Whirl Flutter of Turboprop Aircraft Structures

343 Pages·2015·22.23 MB·English

by  Jiri Cecrdle

Whirl Flutter of Turboprop Aircraft Structures
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Whirl Flutter of Turboprop
Aircraft Structures
ˇ
Jirˇí Cecˇrdle
amsterdam (cid:129) boston (cid:129) cambridge (cid:129) heidelberg (cid:129) london
new york (cid:129) oxford (cid:129) paris (cid:129) san diego
san francisco (cid:129) singapore (cid:129) sydney (cid:129) tokyo
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This book is dedicated to my children, Jan and Anna
List of fi gures
1.1 Aeroelastic (Collar’s) triangle of forces 2
1.2 Principle of airfoil torsional divergence 5
1.3 Principle of control surface reversion 6
1.4 Harmonic motion of airfoil with single DOF – torsion 8
1.5 Harmonic motion of airfoil with single DOF – bending 8
1.6 Harmonic motion of airfoil with 2 DOFs (bending /
torsion – ‘in-p hase’) 9
1.7 Harmonic motion of airfoil with 2 DOFs (bending /
torsion – ‘out- of-phase’ – shift π /2) 9
1.8 Harmonic motion of airfoil with 2 DOFs (bending /
aileron – ‘in-p hase’) 10
1.9 Harmonic motion of airfoil with 2 DOFs (bending /
aileron – ‘out- of-phase’ – shift π /2) 10
2.1 Gyroscopic system with propeller 15
2.2 Independent mode shapes ((a) pitch, (b) yaw) 15
2.3 Backward (a) and forward (b) whirl mode 16
2.4 Stable (a) and unstable (b) state of gyroscopic vibrations
for backward fl utter mode 16
2.5 Aerodynamic forces due to pitching defl ection (angleΘ ) 17
2.6 Aerodynamic forces due to the yawing velocity z˙
(movement around vertical axis) 18
⋅
2.7 Aerodynamic forces due to pitching angular velocity Θ
(movement around lateral axis) 19
2.8 Kinematical scheme of the gyroscopic system 20
2.9 Infl uence of the propeller advance ratio ( V / (Ω R )) on the
∞
stability of an undamped gyroscopic system 24
ix
Whirl Flutter of Turboprop Aircraft Structures
2.10 Infl uences of structural damping and propeller – pivot
point distance on whirl fl utter stability 25
2.11 Static divergence of the gyroscopic system 26
2.12 Whirl fl utter boundaries (Ω = const.) 27
2.13 Whirl fl utter boundaries (K = const.; K = const.) 28
Θ Ψ
2.14 Whirl fl utter boundaries (J = const.) 28
o
2.15 Infl uence of infl ow angle to whirl fl utter boundaries 29
3.1 Lockheed L-188 C Electra II aircraft 34
3.2 Beechcraft 1900C aircraft 36
4.1 NACA wind tunnel model of wing and nacelle 43
4.2 Propeller wind tunnel model 43
4.3 Propeller simple wind tunnel model 44
4.4 Experimental whirl fl utter boundaries 45
4.5 NASA propeller wind tunnel model 45
4.6 Comparison of experimental aerodynamic derivatives
with theory 46
4.7 Effect of thrust on whirl fl utter stability 47
4.8 Hinged blades propeller wind tunnel model 48
4.9 Effect of blades fl apping on whirl fl utter stability 48
4.10 NAL hinged blade propeller model 49
4.11 Effect of blades fl apping on whirl fl utter stability 50
4.12 Semispan wing / engine component model
(NASA Langley) 51
4.13 L-188 C Electra II aeroelastic model WT measurement
(NASA Langley) 53
4.14 L-188 C Electra II aeroelastic model WT measurement
(NASA Langley) 53
4.15 Effect of stiffness reduction on the whirl fl utter
boundary for the starboard outboard engine, ( K / K ) = 1.0;
Θ Ψ
g = 0.014 54
4.16 Effect of stiffness and damping reduction ( K – 67%;
Θ
g – 35% of nominal) on the whirl fl utter boundary for
various starboard engines, (K / K ) = 1.0 or 1.5 55
Θ Ψ
4.17 Effect of structural damping on the whirl fl utter boundary,
K = 3.6e3 [in- lb/rad]; (K / K ) = 1.8 55
Θ Θ Ψ
x
List of fi gures
4.18 Effect of starboard inner propeller overspeed on the whirl
fl utter boundary (others at nominal rpm) 56
4.19 Flapping blades prop-rotor wind tunnel model 58
4.20 Flapping blades prop- rotor – results summary 58
4.21 Flapping blades prop- rotor results – infl uence of blade
fl apping hinge 59
4.22 Flapping blades prop- rotor results – infl uence of stiffness
ratio 60
4.23 Simple table- top prop- rotor model 60
4.24 Prop- rotor model 61
4.25 Four- blade prop- rotor model 62
4.26 Three- blade prop- rotor model 63
4.27 WRATS tilt- rotor aircraft component model 64
4.28 WRATS measurement results – infl uence of WT medium 65
4.29 L-610 commuter aircraft 66
4.30 L-610 complete aeroelastic model at TsAGI T-104 wind
tunnel test section 67
4.31 L-610 aeroelastic model starboard wing/engine component 67
4.32 L-610 aeroelastic model aileron actuation 68
4.33 Aeroelastic model engine nonlinear attachment (1 – engine
mass; 2 – nonlinear attachment; 3 – pitch 1st attachment
4 – yaw attachment; 5 – pitch 2nd and 3rd attachments;
6 – hinge) 69
4.34 W-WING demonstrator nacelle design drawing (1 – motor
and gearbox; 2 – wing spar; 3 – pitch attachment; 4 – yaw
attachment; 5 – mass balancing weight) 70
4.35 W-WING demonstrator, uncoated nacelle 70
4.36 W-WING demonstrator, uncoated nacelle integrated into
wing structure 71
4.37 W-WING demonstrator wing and coated nacelle 71
4.38 W-WING demonstrator wing – strain gauges in half- span
section 72
4.39 Tool for the propeller blade adjustment 73
4.40 W-WING demonstrator FE model (structural) 75
4.41 W-WING demonstrator FE model (aerodynamic) 75
xi
Whirl Flutter of Turboprop Aircraft Structures
4.42 Example of W-WING analytical results – required stiffness
for neutral stability (Ω = 2000 rpm, light blades), parameter:
fl ow velocity 76
4.43 Example of W-WING analytical results – required stiffness
for neutral stability (V = 20 m·s− 1 , Ω = 2000 rpm), parameter:
IP (light/heavy blades) 76
4.44 Example of W-WING analytical results – required stiffness
for neutral stability (V = 20 m·s −1 , heavy blades), parameter:
propeller revolutions 77
5.1 Effective quasi- steady angles 84
5.2 Whirl fl utter critical dimensionless frequency and
damping ( G = (γ /γ ) = 1.0 and γ 2 = ( K / K ) = 1.4) 87
Ψ Θ Ψ Ψ
5.3 Infl uence of the propeller hub distance on the backward
whirl mode critical damping (G = (γ /γ ) = 1.0 and
Ψ Θ
γ 2 = ( K /K ) = 1.0) 89
Ψ Θ
5.4 Stability boundaries – assessment of the stiffness
asymmetry via K (γ = γ = 0.03; Ω = 1020 rpm) 90
RMS Ψ Θ
5.5 Stability boundaries – assessment of the damping
asymmetry (γ = 0.03; K = 12.3e + 6 [in-l b/rad]) 91
AVG RMS
5.6 Arbitrary position of propeller disc 92
5.7 Blade section (angles and velocities) 93
5.8 Blade section lift force components 96
5.9 Blade integrals (fundamental formulation) 98
5.10 Lift curve slope distribution of AV-844 and AV-725
propellers 105
5.11 Aerodynamic derivatives of the (a) AV-844 and (b) AV-725
propellers 106
5.12 Aerodynamic derivatives of the (a) AV-844 and (b) AV-725
propellers 106
5.13 Aerodynamic derivatives of the (a) AV-844 and (b) AV-725
propellers 106
5.14 Aerodynamic derivatives of the (a) AV-844 and (b) AV-725
propellers 107
5.15 Aerodynamic derivatives of the (a) AV-844 and (b) AV-725
propellers 107
xii
List of fi gures
5.16 Aerodynamic derivatives of the (a) AV-844 and (b) AV-725
propellers 107
5.17 Example of the infl uence of the blade lift curve slope
distribution to the whirl fl utter speed: (a) V - g diagram,
(b) V - f diagram 108
5.18 Example of the infl uence of the blade lift curve slope
distributions on the whirl fl utter stability margins 109
5.19 Consideration of the wing fl exibility: (a) rigid wing,
(b) wing bending fl exibility, (c) wing bending and torsional
fl exibility 111
5.20 Infl uence of the wing fl exibility on the whirl fl utter:
(a) rigid wing, (b) wing bending fl exibility, (c) wing bending
and torsional fl exibility 112
5.21 Analytical model with four DOFs including wing bending
and torsional fl exibility 113
5.22 Aerodynamic forces and moments 119
5.23 Flapping blade whirl modes ((r / R ) = 0.13) 127
e
5.24 Scheme of the fl apping blade dynamic system 128
5.25 Forces on blade section 134
5.26 Scheme of the gimballed propeller dynamic system 145
5.27 Twisted blade mode and deformation components 153
5.28 Mechanical instability of the system with fl exible twisted
blades 154
5.29 Stability boundaries for a system with twisted blades
– forward whirl 155
5.30 Stability boundaries for a system with twisted blades
– backward whirl 155
5.31 Velocities at the propeller 157
5.32 Helical coordinate system at the propeller 158
5.33 Doublet–Lattice method 166
5.34 Four- blade large area propeller (C-130E) 167
5.35 Multi- blade swept- tip propeller (A400M) 167
5.36 Twin counter- rotating propeller (An-22) 167
5.37 Typical Campbell diagram of the natural frequencies of
bending of a rotating propeller 169
xiii