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

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

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)

Analysis techniques in operating conditions

OMA OBMA ODS

• 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

Operational Modal Analysis

Run-up time data Auto and cross- powers

290.000.00 s

1.00

0.00Am

plitu

de

760.000.00 Hz

1.00

0.00

Ampl

itude

F AutoPow er Point8:+X

Operational Polymax Modal parameters

f o f v s f v o v vv v d v s f v sv v f o s s v o s sv v f v v v f s sv v f v v v f o v vv s d v v f v v v

f d f o v d s o v vd d f v d v o v v s

o s d v v o f v v v f of s v s v v d v v o v sf v f v v v f s v v s o

o v s f d v d s s s s fv s s d f s o s v v v s fv o v v d v v v v s v o v s ff v v f d v v s v s o v v s fv v s s s s o s d s s v v s f o s fs s s s d s v v d s s v v s f s sf v o o v f o d s v v f s s f v v f v ff o v v v o f f s v v f v v f v vv v fv 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 fs v v s v v v s s v f s v f v s v f v f fv s o s s v o v s s v f s v f v vv f s f fv s f s v s v d s s v s s s d s s f v v sdf s f v v f v v s v v s s s v s v f s v vfv v f s v o d o f v v v s s s v v v f f v fv v f v v v f f f s v v d s s f v v f f s f fv s f s s v v d s s v s d s s s s s f f s v f

o f v f s v o v f v s v v o d v s f v s v v v vv s v d v v v v f o d v v v v s s v s v f s fv s s d s s v v s f s s s s s s s v s s v s sv s v s s s s v d v v s s v s s s f s s s s fv s o v s s s s s s f d s s s o d s s f s s s s df v v d s s s v s v d v s v s s s f s s s s vv s o v d v o s v v f v f s s v o d s s f s v v s fv 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 fs 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 dv 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 fs 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

222222223333333333444444444455555555556Natural

Frequency [Hz]

[50-70]

[60-80]

[120-140] Damping

[%]

[0,2-0,4]

[0,5-0,7]

[0,01-0.15]

End-of-order effect

100.00 600.00 Hz40.00

60.00

dB(Pa)

2

200 150

100.00 600.00 Hz

1200.00

6000.00

rpm

Z-Ax

is: m

easu

red

track

ing

20.00

80.00

dB Pa2

200 150

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

Order Based Modal Analysis

)cos()( 020 ϕ+ωω= trmtfx

)sin()( 020 ϕ+ωω= trmtf y

)(tf x

)(tf y)(ty

output 2 (correlated) inputs m

ω0

r

)()()()()( )(:,)(:, ωω+ωω=ω yfyxfx FHFHY

( ) )()()()( 0)(:,)(:,20 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

Order Based Modal Analysis

)cos()( 020 ϕ+ωω= trmtfx

)sin()( 020 ϕ+ωω= trmtf y

)(tf x

)(tf y)(ty

output 2 (correlated) inputs m

ω0

r Applications

Jet engine

Rotor blade stability

Turbine

Rotating machinery

Order Based Modal Analysis

310.000.00 s

1700.00

100.00

Ampl

itude

rpm

0.07

0.07

Ampl

itude

F 139:Tacho_P2

179.73179.24 s

1181.11

500.00

Ampl

itude

rpm

0.07

0.07

Ampl

itude

F 139:Tacho_P2

310.000.00 s

1700.00

100.00

Ampl

itude

rpm

0.07

0.07

Ampl

itude

F 139:Tacho_P2F 139:Tacho_P2

142.21141.59 s

985.41

500.00

Ampl

itude

rpm

0.07

0.07

Ampl

itude

F 139:Tacho_P2F 139:Tacho_P2

16.000.00 orderPoint5:+X (CH5)

1600.00

200.00

rpm

Tach

o_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 rpmTacho_P2 (T1)

1.00

0.00

Ampl

itude

F Order 11.61 Point5:+X/Point8:+1210.20349.66 rpm

Tacho_P2 (T1)

1.00

0.00

Ampl

itude

F Frequency 24.07 Hz Point5:

140.9954.61 LinearHz

Derived Frequency

-40.50

-80.50

dBg

s s vv v vs s vs s ss s vs s vs s vs s ss s ss s vv s vs s vs s vs s vs s ss s ss s vs s vs s ss s ss s vs s ss s ss s vs s vs s vs s ss s vs s ss s ss s ss s ss s ss s ss s ss s vs s vs s ss s s

424344454647484950515253545556575859606162636465666768697071727374757677787980

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]

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

𝑎𝑛 = 1𝑁�𝑥(𝑛∆𝑡) cos(2𝜋𝑓𝑛𝑛∆𝑡)𝑁

𝑛=1

𝑏𝑛 = 1𝑁�𝑥(𝑛∆𝑡) 𝑠𝑠𝑛(2𝜋𝑓𝑛𝑛∆𝑡)𝑁

𝑛=1

𝑎𝑛 = 1𝑁�𝑥(𝑛∆α) cos(2𝜋𝑜𝑛𝑛∆α)𝑁

𝑛=1

𝑏𝑛 = 1𝑁�𝑥(𝑛∆α) 𝑠𝑠𝑛(2𝜋𝑜𝑛𝑛∆α)𝑁

𝑛=1

Order tracking techniques

𝑎𝑛 = 1𝑁�𝑥(𝑛∆𝑡) cos 2𝜋 � 𝑜𝑛 ∗ ∆𝑡 ∗

𝑟𝑟𝑟60

𝑑𝑡𝑛∆𝑡

0

𝑁

𝑛=1

𝑏𝑛 = 1𝑁�𝑥(𝑛∆𝑡) sin 2𝜋 � 𝑜𝑛 ∗ ∆𝑡 ∗

𝑟𝑟𝑟60

𝑑𝑡𝑛∆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) 10 0 𝑟(𝑛)�

𝑥(𝑛 − 2)𝑥(𝑛 − 1)𝑥(𝑛)

=𝜀(𝑛)

𝑟(𝑛)(𝑦 𝑛 − 𝜂(𝑛))

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)𝑒𝑗Θ(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(𝑠)∆𝑡𝑛

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).

Test cases

Test rig Wind turbine gearbox 8 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 (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

750.000.00 Hz

-40.00

-90.00

dBg2

1.00

0.00

Ampl

itude

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)

Modal analysis on operational wind turbine gearbox

Crosspower for classical OMA analysis Orders 27 extracted for OBMA analysis

Frequency [Hz]

Time [s]

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

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

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

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

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

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!