fatigue life prediction of steam turbine blades during start-up
TRANSCRIPT
Presenter: C Booysen
Academic Mentor: Prof P.S Heyns
Date: 2014/07/25
Fatigue Life Prediction of Steam Turbine Blades during Start-up
Operation Using Probabilistic Concepts
Eskom Power Plant Engineering Institute 2
Outline
• Problem statement
• Fatigue life modelling flow chart
• Experimental material characterisation
• Finite element modelling and analysis
• Probabilistic fatigue life modelling
• Conclusion
• Acknowledgements
University of Pretoria
Eskom Power Plant Engineering Institute 3
Problem statement
• Fatigue in LP turbine blades has been recognised to be one of the primary causes of steam turbine blade failures worldwide
• During start-up operation, blades experience vibration and resonances at critical speeds which produce high dynamics stresses resulting in high cycle fatigue damage.
• Life assessment and prevention of fatigue failures requires the development of a fatigue life model
• Probabilistic model eliminates overly conservative assumptions and allows for uncertainty in key variables to be accounted
University of Pretoria
Fatigue cracking
Fatigue failure
Eskom Power Plant Engineering Institute 4
Fatigue life modelling flow chart
University of Pretoria
Finite element
modelling
and
analysis
Telemetry
testing
Experimental
material
characterisation
Fatigue life
analysis
Eskom Power Plant Engineering Institute 5
Experimental materials characterisation
University of Pretoria
Tensile test specimen
• Material properties required as inputs for the finite element and fatigue life prediction models
• 12% chromium martensitic stainless steel X22CrMoV12-1
Fatigue specimen MTS fatigue test equipment
• Prior to fatigue testing, tensile testing to determine monotonic properties
• Load controlled uniaxial fatigue testing
• Fatigue cycles tested were fully reversed tension-compression and tension-tension with a mean stress
Eskom Power Plant Engineering Institute 6
Experimental materials characterisation
University of Pretoria
• Statistical modelling using linear regression analysis
• Goodness of fit revealed high coefficient of determination, R2
• Sample run-outs not considered
103
104
105
106
100
200
300
400
500
600
Cycles to Failure, Nf [Cycles]
Str
ess A
mplitu
de,
a [
MP
a]
S-N Curve Fitted for Stress Ratio R=0.1
R=0.1
S-N Curve Fit
102
103
104
105
106
200
400
600
800
1000
1200
Cycles to Failure, Nf [Cycles]
Str
ess A
mplitu
de,
a [
MP
a]
S-N Curve Fitted for Stress Ratio R=-1
R=-1
S-N Curve Fit
R2 = 96.14% R2 = 80.32%
Eskom Power Plant Engineering Institute 7
Finite element modelling and analysis
University of Pretoria
• Geometrical scanning to determine the blade topology
• Free-standing last stage LP blade
• Cyclic symmetric model based on principal of sub-structuring
• Higher order 3D 20-node solid elements
• 225009 nodes and 74891 elements
• Surface-to-surface contact
Eskom Power Plant Engineering Institute 8
Finite element modelling and analysis
University of Pretoria
• Modal analysis to characterise blade natural frequencies and mode shapes
• Pre-stressed mode
• Campbell diagram identified potential resonance
• FEM validated against full scale spin test data on LP rotor and OEM results
0 500 1000 1500 2000 2500 30000
50
100
150
200
250
300
350
Rotor Speed, Ns [RPM]
Fre
quency,
f [H
z]
Calculated versus Measured Campbell Diagram
Fn1(FEA)
Fn2(FEA)
Fn3(FEA)
Fn1(OEM)
Fn2(OEM)
Fn1(Meas)
Fn2(Meas)
Fn3(Meas)
Potential resonance
1st Mode stress distribution
Peak stress location
Eskom Power Plant Engineering Institute 9
Finite element modelling and analysis
University of Pretoria
• Transient stress response assessed at resonance for twenty-four variations in blade damping
• A pressure excitation was formulated through approximations from the static steam forces during a turbine start-up
2 4 6 8-300
-200
-100
0
100
200
300
Time, t [s]
Norm
al S
tress,
y [
MP
a]
2 4 6 8-300
-200
-100
0
100
200
300
Time, t [s]
Norm
al S
tress,
y [
MP
a]
2 4 6 8-200
-100
0
100
200
Time, t [s]
Norm
al S
tress,
y [
MP
a]
2 4 6 8-200
-100
0
100
200
Time, t [s]
Norm
al S
tress,
y [
MP
a]
=0.1% =0.2%
=0.3% =0.57%
Max stress at first serration
coincident with crack origin
Eskom Power Plant Engineering Institute 10
Probabilistic fatigue life modelling
University of Pretoria
• Uncertainty and variability in the material fatigue strength parameters and the stochastic nature of the transient stress in the blade root due to variability in blade damping is investigated by random variable simulations using a statistical analysis algorithm written in MATLAB.
• Random curve fitting routines were used to ensure the selection of the random variables used in fatigue life calculations is stochastic in nature
• Random vectors are then chosen from a multivariate normal distribution with mean 𝜇 and covariance Σ to create multivariate normal random curves based on the fitted data
50 100 150 200 250 30040
50
60
70
80
90
100
110
Peak Stress, peak
[MPa]
No.
of
Cycle
s,
n calc
[C
ycle
s]
Data
Median fit
multivariate normal random curve
95% confidence bounds
2 2.5 3 3.5 4 4.5 5 5.5 62.55
2.6
2.65
2.7
2.75
2.8
2.85
2.9
2.95
Log Stress Amplitude, log a [MPa]
Log C
ycle
s t
o f
ailure
, lo
g N
f [C
ycle
s]
Data
Median fit
multivariate normal random curve
95% confidence bounds
Eskom Power Plant Engineering Institute 11
Probabilistic fatigue life modelling
University of Pretoria
• Results represent the number of repetitions, which for this case is turbine start-ups, required to initiate a fatigue crack which was defined as the failure point.
• Fatigue repetitions shown to follow a straight line indicating normality in the data.
7.9 7.95 8 8.05 8.1 8.15 8.2
x 105
0.00050.001
0.0050.01
0.05
0.1
0.25
0.5
0.75
0.9
0.95
0.990.995
0.9990.9995
Fatigue Damage Repetitions, Bf [Cycles]
Pro
babili
ty
Damage Data
Normal Distribution Fit
7.9 7.95 8 8.05 8.1 8.15 8.2
x 105
0
0.2
0.4
0.6
0.8
1
1.2x 10
-4
Fatigue Damage Repetitions, Bf [Cycles]
Density
Damage data
Normal Distribution Fit
Eskom Power Plant Engineering Institute 12
Conclusion
University of Pretoria
• The probabilistic fatigue life model was successfully implemented to
determine the fatigue life of a blade during a turbine start-up.
• The method is shown to adequately quantify variability in material strength parameters and varying root stress
• High dynamic stresses associated to low levels of damping had a low probability of occurrence however in the event they occurred they were shown to have a significant impact on the overall fatigue life
• The probabilistic results findings reinforced those of the discrete life model but showed that the discrete life solution to be more conservative in predicting the life of the blade.
Eskom Power Plant Engineering Institute 13
Acknowledgements
University of Pretoria
Thanks to the following people for their time and expertise:
• Prof. Stephan Heyns – Academic mentorship
• Mr Ronnie Scheepers – Industrial mentorship
• Mr Michael Hindley – Industrial mentorship
• Mr Jacques Calitz – Industrial mentorship
Eskom Power Plant Engineering Institute 14
University of Pretoria
Thank you for your time!