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Emilio Di Lorenzo – Research engineer – Siemens Industry Software nv
PhD candidate at KU Leuven and University of Naples "...
Agenda
1. Introduction
2. Rotor analysis
1. MBC transformation
2. HPS method
3. Validation cases
4. Conclusions
3. Gearbox...
Gearbox analysis
 Development and validation of a methodology for modal analysis of a gearbox in operational
conditions (...
Analysis techniques in operating conditions
OMA OBMAODS
• Peak picking:
• Deformation at a chosen
frequency line
• No damp...
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
0.0...
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:measuredtracki...
Order Based Modal Analysis
)cos()( 0
2
0 ϕ+ωω= trmtfx
)sin()( 0
2
0 ϕ+ωω= trmtfy
)(tfx
)(tfy
)(ty
output 2 (correlated) in...
Order Based Modal Analysis
)cos()( 0
2
0 ϕ+ωω= trmtfx
)sin()( 0
2
0 ϕ+ωω= trmtfy
)(tfx
)(tfy
)(ty
output 2 (correlated) in...
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
118...
Order tracking techniques
 Time domain sampling based Fast Fourier Transform order tracking
 Based upon the standard FFT...
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 ∗ ∆...
Vold-Kalman filter based order tracking
 Any drawback?
 It is not suitable for real time processing because of the long ...
Test cases
Test rig Wind turbine gearbox8 DOF system
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 (sha...
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-b...
Modal analysis on operational wind turbine gearbox
Crosspower for classical OMA analysis Orders 27 extracted for OBMA anal...
Modal analysis on operational wind turbine gearbox
50 Hz component disturbance
End of order spurious peaks
Standard Operat...
Order Based – comparison of new Order Tracking
TVDFT
Vold-Kalman filter
• 1 parameter (number of rotation
per order line)
...
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...
Order tracking techniques for OBMA processing
Gearbox modal parameters
OBMA + TVDFT
Frequency [Hz] Damping [%]
[100-110] 0...
Conclusions
 A methodology for extending the use of Operational Modal Analysis (OMA) to rotating
machineries has been pro...
Emilio Di Lorenzo – Research engineer – Siemens Industry Software nv
PhD candidate at KU Leuven and University of Naples "...
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2015 12-02-opti wind-dynamic-characterisation-gearboxes-siemens

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

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2015 12-02-opti wind-dynamic-characterisation-gearboxes-siemens

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 13. Test cases Test rig Wind turbine gearbox8 DOF system
  14. 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. 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. 16. Modal analysis on operational wind turbine gearbox Crosspower for classical OMA analysis Orders 27 extracted for OBMA analysis Frequency [Hz] Time [s]
  17. 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. 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. 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. 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. 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. 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!

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