large & small blades: design &...
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Copyright © 2004 Wetzel Engineering, Inc.
Kyle K. Wetzel, Ph.D.
Wetzel Engineering, Inc.
Lawrence, Kansas
Sandia National Laboratory
Wind Turbine Blade Workshop
February 24, 2004
Albuquerque, New Mexico
Large & Small Blades:Design & Manufacturing
Tailored Twist-Flap Coupling
Copyright © 2004 Wetzel Engineering, Inc.
Copyright © 2004 Wetzel Engineering, Inc.
Tailored Twist-Flap Coupling
• Tailored twist-flap coupling can be used to shed transient loads, thereby reducing fatigue
• Allow an increase in rotor diameter• Increased Energy Capture• Value of increased energy capture exceeds cost of
implementing coupling• Reduction in the cost of energy
Copyright © 2004 Wetzel Engineering, Inc.
Wetzel Engineering Twist-Flap Coupled Blade Studies
•3-m Blades for a 6-kW Turbine•USDOE Distributed Wind Generation Contract
•9-m Blades for Sandia’s 115-kW LIST Turbine•Subcontractor to Wichita State University
•34/37/39-m Blades for GE Wind’s 1.5-MW Turbine•USDOE STTR Contract•Subcontractor to GE Wind (NGT Program)
Copyright © 2004 Wetzel Engineering, Inc.
Normal Operation
Lift
Drag
TypicalOutboard Section
Resultant ForceOn Blade
Copyright © 2004 Wetzel Engineering, Inc.
High-Speed Gust
Lift
Drag
Resultant ForceOn Blade
Copyright © 2004 Wetzel Engineering, Inc.
Lift
DragResultant ForceOn Blade
High-Speed Gust: Pitch Regulation
Copyright © 2004 Wetzel Engineering, Inc.
Lift
DragResultant ForceOn Blade
High-Speed Gust: Pitch Regulation
• Active Pitch Control will always experience lag
Copyright © 2004 Wetzel Engineering, Inc.
Lift
DragResultant ForceOn Blade
High-Speed Gust: Twist-Flap Coupling
• Active Pitch Control will always experience lag• Passive flap-induced twist will
always respond faster than an active pitch system
Copyright © 2004 Wetzel Engineering, Inc.
Comment on the Governing EquationsThe Common Formulation of Twist-Flap Coupling Used
in Recent Years is Incorrect
Inverted, this yields
−
−=
x
xx
GJggEI
TM
φκ
−=
TM
GJg
gEI x
x
x
1
1
11
2
2
2 α
α
αφκ
GJEIg⋅
=αwhere
( )21 ακ
−=EIM x
xWhen T=0, then which is incorrect!
It can be shown that the classic, well known relationship
EIM x
x =κ
is always true, even when coupling is present
Copyright © 2004 Wetzel Engineering, Inc.
Comment on the Governing EquationsCorrect Formulation
Inverted, this yields
=
TM
GJg
gEI x
x
x
1
1
2
2
α
α
φκ
−
=
x
xx
GJggEI
TM
φκ
α 211
When T=0, then which is Correct!EIM x
x =κ
Previous Conclusions that Twist-Flap Coupling Introduces an Inherent flapwise softening due to the 1-α2 term are incorrect.
No such softening occurs.Rotating axial fibers will obviously reduce the axial stiffness, but no
additional softening occurs due to coupling.
Copyright © 2004 Wetzel Engineering, Inc.
Comment on the Governing Equations
We could use a formulation whichavoids the use of EI, GJ, or g
=
x
xx
KKKK
TM
φκ
2212
2111
This is essentially what we do when we build the stiffness matrix in ADAMS from ANSYS results
We calculate the K terms from ANSYS and plug them into ADAMS
The error is in how we relate the K terms to EI, GJ, & g
Copyright © 2004 Wetzel Engineering, Inc.
If you use the incorrect formulation consistently between models (e.g., ANSYS & ADAMS), you will obtain consistent and correct answers in terms of
deflections, dynamics, etc.That is, Two Wrongs Seem to Make it Right!
Incorrectly putting the 1-α2 term in the Denominator of the Flexibility Matrix Results in an Overestimation of
EI by the factor of approximately α2. However, putting the 1- α2 term in the denominator overestimates the flexure resulting from a given EI by the same factor!
Comment on the Governing Equations
Copyright © 2004 Wetzel Engineering, Inc.
However, if you calculate E and I from a cross-sectional equivalent beam property model, you must
use the correct formulation of the governing equations in order to get the correct answer
Similarly, if you hand EI data calculated using the incorrect formulation to someone using the classic, correct definition of EI, they will obtain a different,
inconsistent, and incorrect answer.
This problem needs to be corrected.
Comment on the Governing Equations
Copyright © 2004 Wetzel Engineering, Inc.
Load Trimming due to Coupling actually permits flapwise softening of the blade without an increase in tip deflection.
Substantial Reductions in Flapwise Fatigue can be Achieved with Coupling
-0.397α + 0.970-0.352α + 0.936-0.347α + 0.912-0.364α + 0.888-0.333α + 0.856-0.392α + 0.870-0.349α + 0.817
60%
80%
100%0.0 0.1 0.2 0.3 0.4 0.5 0.6
Twist-Bend Coupling Parameter -- α
Nor
mal
ized
Fat
igue
Dam
age
Equi
vale
nt B
lade
R
oot F
lapw
ise
Ben
ding
Mom
ent
}}}
∆m=0
∆m=-15%
∆m=-30%
∆m=+15%
∆K11=0∆K11=-15%∆K11=-30%
90%
100%
110%
120%
130%
140%
-50%-40%-30%-20%-10%0%
Change in Blade Flapwise Stiffness -- ∆EI
Nor
mal
ized
Max
imum
Tip
Def
lect
ion
-- x
tip/x
tip,b
asel
ine
α=0.5
α=0.35
α=0.2
x ∆m=-30%+ ∆m=-15%-- ∆m=0% Results of Parametric Studies of
the Dynamics of 37-m Twist-Flap Coupled Blades on a 1.5-MW Pitch-Regulated Turbine
Thanks to GE Wind & Windward Engineering for their Support
Influence of Coupling on Dynamics
Copyright © 2004 Wetzel Engineering, Inc.
37-m Blade Structural Design Studies
0.000.050.100.150.200.250.300.350.400.450.5095
52G
9550
G95
50C
9532
G95
30G
9530
C97
52G
9750
G97
50C
9732
G97
30G
9730
C90
52G
9050
G90
50C
9032
G90
30G
9030
CX
30C
X50
GC
arbo
n 1
Car
bon
2X
5XG
Cases
Effe
ctiv
e Tw
ist-B
end
Cou
plin
g Coupled Skins & Caps
Skins Only
Spar Only
Copyright © 2004 Wetzel Engineering, Inc.
Influence of Coupling on Cost & Fatigue
X5XG
9730G9732G
9730C
9752G
9530G9530C
9750G
9750C
9532G9550C
9550G9552G
9030C9030G
9050C9032G
Carbon2
9050G
9052GX30CX50G
CarbonBaseline
70%
75%
80%
85%
90%
95%
100%
100% 105% 110% 115% 120%
Blade Cost Relative to Baseline
Bla
de R
oot F
lapw
ise
Ben
ding
Fat
igue
DEL
R
elat
ive
to B
asel
ine
Coupled Skins Only
Coupled Skins & CapsCoupled SparOnly
$8/lb Carbon
Copyright © 2004 Wetzel Engineering, Inc.
Influence of Coupling on COE
70%
75%
80%
85%
90%
95%
100%
9552
G95
50G
9550
C95
32G
9530
G95
30C
9752
G97
50G
9750
C97
32G
9730
G97
30C
9052
G90
50G
9050
C90
32G
9030
G90
30C
X30
CX
50G
Car
bon
1C
arbo
n 2
X5X
G
Cos
t of E
nerg
y R
elat
ive
to B
asel
ine
Coupled Skins & Caps Skins Only Spar Only
Includes influence of coupling and massGlass Baseline is at 104%
Copyright © 2004 Wetzel Engineering, Inc.
Influence of Carbon on COENo Coupling
4
5
6
7
8
9
10
11
30 35 40 45 50 55
Blade Length
Bre
ak-E
ven
Car
bon
Cos
t [$/
lb]
Aggressive Designs
Moderate Designs, Increased Diameter
Moderate Designs, No Increased Diameter
Conservative Designs
Current Carbon Fabric Prices
Automotive Carbon Prices
Copyright © 2004 Wetzel Engineering, Inc.
Influence of Coupling on LoadsPitch-Regulated Design Example
0.0
0.2
0.4
0.6
0.8
1.0
1.2
YawMoment
TiltMoment
TT Thrust Hub YawMom
HubPitchMom
LSSTorsion
Root FlapMom
RootEdgeMom
RootTorsion
Nor
mal
ized
Ext
rem
e Lo
ad M
axim
a
GE37a Class3A KW37 Class2A & 3A KW39 Class2A & 3ABaseline 37-m 37-m TBC 39-m TBC
Class IIIA Class IIA Class IIA Baseline 37-m 37-m TBC 39-m TBC
Class IIIA Class IIA Class IIA
Demonstrated Potential to Reduce or Maintain Key Extreme Loads Close to Baseline Values
0
0.2
0.4
0.6
0.8
1
1.2
Flap Moment EdgeMoment
Hub YawMoment
Hub PitchMoment
Yaw Moment Tilt Moment Tower TopThrust
Nor
mal
ized
DEL
37a Class3A KW37 Class2A KW39 Class2A
Key DELs Kept Below Class3A Baseline Values, Even at Class 2 Mean Wind Speeds and Larger Dia.
Baseline 37-m 37-m TBC 39-m TBCClass IIIA Class IIA Class IIA
Copyright © 2004 Wetzel Engineering, Inc.
9.2-m Blade Flapwise FatigueStall-Regulated Turbine (Sandia LIST)
86%
88%
90%
92%
94%
96%
98%
100%
102%
5 7 9 11 13 15 17 19 21 23 Total
Wind Speed Bin [m/s]
WSU 9.2cWSU 9.2TBC10
m=10
WS9.2c is an Uncoupled Carbon/Glass Hybrid BladeWSU9.2TBC10 is a Twist-Flap Coupled Carbon/Glass Hybrid BladeNPS9.2 is the Baseline, Uncoupled All-Glass Blade
Copyright © 2004 Wetzel Engineering, Inc.
Peak Carbon Fiber Strain, 9.2-m Blades
Coupled Blade
Max 2301 µstrain
52% Margin on Static Axial Strain
65% Margin on Axial Strain Fatigue
Uncoupled Blade
Max 3444 µstrain
2% Margin on Static Axial Strain
8% Margin on Axial Strain Fatigue
Copyright © 2004 Wetzel Engineering, Inc.
Shear Stress, 9.2-m Coupled Blade20° Carbon Fibers
32.2 MPa Peak Shear Stress
8% Margin on Static Shear Strength
Shear Fatigue Allowable is Unknown
0° Glass Fibers
21.6 MPa Peak Shear Stress
-7% Margin on Static Shear Strength
Shear Fatigue Allowable is Unknown
Copyright © 2004 Wetzel Engineering, Inc.
Twist-Flap Coupled Blade StudiesConclusions to Date
•Cost of energy benefits seem to improve with increasing coupling – no interim sweet spot has been found•Shear strength and fatigue issues will probably be
the key design challenge•Coupling in the spar caps and skins is preferable
to confining it to either region•Coupling in the spar caps only is preferable to
coupling in the skins only•Must maintain some ±45° material in the skins•Benefits of coupling for stall-regulated turbines is
questionable
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