitch, 0-degree precone hub, 30-degree aft tip sweep.

Figure 16: Design of EC 135 bearingless rotor geom-etry, flexbeam and elastomeric lag damper.



10

0)

4Q>

e 2

Damper Displacement

Cuff

Modal\ Damping

ModalDisplacement

10

o"oCDLL

6 gO

- 4COQ

- 2

200 500 1.000 2,000Damper Stiffness - N/mm

Figure 17: Chordwise kinematics showing cuff andin-plane blade bending (top) which determine themodal displacement and damping of the elastomericlag damper (bottom).

5

QE

6-

4-

2-

20

16-

12-

8-

4-

il 0

600 700 800 900 1000Model Rotor Speed (rpm)

1100

600 700 800 900 1000Model Rotor Speed (rpm)

1100

oCO>,COTJS

Flap Regressing/Roll ModeD

0

a n a Q

*" Limit Cycle

8 O

06°

Q Lag RegressingMode

500 550 600 650 700 750 800 850 900 950 1000Model Rotor Speed (rpm)

•Q.

16--

12--

8--

4-

0-

O

8 oo o

Lag RegressingMode g Q

° ^6

— *" Limit Cycle

8 Oo

Figure 19: Hover air resonance at 9 degree collectivewith Fluidlastic® damper.

500 550 600 650 700 750 800 850 900 950 1000

Model Rotor Speed (rpm)

Figure IS: Hover air resonance of the minimumflight weight configuration with elastomeric dampersat 8-degree collective pitch.

• Test Zp-10000ftA Test Zp-3000 ft• Test Z,« 10000 ft• T0stZ,»2000ft

——— Calculation Z^-10000 ft

Gross Weight 2640-2670 kgNominal Rotor Speed 6.58 HzBlade Lead-Lag Damping 2.0%

o>2Q.E

Regressive Lead-Lag Damping

50 100Level Flight Speed - KTAS

Figure 20: Regressing lag mode damping in forwardflight and comparison with CAMRAD II.



l.UU

0.75

§ 0.50

i~ 0.25O)

'5.E 0COQ

-0.25

-00.50

—— M = 1--- M =9• ••Test Data (Ret. 1)

Stable ^TX

t N•

Lag Regressive, .......1 ————— !_,,... __L... __L. 1 ,

Modei i

200 400 600Rotor speed (RPM)

800 1000

Figure 21: Regressing lag mode damping with in-creasing rotor speed at zero degree blade collectivepitch.

CL(t)

CM(t)

10° 20°

Figure 23: Typical hysteretic lift and moment co-efficients computed with the ONERA dynamic stallmodel.

RETREATINGHOE

ADVANCINGSIDE

lo.s»

——— Dynamic Stall and Wake Theory——— Dynamic StaU Theory— - - - - - Quasisteady Stall Theory

• Test Data

(a)ccs =

(b)as = -1

0.1 0.2 0.3 0.4 0.5 0.6

Advance Ratio Oi)

Figure 22: Schematic illustration of reversed flowregion and dynamic stall region.

Figure 24: Aerodynamic modeling effects on the lagdamping, for a three bladed hingeless rotor blademodel.



Free floatingblade Trailing edge flap

Severedpitch link

active laminate detail:• E-glass 0°/90°Q AFC+450

E-glass +45°/-45°0 AFC-450

Figure 25: Blade with severed pitch link and activelycontrolled trailing edge flap.

trailing edgefairing

low densityfoam core

NACA 0012 airfoil

balance weight

"D-spar" primary structurew/AFC plies

Figure 27: ATR spar structure with active laminatescontaining piezoelectric fibers.

/-». ' ^Sc'**"' ^y-'-^sXlactic Aid*

1 ̂ ^11

. : — -iJ 1i i i

B i C ! D ;

Figure 28: Coupled rotor/flexible fuselage model us-Figure 26: Elastic blade model incorporating a par- ing ACSR platform and actuators,tial span trailing edge flap, with several blade regionsfor time domain aerodynamic approximations.



FHX4 FHY4 FHZ4 MHX4 MHY4 MHZ4

Figure 29: Simultaneous reduction of 4/rev hubshears and moments, // = 0.15, RFA aerodynamics.

FHX4 FHY4 FHZ4 MHX4 MHY4 MHZ4

l-'^^l BASELINE

Figure 30: Simultaneous reduction of 4/rev hubshears and moments, \JL = 0.30, RFA aerodynamics.

Advance Ratio=0.l5

Advance Ratio=0.30

Azimuth (deg)

Figure 31: Flap deflection history at advance ratiosp, — 0.15 and // = 0.30 with RFA aerodynamics.


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