![Page 1: 5. Helicopter Aeroelasticityocw.snu.ac.kr/sites/default/files/NOTE/Aeroelasticity... · 2018. 5. 24. · • Stall flutter in rotorcraft aeroelasticity (Dowell Sec. 7.2) - Single](https://reader035.vdocuments.us/reader035/viewer/2022070212/610786c162908f78bd62b858/html5/thumbnails/1.jpg)
Active Aeroelasticity and Rotorcraft Lab., Seoul National University
5. Helicopter Aeroelasticity
![Page 2: 5. Helicopter Aeroelasticityocw.snu.ac.kr/sites/default/files/NOTE/Aeroelasticity... · 2018. 5. 24. · • Stall flutter in rotorcraft aeroelasticity (Dowell Sec. 7.2) - Single](https://reader035.vdocuments.us/reader035/viewer/2022070212/610786c162908f78bd62b858/html5/thumbnails/2.jpg)
Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
- Single D.O.F. flutter
blade motion (flap, lag, torsion) coupling
hub
divergence, flutter (freq. coalescence)
(e.a., c.g., whirl flutter)
- isolated blade instability (hover) collective pitch
- stall instability (forward flight) cyclic pitch
- aeromechanical instability (rotor, fuselage)
- active control
longitudinal lateral
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
Blade angle Flapping θ β
“90o phase lag”
Resonance system Retreating side Advancing side
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
“hysteresis” feed energy into system
- limit cyclic not destructive
- vibration load
Rotor Type
a) Semi-articulated or teetering(2-bladed,bell)
b) Fully-articulated
c) Hingeless feathering hinge only
d) Bearingless
flapping, pitch, lag elastomeric bearing
13o 14o
16 ~ 17o
Cl
2∏
NACA 0012
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Flapping hinge
z
Ω zB y, yB
xB
r
βs ---- Flapping angle
• Isolated Blade Dynamics
- Articulated Rigid Blade Motion
First let’s consider a single blade with only flapping motion
(hinge located at the axis of rotation)
• Rotor blade structural blade dynamics modeling
- rigid blade + spring concentrated at hub
- elastic blade + geometric coupling
box-beam
Helicopter Aeroelasticity
xB yB zB ---- rotating axis (Ω) x, y, z ---- βs inclination
x
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
- complete cross-section shape
Assumption
From dynamics
A
R
PPP
P
I
FdrHH
Mdt
Hd
0
The blade is slender, assume
I : Inertia : Angular momentum PH
BB zyB III (rotational inertia)
0BxI
If
.
B B B B B B B
P B B B B B B B
p i q j r k
H I I q j I r k
flapping, pitch, lag
elastomeric bearing
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
From dynamics
To relate with Ω,
...232221
131211
kIjjIjiIj
kIijIiiIiI(dyadic)
ByI
A
R
BBBBBBBBBB FdrkqprIjrpqI
0)()(
s
0
0
0
0
cos0sin
010
sin0cos
s
ss
ss
B
B
B
r
q
p
opposite to yB
B
0 0 0
0 0
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
c
θ
Φ Ωr
s
zB
yB
dL
dD
v= inflow
Helicopter Aeroelasticity
For aerodynamics “Hover”
and the equation of motion
sBsBsB rqp cos;;sin
A
R
BssBBsssB FdrjIiI
0
2 )sin2()sincos(
Strip theory “blade element theory” Inflow Momentum theory
r
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
Introduce non-dimensional variables
≈ small
2
2
0
( )
1
2
1
2
A B B
L
d
d F dL k dD dL j
dL r c dr C
dD r c dr C
Profile drag co-efficient
r
r s
4
L
B
rx
R
v
R
C c R
I
: inflow parameter
: Lock no. …. blade motion sensitivity
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
V
V+v
V+
A1
AR
A2
v
Helicopter Aeroelasticity
From total thrust ‘T’
dxxC
C
R
rI
dxxxR
rIdL
L
dB
sB
20
2
22
23
2
0
L
T
l
C
C
dLbT b – No. of blades
R
bc
where, : Solidity ratio
22 )( RR
TCT
: Thrust co-efficient
Momentum theory, 2
TC
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
Flapping eqn. of motion
0
220
4
8 3
242
8 3
R
sA B
d s s sBB
L
r d F j
CIk
C
22 4cos sin
8 8 3
s s s s
< Hover >
and linearizing it 2
2 4
8 8 3
s s s
Damping ratio
16
C.F. : Nat. freq. ω2 = Ω2 Resonant System
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
• Coupled Flap-Lag Equation “Lead-lag instability”
PB
R
APBP aMEFdrHH
0
This accounts for the acceleration
at hinge point
where, MB : mass of the blade
: acceleration of hinge point =
cos sin 0 0 0
sin cos 0 0 0
0 0 1
B s s
B s s
Bs
p
q
r
As before
Pa2
2
Id E
dt
EEEEEE
)()(0 0
βs
e Flap
e Lead-lag
ξs
e: Hinge offset ~ 5% R
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
)( EEE
vvdt
vda pp
p
I
p
EEEdt
Edv
I
p
Helicopter Aeroelasticity
• Neglect the hinge offset for aerodynamic calculation
Then,
(1)
0
0
21[( ) ]
2 ( )
ss l
s
rdL r c dr c
r
, ?pE a
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
The eqn. of motion for 2 D.O.F system
2
2
31 2
2
4 42
8 3 3
s s s s
s s
eCoriolis’ coupling
2
220 0
32
2
8 4 4( ) 2 2
8 3 3 3
s s s s
s d s d
l l
e
C C
C C
where, R
ee
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
Linearize about equilibrium (small perturbation)
0
0
s
s
( = coning angle)
3
4
2
318
0
e
0
200
24 12
3 312
Qd
l l
CC
C Ce e
CQ : rotor torque co-efficient
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
The perturbed equations are
0
3 41 2 2 0
8 2 8 3
s e
00
4 3 82 2 ( ) 0
8 3 2 3
d
l
Ce
C
2 2
2 2
3 31 , ,
2 2
ee e e
R
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Lead
iω
“ Geometric coupling” θs
(pitch –lag)
θξ >0 (positive coupling) ------ θξ <0
Helicopter Aeroelasticity
Fan Diagram
Ω (rpm)
(Hz)
Flap
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
• Stall flutter in rotorcraft aeroelasticity (Dowell Sec. 7.2)
- Single DOF instability in rotorcraft ….. “ Stall flutter”
- primarily associated with high speed flight, maneuvering
- does not constitute a destructive instability, but rather
produces a limit cycle behavior
- Rotor disc in forward flight ….. AOA on the advancing side
is considerably smaller than those on the retreating side
(Typical AOA distribution at μ = 0.33 …. Fig 7.13
- Retreating side ….. large AOA and changes rapidly with
azimuth angle airload prediction needs to include unsteady
effects
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
• Stall flutter in rotorcraft aeroelasticity (Dowell Sec. 7.2)
- Since the stalled region is only encountered over a portion
of the rotor disk, it will not be continuing unstable motion
- complexity of the flow field around a stalled airfoil
experimental data
A.O.A distribution of helicopter rotor at 140 knots (μ = 0.33 )
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
• Stall flutter in rotorcraft aeroelasticity (Dowell Sec. 7.2)
- Single DOF blade motion assumed
Energy eqn. multiply by dα and integrating over one cycle
- Fig. 7.14 ….. time history of the pitching moment coeff.
normal force coeff.
as a function of AOA for an airfoil oscillating at reduced
frequency typical of 1/rev at three mean AOA’s.
)(
2
22
2
MCI
cR
dCI
cRM )(
222
2222
2
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
• Stall flutter in rotorcraft aeroelasticity (Dowell Sec. 7.2)
- large hysteresis loop ….. in the dynamic case when the
mean AOA is small
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
• Stall flutter in rotorcraft aeroelasticity (Dowell Sec. 7.2)
- Pitching moment behaviour ….. in the vicinity of lift stall
average pitching moment increased markedly
(“moment stall”)
time history looks like figure ‘eight 8’
change in energy over one cycle ~
- Value of this integral = area enclosed by the loop
loop is traversed in a counter-clockwise direction …..
integral is negative, dissipation, positive damping.
dCM )(
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
large torsional motion , 2.3 cycles of the torsion
• Stall flutter in rotorcraft aeroelasticity (Dowell Sec. 7.2)
Moment stall occurs statically … no net dissipation of energy
or energy is being fed into the structure (integral is positive)
“stall flutter”
-loss of damping at stall
-marked change in average
pitching moment
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
• Stall flutter in rotorcraft aeroelasticity (Dowell Sec. 7.2)
Fig. 7.15 ….. Typical time history of blade torsional motion
when stall flutter is encountered.
marked increase in the vibratory loads in the blade pitch
control system
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Active Aeroelasticity and Rotorcraft Lab., Seoul National University
Helicopter Aeroelasticity
• Aeromechanical instability in rotorcraft (Dowell Sec. 7.3)
Fig. 7.28 ….. Typical Coleman plot of the rotor-fuselage
coupling. Will induce ground/air resonance.