Vibration and flutter of stiff-inplane elastically tailored composite rotor blades

Mathl. Comput. Modelling Vol. 19, No. 314, pp. 27-45, 1994

Pergamon

Copyright@1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0895-7177/94 $6.00 + 0.00

08957177(94)E0021-E

Vibration and Flutter of Stiff-Inplane Elastically Tailored Composite Rotor Blades E. Aerospace The Pennsylvania

State

C.

SMITH

Engineering

University,

Department

University

Park,

PA 16802,

U.S.A.

Abstract-Aeroelastic response, blade and hub loads, and shaft-fixed aeroelestic stability is investigated for a helicopter with elastically tailored stiff-inplane composite rotor blades. A free wake model for nonuniform rotor inflow is integrated with a recently developed finite-element-based aeroelestic analysis for helicopters with tailored composite blades. Pitch-flap and pitch-lag elastic couplings, introduced through the anisotropy of the plies in the blade spar, have a significant effect on the dynamic elastic torsion response. Positive and negative pitch-flap couplings reduce vertical hub shear forces approximately 20% in the high vibration transition flight regime, however, negative pitch-flap elastic coupling significantly increases inplane hub shear forces at all flight speeds. The influence of pitch-flap, pitch-lag, and extension-torsion elastic couplings on the rotating frame blade bending moments is small. Ply-induced composite couplings have a powerful effect on blade stability in both hover and forward flight. Positive pitch-flap, positive pitch-lag, and positive extension-torsion couplings each have a stabilizing effect on lag mode damping. Negative pitch-lag coupling has a strong destabilizing effect on blade lag stability, resulting in a mild instability at moderate flight speeds.

INTRODUCTION

such as pitch-flap, pitch-lag, or extension-torsion, can be selectively introduced into composite rotor blades through anisotropy of the plies in the blade structure. Research focused on tailoring of elastically coupled composite blades has increased steadily during the past decade. The main objectives of this research have been to explore the potential for improvements in blade aeroelastic stability, rotor-body aeromechanical stability, performance and vibration reduction. Elastic

couplings,

There have been several studies on the aeroelastic stability of tailored composite blades in hover. Pioneering work by Hong and Chopra used a simple composite beam analysis combined with a spanwise finite element discretization of the rotor blade to examine the effects of elastic coupling on the aeroelastic stability of hingeless (soft-inplane and stiff-inplane) and bearingless composite rotors in hover [1,2]. The beam model (and corresponding finite element) used in this study did not include transverse shear deformation and used a simplified model of warping and inplane ply elasticity. Despite the simple composite blade model, this work demonstrated the potential for elastically tailored composite rotors. The aeroelsstic stability of composite blades in hover has recently been investigated using several new composite rotor aeroelastic analyses. Yuan, F’riedmann and Venkatesan formulated an aeroelastic response and stability analysis for straight and swept-tip composite blades in hover [3,4]. The composite cross-section analysis is an extension of that developed by Kosmatka and F’riedmann [5]. The new finite element formulation features a twenty-three degree of freedom beam element including both transverse shear and Presented at the 34th AIAA/ASME/ASCE/AHS/ASC ence, La Jolla, CA, April 19-21, 1993.

Structures, Structural Dynamics and Materials Confer-

27

28

E. C. SMITH

warping restraint effects. Effects of ply orientation and tip sweep on both soft-inplane and stiffinplane composite rotor blade stability were demonstrated. Fulton and Hodges also developed a finite-element-based aeroelastic response and stability code for composite blades in hover [6]. This analysis combines a nonlinear intrinsic formulation for arbitrarily large deformations and a cross-sectional analysis based on variational asymptotic methods. Stability results are presented in [6] for model scale soft-inplane hingeless blades with extension-torsion coupling. Kim and Dugundji extended the nonlinear composite beam formulation of Minguet and Dugundji [7] to include aeroelastic response and stability in hover [8]. Large vibration deformation behavior is considered and a dynamic stall model (developed by ONERA) is incorporated in the blade section aerodynamic loads. The behavior of composite rotors in forward flight has received considerably less attention. Panda and Chopra [9] extended the previous work of [1,2] by examining the dynamics of composite rotors in forward flight. Several soft-inplane and stiff-inplane hingeless rotor designs were analyzed. This work showed the effects of ply orientation and elastic couplings on vibration levels and isolated rotor stability in forward flight. Rand [lO,ll] has also investigated the steady linear periodic response of thin-walled composite helicopter blades in forward flight (p = 0.2). Variations in response, lift distribution, and blade section stresses were demonstrated for soft-inplane blades with extension-torsion and bending-torsion (pitch-flap) couplings. Additional discussions addressing advances in composite rotor blade modeling can be found in several recent review papers [12-141. A comprehensive formulation has recently been developed by Smith and Chopra to study the effects of elastically coupled composite helicopter rotor blades on aeroelastic response, blade and hub loads, rotor aeroelastic stability, and rotor-fuselage aeromechanical stability [15-171. Both hover and forward flight conditions are addressed and the aeromechanical stability analysis includes both air and ground resonance. The blade spar is modeled as a laminated composite box-beam. The box-beam analysis, based on classical lamination theory, includes the nonclassical structural effects of transverse shear, torsion-related out-of-plane warping, and two-dimensional ply elasticity [18]. For the aeroelastic and aeromechanical analysis, the blade is idealized as an elastic beam undergoing moderate deflections in flap and lag bending, elastic torsion, elastic axial deformation, and flap and lag transverse shear. A nineteen degree of freedom shear flexible beam element is introduced for the composite rotor blades. Using the new aeroelastic and aeromechanical analysis, soft-inplane rotors with five different composite spar layups were examined in [15-171: a baseline composite blade with no ply-induced elastic couplings; three symmetric layup composite blades featuring negative pitch-flap elastic coupling, positive pitch-flap elastic coupling, and negative pitch-lag elastic coupling; and an antisymmetric layup blade featuring extension-torsion and bending-shear elastic couplings. Results indicated that elastic couplings introduced through the composite blade spar have a powerful effect on both shaft-fixed blade stability and rotor-body aeromechanical stability. The accentuated role of geometric nonlinearities on shaft-fixed composite blade stability was demonstrated in [17]. The blade elastic torsional response was also significantly affected by the composite couplings. For these soft-inplane configurations, the influence of composite couplings on blade and hub loads was measurable, but less pronounced. The behavior of elastically coupled stiff-inplane hingeless composite rotor blades has not yet been thoroughly addressed. Stiff-inplane rotors have the advantage of not being susceptible to aeromechanical instabilities such as air and ground resonance, however, stiff-inplane hingeless rotors suffer from high blade dynamic loads and high hub vibration [19,20] in forward flight. Stiffinplane rotors may also experience flap-lag or flap-lag-torsion flutter instabilities [19-291. Earlier investigations of the flap-lag flutter phenomenon suggest that this instability is highly sensitive to couplings between flap, lag, and torsional blade motions [19-261. As shown in [25], blade stall can also have a destabilizing effect on stiff-inplane hingeless rotors at high collective pitch settings The importance of modeling elastic torsional deformations for the aeroelastic stability analysis

Vibration

of stiff-inplane that

forward

hingeless

rotors

was established

flight can be very desbabilizing

and Flutter

29

in [27-291. for stiff-inplane

In [26-291 it was also demonstrated hingeless rotors with low torsional

frequencies (w+ M S.O/rev). Use of advanced aerodynamic models in composite rotor analysis has also been very limited. In particular, all previous investigations of composite rotors in forward flight [9-11,15-171 have relied on simple linear or uniform inflow models. These models are generally adequate for stability predictions, although accurate calculation of vibration more refined treatment of the wake structure. In the present

study,

the aeroelastic

response,

with stiff-inplane composite

of helicopters by building

on the recently

new feature

of the present

into the coupled inplane

composite

inplane

tailored

aeroelastic rotor

developed analysis

vibration

rotor blades

aeroelastic

trim and response

and shaft-fixed

is investigated.

analysis

is the incorporation

configurations

composite

levels and trim controls

described

in [15-171.

The dynamic

and compared

requires

aeroelastic

The study

behavior to similar

a

stability

is conducted The

of a free wake nonuniform

solution.

is examined

usually

primary

inflow model of several results

stiff-

for soft-

rotors.

FORMULATION A spatial finite element beam model, based on Hamilton’s principle, is formulated for composite blades undergoing extension, u,, flap and lag bending, vb and Wb, elastic torsion, 4, and transverse shearing deformations, v, and w,. Nonlinear equations governing the moderate deflection of the composite blades are derived. The primary structural member of the blade, i.e., the spar, is idealized as a laminated composite thin-walled box-beam (see Figure 1).

q (0)

(-1516

(30/-30)2

(2

w/3o)2

Tt

wall

(-15&

4

1

Exploded View of Top Wall

Figure 1. Spar schematic and lamination details

Considering displacement

the beam to be undergoing relations are given by

EiC=-(V+~)mt+

small

strains

and moderate

deflections,

the strain-

v: cos(& + 4) + w: sin(B0 + i),

(lb)

w: cos(f30 + 6) + vi sin(&

(lc)

+ i),

where es< = 0 in the horizontal spar walls and E,,, = 0 in the vertical spar walls. In the above equations, the torsion-related out-of-plane warping function is denoted by XT. For a composite

E. C. SMITH

30

box-beam section, an analytical expression for the warping function is derived in [18]. The rigid pitch angle, 00, is given by @c = &s + 6& (z

- 0.75) + el, COS$ + e19 sin@,

(2)

Within the anisotropic laminated plies of the spar walls, the stress-strain

relations are given by

and the total elastic twist C$is given by

{ z:,>

= [z::

gt:]

{ zsi }

horizontal walls,

{z:}

= [g::

::I]

{ :zF}

vertical walls.

(4)

In the above equations, Qll, QG6, Q16 are elastic constants for the composite plies. These constants are functions of ply orientation angle, ply longitudinal and transverse moduli, and ply Poisson’s ratios (see [17,18]). A more detailed modeling of two-dimensional inplane elasticity is used to modify the above relations as described in [17,18]. The variation of strain energy of the composite blade, NJ, can be written as

Substitution of the strain displacement and stress strain equations into the expression for strain energy, results in the desired variational form of the strain energy. An ordering scheme is used to systematically eliminate higher order nonlinear terms from the energy expressions (see [15,17]). The resulting variational form of strain energy is also given in [15,17]. In general, the strain energy is a function of the elastic constants of the blade as shown symbolically below NJ = SUI -I- ixJc, 6u1 = au1 (EA, GJ, EI,, 6uc

= bUc(K12,

EI,,

GA,, GA,, EC?, EC2,

EBl,

-2))

(7)

K13, K14, K25, K36, K45, K46) 9

where 6Ur represents the strain energy components for an isotropic blade and 6Uc represents the additional strain energy components due to composite elastic coupling effects. The nature of these couplings is discussed in detail in [15,17,18]. The variational form of the kinetic energy ST (including shear deformation) is provided in [15,17]. External aerodynamic forces on the rotor blade contribute to the virtual work variational 6W. Aerodynamic forces and moments are calculated using quasi-steady strip theory. The effects of compressibility and reversed flow are also included in the aerodynamic model. In the present investigation, nonuniform inflow is computed using a free wake analysis for trailed vorticity. The free wake geometry consistes of near wake, rolling-up wake and far wake regions. Linear circulation distributions are used for the vortex filaments in the trailed wake. The concentrated tip vortex strength is proportional to the maximum bound circulation on the blade. Modeling of the strong tip vortex is essential for prediction of the high vibration environments in transition and low-speed forward flight. Additional details related to characteristics of the free wake model and its integration into the rotor aeroelssticity code can be found in [30-331.

Vibration

and Flutter

31

The variational form of Hamilton’s principle is discretized using shear flexible beam finite elements. This discretization is shown below, l5l-I=

tZ(6U-bT-6W) C&=0, s t1 tiF N &XI = (cm - 6Ti - SWi) d?JJ= 0,

(8)

JC $1

i=l

with SUi, 6Ti, and SW< defined as the elemental contributions to the strain energy variation, kinetic energy variation, and virtual work, and N as the total number of beam finite elements. Each beam element consists of nineteen degrees of freedom. These degrees of freedom correspond to cubic variations in axial and (flap and lag) bending deflections, quadratic variation in elastic torsion, and linear variation in (flap and lag) shear deformations [15-171. For the aeroelastic response and loads analysis, the finite element equations are transformed to normal mode space to facilitate an efficient solution for the blade response. The nonlinear, periodic normal mode equations are then solved for steady response using a time finite element technique. Steady and vibratory components of the rotating frame blade loads (i.e., shear forces and bending/torsion moments) are calculated using the force summation method. In this approach, blade aerodynamic and inertia forces are directly integrated over the desired length of the blade. Fixed frame hub loads are calculated by summing the contributions from individual blades. A coupled trim procedure is carried out to solve for the blade response, pilot control inputs, and vehicle orientation simultaneously. The coupled trim procedure is essential for composite rotors since the elastic blade deflections play a significant role in the net forces and moments generated by the rotor. Convergence of the coupled trim procedure is achieved when the steady periodic blade response, blade bound circulation, and wake geometry have all converged and the vehicle force and moment equilibrium equations have been satisfied. After the coupled trim response is computed, blade natural frequencies and mode shapes are recalculated about the (time averaged) deflected position. The linearized blade equations are numerically transformed from the rotating frame to the fixed frame using the Fourier Coordinate Transformation (FCT). Quasi-steady aerodynamics is used for all stability calculations. Low frequency unsteady aerodynamic effects are modeled using a three state dynamic inflow model. After the FCT, the fixed-frame blade equations are augmented by the dynamic inflow equations. Forward flight aeroelastic stability analysis is then performed using Floquet theory. Additional details on the aeroelastic analysis can be found in [17,33].

RESULTS

AND DISCUSSION

Aeroelastic response, loads, and shaft-fixed stability of a helicopter with elastically coupled stiff-inplane rotor blades is investigated using the previously described analysis. The properties of the vehicle used in this study are given in Table 1. The vehicle properties, identical to those used in [15-171, are representative of a light hingeless rotor helicopter. The rotor hub, inboard of the pitch bearing, is assumed to be rigid. The rotor spar is designed to yield realistic magnitudes of cross-section stiffness, inertia, and rotating natural frequencies. The box-beam spar consists of 28 laminated plies of AS4/3501-6 graphite/epoxy. Each ply is 0.005 inches thick, the outer box width is 8.0 inches and the outer box depth in 1.5 inches. Ply elastic stiffness properties are EL = 20.59 msi, ET = 1.42 msi, GLT = 0.87 msi, and VLT = 0.42. Due to the very high specific stiffness of the graphite/epoxy spar material, nonstructural mass is required to bring the rotor mass and torsion inertia up to realistic levels. Compared to the spars of the soft-inplane composite rotors investigated in [15-171, the present stiff-inplane blade spar dimensions are wider in the chordwise direction and narrower in depth (flapwise). In the present study, seven different composite spar designs are evaluated. The different laminates used in the spar walls are given in Table Al in the Appendix. Ply orientation angles are

E. C. SMITH

32

Table 1. Baseline vehicle properties. Number of Blades

4

Radius, ft.

16.2

Hover Tip Speed, ft/sec

650

Airfoil

NACA 0015 0.0, 5.73

co, cl 0.0095,

do, dl, dz

0.0, 0.2

clE

0.08

r/R Solidity, (T

0.15 0.10 0.07

CT/U

Precone,

BP

0.0

Lock Number, 7

6.34

Mass per unit length, slug/ft. Torsional Inertia,

s,

0.135

$

0.0001,

0.0004 0.04

Hub Length, xh,r,/R Aerodynamic Long., Lat.

root cutout, CG offsets,

XCG/R,

YCG/R

CG Below Hub, h/R Flat Plate Area,

f lIIR2

0.0,

0.0

0.2 0.01

Tail rotor radius, ft.

3.24

Tail rotor solidity, gtr

0.15

Tail rotor location, xt,/R

1.2

Tail rotor above CG, htr/R

0.2

(cohr,

(c1)tr

Horizontal tail location, xht/R Horizontal tail planform area, &t/HE2 I-

0.10

xroot / R

(CO)ht,

(Cl)ht

0.0, 6.0 0.95 0.011 0.0, 6.0

defined as positive towards the leading edge for the horizontal spar walls (top and bottom) and positive towards the top of the blade section for the vertical spar walls. In Table Al, “right” refers to the spar wall nearest to the trailing edge of the airfoil. The baseline case exhibits no ply-induced elastic couplings. As indicated in Table A2 in the Appendix, the other spar configurations individually feature positive and negative pitch-flap coupling, positive and negative pitch-lag coupling, and positive and negative extension-torsion couplings. A schematic of the blade spar and the lamination details for the blade with negative pitch-flap coupling are shown in Figure 1. Following the conventions defined in [30], positive pitch-flap coupling causes a decrease in blade pitch when the blade flaps upward and positive pitch-lag coupling causes an decrease in blade pitch when the blade lags backward (opposite direction of rotation). Positive extensiontorsion coupling is defined as nose-down blade torsion due to extensional forces. It should also be noted that blades with bending-torsion coupling also exhibit parasitic extension-shear coupling and blades with extension-torsion coupling also exhibit parasitic bending-shear couplings [6,1518]. For the blades examined in the present investigation, effects of these shear related couplings on blade dynamics was not significant. This is mainly due to the low levels of bending-shear couplings relative to direct bending and shearing stiffnesses (see Tables A2-A3). Selection of the test cases was designed to minimize the variations of direct stiffness and natural frequency placement on the comparisons between the baseline and coupled blades. This is helpful for evaluation of elastic coupling effects since differences between elastically coupled blades and the baseline blade cannot be attributed to variations in these important parameters. Elastic stiffness coefficients (including coupling stiffness coefficients) for four of the seven spar configurations are shown in Tables A2-A3. Note that K45 represents pitch-flap elastic coupling, K4e represents pitch-lag elastic coupling, Kr4 represents extension-torsion coupling, K25 and Ksa

Vibration

and Flutter

33

-Baseline 0.15

a

C

P

d

- - - . Positive Pitch-Flap -. NegaWe Piich-Flap

0.12

.

0.06

,

,

,

,

.

,

-

$

a

’

-0.03

I . 0.02

0

’

. ’

’ . ’ .

0.04

0.06

0.08

. ’

’

.

0.1

0.12

. . 0.14

CT/O

Figure 2. Variation of lag mode decay rates with thrust (hover, p = 0.0).

0.18

0.15 a 0 .

0.12

p”

0.09

: A

0.06

R$

0.03

Baseline

- - - PosItMe-Pitch Lag -..

Negative Pitch-Lag

0 -0.03 0.02

0

0.04

0.06

0.08

0.1

0.12

0.14

CT/O

Figure 3. Variation of lag mode decay rates with thrust (hover, p = 0.0).

0.16

0.15

a C

0.12

f

0.09

P A

0.06

aP

0.03

.

Baseline

- - -. Positive Extension-Torsion -..

.-

Negalive Extension-Torsion

. ’ * _*’

0 -0.03 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

CT/0 Figure 4. Variation of lag mode decay rates with thrust (hover, p = 0.0).

E. C. SMITH

34

represent bending-shear couplings, and K12 and Kis represent extension-shear couplings. Signs of all coupling stiffness coefficients in Tables A2-A3 are reversed for the three negatively coupled blades. Rotating natural frequencies for all the test cases are shown in Table A4. Despite the presence of the elastic couplings, there is very little difference between the natural frequencies of the elastically coupled blades and baseline uncoupled blade. The mode shapes, however, exhibit very significant couplings (e.g., flap-torsion) due to the anisotropy of the plies within the spar walls (171. 0.16 -Baseline - - - PositivePitch-nap

0.15

-

C

0.12

-

0” -1,

0.09

:__

s

-. NegativePitch-Flap .

P J $

--_ --__ --_

,

,

.’ _I*

---______-

*--

----.______

a

0 -0.03 0

0.1

0.2

advance

0.3

0.4

ratio, p

Figure 5. Variation of lag mode decay rates with forward speed (CT/~

V.

I

= 0.07).

P -

0.15

Baseline

- - -. Positive-Pitch Lag t

-

-. NegativePitch-Lag

0.12

-

0.09

___-----__ ._-

-.

_---------

---____--

stable

0

0.1

0.3

0.2

advance

0.4

ratio, p

Figure 6. Variation of lag mode decay rates with forward speed (CT/U

Aeroelastic

Stability

= 0.07)

(Hover and Forward Flight)

The lag mode is the least stable mode for stiff-inplane hingeless rotors. Figures 2-7 show the influence of ply-induced elastic couplings on regressive lag mode damping (i.e., nondimensional decay rates, a/n) in hover and forward flight. As indicated in Figures 2 and 3, positive pitch-flap and positive pitch-lag couplings have a powerful stabilizing effect on hover lag mode stability, whereas negative pitch-flap and negative pitch-lag couplings are destabilizing. The stabilizing effect is most significant at moderate and high thrust levels. This stability behavior is consistent with earlier results for stiff-inplane hingeless rotors with kinematic couplings [18-241. In all cases,

Vibration and Flutter

0.18 -

0.15

torsbn)

- - -. Positive-Pitoh Lag (softtorsion)

*..

a

Bssellne (dt

35

-

-. NegativePitchLag (softtorsion)

\

C . “\.. !Y --__ P A

0.06 -

E

0.03 -

K

.

0

t

--__ --________---

stable

0.1

0.2

0.3

0.4

advance ratio, p Figure 7. Variation of lag mode decay rates with

forwardspeed (CT/U = 0.07).

hover stability uniformly increases with thrust level. This trend is also consistent with earlier attached flow results for stiff-inplane hingeless rotors with rigid hubs. Increased structural flap-lag coupling at higher pitch settings is primarily responsible for this trend. The stability behavior of the blades with extension-torsion couplings, shown in Figure 4, is also linked to the magnitude of structural flap-lag couplings. For the blade with positive extension-torsion coupling, nose-down elastic twist (M 3.5 degrees at the blade tip) due to centrifugal forces results in increased blade pitch settings to maintain the specified thrust level. The higher pitch settings resulted in more stabilizing flap-lag structural couplings. Lower pitch settings for blades with nose-up elastic twist resulted in decreased lag mode stability. As indicated in Figures 5 and 6, lag mode stability of the elastically coupled composite blades in forward flight demonstrated the same trends as were observed in the hover condition. Figure 5 illustrates that the stabilizing effects of positive pitchflap elastic coupling are increased at high forward speeds. As shown in Figure 6, the destabilizing effects of negative pitch-lag elastic coupling became more severe in forward flight. In fact, a region of mild instability appears between, ~1= 0.1 and /.J= 0.25. Aeroelastic stability of torsionally soft composite blades was also investigated. Reconfiguring the blade spar laminate to [Os/(lO/ - lO)s/(O) 2] s resulted in a design with V+ = 2.93, ~0 = 1.14, and q = 1.42. As shown in Figure 7, these baseline uncoupled stiff-inplane blades exhibit a characteristic instability at high speeds. Pitch-lag coupling is introduced by unbalancing the (lo/ - 10)s sublaminates within the vertical spar walls. For the torsionally soft blades, positive pitch-lag elastic coupling is stabilizing at high speeds and destabilizing at low and moderate speeds. Negative pitch-lag coupling enhances stability at low speeds and sharply degrades stability at high speeds. Response,

Trim Controls, Blade Loads and Hub Vibration

Results addressing the influence of composite couplings on elastic blade response, trim control settings, blade loads, and hub vibration are presented in Figures 8-22. For blades with elastic pitch-flap or pitch-lag couplings, the blade bending moments are essentially responsible for inducing the coupled elastic torsion deflections. In order to understand the behavior of stiff-inplane composite rotor blades, it is useful to examine the characteristics of the blade root bending moments. Throughout this study, blade root bending moments are presented in nondimensional form as M Nondimensional Moment = (10) moi12 R3’

E. C.

36

SMITH

0.02 4 E P p

0.01

B 5 0 3

0.00

ii P p m

-0.01

.E 9 s 2

-0.02 0

SO

180 v

Figure 8. hot lag bending moments for soft-inplane (CT/U = 0.07).

$

270

360

Wed

and stiff-inplane

rotors

0.02

s E P P

0.01

s & m 5

0.00

d 8 ;

-0.01

/

._ t =s

Rod flap Morn; (XC&, = 0.1 R

RoolFhp Yomwnt (Q,“.

= 0.0 R

-0.02 160

SO

0

Y

360

270

0Jeg)

Figure 9. Root bending moments in forward flight (p = 0.10, CT/U = 0.07).

cn E

0.02

E % m c 5 f m 'j

ROti

bg

(&),“.

0.01

Root Lag Yomml - 0.1 R

(xc&..

moment = 0.0 R

.---\

0.00

B g " m

-0.01

flap

E B E z

t

Root UomMl ('c,&u,. 0.0 R

Root Flap Yoment (Q,,,= 0.1 R

*

-0.02 0

90

160

270

360

Q Ww) Figure 10. Root bending moments in forward flight (p = 0.35, CT/U = 0.07).

Vibration and Flutter

37

Figure 8 shows a comparison between the root lag bending moments of the baseline stiffinplane composite rotor and the baseline soft-inplane composite rotor examined in [15]. Note the severe lag moments characteristic of the stiff-inplane hingeless rotors. The stiff-inplane rotor also experiences a significant increase in lag moment at high speed. Sensitivity of root flap and lag moments to the fuselage center-of-gravity offset from the shaft is illustrated in Figures 9 and 10. The largest flap moments occur at low speed for an aft shift of the fuselage center-of-gravity.

6.00

-

8

Baseline

- - -

g

4.00

-

-

. Positive

Pii-flap

-. Negative Pitch-flap

8 ST P

2.00

4. v ._

0.00

Ir .+ IO = (R S W

-2.00

-4.00

”

0

”

90

l’

”

”

160

“‘I

“I’. 270

360

w (deg)

Figure 11. Tip elastic twist in forward flight (/A=

0.10, CT/U= 0.07, zoo = 0.0).

6.00 8 5 +t

Baseline

- - 4.00

-.

-Positive Pitch-flap . Negative Pitch-Flap

_

g

2.00

2 .z

0.00

f p Iu

-2.00

5

-4.00

W -6.00 0

90

160

270

360

Y Wed

Figure 12. Tip elastic twist in forward flight (/A= 0.35, CT/U = 0.07, IcG

= 0.0).

For the stiff-inplane composite rotors, ply-induced elastic coupling had a very small effect on blade flap and lag responses, however, the torsional response of the blades was dramatically altered. These trends were also observed for soft-inplane rotors with elastically coupled composite spars [15]. Figures 11-14 illustrate the changes in total elastic tip twist angle 4 due to positive and negative pitch-flap elastic couplings. In Figures 11 and 12, tip twist angles for low speed (p = 0.1) and high speed (/.J= 0.35) conditions are presented for a configuration with no longitudinal offset between the vehicle center-of-gravity and the rotor shaft. At both operating conditions, pitch flap couplings result in significant changes in both static and dynamic elastic blade twist. In Figures 13 and 14, elastic tip twist angles are shown for a configuration with an aft longitudinal offset between the vehicle center-of-gravity and the shaft of O.lOR. Increased flapping moments MCM 19-3/4-D

B

&I

e’ 8

’ P 0”

0 0”

N a0

P 0”

Elastic Tip Twist Angle, 9 (deg)

Q B

Elastic Tip Twist Angle, 4 (deg)

z

0

r + 8 B

i

, ,’

I’ : 6’

c’ 8

,’

P 8

LJ 8

f $

Elastic Tip Twist Angle, $ (deg)

A B

m

a

Vibration

and Flutter

39

6.00 -

Baseline

- - -. Positive Pitch-Lag B

4.00

-

. Negative

-.

3 0

Pitch-Lag .--

d F

a z ._ 2 .n

-2.00

-

.

t-

.o x d w

-4.00

._.’

-

-6.00

. 0

’

’

’

90

150

270

. 360

w (de@

Figure 16. Tip elastic twist in forward flight (cl = 0.35, Cl-/o

= 0.07, zCG = 0.0).

in this condition result in even more dramatic increases in the magnitudes of static and dynamic elastic twist. Figures 15 and 16 illustrate the changes in total elastic tip twist angle, 4, due to positive and negative pitch-lag elastic couplings. Changes in elastic blade twist are measurable, but less pronounced than changes in twist caused by pitch-flap couplings. Although lag bending moments are higher than flap bending moments (Figures S-lo), the high lag bending stiffness of the stiff-inplane blades results in lower magnitudes of elastic torsion response. Blades with extension-torsion couplings (results not shown) exhibited approximately 3.5 degrees of static elastic twist, however, dynamic twist was not measurably affected by the couplings. This is understandable due to the static nature of the axial centrifugal loading on the blades.

G

10

B l

5

P

a

i

\ -i::_’ *-

-.

--__

----_____--

eII

__--

%c

-: -10

-. --

jzfi

-.

-._ e1.

r

0

0.1

0.2

advance

0.3

0.4

ratio, p

Figure 17. Variation of trim control angles with forward speed (CT/U = 0.07, zCG = 0.0).

Influence of the composite elastic couplings on the vehicle trim controls is shown in Figures 17 and 18. Figure 17 shows the variation in collective and cyclic pitch trim controls with forward speed for a configuration with no longitudinal offset between the vehicle center-of-gravity and the rotor shaft. A composite spar tailored to introduce positive pitch-flap couplings in examined in Figure 17. For this configuration, elastic twist alters only the collective pitch required to trim the aircraft. For the same composite spar, variation of the trim controls with forward speed is shown

E. C. SMITH

40

-5 0

0.1

0.2

0.3

0.4

advance ratio, p Figure 18. Variation of trim control angles with forward speed (CT/CT = 0.07, zCG = O.lR).

0.015 w E s

-

Baseline

- - - . Positive Pitch-Flap

0.010

-.

. Negative

Pitch-Flap

% z

0.00s

d Ap

0.000

ij B d

-0.005

d m E ._ T

-0.010

f 2

-0.015 0

90

160

270

360

vr (de@

Figure 19. Root lag bending moments in forward flight (p = 0.35, CT/O. = 0.07, ICG = 0). 1

0.015

v

0.010

-

s g

-

I? S 0

0.001

Baseline

. Positive Pitch-Flap -. Negative Pitch-Flap

- - -

-

m

5 2

-0.015 0

90

160

270

360

Y Weg)

Figure 20. Root = O.lR).

XCG

flap bending moments

in forward flight (p = 0.1, C&-/a = 0.07,

Vibration and Flutter

0.09

41

c

0

0.1

0.3

0.2

0.4

advance ratio, 1

Figure 21. Variation of vertical 4/rev hub shear forces with forward speed (CT/U 0.07).

=

0.15 -Baseline

- - -. 5

0.12

-

I Z .c

0.09

-

0.06

-

Positive Pitch-Flap

-- Negative

Pitch-flap

s .g s _t

4

I 0

0.1

0.2

0.3

0.4

advance ratio, p Figure 22. Variation (CT/U = 0.07).

of longitudinal

I/rev

hub shear forces with forward speed

in Figure 18 for a configuration with a O.lOR aft longitudinal offset between the vehicle centerof-gravity and the shaft. For this configuration, increased blade dynamic elastic twist results in significant changes to collective and cyclic pitch controls. Changes in lateral cyclic pitch 81, are required at all speeds, whereas changes required in longitudinal cyclic pitch 131~diminish at higher speeds. Negative pitch-flap elastic couplings resulted in similar trends for required control pitch changes. No significant trim control changes were observed for blades with elastic pitch-lag couplings. High blade loads are a critical

concern

in the design of hingeless

rotors

[19, 211. Results

of the

present investigation indicated that no major changes in blade loads resulted from the elastically tailored blade spars. For example, Figure 19 shows the influence of pitch-flap couplings on nondimensional blade root lag bending moments at p = 0.35. The elastic pitch-flap couplings cause changes of approximately 7% in the peak-to-peak lag moments. Positive pitch-flap couplings slightly increase lag moments and negative pitch-flap couplings slightly decrease lag moments. The influence of pitch-flap couplings on nondimensional blade root flap bending moments is shown in Figure 20 for p = 0.10 and 2CG = O.lOR. This operating condition yields the maximum flap

E. C. SMITH

42

bending moments (see Figure 9). Note once again the mild effects of the pitch-flap couplings on the steady blade hap moments. Changes in blade loads associated with pitch-lag and extensiontorison couplings were even less measurable than those demonstrated for blades with pitch-flap couplings. The relatively weak effects of composite ply-induced elastic couplings on stiff-inplane rotor blade loads is consistent with the trends observed in [15] for soft-inplane elastically

tailored

composite rotors. The vibration behavior of elastically tailored composite rotors is also addressed in the present investigation. Hub vibration is very sensitive to the higher harmonic blade motion, elastic twist distributions, and rotor wake geometry. Elastic pitch-flap couplings resulted in significant changes in hub vibration levels. Figures 21 and 22 show the variation of magnitude of 4/rev vertical and longitudinal hub shear forces with forward speed. The magnitudes of these shear forces are normalized with respect to the steady rotor thrust. Note the large increase in vertical shear force at low speed. This well documented effect is associated with the close proximity of the strong tip vortices to the rotor at low speeds. As shown in Figure 21, both positive and negative pitch-flap couplings are effective in reducing the peak vibration level. At moderate and high speeds, influence of the pitch-flap couplings on vertical hub shears is less significant. Inplane hub shear forces are also sensitive to elastic pitch-flap couplings. Results shown in Figure 22 indicate that negative pitch-flap couplings substantially increase inplane hub shears at both low and high speed. Similar results were observed for lateral inplane hub shears (not shown). Influence of elastic pitch-lag couplings on both vertical and inplane hub vibration was negligible.

CONCLUSIONS A free wake model for nonuniform inflow has been incorporated into a recently developed aeroelastic analysis for helicopters with elastically tailored composite rotor blades. Using the new analysis, aeroelastic behavior of helicopters with elastically tailored stifl-inplane hingeless rotor blades has been investigated. Elastic couplings such as pitch-flap, pitch-lag, and extensiontorsion have been introduced through anisotropy of the composite blade spars. The following conclusions are based on the results of this study. 1) Elastic couplings have a very powerful effect on blade stability in hover and forward.flight. Positive pitch-flap, positive pitch-lag and positive extension-torsion couplings are stabilizing and negative pitch-flap, negative pitch-lag and negative extension-torsion couplings are destabilizing. These general trends are similar to those predicted in earlier investigations [9]. Negative pitch-lag coupling introduces a mild instability at low thrust levels in hover and at low to moderate forward flight speeds. 2) Pitch-flap and pitch-lag elastic couplings generate substantial variations in steady and dynamic elastic blade twist. Magnitude and phase of the dynamic twist varies strongly with flight speed and vehicle center-of-gravity offset. Extension-torsion elastic couplings generate primarily steady twist distributions. 3) Elastic twist associated with pitch-flap elastic couplings results in measurable changes in vehicle trim controls. For vehicles with no longitudinal offset between the center-ofgravity and the rotor shaft, only collective pitch is altered by the elastic couplings. For vehicles with aft longitudinal offsets between the center-of-gravity and the rotor shaft, both collective and cyclic pitch controls are altered by the elastic couplings. 4) Blade root flap and lag bending moments were not dramatically changed by the elastic couplings. For example, pitch-flap elastic couplings resulted in changes of 5-7s in peakto-peak values of blade root bending moments. Changes in blade loads due to pitch-lag and extension-torsion elastic couplings were generally even smaller than changes associated with pitch-flap couplings. 5) Fixed frame hub vibration levels were sensitive to elastic pitch-flap couplings. Peak vertical

Vibration

hub shear forces were reduced negative

pitch-flap

couplings.

and Flutter

approximately Negative

43

20% at low speeds due to both positive

pitch-flap

elastic couplings

resulted

and

in significantly

increased levels of inplane hub shear forces in both low and high speed flight conditions. The influence of elastic pitch-lag couplings on hub vibration was negligible.

REFERENCES

2. 3.

4. 5. 6.

7. 8.

9.

10. 11. 12. 13.

14. 15.

16.

17.

18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

C.-H. Hong and I. Chopra, Aeroelastic stability analysis of a composite rotor blade, Journal of the American Helicopter Society 30 (2), 57-67 (April 1985). C.-H. Hong and I. Chopra, Aeroelastic stability analysis of a composite bearingless rotor blade, Journal of the American Helicopter Society 31 (4), 29-35 (October 1985). I. Yuan, P. Friedmann and C. Venkatesan, A new aeroelastic model for composite rotor blades with straight and swept tips, Proceedings of the 3Yd AIAA/ASME/ASCE/AHS/ASC Struckres, Structural Dynamics and Materials Conference, AIAA Paper No. 92-2259, Dallas, TX, (April 1992). I. Yuan, P. Friedmann and C. Venkatesan, Aeroelastic behavior of composite rotor blades with swept tips, Proceedings of the 48th American Helicopter Society Annual Forum, Phoenix, AZ, (June 1992). J.B. Kosmatka and P.P. Friedmann, Vibration analysis of composite turbopropellers using a nonlinear beam-type finite element approach, AIAA Journal 27 (ll), 1606-1614 (November 1989). M. Fulton and D.H. Hodges, Applications of composite rotor stability to extension-twist coupled blades, Proceedings of the 3yd AIAA/ASME/ASCE/ AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA Paper No. 92-2254, Dallas, TX, (April 1992). P. Minguet and J. Dugundji, Experiments and analysis for composite blades under large deflections, Part 1 Static behavior, Part 2 Dynamic behavior, AIAA Journal 28 (9) (September 1990). T. Kim and J. Dugundji, Nonlinear large amplitude aeroelastic behavior of composite rotor blades a large static deflection, Proceedings of the 3yd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA Paper No. 92-2257, Dallas, TX, (April 1992). B. Panda and I. Chopra, Dynamics of composite rotor blades in forward flight, Vetiicu 11 (l/2), 187-209 (January 1987). 0. Rand, Periodic response of thin-walled composite blades, Journal of the American Helicopter Society 36 (4), 3-11 (October 1991). 0. Rand, Periodic response of thin-walled composite blades, Vertica 14 (3) (1991). D. Hodges, Review of composite rotor blade modeling, AIAA Journal 28 (3), 562-564 (March 1990). P.P. Friedmann, Rotary-wing aeroelasticity with application to VTOL vehicles, Proceedings of the 3fst AIAA/ASME/ASCE/ AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA Paper No. 90-1115, pp. 1624-1670, Long Beach, CA, (April 1990). I. Chopra, Perspectives in aeromechanical stability of helicopter rotors, Vertica 14 (4), 457-508 (1990). E.C. Smith and I. Chopra, Aeromechanical stability of helicopters with composite rotor blades in forward flight, Proceedings of the 48th American Helicopter Society Annual Forum, June 1992, Phoenix, AZ, (Accepted for publication in the Journal of the American Helicopter Society). E.C. Smith and I. Chopra, Aeroelastic response and blade loads of a composite rotor in forward flight, Proceedings of the 3yd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA Paper No. 92-2566, April 1992, Dallas, TX, (Accepted for publication in the AIAA Journal). E.C. Smith, Aeroelastic response and aero-mechanical stability of helicopters with elastically coupled composite rotor blades, Ph.D. Dissertation and UM-AERO Report 92-15, University of Maryland, MD, (August 1992). E.C. Smith and I. Chopra, Formulation and evaluation of an analytical model for composite box-beams, Journal of the American Helicopter Society 36 (3), 22-35 (July 1991). K.H. Hohenemser, Hingeless rotorcraft flight dynamics, AGARDDogmph No. 197, (September 1974). R.A. Ormiston, Investigations of hingeless rotor stability, Verticn 7 (2), 143-181 (1983). W. Johnson, Helicopter Theory, Princeton University Press, Princeton, NJ, (1980). T.M. G&ey, The effect of positive pitch-flap coupling (negative da) on rotor blade motion stability and flapping, Journal of the American Helicopter Society 14 (2) (April 1969). R.A. Ormiston and D.H. Hodges, Linear flaplag dynamics of hingeless helicopter rotor blades in hover, Jountal of the American Helicopter Society 17 (2) (April 1972). D.H. Hodges and R.A. Ormiston, Nonlinear equations for bending of rotating beams with application to linear flap-lag stability of hingeless rotors, NASA TM X-2770 (May 1973). R.A. Ormiston and W.G. Bousman, A study of stall-induced flap-lag instability of hingeless rotors, Journal of the American Helicopter Society 20 (l), 20-30 (January 1975). D.A. Peters, Flaplag stability of helicopter rotor bladea in forward flight, Journal of the American Helicopter Society 20 (4), 2-13 (October 1975). P.P. Friedmann and S.B.R. Kottapalli, Coupled flap-lag-torsional dynamics of hingeless rotor blades in forward flight, Journal of the American Helicopter Society 27 (4), 28-36 (October 1982).

E. C. SMITH

44 28

29. 30. 31. 32. 33.

T.R.S. Reddy and W. Warmbrodt, The influence of dynamic inflow and torsional flexibility on rotor damping in forward flight from symbolically generated equations, Presented at the Second Decennial Specialist’s Meeting on Rotorcraft Dynamics, Ames Research Center, Moffett Field, CA, (November 1984). B. Panda and I. Chopra, Flap-lag-torsion stability in forward flight, Journal of the American Helicopter Society 30 (4), 30-39 (October 1985). W. Johnson, A comprehensive analytical model of rotorcraft aerodynamics and dynamics, Part I: Analysis development, NASA TM 81182 (1980). M.S. Torok and I. Chopra, Rotor loads prediction utilizing a coupled aeroelastic analysis with refined aerodynamic modeling, Journal of the American Helicopter Society 36 (I), 58-67 (January 1991). M.S. Torok and I. Chopra, A coupled rotor aeroelastic analysis utilizing nonlinear aerodynamics and refined wake modeling, Journal of the American Helicopter Society 36 (l), 58-67 (January 1991). G.S. Bir, I. Chopra, E.C. Smith et al., University of Maryland Advanced Rotorcraft Code (UMARC) Theory Manual, UM-AERO Report 92-02, University of Maryland, Maryland, (August 1992).

APPENDIX:

COMPOSITE

SPAR DATA

Table Al. Composite

COMPILATION

spar laminates.

Wall Laminates Baseline Top Bottom

[04/(15/

- I5)3/(30/

- 3O)zl.s

[04/(l5/

- I5)3/(30/

- 3O)~l.s

Right

[04/(l5/

- I5)3/(30/

- 3O)z]s

Left

[04/(l5/

- I5)3/(30/

-

~WS

Negative Pitch-Flap Top

[04/(-I5)6/(30/

- 30)2]s

Bottom

[04/(-I5)6/(30/

- 3O)z]s

Right

[04/(15/

- l5)3/(30/

- 3O)z]s

Left

[04/(l5/

- I5)3/(30/

- 30)2]s

Positive Pitch-Flap Top Bottom

104/(15)6/(30/

- 3O)~l.s

[04/(15)6/(30/

- 3021s

Right

[04/(l5/

- I5)3/(30/

- 30)21s

Left

[04/(l5/

- I5)3/(30/

- 3021s

Top Bottom

[04/(I5/

- 15)3/(30/

- 3O)2ls

[04/(I5/

- l5)3/(30/

- 30)21s

Right

104/(15)6/(30)415

Left

104/(15)6/(30)41S

Negative Pitch-Lag

Positive Pitch-Lag Top Bottom

[04/(15/

- l5)3/(30/

- 3O)z]s

[04/(15/

- l5)3/(30/

- 30)21s

Right

104/(15)6/(30)41S

Left

104/(15)6/(30)41s

Positive Extension-Torsion Top Bottom

[04/(-I5)6/(30/ 104/(15)6/(30/

- 30)21S

- 30)21S

Right

[04/(15)6/(30/

- 30)21S

Left

[04/(-I5)6/(30/

- 30)21S

Negative Extension-Torsion Top Bottom

[04/(15)6/(30/

Right

[04/(-I5)6/(30/

Left

[04/(15)6/(30/

[04/(-I5)6/(30/

- 30)21S - 30)21S - 30)21S - 30)21S

Vibration

and Flutter

Table A2. Composite Stiffness

blade stiffness coefficients.

Baseline

Positive Pitch-Flap

EI,/moR2R4

0.007763

0.007763

EIz/moR2R4

0.1236

0.1236

GJ/moR2R4

0.003693

EA/moR2 R2 GA,/m&2

R2

as.25 15.32

0.003662 88.25 15.32 62.86

K&mt$12R2

0.0000

K13/moR2R2

0.0000

K14/moR2 R3

0.0000

0.0000

K25/moR2 R3

0.0000

0.0000

K36/rnoR2 R3

0.0000

0.0000

K45/moR2 R4

0.0000

0.001334

K46/moR2 R4

0.0000

0.0000

Table A3. Composite Stiffness

0.0000

I

blade stiffness coefficients.

1 Positive Pitch-Lae

1 Positive Exten.-Torsion

EI,/moR2R4

0.007763

0.007763

EI, /moQ2 R4

0.1236

0.1236 0.003652

0.003769

GJ/moR2R4 EA/m&12 R2

699.1

699.1

GA,/moR2R2

88.25

88.25

GA,/moR2R2

12.68

15.32

K12/moR2 R2 K13/rnoR2 R2

0.0000

0.0000

0.0000

-18.09

K14/moR2 R3

0.0000

K25/moQ2 R3

0.0000

Kss/moR2

0.0000

R3

0.4402 0.2200 -0.2207

K45/moR2 R4

0.0000

0.0000

K4slmoR2

0.003225

0.0000

R4

Table A4. Composite Baseline Spar

blade rotating natural frequencies (per/rev), Pitch-Flap

’

699.1

699.1

GA,/moR2R2

Mode

45

Spars

Pitch-Lag Spars

R = 383 RPM. Exten.-Torsion

Flap 1

1.14

1.14

1.14

1.14

Flap 2

3.33

3.29

3.33

3.29

Flap 3

7.20

7.04

7.17

7.05

Flap 4

12.75

12.40

12.68

12.50

Lag 1

1.42

1.42

1.41

1.41

Lag 2

8.50

8.45

8.39

a.43

Torsion 1

4.52

4.50

4.56

4.32

Torsion 2

13.39

13.36

13.54

12.80

Spars