The application of Eulerian laser Doppler vibrometry to the on-line condition monitoring of axial-flow turbomachinery blades

Transcription

1 UNIVERSITY OF PRETORIA The application of Eulerian laser Doppler vibrometry to the on-line condition monitoring of axial-flow turbomachinery blades by Abrie Oberholster Supervisor: Professor Stephan Heyns 01 July

2 Scope Problem statement Eulerian laser Doppler vibrometry Analytical and numerical study Experimental verification Single-blade axial-flow rotor tests Signal processing Phase angle trends Non-harmonic Fourier analysis 2

3 Scope Multi-blade rotor tests Data processing Artificial neural network implementation Conclusions Further work 3

4 Problem statement Turbomachines are critical to most industrial processes Power generation Steam turbines Forced and induced draft fans Air Cooled Condenser (ACC) fans Blade health is of the utmost importance Frequent off-line inspection of blades not possible Online condition monitoring 4

5 On-line blade vibration measurement approaches Contact techniques Strain gauge measurements Good quality data (high SNRs) High frequency resolution Limited sensor lifespan Non-contact techniques Blade tip Time-Of-Arrival Infer blade vibration behaviour from pulses Requires large amount of sensors for useful bandwidth Blade tip sensors Once per revolution sensor 5

6 On-line blade vibration measurement approaches Non-contact techniques (continued) Laser Doppler vibrometry Large stand-off distance (up to 100m) Large measurement bandwidth (0 to 24 MHz) Large dynamic range (50 nm/s to 30 m/s) Direct blade vibration measurement Circumferential or axial Fixed (Eulerian) or moving (Lagrangian) reference frame 6

7 Laser Doppler Vibrometry: Measurement principle Scan mirrors He-Ne laser Detector Bragg cell Target 7

8 Measurement approaches Lagrangian Moving reference frame Tracking laser vibrometry Scanning laser vibrometer Mirrors controlled to follow specific point on blade Not industrially feasible Eulerian Fixed reference frame Laser beam is focussed at fixed spatial point Blades sweep through laser beam Very short signals (max. 1/BPF) Speckle noise 8

9 Eulerian Laser Doppler Vibrometry (ELDV): Analytical study Stationary LDV Moving cantilever beam Euler-Bernoulli formulation: Lagrangian x L x E F LDV v L ( x, t) L = w L ( x, t) t L = j= 1 W j ( x ) L dq j dt ( t) c Chassis Exciter Eulerian x E = ct v E d dt ( c, t) W ( ct ) q () t = j= 1 j j for 0 t l c Amplitude modulation ODS via demodulation 9

10 ELDV numerical simulation c Select and f s Consider Lagrangian vibration responses at N = L c Δt equispaced measurement positions over the entire beam length: L { x x..., x x } x =, L1, L2, L 1 ( N ) ( ) LN at N discrete time instants: { t t..., } T = 1, 2, t N 1, t N c Obtain ELDV for by incrementing the measurement position with each time step 10

11 ELDV numerical simulation L = mm c = m/s f s = 20 khz N = 48 11

12 ELDV numerical simulation Lagrangian Vibration Response Matrix k =1 12

13 ELDV numerical simulation Lagrangian Vibration Response Matrix k k =1 = 2 13

14 ELDV numerical simulation Lagrangian Vibration Response Matrix k k k =1 = 2 = 3 14

15 ELDV numerical simulation Non-integer k: Calculate new Lagrangian response matrix for each new value Computationally expensive Two dimensional interpolation Spatial & time domain Higher values of k reduces error Lagrangian matrix resolution 15

16 ELDV experimental study Cantilever beam Draw wire unit Chassis Rails VibroPet electrodynamic shaker Force transducer 16

17 ELDV experimental study c = 0.54 m/s Sinusoidal excitation ODS extraction Speckle noise White noise excitation FRF peaks visible ODS extraction 17

18 Single-blade test rotor Eliminate multi-blade phenomena Global mode shapes Mistuning Air-jet excitation Air-jet back pressure High efficiency reflective tape Nozzle Laser beam focal point Shaft encoder Simulated damage LDV 1 mm wide slot 0 mm to 16 mm Simulated damage 18

19 Single-blade rotor 720 RPM (12 Hz) ELDV 1.8 ms Δf = 540 Hz TLDV 38.1 ms Δf = 26 Hz Y X Amplitude & phase angle changes Systematic Abrupt 19

20 Non-Harmonic Fourier Analysis (NHFA) NHFA ( m, ω ) = a( ω) C( m, ω) + b( ω) S( m, ω) H y a 0 () t = + ( a cos nω t + b sin nω t) ω0 = 2π 2 n= 1 τ HFA n 0 n 0 a τ 2 τ 2 2 ( ω) = y( t) cos( ωt) dt cos ( ωt)dt τ 2 τ 2 a n = / 2 2 τ τ y τ / 2 () t cos nω t 0 dt b τ 2 τ 2 2 ( ω) = y( t) sin( ωt) dt sin ( ωt)dt τ 2 τ 2 b n = / 2 2 τ τ y τ / 2 () t sin nω t 0 dt y () t = cos( ω t +φ) a b ( ω) = cosφ ( ω) = sinφ () t = cos( kω t +φ) y 0 a b k k = cosφ = sinφ 20

21 a NHFA () t = cos[ ( ω + Δω) t + φ] y ref b 2ω ref sin ( ) ( Δωτ 2) sin( 2ωref + Δω) ω + ref ω τ + sin ωτ τ 2 cos + Δω = ref ref Δω 2ω ref 2ω ref sin ( ) ( Δωτ 2) sin( 2ωref + Δω) ω ref ω τ sin ωτ τ 2 sin + Δω = ref ref Δω 2ωref Phase shift Frequency shift Can be exploited for condition monitoring [ φ + ( ω + Δω) τ 2] [ φ + ( ω + Δω) τ 2] 21

22 Finite Element Model (FEM) Validate experimental measurements Scan curve mesh FRF-based model updating Simulated damage ELDV simulation Node resolution Damage simulation Element deletion Validation 22

23 Unwrapped Phase Angle (UPA) trends FEM frequencies [Hz] Experimental frequencies [Hz] Nozzle FRF peaks Spectral peaks Stationary modal (a) (b) (c) (d) (e) (f) (g) (h) (i) (j)

24 UPA trend sensitivity analysis Experimental: FEM: 24

25 Maximum Absolute UPA Trend (MAUPAT) 25

26 Multi-blade rotor 5-blade rotor Multi-blade phenomena Global mode shapes Erroneous damage detection Damage masking Blade mistuning Blade clamping Epoxy Clamp bolt torque Blade spacing Harmonics 26

27 Multi-blade rotor Test at various rotor speeds 720, 960, 1200, 1440 RPM Phase 1 Phase 2 Multiple blade damage scenarios Two ELDV measurement positions Forced Free 27

28 FEM Solid elements Scan node reduction FRF-based model updating Excitation 28

29 TLDV comparison 29

30 Phase and amplitude irregularities FEM TLDV RMS values Blade 1 st bending mode natural frequency Natural frequency coincides with rotor speed order RMS useful as a damage indicator 30

31 MAUPAT around f 1 31

32 σ MAUPAT around f 1 32

33 Average σ MAUPAT 33

34 Average σ MAUPAT : Multiple blade damage 34

35 Artificial Neural Network implementation Input layer (14 neurons) Output layer (1 neuron) ~ σ MAUPAT,b ~ σ A σ RMS,b σ RMS,b σ A D b σ CORR,b B 35

36 ELDV natural frequency information Run-down and run-up signatures Blade natural frequency coincides with rotor order RMS peaks 36

37 ELDV natural frequency estimation Blade # FRF frequency [Hz] Estimated frequency [Hz] % difference

38 Conclusions ELDV is a feasible on-line rotor blade condition monitoring tool NHFA provides health deterioration indicators MAUPAT RMS, Correlation coefficient Neural network implementation Multiple ELDV measurement positions are advantageous Blade natural frequencies can be estimated from rotor run-down and runup events 38

39 Further work Industrial testing Operating variables Reflectivity Increased laser beam power Safety Phased-based microwave sensors Beam dispersion (spatial averaging) Effect of actual cracks Nonlinear stiffness Rotors with high blade numbers 39

40 Acknowledgements Heavenly Father Prof. Stephan Heyns (University of Pretoria) Mark Newby (Eskom Sustainability & Innovation) Friends & family 40

41 Questions Thank you! 41