Dynamic characterization of wind turbine gearboxes by using operational measurements (Emilio Di Lorenzo/Simone Manzato, Siemens)

1. Emilio Di Lorenzo – Research engineer – Siemens Industry Software nv
PhD candidate at KU Leuven and University of Naples "Federico II"
emilio.dilorenzo@siemens.com
DYNAMIC CHARACTERIZATION OF WIND TURBINE
GEARBOXES BY USING OPERATIONAL MEASUREMENTS
Optiwind Open Project Meeting, Leuven, Belgium 02/12/2015
E. Di Lorenzo, S. Manzato

2. Agenda
1. Introduction
2. Rotor analysis
1. MBC transformation
2. HPS method
3. Validation cases
4. Conclusions
3. Gearbox analysis
1. Operational Modal Analysis
2. Order-Based Modal Analysis
3. Validation cases
4. Conclusions

3. Gearbox analysis
 Development and validation of a methodology for modal analysis of a gearbox in operational
conditions (test rig)
 Building further on existing “Order Tracking” and “Operational Modal Analysis” techniques, a
new method need to be developed
 The developed algorithms will be evaluated by means of numerical simulations (flexible MBS
model) and real experimental data (test rig measurement)

4. Analysis techniques in operating conditions
OMA OBMAODS
• Peak picking:
• Deformation at a chosen
frequency line
• No damping information
• Combination of modes
and forced responses
• Combination of closely
spaced modes
• Phenomena observation
only
• Auto & Cross Powers
• Modal model:
• Natural frequency
• Damping
• Mode shapes
• Structural characteristics
• Separation of closely
spaced modes
• End-of-order related
peaks in the spectrum
• Root causes
• Orders
• Modal model:
• Natural frequency
• Damping
• Mode shapes
• Combines advanced
Order Tracking techniques
with OMA
• Only identifies physical
poles of the system
• Root causes

5. Operational Modal Analysis
Run-up time data Auto and cross- powers
290.000.00 s
1.00
0.00
Amplitude
760.000.00 Hz
1.00
0.00
Amplitude
F AutoPow er Point8:+X
Operational PolymaxModal parameters
f o f v s f v o v v
v v d v s f v s
v v f o s s v o s s
v v f v v v f s s
v v f v v v f o v v
v s d v v f v v v
f d f o v d s o v v
d d f v d v o v v s
o s d v v o f v v v f o
f s v s v v d v v o v s
f v f v v v f s v v s o
o v s f d v d s s s s f
v s s d f s o s v v v s f
v o v v d v v v v s v o v s f
f v v f d v v s v s o v v s f
v v s s s s o s d s s v v s f o s f
s s s s d s v v d s s v v s f s s
f v o o v f o d s v v f s s f v vf v f
f o v v v o f f s v v f v v f v vv v f
v v v v v v d f s s v d s v f s sf v f
f v v o v f f s v v f s v f v v f o v f f
s v v s v v v s s v f s v f v sv f v f f
v s o s s v o v s s v f s v f v vv f s ff
v s f s v s v d s s v s s s d s s f v v sd
f s f v v f v v s v v s s s v s v f s v vf
v v f s v o d o f v v v s s s v v v f f v f
v v f v v v f f f s v v d s s f v v f f s f f
v s f s s v v d s s v s d s s s s s f f s vf
o f v f s v o v f v s v v o d v s f v s v v v v
v s v d v v v v f o d v v v v s s v s v f s f
v s s d s s v v s f s s s s s s s v s s v s s
v s v s s s s v d v v s s v s s s f s s s s f
v s o v s s s s s s f d s s s o d s s f s s s s d
f v v d s s s v s v d v s v s s s f s s s s v
v s o v d v o s v v f v f s s v o d s s f s v v s f
v v v v f o s f s v v o d f f v v v v f s v f v s f s f
s v f s f v v v s v s f s s v s s v v s s s v s s v v d
v s d s d f s f s v v f s v v v v s v s s o v f s s o v s f
s s v s s v s f s v s v s s s s s s s d s v s s s s v v s d
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6Natural
Frequency
[Hz]
[50-70]
[60-80]
[120-140]
Damping
[%]
[0,2-0,4]
[0,5-0,7]
[0,01-0.15]

6. End-of-order effect
100.00 600.00Hz
40.00
60.00
dB
(Pa)
2
200150
100.00 600.00Hz
1200.00
6000.00
rpm
Z-Axis:measuredtracking
20.00
80.00
dB
Pa2
200150
 end-of-order related peaks at 150 Hz (order 1.5 at 6000 rpm) and 200 Hz (order
2 at 6000 rpm) are identified as physical poles of the system
Order 1.5
Order 2
end-of-order
peak
end-of-order
peak
K. Janssens et al. – Order-based resonance
identification using Operational PolyMAX

7. Order Based Modal Analysis
)cos()( 0
2
0 ϕ+ωω= trmtfx
)sin()( 0
2
0 ϕ+ωω= trmtfy
)(tfx
)(tfy
)(ty
output 2 (correlated) inputs
m
ω0
r
)()()()()( )(:,)(:, ωω+ωω=ω yfyxfx FHFHY
( ) )()()()( 0)(:,)(:,
2
0 ω−ωδω−ωω∝ω fyfx jHHY
 Technique to identify modal
parameters from operational
data during a run-up/run-down
 Hypothesis:
the measured response is
mainly caused by rotational
excitation
 The structure is excited by a
rotating mass with increasing
frequency

8. Order Based Modal Analysis
)cos()( 0
2
0 ϕ+ωω= trmtfx
)sin()( 0
2
0 ϕ+ωω= trmtfy
)(tfx
)(tfy
)(ty
output 2 (correlated) inputs
m
ω0
r
Applications
Jet engine
Rotor blade stability
Turbine
Rotating machinery

9. Order Based Modal Analysis
310.000.00 s
1700.00
100.00
Amplitude
rpm
0.07
0.07
Amplitude
F 139:Tacho_P2
179.73179.24 s
1181.11
500.00
Amplitude
rpm
0.07
0.07
Amplitude
F 139:Tacho_P2
310.000.00 s
1700.00
100.00
Amplitude
rpm
0.07
0.07
Amplitude
F 139:Tacho_P2
F 139:Tacho_P2
142.21141.59 s
985.41
500.00
Amplitude
rpm
0.07
0.07
Amplitude
F 139:Tacho_P2
F 139:Tacho_P2
16.000.00 order
Point5:+X (CH5)
1600.00
200.00
rpm
Tacho_P2(T1)
-10.00
-110.00
dB
g
24.07
11.61
Spectrum Point5:+X/Point8:+X WF 700 [202.07-1599.7 rpm]
1600.00200.00 rpm
Tacho_P2 (T1)
1.00
0.00
Amplitude
F Order 11.61 Point5:+X/Point8:+
1210.20349.66 rpm
Tacho_P2 (T1)
1.00
0.00
Amplitude
F Frequency 24.07 Hz Point5:
140.9954.61 Linear
Hz
Derived Frequency
-40.50
-80.50
dB
g
s s v
v v v
s s v
s s s
s s v
s s v
s s v
s s s
s s s
s s v
v s v
s s v
s s v
s s v
s s s
s s s
s s v
s s v
s s s
s s s
s s v
s s s
s s s
s s v
s s v
s s v
s s s
s s v
s s s
s s s
s s s
s s s
s s s
s s s
s s s
s s v
s s v
s s s
s s s
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
Tacho signal Butt-joint correction Order Tracking (OT) technique
Order-based Polymax
Modal parameters
Natural
Frequency
[Hz]
[50-70]
[60-80]
[120-140]
Damping
[%]
[0,2-0,4]
[0,5-0,7]
[0,01-0.15]

10. Order tracking techniques
 Time domain sampling based Fast Fourier Transform order tracking
 Based upon the standard FFT analysis
 Requires time domain data sampled with a constant Δt
 FFT kernel is based on constant frequency sines/cosines
 Angle domain computed order tracking
 Resamples constant Δt sampled data to constant angular intervals
 The angle domain data is processed through the use of FFTs
 Accurate tachometer signal is needed
𝑎 𝑛 =
1
𝑁
� 𝑥(𝑛∆𝑡) cos(2𝜋𝑓𝑛 𝑛∆𝑡)
𝑁
𝑛=1
𝑏 𝑛 =
1
𝑁
� 𝑥(𝑛∆𝑡) 𝑠𝑠𝑠(2𝜋𝑓𝑛 𝑛∆𝑡)
𝑁
𝑛=1
𝑎 𝑛 =
1
𝑁
� 𝑥(𝑛∆α) cos(2𝜋𝑜 𝑛 𝑛∆α)
𝑁
𝑛=1
𝑏 𝑛 =
1
𝑁
� 𝑥(𝑛∆α) 𝑠𝑠𝑠(2𝜋𝑜 𝑛 𝑛∆α)
𝑁
𝑛=1

11. Order tracking techniques
𝑎 𝑛 =
1
𝑁
� 𝑥(𝑛∆𝑡) cos 2𝜋 � 𝑜 𝑛 ∗ ∆𝑡 ∗
𝑟𝑟𝑟
60
𝑑𝑑
𝑛∆𝑡
0
𝑁
𝑛=1
𝑏 𝑛 =
1
𝑁
� 𝑥(𝑛∆𝑡) sin 2𝜋 � 𝑜 𝑛 ∗ ∆𝑡 ∗
𝑟𝑟𝑟
60
𝑑𝑑
𝑛∆𝑡
0
𝑁
𝑛=1
 Time Variant Discrete Fourier Transform
 Instanteneous frequency of kernel matches
frequency of order of interest
 Post-calculation to separate close/crossing orders
 Computationally efficient
 Essentially it is resampling the kernel of the Fourier
transform instead of resampling the data
 Vold-Kalman filter based order tracking
 Extracts orders time histories
 Computationally demanding
 Able to separate close/crossing orders �
1 −𝑐(𝑛) 1
0 0 𝑟(𝑛)
�
𝑥(𝑛 − 2)
𝑥(𝑛 − 1)
𝑥(𝑛)
=
𝜀(𝑛)
𝑟(𝑛)(𝑦 𝑛 − 𝜂(𝑛))

12. Vold-Kalman filter based order tracking
 Any drawback?
 It is not suitable for real time processing because of the long computational
time
 Some math!!!
 Structural equation
 Data equation 𝑦 𝑛 = 𝑥(𝑛)𝑒 𝑗Θ(𝑛)
+ 𝜂(𝑛)
𝑥 𝑛 − 2𝑥(𝑛 + 1) + 𝑥(𝑛 + 2) = 𝜀(𝑛)
Filtered signal = Complex envelope
Measured data
Instantaneous frequency of the sine wave
Noise components
Data equation
describes the
relationship between
the measured data y(n)
and the complex
envelope x(n)
Θ 𝑛 = � 𝜔(𝑖)∆𝑡
𝑛
𝑖=0 Locally, the complex
envelope x(n) is
approximated by a low
order polynomial. The
polynomial order
designates the number
of filter poles (i.e: 2).

13. Test cases
Test rig Wind turbine gearbox8 DOF system

14. Test-rig configuration
Proto Version Ratio
P2 3.0 MW 50 Hz 106.5
P3 3.2 MW 50 Hz 99.5
Step Load Speed
1 0% Standstill (shaker)
2 33% run up, 200-1500 rpm (5 rpm/s)
3 33% constant speed, 1200 rpm
4 33% constant speed, 800 rpm
5 66% run up, 200-1500 rpm (5 rpm/s)
6 66% constant speed, 1200 rpm
7 66% constant speed, 800 rpm
8 100% run up, 200-1500 rpm (5 rpm/s)
9 100% constant speed, 1200 rpm
10 100% constant speed, 800 rpm
P2
P3
Component No. of
measurement
locations
Tested gearbox (gearbox 1)
P3 202
Counter gearbox (gearbox 2)
P2 27
Test rig
Cassette + Motors CASS 27
Total: 256

15. 750.000.00 Hz
-40.00
-90.00
dB
g
2
1.00
0.00
Amplitude
F CrossPow er BH:5:+X/Point8:+X
1
2
3
OBMA processing: Why?
Order-based Modal Analysis
 End-of-order related peaks identified as physical
poles of the system using classical OMA technique:
Frequency
no.
Rpm (P3) Order (P3) Order (P2)
1 1500 8,52 8
2 1500 12,4 11,6
3 1500 27 25,4
Order 8,52 = 8th order counter gearbox
Order 12,4 = 2nd gear mesh (Intermediate Speed Stage)
Order 27 = 1st gear mesh (High Speed Stage)

16. Modal analysis on operational wind turbine gearbox
Crosspower for classical OMA analysis Orders 27 extracted for OBMA analysis
Frequency [Hz]
Time [s]

17. Modal analysis on operational wind turbine gearbox
50 Hz component disturbance
End of order spurious peaks
Standard Operational Modal Analysis
Low quality and low confidence
estimated Modal Model due to end-of
order peaks and harmonic
disturbances

18. Order Based – comparison of new Order Tracking
TVDFT
Vold-Kalman filter
• 1 parameter (number of rotation
per order line)
• Non equidistant order lines
• Low resolution at low frequency
• Phase smoothness depends
strongly on the number of rotation
per order line
• Difficult to fit higher frequency
• 2 parameter (filter selectivity and
number of poles in the filter)
• Very high order resolution (number
of lines equal to the number of
acquired samples)
• Very good quality of the fit
• Non equidistant order lines
• Computationally demanding

19. OMA vs OBMA
Gearbox modal parameters
OMA
Frequency [Hz] Damping [%]
[15-25] 0,26
[45-55] 1,20
[95-105] 1,56
[145-155] 0,49
[180-190] 2,80
[210-220] 1,16
[245-255] 0,35
[300-310] 0,19
[365-375] 0,24
[460-470] 1,14
[510-520] 1,73
[550-560] 1,28
[580-590] 0,61
[610-620] 0,93
[640-650] 0,54
Gearbox modal parameters
OBMA + VK
Frequency [Hz] Damping [%]
[100-110] 1,97
[180-190] 2,10
[200-210] 1,60
[220-230] 3,33
[245-255] 0,37
[270-280] 1,21
[295-305] 1,39
[320-330] 0,67
[360-370] 2,21
[400-410] 2,00
[450-460] 1,45
[460-470] 1,98
[510-520] 2,39
[530-540] 1,91
[550-560] 2,29
[580-590] 1,68
[610-620] 1,26
[640-650] 1,02
End-of-Order related poles

20. Order tracking techniques for OBMA processing
Gearbox modal parameters
OBMA + TVDFT
Frequency [Hz] Damping [%]
[100-110] 0,66
[140-150] 0,19
[180-190] 1,55
[200-210] 1,46
[220-230] 2,34
[360-370] 1,16
[400-410] 0,71
[460-470] 0,21
[510-520] 0,21
[640-650] 0,10
Gearbox modal parameters
OBMA + VK
Frequency [Hz] Damping [%]
[100-110] 1,97
[180-190] 2,10
[200-210] 1,60
[220-230] 3,33
[245-255] 0,37
[270-280] 1,21
[295-305] 1,39
[320-330] 0,67
[360-370] 2,21
[400-410] 2,00
[450-460] 1,45
[460-470] 1,98
[510-520] 2,39
[530-540] 1,91
[550-560] 2,29
[580-590] 1,68
[610-620] 1,26
[640-650] 1,02

21. Conclusions
 A methodology for extending the use of Operational Modal Analysis (OMA) to rotating
machineries has been proposed as a combination of Order Tracking (OT) and OMA
techniques
 Different OT technique have been applied to several test cases both in a simulation and a
test environment
FUTURE DIRECTIONS
• Order-Based Modal Analysis will be applied in the automotive and railway domain
• Some more OT techniques based on the wavelet transform will be analyzed in order to
improve the accuracy of the results

22. Emilio Di Lorenzo – Research engineer – Siemens Industry Software nv
PhD candidate at KU Leuven and University of Naples "Federico II"
emilio.dilorenzo@siemens.com
Thank you!