Document
NASA-CR-196103
ill
ALLEVIATION OF WHIRL-FLUTTER
ON A JOINED-WING TILT-ROTOR
AIRCRAFT CONFIGURATION USING
ACTIVE CONTROLS
Johannes M van Aken Aerospace Engineer Sterling Software Rotorcraft Aeromechanics Branch NASA Ames Research Center Presented at the International Specialists' Meeting on Rotorcraft Basic Research of the American Helicopter Society, ALLEVIATION OF WHIRL-FLU'I3"ER ON A JOINED-WING TILT-ROTOR AIRCRAFT CONFIGURATION USING ACTIVE CONTROLS Johannes M. van Aken Aerospace Engineer Sterling Software Rotorcraft Aeromechanics Branch NASA Ames Research Center ABSTRACT Ci (i=0,1,2) system sensor matrix control sensor matrix Do F The feasibility of using active controls to delay feedback gain matrix the onset of whirl-flutter on a joined-wing tilt- noise level gain vector gm M modal matrix rotor aircraft was investigated. The CAMRAD/JA code was used to obtain a set of linear k th generalized coordinate qk differential equations, which describe the position vector of point P in a rcg,p CAMRAD/JA body axis system with motion of the joined-wing tilt-rotor aircraft.
The hub motions due to wing/body motion is a origin at the aircraft center of gravity, ft standard input to CAMRAD/JA and were obtained from a structural dynamics model of a airframe linear displacement at Up location P representative joined-wing tilt-rotor aircraft.
control vector v The CAMRAD/JA output, consisting of the open- loop system matrices, and the airframe free- Vtrim aircraft trim velocity vector sensor noise vector w vibration motion were input to a separate x state vector program, which performed the closed-loop, first-order state variable active control calculations. An eigenvalue Xs sensor vector analysis was performed to determine the flutter Y stability of both open- and closed-loop systems. 5s longitudinal cyclic pitch, deg Sensor models, based upon the feedback of pure eigenvalue state variables and based upon hub-mounted A diagonal eigenvalue matrix sensors, providing physically measurable pitch angle, deg accelerations, were evaluated. It was shown airframe angular displacement at Op that the onset of tilt-rotor whirl-flutter could location P be delayed from 240 to above 270 knots by roll angle, deg feeding back vertical and span-wise ill yaw angle, deg accelerations, measured at the rotor hub,. to the longitudinal cyclic pitch. Time response damping ratio calculations at a 270-knot cruise condition kth linear displacement vector {k showed an active cyclic pitch control level of k th angular displacement vector 0.009 deg, which equates to a very acceptable 9- (1) angular velocity perturbation vector pound active-control force applied at the rotor natural frequency hub.
f_ rotor rotation rate, rad/sec Indices: a anti-symmetric mode ac active control Ai (i=0,1,2) system matrix center of gravity cg A first-order system matrix F airframe body axis system B0 control matrix FT trim Euler angles B first-order control matrix pilot control, or airframe location P P h hub h,c hub motion , chord-wise direction Presented at the International Specialists' h,s hub motion , span-wise direction Meeting on Rotorcraft Basic Research of the h,v hub motion, vertical direction American Helicopter Society, Atlanta, Georgia, S symmetric mode March 25-27, 1991.
This work is declared a work of the U.S.
Government and is in the public domain.
2-1 II_AGJ[ IEANK (_IOT FILI_IEI,) fly at higher speeds or to reduce its struct_al weight.
The goal of the tilt-rotor concept is to achieve Nasu 10 studied flutter control on a simplified the cruise speed of a fixed-wing aircraft, while tilt-rotor model, consisting of a semi-span retaining the hover capability of a helicopter.
straight wing, a pylon attached to the wing tip, Current tilt-rotor aircraft (XV-15 and V-22) and a three-bladed hingeless rotor. Nasu employ very thick wing airfoils (23% thick) to considered symmetric wing elastic motion (wing obtain adequate wing stiffness and strength to beamwise, chordwise, and torsional bending) and handle the loads imposed by vertical-jump rotor blade chordwise and flapwise bending. His takeoffs and high speed whirl-flutter stability.
feedback control was performed in the state- These thick airfoils result in wing space domain. The author studied the use of compressibility effects limiting the high speed active controls to delay the aeroelastic potential of the tilt-rotor aircraft, e.g. to instability (whirl-flutter) on a tilt-rotor model, M-0.575 for a XV-15 size aircraft. In hover representative of a XV-15 size aircraft 11.
flight the net thrust of the tilt-rotor aircraft is reduced by the vertical drag (download) of the The results of a whirl-flutter alleviation study wing 1 Wolkovitch, et. al. 2, performed an for a joined-wing tilt-rotor aircraft are analytical study to evaluate the application of presented here. Table 1 provides a comparison the joined-wing concept 3 to tilt-rotor aircraft.
of the tilt-rotor models studied in Refs. 10 and Figure 1 shows the baseline cantilever-wing 11 with the present investigation. This study tilt-rotor configuration, representing a XV-15 included rigid-body motion, both symmetric and size tilt-rotor aircraft. Figure2 shows a anti-symmetric elastic body degrees of freedom, typical joined-wing tilt-rotor configuration rotor blade bending and torsion modes, the hub studied in Ref. 2. The joined wing concept can gimbal and the rotor speed degrees of freedom.
reduce the projected wing area in the rotor In addition, feedback control in the state-space downwash in hover, thus potentially reducing the domain as well as feedback control using hover download. The joined wing concept also realistic sensor models (the output of hub- allows for thinner airfoil sections (12% thick), mounted accelerometers) was investigated.
resulting in an increase in the drag-divergence limiting Mach number from 0.575 for the INVESTIGATION APPROACH cantilever-baseline model to 0.69 for the joined- wing model.
The approach followed in this joined-wing tilt- rotor whirl flutter alleviation study is described Reference 2 evaluated various joined-wing tilt- in this section and is schematically shown in rotor configurations in terms of potential Fig. 4.
performance improvements, airframe aeroelastic characteristics, and aircraft whirl flutter A number of XV-15 size joined-wing tilt-rotor speeds. Design parameters that were. varied configurations were studied in Ref. 2, which included front wing sweep angle, front wing used the structural analysis code MSC-PAI_ to airfoil thickness, and nacelle center of gravity calculate the airframe mode shapes, modal location.
frequency, and modal mass. Only the airframe mode shape at the hub is reported in Ref. 2.
Reference 2 showed a potential speed increase of 100 knots by delaying the A typical joined-wing tilt-rotor aircraft compressibility drag effects to higher Mach configuration (model 166CL in Ref. 2) was numbers. However, this performance advantage selected to study the potential of using active was negated by a lowering of the joined-wing controls to delay the occurrence of whirl flutter whirl-flutter speed from 330 to 240 knots.
on a joined-wing tilt-rotor. The airframe Representative results for Ref. 2 are shown in structural dynamic characteristics, consisting Fig. 3.
of the modal frequency, modal mass, and the hub motion due to elastic airframe deformation Studies have been performed in the use of active were obtained from Ref. 2 and are used as an controls to reduce a tilt-rotor's response to a input to the rotorcraft analysis code gust 4-7 and to reduce tilt-rotor blade loads CAMRAD/JA, which provided the mathematical during maneuver@. Other studies have been plant model of the tilt-rotor aircraft. The performed to improve the hover aeromechanical CAMRAD/JA analysis was also used in Ref. 2 to stability of helicopter@. Clearly an area of determine the whirl flutter speed for the various interest for tilt-rotors is flutter control with joined-wing tilt-rotor aircraft configurations.
the objective to allow the tilt-rotor aircraft to The CAMRAD/JA (Comprehensive Analytical 2-2 stability of the aircraft with the closed-lo_op Modelof RotorcraftAerodynamics and Dynamics, Johnson Aeronautics) is described in detail in feedback system. Time response calculations Refs. 12-15 and a summary description is were performed to determine the provided in Appendix A. magnitude/level of the required active control inputs. The effect of sensor noise on the closed- CAMRAD/JA is used to develop the equations of loop aircraft stability was also investigated motion for the airframe motion, the equations of using random noise of a specified magnitude to motion for the rotor, and the expressions for the simulate measurement noise and/or system rotor hub load reactions. The coupled airframe- modelling uncertainty.
rotor equations of motion are obtained by THEORETICAL FORMULATION substituting the hub motion into the equations for the rotor motion and hub loads, and then substituting the hub reactions into the airframe PLANT MODEL DEVELOPMENT equations of motion. The aircraft motion consists of the six rigid body degrees of freedom For the purpose of performing an aeroelastic and the airframe elastic free-vibration modes.
stability analysis, the rotorcraft motion can be CAMRAD/JA accounts for the rigid body motion in described by means of a set of linear differential a quasi-static manner. The CAMRAD/JA analysis equations of the form 12" specifically uses the MSC-PAL data in modeling the airframe dynamics at the rotor hub location A2_(" + Alx + A0x = B0v (1) due to the elastic airframe deformation.
where x is the vector of degrees of freedom, v is For purposes of an aeroelastic analysis, the vector of controls, Ai (i=0,1,2) are the CAMRAD/JA linearizes the aerodynamic and system matrices, and B0 is the control matrix.
inertial forces around the aircraft trim solution Equation (1) represents the rotorcraft plant to derive a mathematical plant model, consisting model, i.e., the tilt-rotor aircraft without of a set of linear differential equations feedback control, referred to hereafter as the describing the perturbed motion of the aircraft basic aircraft. The Ai (i=0,1,2) and Bo matrices about the trim condition.
are obtained from the CAMRAD/JA code and are a function of the cruise flight conditions. For the The CAMRAD/JA plant model was used as an most general case in which Eqn. (1) describes input to a separate program, which allowed for the motion of a rotorcraft, the matrices Ai the evaluation of various feedback control system schemes for their effectiveness in (i=0,1,2) and Bo have periodic coefficients and must be analyzed for stability by the methods of delaying the occurrence of whirl-flutter.
Floquet-Liapunov theory. For the tilt-rotor in Additional input to the closed-loop analysis cruise flight, the rotor operates in a mostly program consisted of the motion sensor model axial-flow environment and the Ai (i=0,1,2) and and the active control feedback specifications.
Bo matrices in Eqn. (1) are constant coefficient The analysis code uses an eigenvalue analysis to determine the stability of the closed-loop matrices. Consequently, the techniques for the system and allows for the calculation of the analysis of time-invariant systems can be used 16.
system time-history response to various types of control inputs, such as an impulse or step control input. The CAMRAD/JA basic aircraft plant model matrices (Eqn. (1)) are input to the closed-loop A separate utility was used to obtain a analysis code which models the airframe motion mathematical formulation describing the output sensor outputs and feedback control system as of the airframe-mounted motion sensors. Input described by Eqns. (2)-(8) below.
to this utility consisted of the geometric definition of the sensor location on the airframe, The control vector v in Eqn. (1) consists of the the airframe mode shape data for the sensor sum of the pilot control inputs, Vp, and the active location, and CAMRAD/JA parameters describing control inputs, Vac: the aircraft trim conditions (i.e., the aircraft velocity and orientation, and its flight path).
v(t) = vp(t) + Vac(t) (2) Sensor models, based on pure state variable The motion sensor output is described by the domain feedback as well as based on realistic observer or sensor vector, y, which is defined sensors, measuring the actual "physical" motion as: of the airframe at the hub were evaluated. An eigenvalue analysis was used to determine the 2-3 degree of freedom to the sensor output sigr_al
Y = C2)(" + C1)( + COX + D0v
(3) represented by the corresponding jth element of the sensor vector y.
where Ci (i=0,1,2) are the system sensor matrices and DO is the control sensor matrix.
The contribution of k th aircraft degree of freedom to the output of a sensor located at a The active control vector, Vac, is defined by: point P can be the due to the local airframe displacement, Xp,k, (through the corresponding vac = Fy (4) Co-matrix element), the velocity at point P, kp,k (Cl-matrix element), or its acceleration ,T(p, k where F is the output feedback gain matrix. No (C2-matrix element).
attempt is made here to model the dynamics of the swashplate actuators.
It is assumed that single-direction motion sensors are employed in the sensor model.
Combining Eqns. (3) and (4) and substituting Therefore each element of the sensor vector y (Vp+Vac) for v in Eqn. (1) leads to the following represents the motion of point P in only one equation for the closed-loop system: direction. Only airframe-mounted sensors are considered. The rotor degrees of freedom do not contribute to the sensor output.
(A2-BoFC2)_ + (A1-BoFC1))_ + (5) (A0-BoFC0)x = (B0+BoFD0)v To determine the element values of the Ci- matrices (i=0,1,2) it is necessary to determine which can be rewritten as: the aircraft body motion at point P where the sensor is located. The derivation for this body motion at point P follows the derivation for the
. , = (6)
hub motion as presented in Ref. 12 and is described below.
Equation (6) is transformed to a first-order state variable form by the substitution: The body axis system is defined as pictured in Fig. 5. From the pilot's perspective the body x- axis is defined positive forward, the body y-axis (7) is positive to the right, and the body z-axis is positive downward. Assume that the sensor is located at a point P, whose location with respect yielding: to the reference body axis system is given by the position vector rp. The sensor at point P will _s = Axs + Bv (8) sense the motion (displacement, velocity and/or acceleration) at P due to both the rigid aircraft An eigenvalue analysis can be perforr:ned to and airframe elastic motions. The motion at determine the stability of the rotorcraft system point P on the aircraft in flight is given by the represented in the state-space form by Eqn. (8).
linear displacement vector, Up, and the angular The natural frequency, (On, and the damping ratio, displacement vector, 0p. These displacements at C, (fraction of critical damping), for each mode is point P are obtained by expanding the motion at obtained from the associated eigenvalue, Z, as point P in a series of orthogonal free vibration (On=l_.lQ/2_ and r.,=-Real(_.)/lZl, respectively, modes, in which the first six modes represent the rigid body motion: where _ is the rotor rpm in rad/sec.
OO up(rp,t) = _.qk(t)_, k(rp) (g) The sensor model used in the feedback control k=l system is defined by Eqn. (3). By appropriate selection of the elements of the Ci (i=0,1,2) by 0p(rp,t) = _qk(t)l,k(rp) (10) setting the elements to "1" or "0", a feedback k=l scheme based upon pure state variables can be obtained. Alternatively, the output of a sensor, such as an accelerometer mounted on the The orthogonality property of the modes implies airframe can be modeled by the proper that the elastic airframe modes produce no net specification of the elements of the Ci matrices.
displacement of the aircraft center of gravity.
The coefficients in the jth row of the Ci matrices represent the contribution of each aircraft 2-4
The first six degrees of freedom in Eqns. (9) and
(10) represent the rigid body motions. The == Ucg - (rcg,p x ) RFT q2 (14) generalized coordinates ql, q2, and q3 are the Eqn. (12) rigid body angular motion around the x-axis (roll $, positive right side down), around the y-axis and (pitch 6, positive nose up), and around the z-axis (yaw u/, positive nose to the right), respectively.
The generalized coordinates q4, q5, and q6 are ep = = RFT q2 (15) the body linear motions along the x-, y-, and z- q3 axis, respectively. The rigid body motion can be specified by the linear perturbation velocity of where rcg,p is the position vector of point P the body center of gravity and the angular relative to the center of gravity, in the body axis perturbation velocity of the body around the body system, _FT is the perturbation rigid body trim c.g. The linear velocity perturbation of the body Euler angle for yaw, and x indicates a vector center of gravity is given by: cross-product.
Therefore the mode shapes for the rigid body motion are: (11) Ucg,rigid = _'F [F_I ... F_6]= [ (-rcg,p x)RFT Z ] (1 6) iF [71 ... 3'6] = [ RFT 0] (17) and the rigid body angular velocity perturbation is given by: where z represent a 3x3 diagonal unit matrix and 0 represent a 3x3 zero matrix.
The total velocity of point P in the body axis
f0 /
system is the sum of the trim velocity, Vtrim, and perturbation velocities: °_F = [RFT]_F_F (12) OO where the subscript F indicates the body axis LJp= Vtrim * _ Clk _k (18) k=l system. The matrix RFT represents the transformation of the body axis system to the Earth-fixed axis system. This matrix defines the The components of Vtrim in the x°, y-, and z- directions are obtained from the CAMRAD/JA aircraft trim attitude with respect to earth axis and is given by: trim solution. The acceleration of point P is the sum of the perturbation accelerations and the inertial acceleration due to the rotation of the trim velocity vector by the body axes angular (13) velocity. Therefore in the body axis system: RFT= 0 cosSFT sinSFTCOSeFTi 0 -sinSFT cosSFTcoseFT (_p=00FxVtrim+ _ EIk_k where eFT and SFT are the trim Euler angles for k=l rigid body pitch and roll. The trim Euler angles are obtained from the CAMRAD/JA trim solution and are dependent upon the flight conditions.
EIk_k (19) = (-Vtrim x ) C12 + The linear and angular displacement perturbation vectors of a point P are therefore given by: Equations (14)-(15), (18), and (19) describe the three components of the displacement, velocity, Up = Ucg + x rcg,p and acceleration of point P, respectively, in the aircraft body axis system.
2-5 t
A separate axis system is defined as being
attached to the sensor at airframe location P. If M( feA(t"c)d'= )M -1Bv (23) the orientation of this sensor axis system does f tO not coincide with the body axis system the displacement vector up, velocity vector tJp, and As previously discussed the system control input acceleration vector _Jp need to be transformed v(t) is defined as: into the sensor axis system by consecutive rotations of the vector around the body z-axis, v(t)=Vp(t)+Vac(t) (2) the new y-axis, and the resulting x-axis. The components of the motion vector in the sensor If the control input v(t) is digitized at time step axis system are used to define the elements of intervals of At and the assumption is made that jth row of the sensor matrices Ci (i=0,1,2), which in turn define the output of a single-direction the control input is constant over the time step motion sensor at point P, represented by the jth At, i.e. v(t)=v(ti) for ti < t < ti+At, then the element of the sensor vector y.
system response Xs at time ti+At can be calculated from the system state at time ti, I]ME_BE,_BQ_,_E Xs(ti), and the system response to a step input of magnitude v(ti) at time ti by using Eqn. (23).
The time history response of the linear system of Eqn. (8) is given by16: xs(ti+At) = MeAAtM "lxs(ti) + ti+At Xs(t) = eA(t't0)xs(t0) + t (24) M feA(ti-t)d_M-1 Bv(ti) ti (2O) eA(t-'0Bv('0d,¢ tO or in matrix form: If the system matrix A has distinct eigenvectors xs(ti+At) = MeAAtM-lxs(ti) + the exponential power eAt can be rewritten as: A-1M{eA&t-z }M "lBv(ti) (25) eAt = Me(M "IAM)t M-1 (21) where z is the diagonal unit matrix.
where M is a matrix of linearly independent The response Xs(ti) in Eqn. (24) represents the eigenvectors. The columns of matrix M, the so- state of the system at time ti. The state called modal matrix, are made up of the velocities ks(ti) are obtained from Eqn. (8).
eigenvectors with columns corresponding to the Knowledge of the first order state variables Xs eigenvalues Zi of matrix A. The matrix and ks at time ti allows the extraction of the manipulation M-1AM results in the displacements x, the velocities k, and the transformation of A into the diagonal eigenvalue accelerations Y( of the aircraft degrees of matrix A: Thus, Eqn. (20) can be rewritten as: freedom in Eqn. (1). The sensor vector y can then be calculated from Eqn. (2) and the active control Xs(t) = MeA(t'to)M'lxs(to) + input Vac from Eqn. (3). The input v to the system t at time step (ti+At) is set equal to (Eqn. (2)): (22) MeA(t"C)M "1Bv('0d'_ (26) v(ti+At) = vp(ti+,',t) + Vac(ti) tO NOISE For a given constant coefficient system, the modal matrix, its inverse, and the control To account for instrumentation signal noise matrix B are constant coefficient matrices. If and/or for sensor modelling uncertainty within it is assumed that the control vector v(t) the sensor model, noise can be simulated by (Eqn. (2)) is constant over the considered time rewriting the sensor vector, y (Eqn. (3)): period from tO to t, then Eqn. (22) can be rewritten as: y(ti) = C2_<'(ti) + Clx (ti) + C0x(h) + Xs(t) = MeA(t't0) M'lxs(to) + D0v(ti) + w(ti) (27) 2-6 of the collective pitch and the lateral a_nd
where w(ti) is a vector representing sensor
noise. For this study the sensor noise is defined longitudinal cyclic pitch.
as: STABILITY OF AIRCRAFT WITHOUT FEEDBACK w(ti) = rgm, -I.0 < r _< +1.0 (28) where r is a random number and gm defines the This section will discuss the results of the sensor noise level or magnitude.
stability analysis for the basic aircraft, i.e., the joined-wing tilt-rotor aircraft without feedback AIRCRAFT MODEL control. The CAMRAD/JA code was used to obtain the mathematical plant model of the basic tilt- An XV-15 size joined-wing tilt-rotor aircraft rotor aircraft in cruise as given by Eqn. (1) for a (model 166CL in Ref. 2) in cruise flight was forward flight range from 150 to 350 knots at considered for this investigation. The aircraft standard sea level conditions. For a tilt-rotor has a three-bladed, 25-foot diameter, gimbal- aircraft configuration in cruise flight the mounted, stiff-inplane proprotor. Table 2 CAMRAD/JA analysis divides the aircraft motion provides a description of the key geometric into uncoupled symmetric and anti-symmetric parameters for the rotor and the airframe as flight modes. Separate system matrices, Ai obtained from Ref. 2 and 17.
(i=0,1,2) and Bo, are calculated for each flight mode. The system matrices for a selected flight The airframe structural characteristics, mode and flight trim condition formed the input consisting of the modal frequency and mass and to the analysis code, which used an eigenvalue of the hub motion due to elastic airframe analysis to evaluate the stability of the aircraft deformation for the joined-wing tilt-rotor without the application of active controls.
aircraft were reported in Ref. 2 for six airframe mode shapes, representing three symmetric and Figure 6 presents the results of the stability three anti-symmetric modes. Table 3 provides analysis for the basic joined-wing tilt-rotor these data for the six elastic airframe degrees aircraft in the form of root-locus plots for both of freedom. This mode shape information at the the symmetric (Figs. 6a and 6b) and anti- hub location is used in the CAMRAD/JA code, symmetric (Figs. 6c and 6d) flight modes. The which provided the mathematical plant model of natural frequency and damping ratio for the three the joined-wing tilt-rotor aircraft. Table4 wing modes were calculated and are shown in presents the location of the aircraft center of Figs. 7 and 8 for the symmetric and anti- gravity and the rotor hubs for the aircraft.
symmetric flight modes, respectively. Wing modes l s and l a are the critical modes for the RESULTS symmetric and anti-symmetric flight modes, respectively. The symmetric flight modes shows The following degrees of freedom were included a whirl-flutter velocity of approximately 243 in the present investigation: six rigid-body knots, while for the anti-symmetric flight degrees of freedom, six (three symmetric and modes the occurrence of whirl-flutter occurs at three anti-symmetric) elastic airframe modes, the higher flight speed of approximately 275 two rotor blade bending and one rotor blade knots. Reference 2 reports a flutter speed of torsion mode, the hub gimbal, and rotor speed approximately 240 and 250 knots for the degrees of freedom. The plant model, as symmetric and anti-symmetric flight modes, calculated by CAMRAD/JA, consisted of the respectively. The discrepancy between the system matrices AI (i=0,1,2) and the control results of the present investigation and of matrix Bo for both symmetric and anti- Ref. 2 for the anti-symmetric flight mode symmetric flight modes. Both the symmetric and flutter speed is not understood.
anti-symmetric plant models consisted of eighteen degrees of freedom per flight mode: CLOSED LOOP RESULTS - State Variable Domain three rigid and three elastic body modes; the flap, chord, and torsion modes for each rotor As noted in the previous section the onset of blade, resulting in nine rotor modes for the three whirl-flutter occurred in the symmetric flight bladed rotor; two hub gimbal and one rotor speed.
Structural damping was set at 3 percent of mode first and therefore the emphasis in the present investigation was towards determining critical damping for the rotor modes and 2 percent critical damping for the elastic airframe the feasibility of using active controls to increase the flutter velocity for this flight modes. The airframe aerodynamic damping was assumed zero. The control vector, v, consisted condition. The flight velocity of 275 knots was 2-7 From comparison of Figs. gb and 11b it is se_n selected as the flight condition for evaluation of various active control schemes.
that at the feedback gain values of 1.6<"qw,ls/Ss <4.0 g/rad where the wing mode ls Accelerometers were considered to be the is damped this critical rotor mode has become preferred sensor to be used in the feedback unstable. Comparison of Figs. 10b and 11b shows that this rotor mode has also become system. Because of the availability of rotor unstable at feedback gain values for cyclic pitch control on the tilt-rotor aircraft in cruise flight it was decided to use the cyclic Clw,ls/_c<-2.5 g/rad, which is the desired gain pitch as the active control input Vac.
level to stabilize wing mode ls. Figure lib References 10 and 11 also used the closed-loop, shows that the magnitude of negative damping cyclic pitch control to improve the whirl-flutter ratio for the critical rotor mode is slightly stability of the cantilever-wing tilt-rotor lower for the required feedback gain levels for models.
CIw,ls/Ss as compared to the required feedback gain levels for ¢Tw,ls/Sc to stabilize the wing The feasibility of whirl-flutter alleviation mode l s. Therefore the longitudinal cyclic pitch, through active controls was first investigated in 5s, was selected as the active control input.
the state space domain. Only state variable accelerations were used in the sensor model.
An obvious choice to stabilize the system is the The matrices C1, Co, and Do in Eqn. (3) were zero additional feedback of the critical lead/lag mode matrices, while the C2 matrix elements had the to cyclic pitch. A sensitivity analysis showed, value of "1" or "0", depending upon whether a however, that this critical rotor mode could be particular state variable acceleration was influenced by feedback of wing modes 2s and 3s incorporated into the closed-loop feedback to either longitudinal or lateral cyclic pitch.
system.
Again the longitudinal cyclic pitch, 8s, was selected at the active control input for feedback Since the first wing mode, qw,ls, was the of wing modes 2s and 3s.
critical mode for the onset of whirl-flutter, the acceleration for this state variable was selected As this study was a preliminary investigation for the sensor output and the longitudinal cyclic into the use of active controls for whirl-flutter pitch, 8s, and lateral cyclic pitch, 8c, were alleviation, no effort was made to optimize the selected for possible active control inputs.
feedback control system. A number of combinations of (_w,ls/Ss, _W,2S/SS, and _W,3S/SS Figure 9 presents the effect of various gain values were evaluated using the closed-loop longitudinal cyclic pitch feedback gains on the analysis code until a stable system (including stability of the elastic wing mode l s at 275 rotor stability) was obtained for the desired knots. A positive feedback gain for CIw,ls/Ss has condition of 275 knots flight velocity.
the desired stabilizing effect on the wing mode Satisfactorily stability was obtained for a l s, has little effect on wing mode 3s, but has a closed-loop system using a _lw,ls/Ss gain of 2.0 destabilizing effect on wing mode 2s.
g/tad and a _w,3s/Ss gain of -1.25 g/rad. The Figure 10 shows the effect of lateral cyclic effect of flight velocity on the stability of this pitch feedback on the frequency and damping closed-loop symmetric flight mode system is ratio of wing modes ls, 2s, and 3s at 275 knots.
shown in Fig. 12. The natural frequencies and A negative feedback gain for _lw,ls/Sc has a damping ratios for the three wing modes for both stabilizing effect on wing mode ls, while having the basic aircraft and the closed-loop system a destabilizing effect on wing modes 2s and 3s.
are shown. Little effect of using this type of Figures 9b and 10b show that all three wing active control on the natural frequency of these modes will be stable for 1.6<'_lw,1s/Ss <4.0 g/rad wing modes is observed (Fig. 12a). However, the or Clw,ls/Sc <-2.5 g/rad.
damping ratio of all three wing modes is changed substantially (Fig. 12b). Wing mode ls shows more damping, while wing modes 2s and 3s show It should be noted here that feeding back the reduced damping from the configuration with no wing mode l s acceleration as described above feedback control. Figure 12 shows that even also influences the frequency and damping of non-optimal feedback in the state domain of other body and rotor degrees of freedom, i.e., their eigenvalue location in the root locus plot wing chord and wing torsional accelerations to longitudinal cyclic pitch can increase the tilt- changes. One rotor mode, a rotor lead/lag rotor whirl-flutter speed from 243 to above 275 bending mode, was significantly influenced by knots, a 13.2% improvement in the flutter the feedback of wing mode l s acceleration, velocity.
Clw,ls, to either the longitudinal or lateral cyclic pitch. This sensitivity is shown in Fig. 11.
2-8 CLOSED LOOP RESULTS - Physical Domain is not necessarily the best location for t_he closed-loop system sensors.
The previous section showed that feedback of The airframe modal information for the hub state variable accelerations to cyclic pitch can location together with the CAMRAD/JA be used to delay the onset of whirl-flutter on the calculated trim information (the cruise velocity joined-wing tilt-rotor aircraft. However, to be vector Vtrim and the trim Euler angles _FT and able to feed back pure state variables requires the identification of the individual system eFT, Eqn. 11} were input to the sensor model modes which would potentially require a large utility (Fig. 4). This utility then determined the number of sensors mounted on the aircraft.
contribution of each aircraft degree of freedom Flutter alleviation studies on fixed-wing to the hub accelerations in body x-, y-, and z- aircraft have shown that it is possible to directions. The assumption was made that the increase the aircraft flutter velocity by feeding contribution of the symmetric rigid body motion back the output of a limited number of to the acceleration at the hub (Eqn. (17)) was accelerometers mounted at appropriate locations eliminated by means of a high pass filter.
near the wing tip to an active control input, such Mathematically this equates to setting the as a wing control surface 18,19 The use of a corresponding Ci-matrix elements to zero. As limited number of accelerometers mounted at mentioned previously, no attempt was made to appropriate locations near the wing tip, whose model the dynamics of the swashplate actuators signal output is then fed back to a blade pitch in the mathematical description of the feedback control was studied in Ref. 11 for a cantilever- control system. The 275-knot flight trim wing tilt-rotor aircraft configuration to condition was again selected for the evaluation of the various feedback control schemes.
increase the whirl flutter speed from 285 to above 300 knots. Use of a limited number of wing mounted accelerometers was also Table 3 shows that for wing mode l s the linear investigated here for the joined-wing tilt-rotor displacement in vertical direction is an order of aircraft. Again the rotor longitudinal cyclic magnitude higher than the linear displacements pitch was selected for the active control input.
in both the chord-wise and span-wise directions.
A single-direction, hub-mounted accelerometer with its sensing direction along the body z-axis The results of the state variable domain analysis was therefore selected for the measurement of discussed in the previous section showed that the wing mode l s degree of freedom. As was the feedback of the accelerations of the wing expected from the results of the state domain modes l s and 3s degrees of freedom to analysis, negative feedback of the hub vertical longitudinal cyclic pitch could be used to acceleration, 0h,v, to the longitudinal cyclic stabilize the joined-wing tilt-rotor aircraft at pitch, 5s, also adversely affected the stability of 275 knots flight speed. It was therefore decided the critical rotor lead/lag mode (at 2.3/rev) as to use wing-mounted, single-direction accelerometers which would measure these two seen in Fig. 13a. A sensitivity analysis showed aircraft degrees of freedom as the sensors in the that this adverse effect could be reduced by feedback system. Only the symmetrical flight eliminating the contributions of wing modes 2s and 3s to the hub vertical acceleration mode was analyzed in the "physical" domain. In measurement as can be seen from comparison of application, wing-mounted sensors would also measure the acceleration due to the anti- Figs. 13a and 13b. Physically this could be symmetric wing elastic deformations and anti- accomplished be means of a notch filter on the symmetric rigid body motion. However, by accelerometer output signal. Mathematically the effect of the notch filter was simulated by placing sensors in the same location on opposite setting the C2-elements' corresponding to the wings and by summing the corresponding sensor mode 2s and 3s contributions to zero.
output signals the contribution of these anti- symmetric flight modes could be eliminated. Eliminating the wing mode 2s and 3s contributions also reduces the effect of the 0h,v/6s feedback on the damping ratios of these As mentioned earlier, Ref. 2 only provided the two wing modes as seen from comparison of elastic airframe mode shape information for the rotor hub location. Therefore hub-mounted Figs. 13a and 13b.
accelerometers, which provide hub accelerations A sensitivity analysis showed that feeding back in the body axis system were considered here.
Reference 11 showed that the location of the the hub acceleration in wing chord-wise direction, 5h,c, and in wing span-wise direction, wing-mounted sensors can be an important parameter in the closed loop active control 0h,s, to longitudinal cyclic pitch, 6s, had a system to increase the whirl flutter velocity on stabilizing effect on the critical rotor mode as a tilt-rotor aircraft. Therefore the hub location shown in Figs. 14a and 14b, respectively. A 2-9 to 350 knots. Comparison of the root locus pl_ts
slight beneficialeffect of such feedbackon the
of Fig. 6 (basic aircraft without feedback
l s wing modedampingratio is alsoobservedin
control) with Fig. 16 (closed-loop system) also
Figs.14a and 14b, althoughthe mode remains
unstable. shows the improved stability for the closed-loop
system, but at the same time illustrates the effect of the feedback system on the damping of
A feedback system was selected consisting of
the various rotor and aircraft degrees of two hub accelerometers measuring vertical and freedom. The rotor lead/lag mode at 2.3/rev span-wise hub accelerations, whose outputs shows an decrease in damping due to the hub were fed back to the longitudinal cyclic pitch.
The hub vertical acceleration measurement was acceleration feedback system and is neutrally assumed to be conditioned by means of a notch stable at approximately 278 knots. Little effect filter so as to eliminate the contribution of wing on the other rotor modes and on the rigid body modes is observed.
modes 2s and 3s from this sensor output signal.
As mentioned before a high pass filter was also used to eliminate the contributions of the rigid TIME RESPONSE CALCULATIONS: body modes to the measured hub accelerations.
This feedback system was analyzed in the To evaluate the magnitude of the required active following manner. The value of the feedback control input, the time response of the aircraft control gain t]h,v/8 s was fixed while the feedback at a 270-knot cruise condition was calculated.
gain Oh,s/Ss was varied systematically within the Time-history response calculations were made closed-loop analysis code. After each Dh,s/_s for both the basic aircraft(no feedback control) and for the closed-loop system, A longitudinal change the code performed an eigenvalue analysis to determine the stability of the cyclic pitch control input, vp (Eqn, (2)), closed-loop system. This process was then representing a square doublet with a 1.0 deg magnitude and a period of 1,0 sac (Fig,17a) was repeated for different Oh,v/8 s values.
used to excite the system at this 270-knot trim condition. The calculated sensor response for Feedback of hub vertical acceleration 0h,v the two accelerometers at the rotor hub is (gain=0.0048g/rad, with a notch filter on the presented in Figs. 17b and 17c for the basic sensor output signal), and hub span-wise aircraft. The response of the higher aircraft acceleration 0h,s, (gain=-0.0035g/rad) to the modes results in the higher frequency response longitudinal cyclic pitch produced a stable in the accelerometer output (Figs.17b and 17c) closed-loop system. This feedback system was during the firstI-1.5 sac (approximate 12 rotor analyzed over the tilt-rotor aircraft velocity revolutions) of the motion. A rapid divergence of range from 150 to 350 knots. Figure 15 the vertical acceleration magnitude is observed compares the stability of the three wing modes (Fig. 17c). The acceleration in the vertical for the basic joined-wing tilt-rotor aircraft (no direction is approximately a factor 5 higher than feedback) and for the closed-loop system. Little the measured span-wise acceleration (Fig. 17c effect on wing natural frequencies is found vs. Fig. 17b).
(Fig. 15a). The effect of flight speed on the damping for the closed-loop system is shown in The time response of the closed-loop system to Fig. 15b. Comparison of Fig. 15b with the the same square doublet is shown in Fig. 18 for results obtained for the state variable domain the first 2 seconds and in Fig. 19 for the first analysis (Fig. 12b) shows similar results for the 15 seconds, which equates to approximately 115 damping ratio for the critical wing mode ls.
rotor revolutions. The closed-loop system Lower damping ratio values are observed for (Fig. 18b) shows slightly higher span-wise wing mode 2s for the closed-loop "physical" accelerations during the first 2 seconds of the domain analysis (Fig. 15b) when compared to the response as compared to the basic aircraft time state variable domain results (Fig. 12b). A large response (Fig. 17b). The vertical accelerations decrease in the wing mode 3s damping ratio was for the closed-loop system (Fig. 18c) are 50% seen in Fig. 12b for the closed-loop system as lower than those observed for the basic aircraft compared to the no feedback case. In contrast, (Fig. 17c) during this 2 second period.
Fig. 15b shows very little influence of the Figure19 shows that after 15 seconds (115 "physical" domain closed-loop feedback system rotor revolutions) the aircraft has not yet on the wing mode 3s damping ratio. Figure 15 reached a steady-state condition. The measured illustrates that again a 13.2% increase in the accelerations in vertical and span-wise whirl-flutter velocity from 243 to 275 knots direction after 15 seconds are approximately was obtained.
one-third (0.5g's and 0.2g's, respectively) the maximum value experienced due to the doublet Figure 16 shows the root locus plot for this excitation (l.9g's and 0.7g's, respectively).
closed-loop system for the speed range from 150 2-10
After 10-12 seconds the hub vertical
characteristics. Second, the frequer_cy acceleration measurement shows a single requirements for the control actuators are within the bandwidth of current electro- frequency content of 3.6 Hz. This corresponds to the first wing mode (mode l s). The time hydraulic actuation flight hardware.
response signal for the span-wise accelerometer is presented in Figs. 18b and 19b and shows a The closed-loop system response to a square doublet was also calculated for two cases where multiple frequency content throughout the 15 seconds of the calculated aircraft time response. the sensor signals were contaminated by noise, Again a higher frequency response is observed in representing signal instrumentation noise and/or the accelerometer outputs (Figs. 18b and 18c), uncertainty regarding the accuracy of the system which is similar in character to the sensor modeling. Based upon the time response output of the basic aircraft (Figs. 17b and 17c) calculations shown in Fig. 19, noise gain levels during the first 1.5 seconds. It is believed that for gm (Eqn. (28)) of 0.1 and 0.5 were selected.
the higher frequency content during the first few This represents a noise level of 0.1 g and 0.5g, seconds is a basic aircraft behavior and is not respectively, for the two hub-mounted the result of the feedback system. However, the accelerometers. The corresponding time influence of these higher frequencies on the responses for the closed-loop system are shown measured signal persist for approximately 10 in Figs. 20 and 21, respectively. Comparison of seconds (Figs. 19b and 19c), and it is thought Fig. 19 (no noise) with Fig. 20 (0.1g noise) that the strong coupling of the rotor lead/lag shows essentially the same time response behavior with the noise contamination.
mode at 2.3/rev with the first wing mode (ls) within the closed-loop system is the main cause Figure21a shows that the 0.5g sensor noise contamination level causes an increase in the of the longer time period for the higher frequency influence to damp out. required level of active longitudinal cyclic pitch control from 0.009 deg (no noise) to 0.010 deg for the first few seconds after disturbing the The longitudinal cyclic pitch active control input system. After 10 seconds an increase in the is shown in Figs. 18a and 19a. A maximum required magnitude of the active control level active control input of 0.009 deg is observed.
from 0.0025-0.0030 deg for the no-noise case The 0.009 deg cyclic pitch input equates to a (Fig. 19a) to approximately 0.005 deg for the rotor active control force of approximately 9 Ibs 0.5g noise case is observed (Fig. 21a). The being applied at the rotor hub to damp the wing periodic character of the active control is not motion and to delay the tilt-rotor whirl-flutter readily observable in Fig. 21a. A decrease in the instability. This level of active control input for magnitude of the hub horizontal and vertical the longitudinal cyclic pitch is of the same accelerations over time is seen (Figs. 21b and magnitude as that predicted by the author for a 21c). The observed response decay rate for the similar flutter alleviation study for a 0.5g noise case (Fig. 21) is smaller than the cantilever-wing tilt-rotor aircraft decay rates observed for the no-noise (Fig. 19) configuration 11 and is a major improvement and 0.1g noise (Fig. 20) cases. However, the over the levels of cyclic pitch control predicted closed-loop system with 0.5g noise by Nasu 7, who showed a required cyclic pitch contamination on the sensors, representing 25% control angle of 0.5 deg. The higher frequency of the maximum observed sensor response level content can also be observed in the active of 2.0g vertical hub acceleration, still shows a longitudinal cyclic control input in Fig. 18a and stable system indicating a robust control in Fig. 19a for the first 10 seconds of the motion. After 10-12 seconds the active control system.
input shows the single frequency content of 3.6 Hz, corresponding to the critical wing mode 1 s.
The present investigation showed that it is For the actual vehicle it is unlikely that possible to delay the onset of whirl-flutter on a actuators can be accurately controlled for 0.009 XV-15 size joined-wing tilt-rotor aircraft deg of pitch input. Control system dynamics through' the use of active controls. The (actuators, swashplate, hydraulic system .... ) will CAMRAD/JA code was used to obtain a set of have to be included in the simulation to achieve linear differential equations, which describe the more realistic results. However, these results motion of the tilt-rotor aircraft in cruise. The provide two important findings. First, the level airframe vibration mode shapes, modal of hub force generation necessary to stabilize frequencies, and modal masses for a the tilt-rotor is very small and can be easily representative joined-wing tilt-rotor aircraft withstood without adverse dynamic loads or were used. The CAMRAD/JA output, consisting of degrading aircraft handling quality the open-loop system matrices, and a sensor 2-11 Eurovean Rotorcraft Forum. Milan, It_y,
model utility output were input to a separate
program, which performed the closed-loop, September 1988.
active control calculations. An eigenvalue 9Straub, F.K., and Warmbrodt, W., "The Use of
analysiswas performedto determinethe flutter
Active Controls to Augment Rotor/Fuselage stability of both open- and closed-loop systems.
Stability, • Journal of the American Helicoc)ter • Sensor models based upon the feedback of Vol. 30, No. 3, July 1985.
pure state variables increased the whirl- 10Nasu, K., "Tilt-Rotor Flutter Control in flutter velocity from 243 to over 275 knots Cruise Flight," NASA TM88315, December by feeding back the first and third wing 1986.
elastic bending degrees of freedom to the 11van Aken, J.M. "Alleviation of Whirl-Flutter longitudinal cyclic pitch.
on Tilt-Rotor Aircraft Using Active Controls," • Whirl-flutter could also be delayed from 243 Proceedings of the 47th Annual Forum of the to above 275 knots by feeding back hub span- American Helicopter Society., Phoenix, Az, wise and vertical accelerations to the May 1991.
longitudinal cyclic pitch.
12Johnson, W., "A Comprehensive Analytical • Time response calculations at a 270-knot Model of Rotorcraft Aerodynamics and Dynamics, cruise condition showed an active cyclic pitch Part I: Analysis Development', NASA TM 81182, control level of 0.009 deg, which equates to a June 1980.
very acceptable 9 pound active control force 1 3 Johnson, W., "Development of a applied at the rotor hub.
Comprehensive Analysis for Rotorcraft - I, Rotor • Contamination of the sensor output signal Model and Wake Analysis," _ Vol. 5, No. 2, with noise, whose magnitude was equal to 1981.
25% of the maximum measured amplitude of 1 4 Johnson, W., "Development of a the sensor output did not adversely effect the Comprehensive Analysis for Rotorcraft II, closed-loop system stability, indicating a Aircraft Model, Solution Procedures and robust control system.
Applications," Vertica, Vol. 5, No. 3, 1981.
15Johnson, W., "A Comprehensive Analytical RF_FEFENCES Model of Rotorcraft Aerodynamics and Dynamics, Johnson Aeronautics Version", Johnson 1Felker, F.F., and Light, J.S., "Aerodynamic Aeronautics, Palo Alto, CA, 1988.
Interactions Between a Wing and a Rotor in 16Ogata, K., State Soace p, nalvsis of Control Hover", Journal of the ArTl_ri_;an HelicoDter Systems, Prentice-Hall, Inc., NJ, 1967.
Society. Vol. 33, No. 2, April 1988.
17Maisel, M, "Tilt Rotor Research Aircraft 2Wolkovitch, J., Wainfan, B., Yitzhak, B.H., and Familiarization Document," NASA TM X-62,407, Johnson, W., "Application of the Joined Wing to January 1975.
Tiltrotor Aircraft', NASA CR-177543, November 1 989. 18Sanford, M.C, Abel, I, and Gray, D.L., "Development and Demonstration of a Flutter- 3Wolkovitch, J., "The Joined Wing: An Suppression System Using Active Controls", Overview", Journal of Aircraft, Vol. 23, No. 3, NASA TR R-450, April 1975.
March 1986,.
19Newsom, J.R., Abel, I., and Dunn, H.J., 4Ham, N.D., and Whitaker, H.P., "A Wind- "Application of Two Design Methods for Active Tunnel Investigation of Tilt-Rotor Gust Flutter Suppression and Wind-Tunnel Test Alleviation Systems," NASA CR-152264, January 1978. Results', NASA TP 1653, May 1980 5Ham, N.D., Bauer, P.H., Lawrence, T.H., and A vvendix A: Comvrehensive Rotorcraft Analysis Yasue, M., "A Study of Gust and Control Response of Model Rotor-Propellers in a Wind Tunnel CAMRAD/JA (for Comprehensive Analytical Model Airstream," NASA CR-137756, August 1975.
of Rotorcraft Aerodynamics and Dynamics, 8Frick, J., and Johnson, W., "Optimal Control Johnson Aeronautics version) is an analysis Theory Investigation of Proprotor/Wing Response designed to calculate rotor performance, to Vertical Gust," NASA TMX-62384, September aerodynamic and structural loads, aircraft 1974.
vibration, gust response, flight dynamics, 7Jenie, S.D., "The Application of Active handling qualities, and aeroelastic stability. The Control Technology to a Gust Alleviation System analysis development is discussed in detail in for the Tilt-Rotor Aircraft with Hingeless References 12-15.
Rotors," NASA CR-152173, February 1978.
8Miller, D.G., and Ham, N.D., "Active Control of The rotor aerodynamic model is based on lifting- Tilt-Rotor Blade In-Plane Loads During line theory, and uses two-dimensional airfoil Maneuvers," Proceedings of the Fourteenth characteristics, and a vortex wake. For the 2-12 aeroelastic stability analysis it is generally analysis these dampings were set to zero. "l(he
sufficient to use the uniform inflow model of
airframe aerodynamic representation is
CAMRAD/JA, i.e. assuminga linear variationof
basically a quasi-static model.
inflow over the rotor disk. The rotor structural
model is based on engineering beamtheory for The aircraft motion consists of the six rigid- rotating wings with large pitch and pretwist. body degrees of freedom and the elastic free Both rigid and elastic blade motion are included.
vibration body modes. A body-axis coordinate A modal method is used to calculate, in vacuum, frame with origin at the aircraft center of the blade bending modes for the rotor. Blade gravity is used for the description of the motion.
torsion modes are not coupled with the bending For the elastic motion of the aircraft in flight, modes, but are calculated independently. The the displacement and rotation at an arbitrary total elastic rotor response is a linear point are expanded in a series of the orthogonal combination of the modal solution in which the free vibration modes. The first six degrees of bending and torsion motion of the rotor are freedom for the elastic aircraft motion at this coupled.
arbitrary point are the rigid body motions, while the remaining body degrees of freedom represent An orthogonal mode representation of the body the elastic modes of the aircraft. (See the elastic motion is used in CAMRAD/JA. The sensor model derivation in the main text).
airframe structural vibration modes need to be obtained from a separate structural analysis (in The rotor equations of motion require the six the present analysis the MSC-PAL finite element components of the hub linear and angular motion structural analysis code was used). The in the shaft axis system due to both the rigid and linearized equations of motion for the rigid body elastic aircraft body motion. This information degrees of freedom are used in the calculation of was obtained from the results of the MSC-PAL the aircraft vibration and transition motion. For analysis as reported in Ref. 2 (see table 3).
this study the aerodynamic forces on the wing- body, horizontal tail and vertical tail are CAMRAD/JA first performs the trim analysis, in modelled, including control surfaces. Static which the equations of motion are solved for the aircraft aerodynamic characteristics were case of a steady state flight condition.
obtained from a wind tunnel test. The Aeroelastic stability is then calculated from the generalized aerodynamic damping and control trim solution by constructing the system forces on the airframe elastic modes can be matrices that describe the linear differential included in CAMRAD/JA and these terms are equations of motion and performing an normally estimated for the frequency of the eigenvalue analysis.
principal excitation of the mode. In the 3resent 2-13 Table 1: Comparison of tilt-rotor model of Refs. 10 and 11 with present investigation.
Nasu (Ref. 10) van Aken (Ref. 11) i Present investigation Cantilever-wing model Cantilever-wing aircraft I Joined-wing aircraft Semi-span wing model: Free flight: Free flight: rigid body motion no rigid body motion rigid body motion symmetric and anti-symmetric symmetric flight mode symmetric and anti-symmetric flight modes flight modes Elastic body modes: Elastic body modes: Elastic body modes: symmetric and anti-symmetric symmetric modes only symmetric and anti-symmetric wing chordwise bending wing chordwise bending wing mode 1 wing beamwise bending wing beamwise bending wing mode 2 wing torsion wing torsion wing mode 3 pylon yaw Rotor: Rotor: Rotor: 3 bladed hingeless rotor 3 bladed hingeless rotor 3 bladed hingeless rotor blade chordwise bending blade chordwise bending blade chordwise bending blade beamwise bending blade beamwise bending blade beamwise bending blade torsion blade torsion rotor speed rotor speed gimbal motion gimbal motion Feedback system: Feedback system: Feedback system: using state variables using state variables using state variables using wing mounted using hub mounted accelerometers accelerometers Table 2: Specifications of joined-wing tilt-rotor aircraft model Rotor: number of blades 3 blade radius 12.5 ft solidity, a 0.0890 airfoil section 64-series rotational speed 458 rpm shaft cant angle -1 deg.
mast height 4.667 ft Wing: semispan 16.1 ft forward wing: chord 3.5 ft sweep (forward) 6.5 deg airfoil thickness 12% aft wing: chord 1.7 ft sweep (forward) 15 deg airfoil thickness 120/o airfoil section 64A212 Aircraft weight 13,000 Ibs 2-14
Table3: Wing mode shape information at right hub _"
symmetric modes mode ls mode 2s mode 3s 3.65 5.56 7.30 !frequency, Hz 1.833 0.832 O.375 modal mass, slug/12 linear displacements: -0.0735 0.1265 0.0341 x, in 0.0771 -0.1318 -0.0340 y, in z, in -0.4530 -0.1439 -0.0655 angular displacements: -0.00313 -0.00001 0.0015 x, rad.
0.00515 0.00400 0.00178 y, rad.
0.0011 -0.001 99 -0.00049 z, rad.
anti-symmetric modes mode la mode 2a mode 3a 4.75 7.42 8.13 frequency, Hz 0.639 0.393 1.295 modal mass, slug/12 linear displacements: x, in -0.0025 0.0324 0.1576 -0.0089 -0.0104 -0.1706 y, in 0.2578 -0.0841 0.0339 z, in angular displacements: 0.0011 0.0017 0.0010 x, rad.
-0.0053 0.00253 -0.0006 y, rad.
0.0001 -0.00048 z, rad. -0.00235 Table 4: Location of c.g. and rotor hubs on joined-wing tilt-rotor aircraft.
Body axis system coordinates X Z Y (inches I (inches) (inches) Component location: Oo O. .
center of gravity 49.40 192.99 -26.44 right hub left hub 49.40 -192.99 -26.44 2-15 I Fig. 2: Typical joined-wing tilt-rotor Fig. 1: Baseline cantilever-wing tilt-rotor configuration.
configuration.
2-16
/
baselinecantileverwing anti-symmcuic model 16&:l = ¢ 260 .......... "0' ...... e symmetnc ' I I I I 280 282 284 286 288 290 Nacelle c.g. fuselage station,inches Fig. 3: Effect ofnacelle c.g. location on the flutter speed of the joined-wing tilt-rotoraircraft (baseline cantilever-wing aircraftflutterspeed shown for comparison).
(source: Ref. 2) Tilt-rotor aircraft structural specifications analysis (ReL 2) mode [ hub motion _,[ rotorcraft I i vibraUon I I CAMRAD/JA I
'"" I "I"°'''''" I
....... [" trlmVt rlE'mlsr i :::dilions , ,model, Yp control __ closed-loop
'-- t I
specifications analysis z F oigenvalue time response analysis calculations active Fig. 5: Body axis system stability control magnitude Fig. 4: Methodology of whirl-flutter alleviation study 2-17 Vdoci_ 10 (kno_) +a (b) exploded view o 150 • (a) symmetric flight mode rotor el_ I u 175 2.5 8 ° a • 200
1oo, flapping °u o x + a_
t_ x 225 rotorlead-lag + 250 6 e&+)_ D A 275
xo_
"_ 1.5 t • _ ,,_ rotortorsio.
• 300 e II 325
4 1
wing mode 3s a • 350 wing mode 2s_ 0.5 _(+&O le °ao x wing mode ls -,;j 0 0 I ' I l _ ' (c) anti-symmetric flight mode (c) anti-symmetric flight mode @ rotor ,_:A+ x rotor _._x, r_ flapping • _ | :Qz • = 6 torsion torsion C_+ ° A+_D_7 rotor _+. a+>al_,4"/mt°r _0 _0 .E_ 4
. fi d!
! I -2 -0.5 0 0.5 -2 -1.5 -I -0.5 0 0.5 real axis real axis Hg. 6: Root locus plots for basic joined-wing aircraft without active controls.
(a) symmetric flight mode (b) symmetric flight mode exploded view (c) anti-symmetric mode (d) anti-symmetric mode exploded view 2-18 Ca) mode 3a_ (a) N .... • .... O'- - - = 'O- - - - .O. - - - -O--x_-- O.-- - - ¢- ....
tq t'q ..... o .... o---- o-- ---o L;¢,-o.... o .... o- ....
3.... m.... _---t_--. o__k._ .... m----_---_ mode 3s /
\
= 6
0 6 mode 2a
I----o .... _---- trj¢- o----o .... m.... o- ....
mode 2s j ) .... ® .... 0"'" 0 "_If 0''''0 .... O- mode la / ---O----, _----0 .... O-v_. 0..__3..o. 0 .... 0----0- ....
Z z -- mode ls 0 0 I I I I i I 0.08 0.08
(b) (b)
0.07 0.07 .0.
0.06 0.06 "o, ,,,_,,,/ mode la o" 0.05 ._ 0.05 'o 0.04 ._ 0.04 ',"., mode 2a ca, =.
. . mode 3s O ', - --.43 --[B"qK'i3" ....
0.03 0.03 / .--_J--_ .... O---- I.... ::::::::::::::::::::::::.,. .... _ ....
.... o----'g.---o-: :: _ :.
0.02 0.02 • mode 3a i _L "" L 0.01 0.01 L mode ls , ,,_'" o.
, mode 2s -.
I I '_' I I I I 150 200 250 300 350 150 200 250 300 350 Flight Speed V, knots Flight Speed V., knots Fig. 8: Natural frequency and damping ratio of wing modes for Fig. 7: Natural frequency and damping ratio of wing modes for basic aircraft without active controls, anti-symmetric flight basic aircraft without active controls, symmetric flight condition; condition; (a) Natural frequency, Hz (a) Natural frequency, Hz (b) Damping ratio, (b) Damping ratio, 2-19
I0
I0 (a) mode qw,3s mode qw,3s N N --.---.--.--.-'.---..--.--.-- ---,---.--.--.'-.-.-,.--._.._., = mode qw 2s = 6 mode qw,2s _ O --[_ - B - B -- B -- 6"1 -El- -E3_ _E}_ _El._ _ "_ 4 "_ 4 Z Z _0_. 0=_ OTTO... o..- -o- -o- -°" -°" - _e__ e._ e._ 4a-- -e- -e- "_" "e- -{ -- mode qw,l s mode qw, 1 s (a) I I I ! I I 0.15 0.050 (b) __._,_._- _--- _--- _ =: 4 _-'B- --0--- _'f "_
/
0.10 0.0 O,,,, mode %,2s mode qw,3s _' o" .= 0.050 .= IN b, -0.050 stable ___._.. / _.
mode qw, Is
A"
E 0.0 • _ modeqw,2s -0.10 -0.050 \ i oi" e'" -_mode qw,ls (b) -0.10 -0.15 , , , I ! I -5 -2.5 0 2.5 5 -5 -2.5 0 2.5 5 Feedbackgain_w,ls]8 s, g/rad Feedback gainL,is/_ c, g/rad Fig. 9: Natural frequency anddamping ratio for wing modes Fig. I0: Natural frequency anddamping ratio for wingmodes for closed loop system (symmetric flight mode) when for closed loop system (symmetric flight mode)when feeding back wingmode state variable acceleration, feeding back wingmodestate variable acceleration, qwJs' to longitudinal cyclic pitch, 8¢ at 275knots _w,ls' tolateral cyclic pitch, 8c, at275knots (a) Natural frequency, Hz (a) Natural frequency, Hz Co) Damping ratio, CO)Damping ratio, 2-20 17.5 (a) (a) dashed lines: no feedbac_ solid lines: with feedbackl _r-'4 ..._..I N t"4 "_ gl ", /_w,ls/_C s,.. s m 17.0 if, o _w,l _/ks "o.
-_ 4
2 16.5 Z Z ck ra 16.0 I I I 0.10 0.04 [ (b) (b) [ dashed lines: no feedback ] feedback 0.08 solid lines: with
\
0.03 0.06 0" _t
0.04
\
o._'._:.__.. .... ._ o
o_ stable ._ 0.02 _ 0.02 _", mode 2s 0.00 0.01
m og"
-0.02 / qw, ls -0.04 0.00 I I I -5 -2.5 0 2.5 150 200 250 300 350 Feedback gain, g/rad Flight Speed V**, knots Fig. 12: Fig. 1 h Natural frequency and damping ratio for critical'rotor Natural frequency and damping ratio for wing modes mode for closed loop system (symmetric flight mode) for basic aircraft and for closed loop system using sensors measuring state variable accelerations (symmetric when feeding back wing mode, _w, ls acceleration to flight mode): _w,ls/_is = 2.0 g/rad, _w,3s/_s = -1.25 g/rad longitudinal (Ss) or lateral (8) cyclic pitch at 275 knots.
(a) Natural frequency, Hz (a) Natural frequency, Hz (b) Damping ratio, r (b) Damping ratio, 2-21 0.04 0.04 (a) _wing mode 3s. . a wing mode 3Sx 0.03 - _k...._ _.._ _ ._I __ _......o_ ._ ° 0.02 _o._e.-a,--,e--o-_--a":_--'°_t- stable _'. _" _- -e-__ 0.02 a _-- _ - _wing mode 2s 0.01
o.oo
.= .. a" wing mode 2s o_ • -" I_""lslabl e _" _ bTA A b_ 0.00 rotor mode _ .0.02 _ -0.01 -0.02 4).04 *0.03 -0.04 *0.06 I ' I ' I ' I " I ' I I I I 0.04 0.04 wing mode 2s (b) / wing mode 3s 0.03 _-. __ wing mode 3s _.
" - o-- _"- m-.-_- ._- -_- -o- .-o_.,_o
0.02 __ _ _ _-. _ -B--.. -_'" j_ 0.02 / # k.P stable -s.
stable • . a- -" "_" \ d d 0.01 I a-" "'R, wingmode2s '= 0.00 1,9 0.00 .=.
rotor mode " -0.02 -0.01 -0.02
•.04
*0.03
(b)
-0.04 , , , , -0.06 ' ; , i , *0.005 *0.003 .0.001 0.001 0.003 0.005 • 0.005 43.003 .0.001 0.001 0.003 0.005 Feedback gain, g/lad Feedback gain _h,v/Ss, g/tad Fig. 13: Damping ratio for wingandcritical rotor modesfor Fig. 14: Damping ratio for wing and critical rotor modes for closed loop system (symmetric flight mode) with closod loop system (symmetric flight mode) whenfeeding feedbackto longitudinal cyclic pitch.
back vertical hubacceleration 7h, vtolongitudinal cyclic pitch.
(a) feeding back chord-wise hubacceleration,'ffh,c (a) without a notchfiller on verticalaccelerometer output (b) feeding back span-wise hubaccelemtion,'_h: 5 (b) with a notchfilteron vertical accelerometer output 2-22 I0 0.04
(a)
I no I
dashed lines: no fe_back I solid lines: with fccdbac.._J N I solid lines: withfeedback I 0.03 n: mode 3s o"
"7
"_ °oo - .o .
= 0.02 mode 2s Z 0.01 'i 1:1 i _-_e 2s "'..
0.00 I i _ [ , I l 150 200 250 300 350 150 200 250 300 350 Flight Speed V, knots Hight Speed V=, knots Fig. 15: Natural frequency and damping ratio for wing modes for basic aircraft and for closed loop system using scasor at hubmeasuring "physical" accelerations: °,,°t_/_ = 0.0048 g/tad, =°_ = -0.0035 g/rad (a)Natural frequency, Hz (b) Damping ratio, Velocity I0 (knots) (b) exploded view (a) symmetric flight mode
I '+,,_ o ,5o
l[ 4 rotor, q_ M 175 2.5 o& flapping Ora rotor _.,. :A+ o t x +4It • 200 tq flapping _ _c k ..= • 1.5 275 c_ ca rotor torsion ._ 300 x $ A+°@ _ 1 wingmode 3s e 350 wing mode 2se<o-ae _• 0.5 -I i-_e _, O_3° x , wingmode Is 0 "tits I I -1.5 -I -0.5 0 0.5 -0.2 -0.15 -0.1 -0.05 0 0.05 0.I real axis real axis Fig. 16: Root locus plots for closed-loop system using feedback of vertical and spanwise accelerations at the hub to longitudinal cyclic pitch.
(a) symmetric mode (o) symmetric mode exploded view 2-23 ( 0.010 1.5 (a) 1.0 ub I 0.005 0.5 ._, 0.0
0.0oo
-0.5 O g r..)
• -0.0o5
< -1.0 -1.5 -0.010 I " I l l I 1.0 1.0 (b) tm a_ 0.6 ._ 0.6
0.2
._ 0.2 o _-0.2 -0.2 _ -0.6 -1.0 -1.0 I • I I I l l l I ' 3 3 (c) (c) 2 2 d_
f
o 0 O O -1
tI
o O > -2 > -2 -3 -3 I I I ! • J J l [ 0 0.4 0.8 1.2 1.6 2 0 0.4 0.8 1.2 1.6 2 Elapsed time, see Elapsed time, see Fig. 18: Closed-loop time response to a square doublet Fig. 17: Basic aircraft time response to a square doublet 5s S longitudinal cyclic pitch input; input; (a) Active control input/is, deg (a) Active control input _s' deg (b) Span-wise acceleration _,s' g (b) Span-wise acceleration _,s' g 2-24 (c) Vertical acceleration'rib,v, g (c)Vertical acceleration _h,v' g < 1.0
(b)
0.6 0.6 1.0 ! CO) •_ 0.2 0.2 -0.2 -0.2 o -0.6 -0.6 O_ -1.0 -1.0 ! ! ! !
0 5 10 15 0 5 10 15 Elapsed time, sec Elapsed time, sec Fig. 19: Closed-loop time response to a square doublet 8 Fig. 20: Closed-loop time response to a square doublet 8 S S input.
input with a 0.1g sensor noise contamination.
(a) Activecontrolinput 8¢ deg (a) Activecontrolinput 8s' deg (b) Span-wiseacceleration_h,s' g (b) Span-wiseacceleration_a,s,g (c) Verticalacceleration'_,v, g 2-25 (c) Verticalacceleration_h,v'g 0.010 _ 0.006
i
_ -0.002
_ -o._6
_.010 (b) 0 5 10 15 Elapsed time, sec Fig. 21: Closed-loop time response to a square doublet 8s input with a 0.5gsensor noise contamination.
(a) Active control input 8s' deg (b) Span-wise acceleration _ ,g n,$ (c) Vertical acceleration'Uh,v, g 2-26