EWEA 2011 Brussels, Belgium: Europe’s Premier Wind Energy Event
description
Transcript of EWEA 2011 Brussels, Belgium: Europe’s Premier Wind Energy Event
EWEA 2011 Brussels, Belgium:Europe’s Premier Wind Energy Event
EWEA 2011 Brussels, Belgium:Europe’s Premier Wind Energy Event
Structural reliability analysis of rotor blades in ultimate loading
K. C. Bacharoudis1, D. J. Lekou2, T. P. Philippidis1 1. University of Patras, Dept. of Mechanical Engng & Aeronautics, Greece2. Centre for Renewable Energy Sources, Wind Energy Division, Greece
Brussels, 14-17 March 2011
The objectives are:
• Reliability assessment of a given design (safety factors, Target reliability)
• New probabilistic design, sensitivity studies (Improve/optimize blade structural design)
Probabilistic Strength AnalysisProbabilistic Strength Analysis
Brussels, 14-17 March 2011
• Sectional analysis based on thin wall multi cellular theory was performed by a numerical tool (THIN)
• Monte Carlo, Edgeworth expansion method and Response Surface method/Monte Carlo were used
• Stress resultants, engineering elastic constants (E1, E2 , v12 , G12) and failure stresses (XT, XC, YT, YC, S) in the principal coordinate system of the UD ply were considered random variables (RV)
Probabilistic Strength AnalysisProbabilistic Strength Analysis
Brussels, 14-17 March 2011
• Stochastic representation of material properties• Stochastic modeling of the stress resultants acting on
the blade section• Implementation of fast and accurate reliability
methods
The effort consists of three major tasks:
Probabilistic Strength AnalysisProbabilistic Strength Analysis
Brussels, 14-17 March 2011
Sec 9.2m
Thin model
Blade model
Blade section
Rotor Blade ModelRotor Blade Model
Brussels, 14-17 March 2011
Laminate
Material Property
Mean Std. Rd
Ex (GPa) 22.9 2.1 22.9
Ey (GPa) 7.9 1.6 7.9
vxy0.3 0.05 0.3
Gxy (GPa) 1.7 0.4 1.7
XT (Mpa) 241.2 34.4 134.2
XC (Mpa) 199.5 19.9 123.6
YT (Mpa) 22.0 3.6 11.5
YC (Mpa) 89.3 9.1 55.1
S (Mpa) 9.7 1.4 5.4
Material properties were considered normally distributed
Material properties at the ply level
Stochastic Material PropertiesStochastic Material Properties
Sec 9.2m
THIN model
Blade section
Brussels, 14-17 March 2011
z
Nz
Mz
Nx
xMx
NyMy
y
Extreme Load Analysis (IEC-61400 ed.3)Extreme Load Analysis (IEC-61400 ed.3)
Directions of the stress resultants of the blade under extreme loading
Brussels, 14-17 March 2011
0
200
400
600
800
1,000
1,200
1,400
1,600
1,800
2,000
1000 1200 1400 1600 1800 2000
Flap
mom
ent [
kN*m
]
Sample #
Time series from aero elastic codes
z
Nz
Mz
Nx
xMx
NyMy
y
Extreme Load Analysis (IEC-61400 ed.3)Extreme Load Analysis (IEC-61400 ed.3)
Brussels, 14-17 March 2011
0
200
400
600
800
1,000
1,200
1,400
1,600
1,800
2,000
1000 1200 1400 1600 1800 2000
Flap
mom
ent [
kN*m
]
Sample #
Sample valuesThresholdMax
z
Nz
Mz
Nx
xMx
NyMy
y
Extreme Load Analysis (IEC-61400 ed.3)Extreme Load Analysis (IEC-61400 ed.3)
Pick local maxima according IEC 61400-1 Ed.3
Thrs.=mv+1.4*sd
Brussels, 14-17 March 2011
-2
0
2
4
6
8
10
12
14
1300 1500 1700 1900 2100
-Ln(
-Ln(
F max
))
Flap moment [kN*m]
EmpiricalLognormalWeibull3pWeibullGumbelGumbel_1
Find best-fit probability distributions for every mean wind speed bin
z
Nz
Mz
Nx
xMx
NyMy
y
Extreme Load Analysis (IEC-61400 ed.3)Extreme Load Analysis (IEC-61400 ed.3)
Brussels, 14-17 March 2011
1.00E-12
1.00E-11
1.00E-10
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
300 1300 2300 3300
P(F e
xt>=
F/T=
10 m
in)
Flap moment [kN*m]
Lognormal
Weibull
3pWeibull
Gumbel
Gumbel_1
P=3.8e-7
Maximum observation
Pr , Pr ,ob F F T P F T ob F F V T p V dVext e extV
V
in
out
z
Nz
Mz
Nx
xMx
NyMy
y
Extreme Load Analysis (IEC-61400 ed.3)Extreme Load Analysis (IEC-61400 ed.3)
Brussels, 14-17 March 2011
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
2730 2830 2930 3030 3130 3230 3330
P(F e
xt<F
/T=2
0 yr
s)
Flap moment [kN*m]
EmpiricalNormalLognormalWeibull3pWeibullGumbel
P F F T yr P F F Text ext
N
20 1 10min
z
Nz
Mz
Nx
xMx
NyMy
y
Extreme Load Analysis (IEC-61400 ed.3)Extreme Load Analysis (IEC-61400 ed.3)
Brussels, 14-17 March 2011
Stress resultants are modeled as Gumbel distribution
F x e e
x b
a
z
Nz
Mz
Nx
xMx
NyMy
y
Extreme Load Analysis (IEC-61400 ed.3)Extreme Load Analysis (IEC-61400 ed.3)
Section 9.2mFd a b
Nx [kN] 306.00 1.297 243.6Ny [kN] 200.50 5.163 155.6Nz [kN] 145.87 4.289 112.7
Mx [kNm] 17.80 0.667 13.6Mz [kNm] 1872.50 50.610 1451.3My [kNm] 1253.75 35.510 970.4
Brussels, 14-17 March 2011
0
0.2
0.4
0.6
0.8
1
1 6 11 16 21 26 31 36
Corr
elati
on
Sample #
Edge M.-TorsionEdge M.-Flap M.Edge M.-Flap F.Edge M.-Edge M.Edge M.-Edge F.Correlation matrix of stress resultants for section
9.2m from root
Tor. Flap M. Flap F Edge M. Edge F.
Tor. 1 0.48 0.53 0.77 0.79
Flap M. 0.48 1 0.95 0.33 0.32
Flap F. 0.53 0.95 1 0.28 0.27
Edge M. 0.77 0.33 0.28 1 0.99
Edge F. 0.79 0.32 0.27 0.99 1
z
Nz
Mz
Nx
xMx
NyMy
y
Extreme Load Analysis (IEC-61400 ed.3)Extreme Load Analysis (IEC-61400 ed.3)
Brussels, 14-17 March 2011
z
Nz
Mz
Nx
xMx
NyMy
y
Element failure probabilityElement failure probability
i j
Laminate
i j
Assuming :•Laminate is a series system of layers•Each ply has one failure mode described by the specified failure criterion•Positive correlated failure modes among the layers
Brussels, 14-17 March 2011
z
Nz
Mz
Nx
xMx
NyMy
y
Element failure probabilityElement failure probability
i j
Laminate
i j
1
1
max , ,
max , ,
max ,
node i layer layer n
node j layer layer n
element node i node j
f f f
f f f
f f f
P P P
P P P
P P P
Brussels, 14-17 March 2011
z
Nz
Mz
Nx
xMx
NyMy
y
Failure criterionFailure criterion
i j
Laminate
i j
Limit state function for every ply formulated by Tsai-Hahn failure criterion
1
1
max ,
max , ,
max , ,
element node i node j
node i layer layer n
node j layer layer n
f f f
f f f
f f f
P P P
P P P
P P P
0 , 0g fail g safe 1g X R
Brussels, 14-17 March 2011
Reliability methods: Monte CarloReliability methods: Monte Carlo
Basic Variables (RVs)
E1, E2, v12, G12
XT, XC, YT, YC, SNx, Ny, Nz, Mx, My, Mz,
THIN analysis Output Variable (RV)
εx, εy, εs
Limit state function
g x R 1
• Random number generation for the basic variables•THIN analysis•Evaluation of limit state function• Layer failure probability
•Estimation of element failure probability• 2,000,000 simulations
0layer
failsf
total
nP P g n
Brussels, 14-17 March 2011
2
3 4 63 343 322 222 2
22 2
1 2, 2 2, 3,2 21 1 1
1 1 103
4! 6!3!
1, , ...
2
0layer
g
M M M
i i ii i ii i i i
f
F g g g g g
g g g gg
X X X X
P P g
Reliability methods: EDWReliability methods: EDW
Basic Variables (RVs) Output Variable (RV)
Limit state function
g x R 1
E1, E2, v12, G12
XT, XC, YT, YC, SNx, Ny, Nz, Mx, My, Mz,
Brussels, 14-17 March 2011
Reliability methods: RSM/MCReliability methods: RSM/MC
Basic Variables (RVs) Regression models Output Variable (RV)
Limit state function
g x R 1
• Random number generation for the basic variables•Stress-strain analysis through regression models•Evaluation of limit state function• Layer failure probability
•Estimation of element failure probability• 2,000,000 simulations
0layer
failsf
total
nP P g n
εx, εy, εs (top and bottom layers)
E1, E2, v12, G12
XT, XC, YT, YC, SNx, Ny, Nz, Mx, My, Mz,
Brussels, 14-17 March 2011
εx, εy, εs (top and bottom layers)
Reliability methods: RSM/MCReliability methods: RSM/MC
Input Variables (RVs)
E1, E2, v12, G12
Nx, Ny, Nz, Mx, My, Mz,
Regression models Output Variable (RV)
Limit state function
g x R 1
Building regression models
Design of Experiment10 input variables5 levels to be tested for every input variable (circumscribed CCD)6 output parameters (strains at the lower face of the bottom and the upper face of the top ply of the laminate).149 THIN analyses
Brussels, 14-17 March 2011
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50
Failu
re p
roba
bilit
y
# element
MC
RSM
EDW
Very good agreement between MC and RSM/MC.EDW is less accurate. (Correlation was not considered)
Failure Probability (IFF): Section 9.2mFailure Probability (IFF): Section 9.2m
[90][90]
[90]
[90][90]
[90]
[90]
[45] [45] [45]
[45]
[45]
[45]
[45]
[-45]
[-45][45]
[45][-45]
[-45]
[-45]
[90][90]
[90][90][90][90][90]
[90]
[90]
[90]
[90][90]
[90]
[90]
[90]
[45]
[-45]
[90]
[45]
Layer #
1
6
1220
26
32
40
41
44
45
48
Element #
Brussels, 14-17 March 2011
Failure Probability (IFF): Section 9.2mFailure Probability (IFF): Section 9.2m
[90][90]
[90]
[90][90]
[90]
[90]
[45] [45] [45]
[45]
[45]
[45]
[45]
[-45]
[-45][45]
[45][-45]
[-45]
[-45]
[90][90]
[90][90][90][90][90]
[90]
[90]
[90]
[90][90]
[90]
[90]
[90]
[45]
[-45]
[90]
[45]
Layer #
1
6
1220
26
32
40
41
44
45
48
Element #
Reliability analysis3h-MC, 30 min-RSM/MC, 10 sec-EDW
Brussels, 14-17 March 2011
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50
Failu
re p
roba
bilit
y
# element
MC
RSM
EDW
ConclusionsConclusions
• Assessment of the reliability level of a rotor blade already designed according to IEC ed. 3 at the ply level was performed
• The stochastic modeling of sectional stress resultants of the blade under extreme loading was achieved
•The probabilistic analysis was performed by using MC, RSM/MC, EDW
• A numerical tool was developed that can be combined with aero elastic codes and can be used for reliability analysis and probabilistic design
Brussels, 14-17 March 2011