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

Transcription

1 The application of Eulerian laser Doppler vibrometry to the on-line condition monitoring of axial-flow turbomachinery blades by Abraham Johannes Oberholster Submitted in partial fulfilment of the requirements for the degree Philosophiae Doctor (Mechanical Engineering) in the Faculty of Engineering, the Built Environment and Information Technology, University of Pretoria, Pretoria 2010 Supervisor: Professor P.S. Heyns University of Pretoria

2 Summary The application of Eulerian laser Doppler vibrometry to the on-line condition monitoring of axial-flow turbomachinery blades by Abraham Johannes Oberholster Summary Supervisor: Professor P.S. Heyns University of Pretoria Department of Mechanical and Aeronautical Engineering Degree: PhD (Mechanical Engineering) The on-line condition monitoring of turbomachinery blades is of utmost importance to ensure the long term health and availability of such machines and as such has been an area of study since the late 1960s. As a result a number of on-line blade vibration measurement techniques are available, each with its own associated advantages and shortcomings. In general, on-blade sensor measurement techniques suffer from sensor lifespan, whereas non-contact techniques usually have measurement bandwidth limitations. One non-contact measurement technique that yields improvements in the area of measurement bandwidth is laser Doppler vibrometry. This thesis presents results and findings from utilizing laser Doppler vibrometry in an Eulerian fashion (i.e. a fixed reference frame) to measure on-line blade vibrations in axial-flow turbomachinery. With this measurement approach, the laser beam is focussed at a fixed point in space and measurements are available for the periods during which each blade sweeps through the beam. The characteristics of the measurement technique are studied analytically with an Euler-Bernoulli cantilever beam and experimental verification is performed. An approach for the numerical simulation of the measurement technique is then presented. Associated with the presented measurement technique are the short periods during which each blade is exposed to the laser beam. This characteristic yields traditional frequency domain signal processing techniques unsuitable for providing useful blade health indicators. To obtain frequency domain information from such short signals, it is necessary to employ non-standard signal processing techniques such as nonharmonic Fourier analysis. ii

3 Summary Results from experimental testing on a single-blade test rotor at a single rotor speed are presented in the form of phase angle trends obtained with non-harmonic Fourier analysis. Considering the maximum of absolute unwrapped phase angle trends around various reference frequencies, good indicators of blade health deterioration were obtained. These indicators were verified numerically. To extend the application of this condition monitoring approach, measurements were repeated on a five-blade test rotor at four different rotor speeds. Various damage cases were considered as well as different ELDV measurement positions. Using statistical parameters of the abovementioned indicators as well as time domain parameters, it is shown that with this condition monitoring approach, blade damage can successfully be identified and quantified with the aid of artificial neural networks. Keyterms: Laser Doppler vibrometry, Eulerian measurements, Lagrangian measurements, on-line blade vibration, condition monitoring, non-harmonic Fourier analysis, phase angle trends, finite element modelling, artificial neural networks. iii

4 Opsomming Die toepassing van Euler laser Doppler vibrometrie op die operasionele toestandsmonitering van aksiaalvloei turbomasjinerie lemme deur Abraham Johannes Oberholster Opsomming Studieleier: Professor P.S. Heyns Universiteit van Pretoria Departement Meganiese en Lugvaartkundige Ingenieurswese Graad: PhD (Meganiese Ingenieurswese) Die operasionele toestandsmonitering van turbomasjinerie lemme is van uiterste belang met betrekking tot die langtermyn integriteit en beskikbaarheid van hierdie masjiene en is n gebied wat al sedert die laat 1960 s bestudeer word. Gevolglik is daar n aantal operasionele lemvibrasie meettegnieke beskikbaar, elk met sy eie sterken swakpunte. In die algemeen word sensors wat direk op die lemme geïnstalleer word, hoofsaaklik beperk deur sensorleeftyd. Nie-kontak tegnieke aan die ander kant, het gewoonlik meetbandwydte beperkings. n Nie-kontak meettegniek wat verbeterings bied op die gebied van meetbandwydte, is laser Doppler vibrometrie. Hierdie proefskrif bied resultate en bevindings aan ten opsigte van die implementering van laser Doppler vibrometrie in n Euler verwysingsraamwerk, ten einde operasionele lemvibrasies te meet op aksiaalvloei turbomasjinerie. Met hierdie meetbenadering word die laserstraal gefokus op n vaste ruimtelike punt en is metings dan beskikbaar vir die periodes waartydens elke lem deur die laserstraal beweeg. Die eienskappe van die meettegniek word analities bestudeer met behulp van n Euler- Bernoulli kantelbalk waarna eksperimentele verifiëring uitgevoer word. n Metode om die meettegniek numeries te simuleer word dan aangebied. Gepaardgaande met hierdie meettegniek is die kort periodes waartydens elke lem blootgestel word aan die laserstraal. Tradisionele seinprosesseringstegnieke is as gevolg daarvan nie geskik om bruikbare lemtoestandsaanwysers te lewer nie. Om frekwensiedomein inligting vanaf sulke kort seine te kry, is dit nodig om van niestandaard seinprosesseringstegnieke soos nie-harmoniese Fourier analise gebruik te maak. iv

5 Opsomming Resultate vanaf eksperimentele toetse op n enkellem toetsrotor by n vaste rotorspoed word aangebied in die vorm van fasehoek grafieke wat verkry is deur nie-harmoniese Fourier analise. Deur die maksimum van die absolute van ontvoude fasehoek grafieke te evalueer, word goeie aanduiders van lemtoestandsverswakking verkry. Die resultate word numeries geverifiëer. Om hierdie toestandsmoniteringtegniek verder te verifiëer, word die metings herhaal op n vyf-lem toetsrotor teen verskillende rotasiesnelhede. Verskeie lemskade gevalle word beskou so wel as verskillende Euler meetposisies. Deur statistiese karakteristieke van die bogenoemde aanduiders asook tyddomein aanduiders te evalueer, word dit bewys dat met hierdie toestandsmoniteringtegniek lemskade suksesvol geïdentifiseer en gekwantifiseer kan word deur gebruik te maak van kunsmatige neurale netwerke. Sleutelterme: Laser Doppler vibrometrie, Euler metings, Lagrange metings, operasionele lemvibrasie, toestandsmonitering, nie-harmoniese Fourier analise, fasehoek grafieke, eindige element modellering, kunsmatige neurale netwerke. v

6 Acknowledgements Acknowledgements First and foremost, I thank God for the opportunity to have done this research. I could easily double the number of pages in this document if I had to write about all the grace and favour I received from Him during this project. I also wish to thank the following people and companies for their contributions to this project: Professor Stephan Heyns for his guidance and drive for excellence Mark Newby (Eskom Research and Innovation Division) Kobus Babst, Saluja Ramluckun and Gladman Mkwai (Eskom Kendal Power Station) Professor Schalk Els, Michael Thoresson and Burkhardt Freyer (University of Pretoria) Kris Peeraer (Polytec) Kobus van der Westhuizen (Ideas Solutions) Professor Steve Vanlanduit (Vrije Universiteit Brussel) Annamarie Bezuidenhout, Marietjie Calder (University of Pretoria) The Turbomachinery Technogroup Esteq Engineering Furthermore, I want to thank the following people for their personal support: My lovely wife, Karin Oberholster My parents, Jan and Magdaleen Oberholster Mark and Christina Burger Clive and Wendy Willoughby Werner and Cindy Steyn Dr. Amanda Kotze-Streicher Caryn Seago All my other friends at Harvest Church International The fear of the LORD is the beginning of knowledge (Proverbs 1:7) vi

7 Table of contents Table of contents Summary...ii Opsomming...iv Acknowledgements...vi Table of contents...vii Glossary...xi Abbreviations...xi Symbols...xii Greek symbols...xv Chapter 1 Introduction and Literature Study Introduction Blade vibration Operational blade excitation Rotational effects Blade manufacturing tolerances Blade roots Mistuning Blade damage and failure modes Fatigue Stress-corrosion Foreign object damage Flutter Transient load events Blade health indicators Natural frequencies Damping Amplitude Phase angle Operational modal analysis Blade vibration measurement techniques Strain gauges Blade tip TOA Probe Types Aliasing Probe configuration Assumptions Signal processing...16 vii

8 Table of contents Pressure signals Shaft torsional vibration measurements Audio signals Fibre Bragg Grating sensors Interferometry Laser Doppler velocimetry Laser Doppler Vibrometry Eulerian Laser Doppler Vibrometry Lagrangian Laser Doppler Vibrometry Tracking Laser Doppler Vibrometry Continuous Scanning Laser Doppler Vibrometry Radar proximity sensors Blade vibration measurement systems Available systems Shortcomings of available systems Experimental related issues Non-contact blade excitation techniques Finite element modelling Model updating based on Frequency Response Functions Issues with regards to Laser Doppler Vibrometry Speckle noise The nature of speckle noise Noise cancellation Effect of geometry on measurements Practical issues Signal processing Scope of research Document layout Publications...34 Chapter 2 Eulerian Laser Doppler Vibrometry Introduction Analytical and numerical study Cantilever beam theory ELDV analytical formulation Numerical simulation of ELDV Effect of scanning speed Modulation frequency Frequency resolution...46 viii

9 Table of contents Condition monitoring feasibility study Experimental study of ELDV Discrete frequency excitation White noise excitation ELDV on rotating axial-flow blades Rotor-circumferential ELDV Rotor-axial ELDV Conclusions...56 Chapter 3 Rotor-axial Eulerian Laser Doppler Vibrometry applied to a single-blade axial-flow test rotor Introduction Experimental setup Measurement and control Laser alignment Experimental measurements Finite element model Phase angle as a damage indicator Non-Harmonic Fourier Analysis Signal shift detection using NHFA Sensitivity analysis Damping Results comparison Experimental measurement uncertainty Conclusions...86 Chapter 4 Rotor-axial Eulerian laser Doppler vibrometry applied to a five-blade axialflow test rotor Introduction Test setup Test control and measurement FEM Model updating TLDV simulation Experimental results MAUPAT analysis Time domain analysis ANN implementation Natural frequency estimation Measurement uncertainty sensitivity analysis ix

10 Table of contents MAUPAT results Time domain results Discussion Conclusions Chapter 5 Conclusions and further work Conclusions Further work References Appendix A Rotor-Circumferential ELDV A.1 Introduction A.2 RC ELDV mathematical definition A.2.1 Vector-loop equations A.2.2 Rigid Body Velocity Component A.2.3 The influence of BLEP variance from the MBLEC A.3 Experimental verification A.4 Response matrix interpolation for non-constant scanning speeds A.5 Conclusions x

11 Glossary Glossary Abbreviations Abbreviation AC ADC AIC ANN AR ARMA BLEP BPF CLSF-IO CSLDV DC DEN ELDV ESPI EV EVR FBG FEM FFT FOD FPE FRF HCF HFA HI HP INVE LCF LDV Description Alternating Current Analogue to Digital Converter Akaike Information Criterion Artificial Neural Network Autoregressive Autoregressive Moving Average Blade Leading Edge Profile Blade Pass Frequency Combined Non-Linear Least Squares Frequency Method On Input Output Spectra Continuous Scanning Laser Doppler Vibrometry Direct Current Denominator Eulerian Laser Doppler Vibrometry Electronic Speckle Pattern Interferometry Eigenvector Eulerian Vibration Response Fibre Bragg Grating Finite Element Model Fast Fourier Transform Foreign Object Damage Final Prediction Error Frequency Response Function High Cycle Fatigue Harmonic Fourier Analysis Holographic Interferometry High Pressure Iterative Noise Variance Estimation Low Cycle Fatigue Laser Doppler Vibrometer / Vibrometry xi

12 Glossary LP LVR LVRM MAUPAT MBLEC MDL MPC MUSIC MW mw NExT NHFA NOM ODS PI PPCRE PPR PSD RBVC RC RMS RPM SCC SLDV SNR TLDV TOA UPA VI Symbols Symbol A a Low Pressure Lagrangian Vibration Response Lagrangian Vibration Response Matrix Maximum Absolute Unwrapped Phase Angle Trend Mean Blade Leading Edge Curve Minimum Description Length Multi-Point Constraint Multiple Signal Classification Megawatt milliwatt Natural Excitation Technique Non-Harmonic Fourier Analysis Nominator Operational Deflection Shape Proportional-Integral Predicted Percent Reconstruction Error Pulses-Per-Revolution Power Spectral Density Rigid Body Velocity Component Rotor Circumferential Root-Mean-Square Revolutions Per Minute Stress Corrosion Cracking Scanning Laser Doppler Vibrometer / Vibrometry Signal to Noise Ratio Tracking Laser Doppler Vibrometry Time-Of-Arrival Unwrapped Phase Angle Virtual Instrument Description ELDV measurement position Fourier cosine coefficient xii

13 Glossary B b C c ELDV measurement position Blade number Cosine operator Scanning speed c ref Reference scanning speed c max Maximum scanning speed D b d E j F F b f Blade-specific damage level [mm] Fourier sine coefficient j th modal constant Force Simulated blade force Frequency f actual Actual frequency f aliased Aliased frequency f NQ Nyquist frequency f R f s MAUPAT reference frequency Sampling frequency Δ f min Minimum required ELDV frequency resolution Δ f G g H h J j k l m N N k Frequency resolution NHFA signal approximation Probe group size Mobility FRF amplitude Vector-loop diagram vector number ELDV RMS run-down peak number Mode / natural frequency number Scanning speed ratio Cantilever beam length Harmonic number Sample length Interpolation sample length xiii

14 Glossary N ref Reference sample length n P b Sample number Average nozzle back-pressure waveform q j j th generalized modal coordinate R 1 R 2 R 3 R 4 R 5 R h R h r S t t 0 MBLEC offset vector Relative MBLEC measurement position vector Laser orientation vector Laser offset vector Absolute MBLEC measurement position vector Vector-loop diagram vector R h amplitude Angular ELDV measurement radius Sine operator Time Zero-based time vector t N Sample time span Δ t ˆ LVRM V L, c ref VL, ψ ref Time increment ˆ Angular LVRM v E v E v L v L Eulerian vibration velocity EVR vector Lagrangian vibration velocity LVR vector v RB RBVC W j w E w L X j th characteristic function Eulerian vibration displacement Lagrangian vibration displacement X-axis xiv

15 Glossary x E x L Δ x Y y Z Eulerian measurement position Lagrangian measurement position Measurement position increment Y-Axis Time signal Z-axis Greek symbols Symbol β j δ ε Φ φ φ d η h ϑ ϕ E ϕ L μ b θ σ Description j th modal root ε offset Rotor order vector NHFA detected phase angle Phase angle Damped phase angle R h angle Angular measurement range Eulerian angular measurement position Lagrangian angular measurement position Pressure waveform normalization constant Rotor angle Standard deviation σ CORR Correlation coefficient standard deviation σ MAUPAT MAUPAT standard deviation σ RMS RMS standard deviation ~ σ MAUPAT Mean MAUPAT standard deviation τ ϖ ϖ 0 Total signal time span Arbitrary frequency Signal fundamental frequency ϖ ref NHFA reference frequency Δ ϖ Frequency offset xv

16 Glossary Ω j ω ω d ω j ω 1 j th modulation frequency ω 1 estimate vector Damped natural frequency j th natural frequency Blade first bending mode frequency ω 1,est ω 1 estimate Ψ ψ Rotation speed vector Rotor speed ψ ref Reference rotor speed ζ Structural damping coefficient xvi