Development of Blade Tip Timing Techniques in Turbo Machinery

Development of Blade Tip Timing Techniques

in

Turbo Machinery

A thesis submitted to The University of Manchester for the degree of

Doctor of Engineering

In the Faculty of Engineering and Physical Sciences

2013

Olivier Jousselin

Rolls-Royce Plc

School of Mechanical, Aerospace and Civil Engineering

Dynamics and Aeroelasticity Research Group

Table of Contents

2

Table of Contents

Table of Contents .................................................................................................................................. 2

Abbreviations........................................................................................................................................ 7

Nomenclature ....................................................................................................................................... 9

List of Figures .......................................................................................................................................12

List of Tables ........................................................................................................................................18

Abstract ...............................................................................................................................................19

Declaration ..........................................................................................................................................20

Copyright Statement ............................................................................................................................21

Acknowledgements ..............................................................................................................................22

Chapter 1 Introduction ....................................................................................................................24

1.1 Blade Tip Timing Principles ....................................................................................................... 25

1.1.1 BTT Data Acquisition ............................................................................................................ 25

1.1.2 General Overview of BTT Data Processing ........................................................................... 27

1.2 Scope, Aim and Contributions of the Research ......................................................................... 30

1.2.1 Aim and Objectives ............................................................................................................... 31

1.2.2 Thesis Contributions to Industry and Research Impact ........................................................ 31

1.3 Thesis Contributions to Knowledge ........................................................................................... 34

1.4 Thesis Overview ........................................................................................................................ 34

Chapter 2 BTT Industry Best Practices .............................................................................................37

2.1 Current Vibration Measurement System for Rotating Components ......................................... 38

2.1.1 Strain Gauge Based Measurements ..................................................................................... 39

Table of Contents

3

2.1.2 Frequency Modulated Grid Measurements ......................................................................... 39

2.1.3 Scanning Laser Doppler Vibrometer Measurements ........................................................... 40

2.2 Blade Tip Timing Measurements .............................................................................................. 41

2.2.1 Previous BTT Data Processing Methods ............................................................................... 41

2.2.2 Current Rolls-Royce BTT Methods (due to Russhard [9]) ..................................................... 48

2.2.3 Other Proprietary BTT Systems (AEDC, Agilis, BSSM, Hood Systems) .................................. 51

2.3 Summary of Chapter 2 .............................................................................................................. 52

Chapter 3 BTT Improved Processing Methods .................................................................................54

3.1 Current Data Preparation & Processing Methods .................................................................... 54

3.1.1 Probe/Blade Data Alignment – Step 1 .................................................................................. 56

3.1.2 Conversion of TOA Data to Displacements – Step 2............................................................. 59

3.1.3 Stack Pattern Verification – Step 3 ....................................................................................... 59

3.1.4 Generation of the Blade Activity Mask– Step 4 .................................................................... 60

3.1.5 Application of the Noise Filter Removal – Step 5 ................................................................. 60

3.1.6 Removal of the Probe Steady State Offset – Step 6 ............................................................. 61

3.1.7 Russhard’s Six Step Process Summary ................................................................................. 61

3.2 New Improved Model for Single Frequency Response .............................................................. 62

3.2.1 Single Non-Integral Engine Order Response Matrix-Based Model ....................................... 63

3.2.2 Single Integral Engine Order Response Matrix-Based Model............................................... 72

3.2.3 Non-Integral / Integral Engine Order Matrix-Based Model Displacement Interface ........... 78

3.3 Multiple Simultaneous Frequency Responses ........................................................................... 81

3.3.1 Multiple Non-Integral Engine Order Responses ................................................................... 82

3.3.2 Multiple Integral Engine Order Responses ........................................................................... 84

3.3.3 Conclusions to Section 3.3.................................................................................................... 86

3.4 Quantitative and Qualitative Improvements of New Filtering Techniques ............................... 87

3.4.1 Single Non-Integral Engine Order Response Matrix-Based Model ....................................... 89

3.4.2 Single Integral Engine Order Response Matrix-Based Model............................................. 102

3.5 New Tracking Process for Extracting Blade Modal Amplitude Responses .............................. 115

3.6 Nodal Diameter Extraction Method ........................................................................................ 118

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3.7 Real-Time Analysis Improvements .......................................................................................... 123

3.8 Summary of Chapter 3 ............................................................................................................ 124

Chapter 4 Adapting BTT for Equally Probe Spacing Constraints ..................................................... 125

4.1 Processing Issues Linked To Equally Spaced Probe Configuration .......................................... 126

4.2 Virtual Probe & Engine Order Optimisation Process ............................................................... 130

4.2.1 Multiple Simultaneous Non-Integral Engine Order Virtual Matrix Model ......................... 131

4.2.2 Multiple Simultaneous Integral Engine Order Virtual Matrix Model ................................. 136

4.3 Virtual Optimisation Process - Theoretical Example ............................................................... 141

4.3.1 Step No 1 - Selection of Best Virtual Engine Order and Virtual Probe Position .................. 141

4.3.2 Step No 2 - Combined Probe Virtual and Measured Displacements .................................. 143

4.3.3 Step No 3 - Extraction of Targeted and Virtual Vibratory Information ............................... 146

4.3.4 Step No 4 - Verification and Confirmation of Assumptions ................................................ 149


Chapter 5 BTT Signal to Noise Ratio & Uncertainties ..................................................................... 154

5.1 Extraction of Residual Blade Tip Displacements ..................................................................... 155

5.1.1 Asynchronous (non-integral) residual blade tip displacements ......................................... 155

5.1.2 Extraction of the synchronous (integral) residual blade tip displacements ....................... 156

5.2 Blade Tip Timing Uncertainty Model ...................................................................................... 157

5.3 Quantification of the Systematic Measurement Error Uncertainty ........................................ 159

5.4 Quantification of the Random Measurement Error Uncertainty ............................................ 161

5.5 Verification of Noise and Uncertainty Extraction Methods .................................................... 161

5.5.1 Probe Selection .................................................................................................................. 163

5.5.2 Uncertainty Levels vs. Confidence Intervals ....................................................................... 164

5.5.3 Uncertainty Levels vs. Number of Averaging Revolutions ................................................. 169

5.5.4 Uncertainty Levels vs. Matrix Condition Numbers ............................................................. 173

5.5.5 Signal to Noise Ratio ........................................................................................................... 176


Table of Contents

5

Chapter 6 Validation of Improved BTT Capabilities........................................................................ 180

6.1 Validation for Non-Integral Engine Order Blade Tip Activities ................................................ 181

6.1.1 Single Asynchronous Compressor Blade Response ............................................................ 181

6.1.2 Multiple Asynchronous Compressor Blade Responses ...................................................... 191

6.2 Validation for Integral Engine Order Blade Tip Activities ....................................................... 197

6.2.1 Single Synchronous Compressor Blade Response .............................................................. 197

6.2.2 Validation of Equally Spaced Probe Method ...................................................................... 201

6.3 Validation for Signal to Noise Ratio and Uncertainty Measurements .................................... 207


Chapter 7 Method for Extracting BTT Axial Displacement & Untwist ............................................. 212

7.1 BTT Blade Axial Displacement ................................................................................................. 213

7.2 Turbine Blade Axial Shift & Untwist ........................................................................................ 215

7.2.1 BTT Turbine Data Blade Acquisition ................................................................................... 215

7.2.2 BTT Turbine Axial Displacement and Untwist .................................................................... 216

7.3 Conclusions of Chapter 7 ........................................................................................................ 220

Chapter 8 Commercial Aspects & Context of the Research Work .................................................. 222

8.1 Cost Reduction Benefits associated with BTT ......................................................................... 223

8.2 Rolls-Royce’s BTT Strategy ...................................................................................................... 224

Chapter 9 Conclusions & Future Work ........................................................................................... 225

9.1 Conclusions ............................................................................................................................. 225

9.2 Future Work ............................................................................................................................ 226

9.3 Closing Remarks ...................................................................................................................... 228

References ......................................................................................................................................... 229

Appendices ........................................................................................................................................ 235

Table of Contents

6

A Multiple Asynchronous Compressor Blade Response Comparative Displays .............................. 236

B Single Synchronous Compressor Blade Response Comparative Displays .................................... 240

C Multiple Synchronous Compressor Blade Response Comparative Displays ................................ 243

D SNR and Uncertainty Blade Response Comparative Displays ..................................................... 247

E BTT Test Facility Laboratory – University of Manchester ............................................................ 252

The final word count of this thesis is 37.483.

Abbreviations

7

Abbreviations

AABM Asynchronous Averaging Built-in Matrix

ABM Averaging Built-in Matrix

AATAS Agilis Arrival Time Analysis Software

ABD Acquire Blade Data

ABV Analyze Blade Vibration

ACARE Advisory Council for Aeronautics Research in Europe

AEDC Arnold Engineering Development Centre

AMS Agilis Measurement System

BA Block Average

BHM Blade Health Monitoring

BP Batch Processor

BSSM Berührungslose Schaufelschwingungsmessung

BTT Blade Tip Timing

BVM Blade Vibration Monitoring

CCACR Critical Capability Acquisition and Capability Review

CI Confidence Interval

COST Commercial Off The Shelf

CO2 Carbon Dioxide

DC Direct Current

EASA European Aviation Safety Agency

EFE Environmental Friendly Engine

EM Electromagnetic

ESP Equally Spaced Probes

FE Finite Element

FEM Finite Element Model

FFT Fast Fourier Transform

FM Frequency-Modulated

FoV Factor of Validity

FoC Factor of Conformity

GAR Global Auto-Regressive

GARIV Global Auto-Regressive with Instrumented Variables

Abbreviations

8

HCF High-Cycle-Fatigue

HP High Pressure

HPC High Pressure Compressor

HPT High Pressure Turbine

HPTB High Pressure Turbine Blade

IP Intermediate Pressure

ISA International Society of Automation

LASER Light Amplification by Stimulated Emission of Radiation

LPT Low Pressure Turbine

mm Millimetre

MTU Moturen und Turbinen Union

NI Non-Integral

NGV Nozzle Guide Vane

NOx Nitrogen Oxides

NSMS Non-intrusive Stress Measurement System

ODS Operational Deflection Shape

OPR Once-Per-Revolution

pk-pk peak-to-peak

P&W Pratt & Whitney

PSR Probe Spacing at Resonance

RPM Revolution per Minute

R&D Research & Development

R&T Research & Technology

SABM Synchronous Averaging Built-in Matrix

SVD Singular Value Decomposition

SNR Signal-to-Noise Ratio

SMA Simple Moving Average

SRA Strategic Research Agenda

TET Turbine Entry Temperature

TOA Time-Of-Arrival

TRL Technology Readiness Level

XWB eXtra Wide Body

2PP Two Parameter Plot

Nomenclature

9

Nomenclature

b Blade number relative to the blade expected to pass probe 1.

i Revolution number.

j Probe number.

Fixed number of probes chosen from the original probe configuration.

r Modal frequency response.

n Number of probes in the original probe configuration.

Number of blades on the rotor.

q Probe no from the best permuted probe selection.

t Unused probe number.

u Virtual modal frequency response number.

Number of virtual probes.

Blade tip radius.

Number of selected revolution in the average.

Rotational speed of bladed disc.

Width of the blade window calculated for each revolution.

Time period for one revolution as measured by the OPR probe.

Actual recorded timing value of a blade at a probe.

Expected arrival time of the same and non-vibrating blade at probe j

positioned at angle .

Relative spacing of probe 1 to probe j.

OPR offset.

Measured blade tip displacement at revolution i at probe j.

Measured blade tip displacement at revolution i at probe q.

Measured blade tip displacement at revolution i at probe t.

Added blade tip displacement for virtual modal response u at revolution i at

probe q.

Extracted displacement at probe j at revolution no. i for asynchronous modal

response.

Extracted displacement at probe j at revolution i for synchronous modal

response.

Nomenclature

10

Extracted displacement at probe j at revolution i for asynchronous modal

response r.

Extracted displacement at probe j at revolution i for synchronous modal

response r.

Extracted displacement at probe q at revolution i for asynchronous modal

response r.

Extracted displacement at probe q at revolution i for virtual asynchronous

modal response u.

Extracted displacement at revolution i for asynchronous modal response r at

unused probe t.

Extracted displacement at revolution i for synchronous modal response r at

unused probe t.

User-defined value for blade tip amplitudes for virtual engine order response

u.

Individual probe steady position error.

Sine and cosine terms of asynchronous modal response.

DC component in the synchronous modal response.

Sine and cosine terms of synchronous modal response.

Sine and cosine terms of asynchronous modal response r.

Sine and cosine terms of synchronous modal response r.

Sine and cosine terms of virtual engine order response u.

Residual displacement term at probe j at revolution i.

Residual displacement term at probe q at revolution i.

Steady state position for asynchronous modal response at probe j.

Steady state position for synchronous modal response at revolution i.

Angular circumferential position of probe j.

Angular circumferential position of probe q.

Probe j corrected circumferential angular position at revolution no. i.

Corrected circumferential angular position of probe j at revolution i for modal

response r.

Corrected circumferential angular position of probe q at revolution i for modal

response r.

Nomenclature

11

Corrected circumferential angular position of probe q at revolution i for virtual

modal response u.

Fitted engine order.

Fitted engine order for modal response r.

Angular circumferential probe position offset for fitted engine order .

Angular circumferential probe position offset for fitted engine order for

modal response r.

Angular circumferential probe position offset for fitted engine order for

virtual modal response u.

Maximum number of nodal diameters.

Number of blades.

Frequency of travelling wave in rotating frame of reference.

Frequency of travelling wave in static frame of reference.

Phase difference of observed frequency at two probes.

Circumferential angular separation of two selected probes.

Overall measurement uncertainty associated to modal response r.

Random measurement uncertainty associated to modal response r.

Systematic measurement uncertainty attributed to modal response r.

Overall measurement uncertainty associated to tip displacement of targeted

asynchronous modal response r.

Overall measurement uncertainty associated to tip displacement of targeted

synchronous modal response r.

Sample size defined by number of selected revolutions and number of probes.

Selected t-value for confidence level of 99.9% for sample size N.

Sample standard deviation of residual displacement terms.

Mean value of residual displacement terms.

Systematic measurement uncertainty of targeted asynchronous modal

response r.

Systematic measurement uncertainty of targeted synchronous modal

response r.

List of Figures

12

List of Figures

Figure 1.1 - BTT Measurement System ....................................................................................................... 25

Figure 1.2 – Mounted Optical Probe .......................................................................................................... 26

Figure 1.3 – 2nd

Engine Order Response ..................................................................................................... 27

Figure 2.1 - Arrangement of magnet of grid [18] ....................................................................................... 40

Figure 2.2 – Optical Probe Spot Size ........................................................................................................... 42

Figure 2.3 – BTT Displacement ................................................................................................................... 42

Figure 2.4 – Simulated Probe Data [9] ....................................................................................................... 43

Figure 2.5 – Real Engine Probe Data [9] ..................................................................................................... 44

Figure 2.6 – 2PP on Simulated Data [9] ...................................................................................................... 45

Figure 2.7 – 2PP on Real Engine Data [9] ................................................................................................... 46

Figure 2.8 – 2PP Elliptical Fits [9] ............................................................................................................... 46

Figure 2.9 – Russhard’s Linear Interpolation [9] ........................................................................................ 49

Figure 2.10 – Probe Responses and Noise [9] ............................................................................................. 50

Figure 2.11 – 31 Tap Savitzky-Golay Filter [9] ............................................................................................ 50

Figure 3.1 – BTT Six Step Process Data Preparation ................................................................................... 56

Figure 3.2 - Recorded Raw BTT TOA Data .................................................................................................. 57

Figure 3.3 - BTT Rotor Blade Displacement ................................................................................................ 59

Figure 3.4 - Stack Plot ................................................................................................................................. 60

Figure 3.5 – Russhard’s Linear Interpolation .............................................................................................. 61

Figure 3.6 – Targeted asynchronous response over 2 revolutions ............................................................. 68

Figure 3.7 – Offset of targeted asynchronous response over 2 revolutions ............................................... 68

Figure 3.8– All measured probe displacements displayed on first revolution ............................................ 69

Figure 3.9 – Steady state offsets displayed over two revolutions .............................................................. 75

Figure 3.10 – Steady state offsets displayed over one revolution .............................................................. 75

Figure 3.11 – Single Probe BTT Travelling Wave Plot ................................................................................ 81

Figure 3.12 – Definition of Level of Confidence (LC) ................................................................................... 88

Figure 3.13 – Extracted amplitudes using AABM & Russhard’s filtering techniques for a 0.04 mm peak

targeted amplitude .................................................................................................................................... 90

List of Figures

13

Figure 3.14 – 95% CI mean Values for AABM and Russhard’s filtering techniques for a 0.04 mm peak

targeted amplitude .................................................................................................................................... 91

Figure 3.15 – 95% CI mean differences between the ‘AABM / Russhard’ extracted amplitudes for a 0.04

mm peak targeted amplitude .................................................................................................................... 92

Figure 3.16 – Absolute mean errors for a 0.04 mm peak targeted amplitude ........................................... 93

Figure 3.17 – 95% CI mean error values for a 0.04 mm peak targeted amplitude ..................................... 94

Figure 3.18 - 95% CI mean differences between the extracted AABM and Russhard amplitudes for a 0.04


Figure 3.19 - Absolute mean errors for targeted amplitudes of 0.02 and 0.04 mm peak .......................... 97

Figure 3.20 – 95% CI for Absolute Mean errors for targeted amplitudes of 0.02 and 0.04 mm peak ........ 98

Figure 3.21 – 95% CI mean differences between the ‘AABM / Russhard’ extracted amplitudes for a 0.02


Figure 3.22 – 95% CI for Absolute Mean errors for targeted amplitudes of 0.02 and 0.04 mm peak using

AABM process .......................................................................................................................................... 100


AABM process .......................................................................................................................................... 101

Figure 3.24 – Extracted amplitudes using SABM & Russhard’s filtering techniques for a 0.04 mm peak

targeted amplitude .................................................................................................................................. 103

Figure 3.25 – 95% CI mean Values for SABM and Russhard’s filtering techniques for a 0.04 mm peak

targeted amplitude .................................................................................................................................. 104

Figure 3.26 – 95% CI mean differences between the ‘SABM / Russhard’ extracted amplitudes for a 0.04

mm peak targeted amplitude .................................................................................................................. 105

Figure 3.27 – Absolute mean errors for a 0.04 mm peak targeted amplitude ......................................... 106

Figure 3.28 – 95% CI mean error values for a 0.04 mm peak targeted amplitude ................................... 107

Figure 3.29 - 95% CI mean differences between the extracted SABM and Russhard amplitudes for a 0.04


Figure 3.30 - Absolute mean errors for targeted amplitudes of 0.02 and 0.04 mm peak ........................ 110

Figure 3.31 – 95% CI for Absolute Mean errors for targeted amplitudes of 0.02 and 0.04 mm peak ...... 111

Figure 3.32 – 95% CI mean differences between the ‘SABM / Russhard’ extracted amplitudes for a 0.02



SABM process ........................................................................................................................................... 113

List of Figures

14


SABM process ........................................................................................................................................... 114

Figure 3.35 – Finite Element Predictions .................................................................................................. 115

Figure 3.36 – New Tracking Method Process ........................................................................................... 116

Figure 3.37 – Two Nodal Diameter Pattern .............................................................................................. 118

Figure 3.38 – Static frame of reference FFT performed using a single probe ........................................... 121

Figure 4.1 – HPT Blade and Segment ....................................................................................................... 125

Figure 4.2 – HPT Segment at Maximum TET ............................................................................................ 126

Figure 4.3 – ESP Configuration – 10EO Signal .......................................................................................... 127

Figure 4.4 – ESP Configuration – 10EO Signals with two different choices of phase ............................... 128

Figure 4.5 – Overall Virtual Probe and EO Optimisation Process ............................................................. 130

Figure 4.6 – ESP Configuration – Targeted 10EO + 17.7EO Virtual Signals .............................................. 146

Figure 5.1 – Condition Numbers ............................................................................................................... 164

Figure 5.2 0.04 mm peak Targeted Amplitude – Fractional Uncertainty Differences - 8 Probes ............. 165



Figure 5.5 0.5 mm peak Targeted Amplitude – Fractional Uncertainty Differences - 8 Probes ............... 167



Figure 5.8 - Fractional Uncertainty Differences Method 1 vs. 90% CI Method 2 ...................................... 169

Figure 5.9 – 90% CI Fractional Uncertainty Differences at Averaging Revolution Number ...................... 171

Figure 5.10 - 90% CI for Fractional Uncertainty Differences at Averaging Revolution Numbers ............. 172

Figure 5.11 – SVD Fractional Uncertainties .............................................................................................. 174

Figure 5.12 – Maximum SVD Fractional Uncertainty Differences ............................................................ 175

Figure 5.13 - Extracted Signal / Noise Ratios for BTT Mode 1 .................................................................. 177

Figure 5.14 - Extracted Signal / Noise Ratios for BTT Mode 2 .................................................................. 177

Figure 5.15 – Differences in Theoretical and Computed SNRs for BTT Mode 1 ........................................ 178

Figure 5.16 – Differences in Theoretical and Computed SNRs for BTT Mode 2 ........................................ 178

Figure 6.1 – BTT Travelling Plot of Targeted Asynchronous Blade Response ........................................... 181

Figure 6.2 – FEM Predicted Frequency Response ..................................................................................... 182

Figure 6.3 – Single Asynchronous Engine Order – BTT Replay vs. AABM ................................................. 183

Figure 6.4 – Single Asynchronous Frequency – BTT Replay vs. AABM ...................................................... 183

List of Figures

15

Figure 6.5 – Single Asynchronous Coherence – BTT Replay vs. AABM ..................................................... 184

Figure 6.6 – Single Asynchronous Amplitude – BTT Replay vs. AABM ...................................................... 185

Figure 6.7 – BTT Replay vs. AABM Differences in Amplitude (mm) .......................................................... 185

Figure 6.8 – BTT Replay vs. AABM Differences in Amplitude (%) ............................................................. 186

Figure 6.9 – Statistical Analysis of BTT Replay vs. AABM Differences in Amplitude ................................. 186

Figure 6.10 – Statistical Analysis of Differences in Amplitude between 35 to 60 sec ............................... 188

Figure 6.11 – Statistical Analysis of Differences in Amplitude between 60 to 90 sec ............................... 188

Figure 6.12 – Single Asynchronous SNR – BTT Replay vs. AABM .............................................................. 189

Figure 6.13 – Single Asynchronous Uncertainty – BTT Replay vs. AABM ................................................. 190

Figure 6.14 – BTT Travelling Plot of Two Simultaneous Asynchronous Blade Responses ........................ 191

Figure 6.15 – FEM Predicted Frequency Responses.................................................................................. 191

Figure 6.16 – Asynchronous Mode ‘A’ Engine Order – Batch Processor vs. AABM .................................. 192

Figure 6.17 – Asynchronous Mode ‘B’ Engine Order – Batch Processor vs. AABM................................... 192

Figure 6.18 – BP vs. AABM Mode ‘A’ Differences in Amplitude (mm) ...................................................... 193

Figure 6.19 – BP vs. AABM Mode ‘B’ Differences in Amplitude (mm) ...................................................... 193

Figure 6.20 – BP vs. AABM Mode ‘A’ Differences in Amplitude (%) ......................................................... 194

Figure 6.21 – BP vs. AABM Mode ‘B’ Differences in Amplitude (%).......................................................... 194

Figure 6.22 – Statistical Analysis of BP vs. AABM Mode ‘A’ Differences in Amplitude ............................. 195

Figure 6.23 – Statistical Analysis of BP vs. AABM Mode ‘B’ Differences in Amplitude ............................. 195

Figure 6.24 – Asynchronous Mode ‘A’ and ‘B’ Coherence – Batch Processor vs. AABM .......................... 196

Figure 6.25 – FEM Predicted Frequency Response ................................................................................... 197

Figure 6.26 – BTT Travelling Plot of Targeted Synchronous Blade Response ........................................... 198

Figure 6.27 – Synchronous Engine Order – BTT Replay vs. SABM ............................................................ 198

Figure 6.28 – Synchronous Frequency – BTT Replay vs. SABM ................................................................. 199

Figure 6.29 – Synchronous Amplitude – BTT Replay vs. SABM ................................................................. 199

Figure 6.30 – Replay vs. 5 Revs SABM - Synchronous Amplitude Differences .......................................... 200

Figure 6.31 – Blade Tip Amplitude of Targeted Response – SABM vs. SABM~Virtual .............................. 203

Figure 6.32 – SABM vs. SABM~Virtual Differences in Targeted Response ............................................... 204

Figure 6.33 – Targeted Synchronous Engine Orders – SABM vs. SABM~Virtual....................................... 204

Figure 6.34 – Targeted Synchronous Frequencies – SABM vs. SABM~Virtual .......................................... 205

Figure 6.35 – Synchronous Coherences – SABM vs. SABM~Virtual .......................................................... 205

Figure 6.36 – Targeted Synchronous Uncertainties – SABM vs. SABM~Virtual ........................................ 205

List of Figures

16

Figure 6.37 – FoV and FoC – SABM~Virtual .............................................................................................. 206

Figure 6.38 – Targeted Synchronous Uncertainties – SABM vs. SABM~Virtual ........................................ 206

Figure 6.39 – Synchronous Amplitude – Non-Zeroing BTT Replay vs. SABM ............................................ 208

Figure 6.40 – Synchronous Amplitude – Zeroing BTT Replay vs. SABM .................................................... 208

Figure 6.41 – BTT Replay Zeroing vs. Non-Zeroing Amplitude Differences .............................................. 209

Figure 6.42 – Synchronous Uncertainty Comparison - BTT Replay vs. SABM ........................................... 209

Figure 6.43 – SABM SNR Extracted Information ...................................................................................... 210

Figure 7.1 - Compressor Blade Tip vs. Turbine Blade Tips ........................................................................ 212

Figure 7.2 - Definition of Blade Lean and Blade Sweep [49] .................................................................... 213

Figure 7.3 - Definition of BTT Axial and Radial Displacements ................................................................ 214

Figure 7.4 - Definition of Shrouded Turbine Blade TOA Data points ....................................................... 215

Figure 7.5 - Shrouded Turbine Blade Tip Manufacturing Information .................................................... 217

Figure 7.6 - Definition of Shrouded Turbine Blade Tip Axial Displacement ............................................. 218

Figure 7.7 - Zoomed Definition of Shrouded Turbine Blade Tip Axial Displacement ................................ 220

Figure A1 – Asynchronous Mode ‘A’ Amplitude – Batch Processor vs. AABM.......................................... 236

Figure A2 – Asynchronous Mode ‘A’ Engine Order – Batch Processor vs. AABM ..................................... 236

Figure A3 – Asynchronous Mode ‘A’ Frequency – Batch Processor vs. AABM .......................................... 237

Figure A4 – Asynchronous Mode ‘B’ Amplitude – Batch Processor vs. AABM .......................................... 237

Figure A5 – Asynchronous Mode ‘B’ Engine Order – Batch Processor vs. AABM ..................................... 237

Figure A6 – Asynchronous Mode ‘B’ Frequency – Batch Processor vs. AABM .......................................... 238

Figure A7 – Asynchronous Mode ‘A’ and ‘B’ Coherence – Batch Processor vs. AABM ............................. 238

Figure A8 – AABM Asynchronous Modes ‘A’ SNR ..................................................................................... 238

Figure A9 – AABM Asynchronous Modes ‘B’ SNR ..................................................................................... 239

Figure A10 – Asynchronous Mode ‘A’ Uncertainty – Batch Processor vs. AABM ..................................... 239

Figure A11 – Asynchronous Mode ‘B’ Uncertainty – Batch Processor vs. AABM ..................................... 239

Figure C1 - Targeted Synchronous Amplitudes – SABM vs. SABM~Virtual ............................................... 243

Figure C2 - Targeted Synchronous Engine Orders – SABM vs. SABM~Virtual .......................................... 243

Figure C3 - Targeted Synchronous Frequencies – SABM vs. SABM~Virtual .............................................. 243

Figure C4 - Synchronous Coherences – SABM vs. SABM~Virtual .............................................................. 244

Figure C5 - Synchronous SNRs – SABM vs. SABM~Virtual ........................................................................ 244

List of Figures

17

Figure C6 - Targeted Synchronous Uncertainties – SABM vs. SABM~Virtual ........................................... 244

Figure C7 - Virtual Synchronous Amplitude Response .............................................................................. 245

Figure C8 - Virtual Synchronous Frequency Response .............................................................................. 245

Figure C9 - Virtual Synchronous Engine Order Response ......................................................................... 245

Figure C10 - Virtual Uncertainty Response ............................................................................................... 246

Figure C11 - Virtual SNR Response ........................................................................................................... 246

Figure C12 - FoV and FoC – SABM~Virtual ............................................................................................... 246

Figure D1 - Synchronous Amplitude – Non-Zeroing BTT Replay vs. SABM ________________________ 247

Figure D2 - Synchronous Engine Order – Non-Zeroing BTT Replay vs. SABM ______________________ 247

Figure D3 - Synchronous Frequency – Non-Zeroing BTT Replay vs. SABM ________________________ 247

Figure D4 - Synchronous Coherence – Non-Zeroing BTT Replay vs. SABM ________________________ 248

Figure D5 - SABM Synchronous SNR _____________________________________________________ 248

Figure D6 - SABM Synchronous Uncertainty _______________________________________________ 248

Figure D7 - Synchronous Amplitude – Zeroing BTT Replay vs. SABM ____________________________ 249

Figure D8 - Synchronous Engine Order – Zeroing BTT Replay vs. SABM __________________________ 249

Figure D9 - Synchronous Frequency – Zeroing BTT Replay vs. SABM ____________________________ 249

Figure D10 - Synchronous Coherence – Zeroing BTT Replay vs. SABM ___________________________ 250

Figure D11 - SABM Synchronous SNR ____________________________________________________ 250

Figure D12 - SABM Synchronous Uncertainty ______________________________________________ 250

Figure D13 - Synchronous Uncertainty Comparison - BTT Replay vs. SABM ______________________ 251

Figure E1 – Test Facility Laboratory Hardware _____________________________________________ 252

Figure E2 – HPT Blade and Mass Block ___________________________________________________ 252

Figure E3 – Chopped Air Jet Exciter ______________________________________________________ 253

List of Tables

18

List of Tables

Table 4.1 - Original Equally Spaced Probe Configuration ......................................................................... 142

Table 4.2 – Permuted Configuration with Virtual Probe and Virtual Engine Order .................................. 142

Table 4.3 – ESP General Information ........................................................................................................ 143

Table 4.4 – Targeted EO Information ....................................................................................................... 144

Table 4.5 – Targeted + Virtual EO & DC Information ............................................................................... 145

Table 4.6 – Summarised ESP Test Cases ................................................................................................... 152

Table 5.1 – Simulated SNR and Uncertainty Parameters ......................................................................... 162

Table 5.2 – Maximum differences in fractional uncertainty .................................................................... 172

Table 6.1 – Original Probe Configuration Parameters ............................................................................. 202

Table 6.2 – New BTT Configuration Parameters ...................................................................................... 202

Abstract

19

Abstract

In the current gas turbine market, the traditional design-test-redesign loop is not a viable

solution to deploy new products within short timeframes. Hence, to keep the amount of testing

to an absolute minimum, theoretical simulation tools like Finite Element Modelling (FEM) have

become a driving force in the design of blades to predict the dynamic behaviour of compressor

and turbine assemblies in high-speed and unsteady flows. The predictions from these

simulation tools need to be supported and validated by measurements. For the past five years,

Rolls-Royce Blade Tip Timing (BTT) technology has been replacing rotating Strain Gauge

systems to measure the vibration of compressor blades, reducing development times and costs

of new aero engine programmes.

The overall aim of the present thesis is to progress the BTT technology to be applied to aero

engine turbine modules. To this end, the two main objectives of this project are:

i. To improve the current validated Rolls-Royce BTT extraction techniques, through the

development of novel algorithms for single/multiple asynchronous and responses.

ii. To validate the improved extraction using simulated and real engine test data in order to

bring the Turbine BTT technology to a Rolls-Royce Technology Readiness Level (TRL) of 4

(i.e. component and/or partial system validation in laboratory environment).

The methodology adopted for the development of the novel algorithms is entirely based on

matrix algebra and makes extensive use of singular value decomposition as a means for

assessing the degree optimisation achieved through various novel manipulations of the input

(probe) raw data. The principle contributions of this thesis are threefold:

i. The development of new BTT matrix-based models for single/multiple non-integral and

integral engine order responses that removed certain pre-processing assumptions required

by the current method.

ii. The development of BTT technology to operate under the constraint of having equally

spaced probes, which is unavoidable in turbines and renders current BTT methods

unusable for turbine applications.

iii. The development of methods for extracting measurement uncertainty and signal to noise

ratios that are based solely on the raw data, without reliance on simulated reference data.

Following the verification and validation of the new processing algorithms against simulated

data and against validated software with numerous examples of actual engine test data, a Rolls-

Royce’s Research & Technology (R&T) Critical Capability Acquisition and Capability Readiness

(CCAR) review has accredited the novel techniques with a TRL of 4.

Declaration

20

Declaration

No portion of the work referred to in the thesis has been submitted in support of an application

for another degree or qualification of this or any other university or other institute of learning.

Copyright Statement

21

Copyright Statement

Copyright in text of this thesis rests with the Author. Copies (by any process) either in full, or of

extracts, may be made only in accordance with instructions given by the Author and lodged in

the John Ryland’s University Library of Manchester. Details may be obtained from the Librarian.

This page must form part of any such copies made. Further copies (by any process) of copies

made in accordance with such instructions may not be made without the permission (in writing)

of the Author.

The ownership of any intellectual property rights which may be described in this thesis is vested

in Rolls-Royce, subject to any prior agreement to the contrary, and may not be made available

for use by third parties without the written permission of the Rolls-Royce, which will prescribe

the terms and conditions of any such agreement.

Further information on the conditions under which disclosures and exploitation may take place

is available from the Head of the School of Mechanical, Aerospace and Civil Engineering

Acknowledgements

22

Acknowledgements

I would like to express my gratitude to Dr. Peter Russhard and Jason Back for their technical

expertise and support for this project. I would also like to thank my supervisor, Dr Philip Bonello

for his valuable advice and guidance throughout the course of this work. I am grateful to

Professor Jan Wright for his guidance in the early stages of this project.

Thanks are extended to Dr Jose Garcia (Rolls-Royce), Scott Courtney (Rolls-Royce), Dr Paul N.

Bennett (Rolls-Royce), Jamie Gallagher (Rolls-Royce) and Pierpaolo Murtas.

I would like to acknowledge Rolls-Royce and the Engineering and Physical Sciences Research

Council (EPSRC) of the United Kingdom for its support of this research project trough grant N

EP/H00128/X1, as part of Work Package 1.7 Project N 1 of SAMULET (Strategic Affordable

Manufacturing in the UK with Leading Environmental Technology) consortium.

Finally I would like to express my sincere thanks to Dr Sophoclis Patsias (Rolls-Royce) and Dr

Adam Pickard (Rolls-Royce) whose help in the preparation of the thesis have been without

doubt invaluable.

23

To Marta

Chapter 1 Introduction

24


Caused by excessive levels of vibration, engine failure is an expensive reality for the aviation

industry. Even when they are not safety-critical, acceptable levels of vibration are a primary

target for any new engine design to reduce noise emissions and to improve passenger comfort.

One of the main threats for the rotor blades of a gas turbine engine is vibration. Of the problems

encountered during development of modern aircraft gas turbine engines, 40% are related to

High-Cycle-Fatigue (HCF) [1]. This accounts for approximately 5% of the commercial field

maintenance costs [2].

In the current market, the traditional design-test-redesign loop is not a viable solution to deploy

new products in short periods of time. Hence, to keep the amount of testing to an absolute

minimum, theoretical simulation tools have become a driving force in the design of blades to

predict the dynamic behaviour of compressor and turbine assemblies in high-speed and

unsteady flows. The predictions from these simulation tools need to be supported and validated

by measurements. Hence, a cost-effective blade vibration measurement system is essential to

aero engine development.

To reduce the cost and the development times of new aero engine programmes, Rolls-Royce

Blade Tip Timing (BTT) technology has for the past five years, been replacing rotating Strain

Gauges in measuring compressor rotor blade vibrations. This technique makes measurements

of the passing times of blade tips under stationary points.

Operated in a benign environment, strain gauges can give reliable results for many years.

Applied in harsh environments, many factors can reduce their circuit life such as:

Build damage.

Exposure to extreme temperatures.

Rapid build up of fatigue cycles through component vibration.

High/Low frequency loads (e.g. g-loading and thermal stresses).

Abrasive particles in the gas stream.


25

Oxidation or other metallurgic changes within the gauge element, leads and solder

joints.

Chemical attack by oil and other liquids.

Damages to the gauge or lead wires through contact between rotating and stationary

parts.

For high-pressure turbine blades, strain gauge mortality is extremely high and re-test costs are

prohibitive. To achieve reductions in cycle times, material waste and improvement in

productivity, Rolls-Royce has decided to investigate using BTT technology instead of strain

gauges for High Pressure Turbine Blade (HPTB) component certification. The research and

development programme SAMULET (Strategic Affordable Manufacturing in the UK with Leading

Environmental Technology) led by Rolls-Royce, focuses on making BTT technology the

preferred measurement system. This is to be accomplished by improving some of the existing

capabilities and by developing new techniques to remove some of the constraints preventing

the use of BTT on HPTB components.

1.1 Blade Tip Timing Principles

1.1.1 BTT Data Acquisition

Blade Tip Timing is a turbo-machinery testing

technology defined as a non-contacting and non-

intrusive measurement system. This utilises a

number of external sensors mounted in the casing

at pre-determined circumferential and axial

positions, to accurately measure the passing time

of the blade tips (see Figure 1.1). Different types

of sensors based on different concepts (e.g. eddy

current probes, optical laser probes, capacitive

and inductive probes) can be used for detecting

the passing times of the blades.

Figure 1.1 - BTT Measurement System


26

It is generally accepted that intrusive and contacting

sensors such as strain gauges provide better

accuracy than non-intrusive and non-contacting

transducers. However, the optical probes, for

example, provide more information and do not alter

the dynamic characteristics of the bladed disc under

investigation [3]. For engine development

programmes, optical probes are the preferred

sensors due to minimal engine modifications for

their implementation (see Figure 1.2). These are

developed and designed specifically for Rolls-

Royce’s Turbomachinery applications in order to

keep implementation and operational costs as low as possible.

Using the Once-Per-Revolution (OPR) sensor, the reference time enables the determination of

the free-passing Time-Of-Arrivals (TOA) of each blade (i.e. no blade vibration) at each probe

mounted circumferentially on the casing. However, in the presence of vibration, the blade tip

TOA will be measured earlier or later than the free-passing TOAs at each probe, depending on

the blade vibratory motion.

The comparison of the measured and the free-passing times of each blade results in a time

offset which can be converted into displacement using the speed of the rotor and its radius at

each probe. These calculated “measured” blade deflections are displacements in the

measurement plane of the blade tip timing system which are at differing circumferential

positions around the casing and are not blade tip amplitudes.

Figure 1.3 shows the measured defections for a single blade using fives probes (i.e. P1 to P5)

over two revolutions for a 2nd

engine order (EO) response (note that a kth EO (“kEO”) response

means that the frequency of the blade vibration is k times the rotational speed).

Figure 1.2 – Mounted Optical Probe


27

Figure 1.3 – 2nd

Engine Order Response

By carrying out the BTT data processing described in Section 1.1.2, the curve fitting process will

determine that, for example in Figure 1.3, the measured blade defections are indeed linked to a

resonant frequency equal to twice the rotational speed of the engine (i.e. Engine Order = 2).

1.1.2 General Overview of BTT Data Processing

In addition to supplying the hardware of a Blade Tip Timing measurement system, a number of

company engineering services (see Section 2.2.3) include using proprietary algorithms to

convert the captured TOA data into modal amplitude, frequency, phasing and nodal information

including measurement uncertainties.

The algorithms are mainly used to extract the vibratory characteristics of two distinct classes of

blade responses; the synchronous response and the asynchronous response.

Also referred to as integral engine order vibration (i.e. kEO, where k is an integer), synchronous

vibrations are excited by elements which are stationary relative to the engine casing and located

in the path flow. The two main characteristics associated with this type of vibration are that:

1. The blade deflections reach maximum peaks at points of resonance.


28

2. The frequencies associated with these blade vibrations are in phase (hence

synchronous responses) with the rotational speed of the engine.

In contrast to the above asynchronous vibrations, also referred to as non-integral engine order

vibration (i.e. kEO, where k is a non-integer), are excited by elements which are typically not

stationary relative to the engine casing and therefore not tied to the rotational speed of the

engine. Caused by the energy entering the system, the blades are forced to vibrate along their

natural modal frequencies.

Using theoretical and real engine data, many analysis techniques have been developed over

the past two decades associated with specific requirements [4] (e.g. number of probes,

circumferential probe distribution for specific engine order), hence limiting the BTT analysis

capabilities as a whole. However, any type of vibration events which could lead to blade HCF

events [1] during engine test development programmes must be captured and analysed without

any restrictions. For this reason, the works of Heath [5], Desforges [6], Dimitriadis [7],

Carrington [8] and Gallego-Garrido [4] were unsuitable for engine test development

programmes, but showed promising characteristics for in-service Blade Health Monitoring

(BHM) algorithms, where the number of probes are limited [9]. This will be described further in

Chapter 2.

The limitations of the aforementioned works were identified by Russhard [9], who developed

new analysis routines to extract blade vibratory responses from the recorded BTT TOA data,

without such restrictions.

The following example provides a basic overview of a BTT analysis technique to extract the

dynamic displacement amplitudes of the blades and their frequency of vibration. Assuming that

the synchronous engine order vibration response of a blade is a simple sinusoidal motion [9]

then the measured blade tip displacement at each probe can be expressed as follows:

1.1

where is the measured tip displacement of a particular blade at probe no. p (p = 1...n) at

circumferential position on the engine casing, and EO is the targeted engine order excitation.


29

For a number of probes, n, the measured blade tip displacements at each probe can be

expressed in a matrix form as:

1.2

where

1.3

1.4

1.5

The , and terms are the coefficients to be determined, from which the steady state

position, the dynamic displacement amplitude and the phase at each blade tip can be calculated

for the targeted engine order. Using Singular Value Decomposition (SVD) [10], the matrix M

(see Equation 1.4) can be factored as:

1.6

where is a n × n orthogonal matrix whose columns are the eigenvectors of , is a 3 × 3

orthogonal matrix whose columns are the eigenvectors of , and is a n × 3 matrix of the

form of:

1.7

where the 0’s denote appropriately sized zero matrices and the diagonal matrix in the top left

hand corner is composed of the singular values of M, which are the positive square roots of the

non-zero eigenvalues of , 1≥2...≥r≥0 where . Problems arise when one of

the ’s is so small that its value is dominated by round-off error. The more the ’s are affected

by this issue, the more is badly conditioned.


30

The above extraction method provides a way of determining the sensitivity of a matrix to

numerical operation and this concept is linked with the condition number of , the ratio of its

largest singular value to its smallest singular value. The scale on which the condition number is

measured ranges from one to infinity, where a robust system will have a condition number of

unity.

The extractions of the , and coefficients are performed by computing the Moore-

Penrose inverse of Equation 1.2:

1.8

where

1.9 and

1.10

The denotes the calculated version of . The calculated dynamic displacement amplitude of

the blade is then given by:

1.11

The coherence between the actual displacement measurements and their calculated

counterparts can then be calculated using the Pearson correlation formula [11].

1.2 Scope, Aim and Contributions of the Research

Over the past 20 years, Rolls-Royce has invested and dedicated resources in developing Blade

Tip Timing technologies to a level of maturity that allows the replacement of rotating blade strain

gauges in engine-compressor modules through sponsoring different research programmes

(Heath in 1996 [5], Desforges in 1997 [6], Dimitriadis in 2000 [7], Carrington in 2002 [8],

Gallego-Garrido in 2005 [4] and Russhard in 2010 [9]).

In particular, Russhard’s work [9] brought the BTT technology successfully to a Rolls-Royce

Technology Readiness Level (TRL) of 6 (i.e. full system / subsystem validation in a relevant

environment) for aero engine fan/compressor module applications [12].


31

1.2.1 Aim and Objectives

The overall aim of the present thesis is to advance BTT technology to aero engine turbine

module application. To this end, two main objectives were set for this research:

1. To improve the current validated Rolls-Royce BTT extraction techniques, through

the development of novel algorithms, to achieve extremely low displacement

measurements (typical of high pressure turbine modules) for single/multiple non-

integral and integral engine order responses.

2. To validate the improved extraction using theoretical and real engine test data in

order to bring the Turbine BTT technology to a Rolls-Royce Technology Readiness

Level (TRL) of 4 (i.e. component and/or partial system validation in laboratory

environment).

1.2.2 Thesis Contributions to Industry and Research Impact

The thesis contributions in the industrial context can be listed as follows.

1. This research has initially highlighted areas for improvement in the data zeroing and

filtering methods developed by Russhard [9], leading to the development of new BTT

matrix-based models for single/multiple non-integral and integral engine order

responses in Chapter 3. By doing so, the new models have:

a. Removed the need to identify and isolate resonances.

b. Stopped the alteration of the dynamic content of the raw data before the

extraction of blade tip amplitudes at targeted resonances.

These new techniques have been verified using simulated data in Chapter 3 and

validated using and real engine test data in Chapter 6. The verification/validation is

performed by comparing the outputs from the novel methods to those from Russhard’s


32

methods [9] in Chapter 3 and proprietary Rolls-Royce software also based on Russhard

[9] in Chapter 6 (which have been previously validated against rotating strain gauges).

2. The implementation of BTT technology for Turbine applications is constrained by the

circumferential position of the probes which is governed by the level of distortion, the tip

clearance losses, the predicted life of the component and the inter-segment leakages.

Indeed, these constraints force the BTT system to have an Equally Spaced Probe

(ESP) configuration, which with current BTT analysis techniques makes the extraction

of the Turbine blade tip amplitudes for specific engine orders erroneous. To remove this

processing limitation, a new technique has been developed in Chapter 4, verified and

validated in Chapter 4 and Chapter 6 respectively.

3. This research work has also delivered new validated methods for extracting

measurement uncertainties and signal to noise ratios (Chapter 5), improving the

Russhard’s initial work in assessing measurement uncertainties [9] based on theoretical

simulations. The advantages of these methods which are verified and validated in

Chapter 5 and Chapter 6 respectively, are based on the usage of BTT data only to

determine the systematic and the random errors associated with the reported vibratory

information.

4. An algorithm has been developed (see Chapter 7) to determine untwist values and BTT

axial displacements for shrouded turbine blades based solely on the raw BTT time-of-

arrival data points. There are critical parameters when assessing the blade tip

displacements against FEM predictions. Unfortunately, the limitations of the test

facilities could not validate these methods.

5. Finally, the test facility hardware for characterising turbine blade vibration response(s)

and finite element prediction validation has been set up as part of this project (see

Chapter 9 and Appendix E). This will form the basis of a future project which will

integrate the above contributions with the test facility to create an end-to-end verification

of this improved BTT methodology for turbine blade applications.


33

The impact of the above contributions (1-3) is already felt at Rolls-Royce, and can be

summarised as follows:

The above methods have been successfully used on FUTURE (Flutter-Free

Turbomachinery Blades), a project sponsored by the European Union, to characterise

the structural dynamics of test rotors in vacuum under rotation [13].

The research work has resulted in the following four patent applications:

o GB1309624.3 - “Simultaneous BTT Analysis of Non-Integral & Integral

Responses using Non-Zeroed”, 30th May 2013.

o GB1309623.5 - “High Resolution BTT Algorithm for Extracting Synchronous

Blade Tip Amplitudes”, 30th May 2013.

o GB1203181.1 - “Determination of Blade Tip Displacement Uncertainties &

System Amplitude Threshold from Blade Tip Timing Measurements”, 4th

February 2012.

o GB1309622.7 - “Measurement of Turbine Blade Axial Movement using Blade

Tip Timing”, 30th May 2013.

Following the verification and validation of the new processing algorithms against

simulated data and against validated software with numerous examples of actual

engine test data, a Rolls-Royce’s Research & Technology (R&T) Critical Capability

Acquisition and Capability Readiness (CCAR) review has accredited the novel

techniques with a TRL of 4 [14]. Unfortunately, the planned engine test experiment

failed to deliver data and hence this research work could not progress the technology to

TRL6 (i.e. full system / subsystem validation in a relevant environment).


34

1.3 Thesis Contributions to Knowledge

The major contributions of this research work to knowledge on BTT measurement technology

are the following.

Chapter 3 (and further validated in Chapter 6) shows the deployment of new BTT

matrix-based models for single/multiple non-integral and integral engine order

responses with the advantages of removing certain pre-processing assumptions

required by the current processing methods.

Chapter 4 (and further validated in Chapter 6) shows the development of new BTT

algorithms which overcome the current processing constraints introduced by equally

spaced probe configurations. Indeed, those restrictions can now be surpassed through

replacement of an actual probe with a virtual probe and the introduction of a virtual

engine order response.

Chapter 5 (and further validated in Chapter 6) defines the calculation of the

measurement uncertainties and signal-to-noise ratios using the residual displacement

terms at each probe. The advantages of the new method are defined by assessing

uncertainty from measured data as opposed to uncertainty from processing theoretical

simulations [15]. This has the added bonus of considering the effects of noise

associated with the targeted component which was not considered with the previous

method.

1.4 Thesis Overview

The work developed during the research project and presented in this thesis covers the

following sequence:

o Chapter 2 provides a critique of previous and established (current) methods. It

highlights why some of techniques failed in the past when using real engine test data

and provides an insight of possible areas of improvement for Blade Tip Timing in

Turbine applications.


35

o Chapter 3 starts by providing a detailed narrative of Russhard’s processing techniques

[9]. It then offers a mathematical description of the novel matrix-based models for non-

integral and integral engine order responses with a quantitative and qualitative

assessment of the improvements. The information given in this chapter is protected by

Patent GB1309624.3 (see Section 1.2.2).

o Chapter 4 exposes the constraints imposed by the Turbine segments which force a BTT

implementation based on Equally Spaced Probe (ESP) configurations. By identifying

the issues associated to the current techniques to extract accurate blade amplitudes, a

new method is described and verified using simulated data showing that those previous

limitations have been removed. The information given in this chapter is protected by

Patent GB1309624.3 (see Section 1.2.2).

o Chapter 5 presents a new method asserted with a verification statement for extracting

BTT measurement uncertainties and signal-to-noise ratios. The information given in this

chapter is protected by Patent GB1309624.3 and GB1309624.3 (see Section 1.2.2).

o Chapter 6 uses experimental data (from real engine tests and a turbine blade rotating

test rig), to validate the new improved BTT capabilities for turbine applications against

Rolls-Royce’s validated tools originally developed by Russhard [9].

o Chapter 7 contains the details of the novel algorithms for the determination of the

untwist values and BTT axial displacements for shrouded turbine blades, listed as

contribution no. 4 in Section 1.2.2.

o Chapter 8 provides details about the commercial implications of the research work

including the driving forces in the development and implementation of the technology for

High Pressure Turbine blade components.

o Chapter 9 draws conclusions of the research presented in this thesis and considers

future developments and applications for the technique. In particular, an overview is

given of the BTT Test Facility Laboratory at the University of Manchester, which is listed

as contribution no. 5 in Section 1.2.2.


36

o Appendices A to D provide supplementary results from the thorough validation process

presented in Chapter 6. Appendix E displays some of the test hardware available at the

University of Manchester, listed as contribution no. 5 in Section 1.2.2.

Chapter 2 BTT Industry Best Practices

37


Fourteen year ago, Heath [5] compiled a list of requirements for an ideal Blade Tip Timing

measurement system. The list was subsequently revised by Russhard [9]. To promote the BTT

technology as the preferred vibration measurement system for High Pressure Turbine Blades,

the list needs to be reassessed and prioritised once more in order to attract the necessary

funding and resources for a successful implementation.

Divided into two categories, the requirements defined in the revised list are classed as follows:

a. Analytical requirements for BTT processing algorithms:

1. Be able to determine the natural frequency of vibration.

2. Be able to determine a damping for each blade.

3. Be able to determine the response amplitude and deflection due to forced

vibration.

4. Be able to detect variations in blade response amplitude with sufficient

accuracy to be related to manufacturing tolerances, known as mistuning.

5. Be able to support an FE predicted mode shape.

6. Be able to determine nodal diameter associated with the assembly.

7. Be able to extract vibratory information for a majority of blades.

8. Verification evidence for the technique should exist and be traceable.

9. Validation evidence for the operational results from a realistic environment

should support the technique.

10. A value for uncertainty should be readily calculated for each application.

Since this list was compiled and based on past experience, it has become necessary to

add the following three needs to the analytical requirement list:

11. A measurement of the Signal-to-Noise Ratio (SNR).

12. A value of the blade axial displacement.

13. Values of the blade untwist.


38

b. Operational requirements for BTT measurement system:

1. The application of the system must be achievable within the cost and time

constraints placed upon it.

2. The system must be able to operate in a realistic environment,

3. Its application should be minimally intrusive and should not change the

characteristics of the component being observed,

4. The system should provide real time quantitative data about the blades

behaviour,

5. Off-line analysis should provide a more comprehensive set of results to the real

time analysis.

Since, in practice, BTT data is under sampled because of the limited number of recorded data

points (i.e. number of probes), a Blade Tip Timing measurement system cannot deliver on its

own all the analytical and operational requirements listed above.

Hence, Finite Element Model predictions, laboratory bench calibrations and information

extracted from any other measurement devices are key activities to guide extraction, analysis,

correlation and validation of component behaviours, leading to compliance with the latest safety

and environmental legislation.

2.1 Current Vibration Measurement System for Rotating Components

In the past, conventional methods for rotor blade vibration measurement have mainly involved

the use of Strain Gauges (SG) or Frequency Modulated (FM) grids. In recent years, additional

measurement techniques, Scanning Laser Doppler Vibrometer (SLDV) and Blade Tip Timing

(BTT), have been developed and used to detect, assess, quantify and characterise vibrations in

rotating Turbomachinery. Each of these measurement systems can be classified as

contacting/non-contacting and intrusive/non-intrusive.


39

2.1.1 Strain Gauge Based Measurements

Described as the preferred transducer for blade vibration measurement [16], strain gauges are

a field proven technology for extracting accurate real-time information [5] relating to the

alternating strains arising in critical areas of a blade. In addition, strain gauges have proven to

be well established and reliable when applied to non-rotating components for most applications.

However for rotating components, SG measurement systems suffer from a low operating life.

This limited life expectancy is often due to the use of the slip ring or telemetry systems to

transmit the strain gauge signals from the rotating structure to the stationary analysis hardware

(e.g. wear of slip ring, failure of the telemetry systems due to high temperature and embedded

electronic system fatigue). However, it can also be due to the hostile environments to which the

strain gauges are exposed. The slip ring or telemetry systems are often a considerable source

of noise, and the Signal-to-Noise Ratio (SNR) is a very important measurement parameter [17].

In addition, the strain gauges attached to the component under observation and the wire paths

can alter the blade structural characteristics as well as interfering with the local fluid flow field,

hence restricting the number of strain gauges to a few blades per rotor stage [3]. Associated

with this test method, the strain gauge measurements can provide valuable information on

certain parts of the blades but are statistically inaccurate due to blade-to-blade differences in

response caused by mistuning [16].

2.1.2 Frequency Modulated Grid Measurements

Capable of providing continuous real-time blade amplitude and frequency information, the

Frequency-Modulated (FM) grid [18], is a non-contacting but intrusive measurement system,

built of a small magnet inserted in the blade tip and a precision made meander-shaped wire

placed inside the casing, just above the rotor blade tips (see Figure 2.1).


40

Figure 2.1 - Arrangement of magnet of grid [18]

When the engine is under rotation, a series of electrical impulses is generated in the zigzag

conductor by the magnet. If, however, the blade vibrates, a substantially sinusoidal voltage

wave will be induced as the magnet passes the parallel wires. The frequency of the impulses

will vary directly with the velocity with which the magnet is moving past the grid, so that the

frequency component due to the vibration is isolated to give an output proportional to a blade

Amplitude-Frequency (AF) value.

The main limitations associated to the FM grid system are that vibratory information can only be

provided for the blade(s) fitted with a magnet and the costs associated with the modification of

the casing to fit the conductor.

2.1.3 Scanning Laser Doppler Vibrometer Measurements

Scanning Laser Doppler Vibrometer (SLDV) systems measure time domain velocity of a

component on which an FFT can recover its vibration behaviour, for example an Operational

Deflection Shape (ODS). The system requires adequate optical access and is hence unusable

for measuring the vibrations of rotating bladed discs inside a casing.


41

However, the techniques associated to SLDV measurement have been further developed in

recent years and high accuracy data using SLDV on a bladed disc under rotating conditions can

now be carried out successfully in a controlled environment [17] [19]. Unfortunately, despite the

promising new capabilities, the SLDV measurement techniques are still impractical for the

Intermediate Pressure (IP) compressor, the High Pressure (HP) compressor and the turbine

stages because there is no optical access.

2.2 Blade Tip Timing Measurements

Despite their limited life in hostile environment, strain gauges have been the preferred

measurement system for many years assessing targeted modal vibratory responses for a

limited number of blades.

Blade Tip Timing has now become the preferred measurement system to support the simulation

tools which have become the driving force in the design of rotor blades. This is because the

system aids validating and deploying new products faster than the traditional design-test-

redesign approach while keeping the amount of testing to an absolute minimum and therefore

reducing the development and operational costs.

2.2.1 Previous BTT Data Processing Methods

Described by Russhard [9], the probe laser light illuminating the portion of the blade defines the

location where the blade TOA is triggered and captured using a Blade Tip Timing measurement

system. Typically, the laser spot size is between 100m and 1mm (see Figure 2.2 [9]).

The recorded raw time-of-arrival data are then converted into blade tip deflections, BTT (see

Figure 2.3), using the blade tip radius and the rotational speed of the engine. Note that the BTT

blade tip defections are measured in the direction of rotation (see Figure 2.3 [9]) at each probe.

In reality, the direction of the blade vibration defined by , is at an arbitrary angle to the

direction of rotation which can be predicted by a validated Finite Element (FE) model.


42

Figure 2.2 – Optical Probe Spot Size Figure 2.3 – BTT Displacement

Over the past twenty years or so, a number of analysis methods for asynchronous and

synchronous responses have been developed. Different BTT analysing methods have been

listed by Gallego-Garrido [4] who added to the original list produced by Carrington [20]. Based

mainly on simulated data and on the availability of real engine data, they have shown that each

processing technique has different requirements regarding the relative position between the

sampling points.

Established over many years as the norm, Equally Spaced Probe (ESP) configurations (i.e.

probes equally spaced from each other) used in the Desforges [6], Heath [21] and Wilson [22]

processing techniques and in the Auto-Regressive (AR) methods developed by Carrington [8]

and Dimitriadis [23] have since been abandoned following a better understanding of the real

nature of the recorded BTT blade vibrations.

In fact, Russhard [9] stated that any probe configuration that is only sensitive to a particular

resonance has a limited use in the real world where several equally important events need to be

captured and quantified along with a stated uncertainty. By carrying out a comparative analysis

between some of the previous analysis methods, Russhard [9] pointed out their limitations

based on real engine data.


43

2.2.1.1 Single Parameter Method

Zablotskiy and Korostelev [24] claimed that the maximum amplitude for a synchronous

response can be quantified using a single parameter (i.e. probe). Such a method cannot provide

frequency information. This claim can only be true if the blade displays a 180 degrees phase

shift at resonance which is not true in reality and in most of the cases, due to the increase of

engine speed and the duration of the resonance.

Russhard [9] demonstrated using simulated data (see Figure 2.4) that the identification of blade

resonance and the extraction of its amplitude can be performed well. The simulated data

described in Figure 2.4 is based on a 4th engine order resonance, 1mm peak-to-peak amplitude

and four probes equally spaced at 30 degrees over a 4000 RPM speed.

Figure 2.4 – Simulated Probe Data [9]

However, when dealing with data from real applications (see Figure 2.5), the technique shows

some limitations since the majority of the probe signals also contain blade lean, blade untwist

and noise information. Indeed, in order to accurately identify resonances and amplitudes, those

unwanted signals need to be assessed.


44

Figure 2.5 – Real Engine Probe Data [9]

2.2.1.2 Two Parameter Plot Method

The Two Parameter Plot (2PP) method developed by Heath [5] requires data from two probes

over several revolutions while traversing a resonance of the assembly. The recorded data from

the two probes for an accelerating manoeuvre and a decelerating manoeuvre are then plotted

against each other, leading to an elliptical shape at the blade resonance. Using the simulated

data defined in Section 2.2.1.1 (see Figure 2.4), the processed data using the 2PP technique is

shown in Figure 2.6.


45

Figure 2.6 – 2PP on Simulated Data [9]

With previous knowledge of the probe positions, the blade tip amplitude and engine order

response can be calculated using the Probe Spacing at Resonance (PSR) equations developed

by Heath [5] (i.e. the probes need to be set within a specific PSR range to target specific

resonance).

However, Dimitriadis [7] highlighted on different occasions that the 2PP technique becomes

more unreliable with real engine test data than when using simulated data due to probe noise

and steady offsets introduced by the measurement system. This observation was confirmed by

Russhard [9] using the real engine probe data displayed in Figure 2.5 which resulted in the 2PP

processed data in Figure 2.7 for which elliptical fits based on Heath’s equations [5] are shown in

Figure 2.8.


46

Figure 2.7 – 2PP on Real Engine Data [9]

Figure 2.8 – 2PP Elliptical Fits [9]

Indeed, the different elliptical fits displayed in Figure 2.8, highlight the difficulties in extracting

the blade tip amplitude(s) and its associated engine order(s) with confidence using the PSR


47

equations defined by Heath [5]. Note, that the blade tip amplitude is calculated by averaging the

lengths of the minor and major axes defining each of the elliptical fits.

In summary, the main problems associated to the 2PP techniques are:

a. The uncertainties associated with the technique are extremely high and the method

unreliable.

b. The quantification of small resonances is impossible due to inability to identify and

to extract the probe noise and the steady state offsets from the recorded raw data.

c. The elliptical shape at the blade resonance is highly dependent on the number of

revolutions selected, which impact on the final results.

2.2.1.3 Auto-Regressive Methods

The Auto-Regressive (AR) methods developed by Carrington [8], Dimitriadis [7] and Gallego-

Garrido [4] are extensions of Heath’s work [5] based on new simulated TOA data which

introduces probe noise and steady state offset. These methods are also based on limited real

engine test data. By adding additional probes at equally spaced intervals, the new methods

have shown that blade amplitude and frequency at a single resonance can be extracted without

prior knowledge of the excitation.

Highly dependent on the PSR range as mentioned earlier (see Section 2.2.1.2), the quality of

the processed information based on a single targeted response is affected by the noise and the

steady state offsets contained in the data. To reduce the bias error associated with the results,

Carrington [8] developed new techniques based on multi-blade and multi-revolutions:

1. Global Auto-Regressive (GAR).

2. Global Auto-Regressive with Instrumented Variables (GARIV).

However, these techniques came with additional restrictions linked to the mistuning and the

acceleration rate of the rotor. Indeed, a rotor assembly can exhibit severe mistuning and the


48

responses of individual blade can be significantly different including their frequency response.

With regards to multi-revolutions, the averaging technique can only be applied where the

acceleration of the rotor is slow.

Russhard [9] carried out a comprehensive comparative analysis of the above two techniques

using data recorded on a UK/US durability engine demonstrator. The results [25] indicated that

for the majority of the selected tests, the calculated engine orders were in error, hence leading

to the wrong computation of the blade tip amplitudes with insufficient levels of confidence based

on a number of manoeuvres.

2.2.2 Current Rolls-Royce BTT Methods (due to Russhard [9])

Russhard [9] stated that the Blade Tip Timing simulators developed by previous researchers

have been over complicated in simulating the behaviour of the rotor instead of the movement of

the tip of the blade. Indeed prior to Russhard’s work [9], all the developed techniques have

failed to consistently extract individual blade tip amplitudes and frequencies with a good level of

confidence.

Russhard’s breakthrough in extracting blade tip vibratory information from real engine and

simulated data sets was to convert the recorded TOA data points for each blade into

displacement as soon as possible within the measurement process, instead of defining models

(see Section 2.2.1.3) based solely on time values. Indeed, Russhard’s new technique described

thoroughly in Section 3.1 performs successfully and consistently well in dealing with the noise

and steady state offsets contained in the recorded TOAs where previous methods have failed to

do so. However, there are some issues associated with Russhard’s technique.

The most challenging one is the data zeroing process. Based on an algorithm initially developed

by Carrington [8], and subsequently improved by Russhard [9], areas are identified where

integral engine order response(s) may be present by carrying out a revolution-by-revolution

cross correlation of the probe data. Where integral engine order responses are found, the

average values at the beginning and at the end of each period are calculated based on forty

revolutions to generate linear interpolations of values for the zeroing to be applied (e.g. red line

as per Figure 2.9). If incorrectly applied, the zeroing process in turn incorrectly alters the data if

it is allowed to continue into or across the event (e.g. red dashed line as per Figure 2.9) and


49

renders the analysis open to indeterminate error(s) (i.e. reduces the confidence in both

amplitude and phase for synchronous responses).

Figure 2.9 – Russhard’s Linear Interpolation [9]

In addition, Russhard [9] stated that his non-integral engine order analysis method could not

distinguish the asynchronous response and noise term apart, leading to greater uncertainties.

This statement is reinforced by the fact that a Savitzky-Golay filter [9] [26] is applied on the raw

displacements to filter the noise components.

Figure 2.10 displays simulated data of five probes subject to some random noise with the

illustration of the Savitzky-Golay filter applied to this same data displayed in Figure 2.11.


50

Figure 2.10 – Probe Responses and Noise [9]

Figure 2.11 – 31 Tap Savitzky-Golay Filter [9]

This inevitably introduces errors in the extracted blade tip amplitudes and phases despite best

efforts of preserving the maxima and minima of the probe responses at resonance (see Figure


51

2.10 and Figure 2.11). Indeed, depending on the selected length of the filter (i.e. user

dependant), uncertainties are being introduced in the displacement observed at each probe.

In 2009, to eliminate the errors encountered by the Gauss-Jordan method [27] [28] used by

Russhard [9], and to improve accuracy, Rolls-Royce took the decision to instead implement the

Singular Value Decomposition (SVD) method [29]. A test program was carried out in comparing

and validating the differences [30] which led to its implementation in the Rolls-Royce BTT

software suite.

2.2.3 Other Proprietary BTT Systems (AEDC, Agilis, BSSM, Hood Systems)

The aforementioned research and development of BTT systems (Sections 2.2.1 and 2.2.2) have

principally been spearheaded by Rolls-Royce researchers. However, in the aero engine

industry, there are another four proprietary BTT measurement systems used by other

companies for extracting blade displacements, which are listed below.

1. The AEDC System, first implemented 30 years ago, consisted of a single probe

connected to an oscilloscope and spectrum analyser. Since then, Arnold Engineering

Development Centre (AEDC) has matured its 4th generation Non-intrusive Stress

Measurement System (NSMS) [31] which is based on several probes mounted

circumferentially on the casing and proprietary blade tip displacement analysis

techniques.

2. The Agilis Arrival Time Analysis Software (AATAS) [33] is a commercial venture based

on technology and analysis methods developed at Pratt & Whitney (P&W). The Agilis

Measurement System (AMS) develops and licences proprietary software based on

TOAs captured by a number of probes also mounted circumferentially on the casing.

3. The Berührungslose Schaufelschwingungsmessung (BSSM) [32], an in-house

development by Moturen und Turbinen Union (MTU) is based on a number of sensors

distributed in an axial plane, targeting a single blade tip at the same time. This differs

from the majority of the known techniques which instead use TOA data taken from

circumferential spaced probes. The technique does not require an OPR and relies

heavily on the FEM predictions to extract blade tip amplitudes and frequencies.


52

4. The Blade Vibration Monitoring (BVM) system [34] developed by Hood Technology

Corporation is a self contained commercial NSMS system intended mainly for gas

turbine engine diagnostic and prognostic. Since, Hood Technology Corporation has

developed a more advanced analysis tool named Analyze Blade Vibration (ABV). The

ABV software processes the TOA data captured by their own Acquire Blade Data (ABD)

software using probes also mounted circumferentially around the casing, to extract

blade tip amplitudes and frequencies.

Because of their proprietary status, the information released for each of the described systems

regarding their associated benefits and drawbacks is limited. Hence, the present thesis follows

along the Rolls-Royce branch of BTT research and development.

2.3 Summary of Chapter 2

Different techniques based on different probe distributions have been developed over the years,

with some methods more successful than others as shown in the above sections. Indeed only a

few international companies like Rolls-Royce (Section 2.2.2) and others (Section 2.2.3), have

successfully developed proprietary techniques to extract blade tip amplitudes and frequencies

for integral and non-integral engine order responses.

Rolls-Royce Blade Tip Timing (BTT) technology which over the past five years [35] has

successfully replaced rotating Strain Gauge systems on Low, Intermediate and High Pressure

(LP, IP and HP) compressor modules, is aiming as discussed in Chapter 1, for a similar success

for the High Pressure Turbine Blades (HPTB) based on the techniques developed by Russhard

[9].

However, the predicted FEM tip displacements for the HPTB modes of interest are much

smaller than the ones predicted for compressor blades which, using today’s BTT algorithms

cannot be detected.

Therefore, to successfully implement the BTT technology into turbines, the issues with the

techniques that were briefly discussed in Section 2.2.2, need to be resolved by advancing the

current capability through novel algorithms. This provides the motivation for the present thesis.


53

The first step towards achieving this aim is to carry out an assessment of Russhard’s methods

in terms of dealing with noise, blade steady state offsets, the detection of blade resonances, the

filtering techniques and the selected number of revolutions for defining the linear interpolation.

This detailed assessment is done in the first part of the following chapter.

Chapter 3 BTT Improved Processing Methods

54


The main difficulty associated with Blade Tip Timing technology for generating accurate off-line

and real-time results is the removal of the steady state displacement errors in the probes whilst

leaving the required steady state data intact.

Indeed, due to the under-sampling effect linked to the Blade Tip Timing technology, a

synchronous resonance manifests itself as a slow change in the blade’s steady state

displacement.

Methods and algorithms have been developed in the past to overcome this difficulty by

averaging the collected probe data over a number of revolutions of the rotor.

This chapter starts by detailing the current data preparation and processing methods. It then

details new processing methods based on two different models (i.e. one for asynchronous

activities and one for synchronous responses), including seamless automated averaging built-in

matrix techniques and frequency-domain adaptive filters.

The new methods have been assessed against previous validated techniques, which are

actually being used at Rolls-Royce plc, by carrying out a qualitative and quantitative analysis.

Advantages of the new models are detailed in Section 3.2 (main features).

3.1 Current Data Preparation & Processing Methods

Previous models [22] used to extract blade tip amplitudes and phase information which relied

heavily on simulated data and modelling of the rotor blade behaviour, have failed to successfully

recognise that based on practical applications, unwanted signals contained in the raw data

increase the measurement uncertainty if not removed.

With the constraints of the real life operation and industrial environmental issues, the work

carried out by Russhard [9] highlighted successfully unwanted components from the raw Time-

Of-Arrival (TOA) data.


55

The currently used model to extract blade tip displacement at each probe, suggested by

Russhard [9] is defined as follows:

3.1

where

is the actual measured blade tip displacement at probe .

is the individual probe steady position error.

are constants from which the DC component, amplitude and phase of

the synchronous response can be calculated.

are constants from which the amplitude and phase of the asynchronous

response can be calculated.

is an integer engine order excitation.

is an estimate of the non-integral engine order excitation.

is the angular position of probe .

is the unwanted(noise) term.

To determine the coefficients and of the synchronous and/or asynchronous blade

response, Russhard [9]has developed a six step robust process to extract, from the raw TOA

data, the individual probe steady position error and the noise (i.e. the unwanted components).

The flowchart shown in Figure 3.1 describes his process to extract the “ ” and “ ” terms

from the recorded raw TOA data files.


56

Figure 3.1 – BTT Six Step Process Data Preparation

3.1.1 Probe/Blade Data Alignment – Step 1

The radial spacing of the probes and the possibility that the acquisition system may contain lost

or surplus TOA data points means that the data arriving at the acquisition system is misaligned

Recorded Raw Time-Of-Arrival Data File for Probe j

Probe/Blade Data Alignment

Conversion of Probe j TOA to displacements

Stack Pattern Verfication

Generation of the blade activity mask

Application of the noise removal filter

Removal of the probe steady state offset

BTT data ready

for processing

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6


57

by default. Depending of the arrangement and the number of probes, the timing values are

recorded as shown in Figure 3.2 - , where ‘b’ is the total number of blades.

Figure 3.2 - Recorded Raw BTT TOA Data

The time for each revolution is recorded by the Once-Per-Revolution (OPR) probe allowing

each revolution to be divided into windows, each one blade pitch wide (see Equation 3.2).

3.2

where

is the width of the blade window calculated for each revolution.

is the time period for one revolution as measured by the OPR probe.

is the number of blades on the rotor.

A timing value from a probe can now be tagged with a blade number ‘b’ if it lies between the

window limits given by Equation 3.3.

3.3

where

is the actual recorded timing value of a blade at a probe.

is the blade number relative to the blade expected to pass probe no. 1 at time t = 0.


58

The next step is to define the relative spacing of probe 1 to probe j as an integer number of

blades (or windows), see Equation 3.4.

3.4

where

is the relative spacing of probe 1 to probe j (j = 1 ...n).

is the angular circumferential position of probe j ( j = 1...n ).

Before updating Equation 3.3 with the relative probe spacing term, the window equation needs

to be written with respect to the OPR signal. However, in reality the position of the OPR is not

precisely known, or recorded as it is often a temporary feature in any engine (from a protruding

feature such as a bolt head of slot). Known as the OPR offset ( ), this results into an

additional offset being manually selected at the time of the test. The Equation 3.3 can be re-

written as:

3.5

The window value is dynamic and has to be recalculated for every revolution. The action of

windowing doesn’t change the data. It is used to align the data arrays in a logical order.


59

3.1.2 Conversion of TOA Data to Displacements – Step 2

At each revolution i, the Time-Of-Arrival

( ) of a blade n at a probe j is measured

and recorded.

Knowing the rotational speed () of the

bladed disc, the expected arrival time of the

same and non-vibrating blade at a probe j

positioned at an angle is given by:

3.6

where

is the angular position of probe in

rad.

is the rotational speed in rad.s-1

.

Finally, the measured blade tip displacement at a probe j, for a given blade tip radius is given

by:

3.7

3.1.3 Stack Pattern Verification – Step 3

The stack plot (see Figure 3.4 ) is used to confirm that probe/blade alignment operation defined

in Section 3.1.1 for a selected data set is correct. By calculating the correlation coefficient

between each probe stack pattern against the data from probe one, it is possible to generate a

value for the integrity of the data set and also to correct the data set for alignment errors prior to

attempting data analysis. Misalignment data will produce errors in subsequent analysis.

Figure 3.3 - BTT Rotor Blade Displacement


60

Figure 3.4 - Stack Plot

3.1.4 Generation of the Blade Activity Mask– Step 4

Due to the mistuning effects caused by minor physical differences between blades, areas of

resonance for each blade need to be identified. Using a revolution-by-revolution correlation

technique, the generation of the mask identifies where the probe-to-probe correlation indicates

possible integral engine order vibration events.

3.1.5 Application of the Noise Filter Removal – Step 5

A suitable algorithm for preserving the local minima and maxima of time-series that would be

affected in normal conditions by averaging techniques is the Savitzky-Golay filter [26].

Successfully used by Russhard [9] for dealing with non-integral engine order and noise

components, the smoothing filter performs essentially a local polynomial regression of kth

degree on the input data, to determine a smoothed value for each point. The operation defines

the ‘noise’ term in Equation 3.1.


61

3.1.6 Removal of the Probe Steady State Offset – Step 6

The last step before attempting an

extraction of the blade tip amplitudes is to

remove the unwanted steady offset of each

probe and to retain the dynamic portion of

the signal. Using the information developed

in Section 3.1.4, for data outside the

identified areas of activity, local averages

are generated. Where a resonance is

identified then a linear interpolation of the

values is carried out between the start and

the end of the identified integral engine

order event. This operation is called

‘zeroing’ and it enables to calculate the unwanted probe offset ‘ ’ term in Equation 3.1.

3.1.7 Russhard’s Six Step Process Summary

For practical applications, the previous attempts on creating models to extract information from

the TOA data have failed to take into account and/or to find a robust method in the exception of

Russhard [9], for the following:

1. The measured components of displacements at each probe contain other components

than sinusoidal motions

2. The TOA data is subject to external unwanted sources of interference, such as noise,

manufacturing uncertainty of the circumferential positions of the probes on the casing,

jitter in the once-per-revolution (OPR).

With all the challenges linked to BTT, Russhard has successfully provided a clear

understanding of the different steps to follow to assess blade activities from a vibratory point of

view.

Figure 3.5 – Russhard’s Linear Interpolation


62

3.2 New Improved Model for Single Frequency Response

The new model to extract vibratory information from the TOA data for each blade at each

revolution is based purely on the usage of matrices for both synchronous and asynchronous

blade frequency responses, eliminating the need of the steps 4 to 6 from Russhard’s six step

process (see Section 3.1, Figure 3.1). Previous reported analysis methods (see Section 2.2.1)

were based on extracting vibratory integral engine order information based on predicted Finite

Element Model (FEM) information.

The matrix-based model is instead tracking the predicted blade frequency modal response

based on the FEM predictions over the entire speed range. For each revolution of the engine,

the best fitted frequency for the targeted subject is reported with all its relevant vibratory

information.

One of the main challenges is to be able to cope seamlessly with asynchronous and

synchronous activities for each targeted blade frequency response. Based on the six step

process developed by Russhard [9], this section describes the new matrix-based model which

offers a new tracked modal extraction analysis technique from BTT displacement data.

The main features of the new matrix-based models compared to the previous reported models

are:

1. For asynchronous responses, each probe is defined with a steady state offset

component.

2. For synchronous responses, one steady state position component is defined for each

revolution.

3. For both asynchronous and synchronous targeted responses, a residual displacement

term component for each probe is extracted.

4. The minimum number of revolutions required for the new improved models to satisfy all

the requirements is two revolutions and the reasons will be explained in Section

3.2.1.1.


63

5. Nodal diameter information associated with asynchronous response is no longer

required.

6. Reduction of the processing latency for real-time monitoring,

In addition to the features listed above, the new models for asynchronous and synchronous

responses have provided key improvements over current methods in terms of speed. Indeed,

the new tracking methods offer few less preparatory steps than the analysis techniques

developed by Russhard [9].

Indeed, summarised in see Section 3.1, Russhard’s process is based on six steps before

attempting the extraction of the vibratory information of the targeted responses. With the new

processing techniques (see Sections 3.2 and 3.3), three of the six preparatory steps have been

removed and they are:

o Generation of the blade activity mask,

o Application of the noise filter removal,

o Removal of the probe steady state offset.

By removing the three tasks described above, it is clear that the analysis process has been

improved in terms of speed and efficiency. However, the quantification of the improvements will

be feasible and practical only by:

o Integrating the new algorithms with the initial preparatory steps,

o Writing efficient and optimised code using for example, the C++ programming

language.

3.2.1 Single Non-Integral Engine Order Response Matrix-Based Model

For extracting non-integral engine order vibratory activities, a new matrix-based model has been

developed and its main features are described in Equations 3.8 to 3.10. The new model

provides a seamless automated Asynchronous Averaging Built-in Matrix technique (AABM),

which will be described in Section 3.2.1.2.


64

3.8

3.9

3.10

where

is the measured blade tip displacement at the revolution no. i (i = 1...m) for a particular blade at probe no. j (j = 1...n).

is the extracted probe displacement for an asynchronous modal frequency response at the revolution no. i (i = 1...m) for a particular blade at probe no. j.

is the residual displacement term at the revolution no. i (i = 1...m) at probe no. j (j = 1...n).

are constants from which the amplitude and phase of an asynchronous modal frequency response for a particular blade can be extracted.

is the steady state position for an asynchronous modal frequency response for a particular blade at probe no. j (j = 1...n).

is the fitted engine order excitation.

is the angular circumferential position of probe j (j = 1...n).

is the angular circumferential probe position offset for the fitted engine order .

is the corrected circumferential angular position of probe j (j = 1...n) at the revolution no. i (i = 1...m).

Therefore, for m revolutions and for an n probe configuration, Equations 3.8 and 3.9 can be


3.11


65

where

3.12

3.13

3.14

3.15

with

3.16

3.17


66

The two main features of the new-matrix model for asynchronous responses are:

Feature No 1:

The ability to extract asynchronous vibratory information over a selected number of

revolutions by introducing an angular circumferential probe offset,

, into the matrix (see Equations 3.10 and 3.16).

Feature No 2:

The ability to remove seamlessly the average steady state offset for each probe at the

same time as extracting the best fitted engine order for the selected BTT displacement

data by introducing this novel BTT averaging built-in matrix technique (see Equation

3.17).

3.2.1.1 Feature No 1 – Introduction of Angular Circumferential Probe Position Offset

By introducing the angular circumferential probe position offset into Equation 3.10 hence

Equation 3.16, it enables the search for the best fitted engine order over a number of

revolutions, therefore the extraction of the blade tip amplitude for a targeted modal frequency

response.

Knowing the engine order ( ) to be fitted, then the angular circumferential probe position

offset is determined by:

3.18

Note, the ‘floor’ function rounds the fitted engine order excitation to the nearest integer, less

than or equal to .

This can be demonstrated using an eight probe configuration over two revolutions, with

simulation shown in Figure 3.6, Figure 3.7 and Figure 3.8.


67

The circumferential angular probe positions in degrees are:

8.74 170 74 188 74 206.74

224.74 242.74 296.74 314.74

The fitted engine order in this example has been set to a value of 1.6. Figure 3.6 displays

the targeted signal over two revolutions with the two sets of probe displacements for each

probe.

Using Equation 3.18 and the above information:

Figure 3.7 indicates the angular circumferential probe position offset (equivalent to 135

degrees), with the first revolution as reference.

Finally, the measured displacements of each probe for the second revolution can be folded

back onto the first revolution at their respective new calculated probe positions using Equation

3.10. Note that if the new calculated probe angular position is greater than 2, then a value of

2 has been removed from the new calculated probe positions as done for theta 2.6, 2.7 and

2.8.

The new calculated circumferential angular probe positions in degrees are:

368.74 - (1 * (360 - 135)) = 143.74 530. 74 - (1 * (360 - 135)) = 305.74

548.7474 - (1 * (360 - 135)) = 323.74 566.74 - (1 * (360 - 135)) = 341.74

584.74 - (1 * (360 - 135)) = 359.74 602.74 - (2 * (360 - 135)) = 152.74

656. 74 - (2 * (360 - 135)) = 206.74 674. 74 - (2 * (360 - 135)) = 224.74

The collected information from the second revolution folded into the first revolution by

introducing the angular circumferential probe position offset is displayed on Figure 3.8.


68

Figure 3.6 – Targeted asynchronous response over 2 revolutions

Figure 3.7 – Offset of targeted asynchronous response over 2 revolutions


69

Figure 3.8– All measured probe displacements displayed on first revolution

By introducing the angular circumferential probe offset into the new-matrix model to extract the

vibratory characteristics of each blade for selected engine conditions, Blade Tip Timing data can

be processed over an unlimited number of revolutions.

3.2.1.2 Feature No 2 - Averaging Built-in Matrix

Early forms of the non-integral engine order data processing technique were based on capturing

and presenting peak-to-peak displacement values over a number of revolutions average as

results (see Section 2.2 and Gallego-Garrido [4] where further explanation is given). However,

knowledge of the component frequency responses was required to understand those calculated

values in addition to the nodal diameter information (i.e. different probes will present different

amplitudes).

Another method was to carry out a Simple Moving Average (SMA) to remove the steady state

component of the asynchronous blade data (Gallego-Garrido [4] where further explanation is

given). However problems arose with the aliasing effects; the observed frequency changing with

the rotational speed of the engine, demonstrated by Russhard [9].

For these reasons, Russhard [9] developed a new method to remove the unwanted probe

steady offset ( at each probe (see Equation 3.1) for asynchronous responses. The method is


70

based on a Block Average (BA) where only a single value is calculated for each probe over a

fixed number of revolutions. The calculated BA value for each probe is then subtracted from the

measured blade tip displacements. Equation 3.19 summarises this technique.

3.19

where

, is the number of revolution in the average.

The two main issues with Russhard’s technique are:

1. How to select the best number of revolutions required for the Block Average

technique.

2. The alteration of measured blade tip displacement data prior to any extraction of the

blade vibratory information.

With the introduction of the angular circumferential probe offset, the implementation of a

seamless automated Asynchronous Averaging Built-in Matrix technique (AABM, see Equation

3.17) is now feasible. This AABM is also linked with a frequency-domain adaptive filter (see

Equation 3.16). It provides a method of separating , for a targeted frequency , from the

measured blade tip displacement .

To demonstrate theoretically its equivalence to the BA method, the following assumptions are

made. All the terms in Equations 3.13 and 3.15 are equal to zero, the number of probes is set to

three and the data processing is carried out over two revolutions. Therefore Equation 3.11 can

be written as:

3.20


71

Equation 3.20 can be decomposed and the singular values , and can be extracted.

3.21

The results displayed in Equation 3.21 demonstrate that the AABM technique is equivalent to

the BA method developed by Russhard.

All the different processes required to analyse BTT data for non-integral engine order responses

when compared to previous methods have been covered and the new matrix model for non-

integral engine order frequency responses can be re-arranged and expressed as follows (see

Equation 3.22).

3.22

Equation 3.22 demonstrates that the non-integral engine order frequency blade modal

responses can be extracted from a single step operation when compared against the six-step

process defined by Russhard [9].

Note that the residual matrix is not included in Equation 3.22 because is the result of the

difference between this equation and Equation 3.11.


72

3.2.2 Single Integral Engine Order Response Matrix-Based Model

A Synchronous Averaging Built-in Matrix (SABM) model for extracting integral engine order

vibratory activities has also been developed and its features are different from the one created

for the non-integral engine order activities (see Equation 3.22). The new synchronous matrix-

based model requires some of the information extracted from the asynchronous matrix-based

model and the link between the two new models will be described later in this section.

The new matrix-based synchronous model is based on the following two equations.

3.23

3.24

where

is the measured blade tip displacement at the revolution no. i (i = 1...m) for a particular blade at probe no. j ( j = 1...n ).

is the extracted probe displacement for a synchronous modal frequency response at the revolution no. i (i = 1...m) for a particular blade at probe no. j.

is the residual displacement at the revolution no. i (i = 1...m) at probe no. j ( j = 1...n ).

are constants from which the amplitude and phase of a synchronous modal frequency response for a particular blade can be extracted.

is the steady state position for a synchronous modal frequency response for a particular blade at the revolution no. i (i = 1...m).

is the fitted engine order excitation.

is the angular circumferential position of probe j ( j = 1...n )



3.25


73

where

3.26

3.27

3.28

3.29

with

3.30

3.31


74

Similar to the asynchronous matrix-based model, the new model for synchronous responses

offers some integrated features.

Feature No 1:

The ability to extract synchronous vibratory information over a selected number of

revolutions. For integral engine order responses, the angular circumferential probe

position offset is equal to zero therefore (see Equations 3.10 and

3.18).

Feature No 2:

The ability to calculate the steady state offset at each revolution contained within a

selected range of revolutions.

Feature No 3:

The ability to subtract seamlessly the calculated steady state offset value from the blade

tip displacements measured at each probe, at each selected revolution for each fitted

integral engine order.

In the following paragraph, Features No 2 and N

o 3 will be discussed. However, because of the

similarities of the Feature No 1 to the one described for the non-integral engine order response

matrix-based model (see Section 3.2.1), this feature won’t be addressed further in this section.

3.2.2.1 Feature No 2 – Extraction of the Steady State Offset per Revolution

Figure 3.9 describes the theoretical blade tip displacements over two revolutions for a

synchronous response. The response has been created based on an eight probe configuration

with two equal steady state offset values for each revolution. Both offsets are equal in amplitude

but opposite in sign.


75

Figure 3.9 – Steady state offsets displayed over two revolutions

As mentioned earlier, fitted integral engine orders provides an angular circumferential probe

position offset equal to zero. This is highlighted in Figure 3.10 where the measured blade tip

displacements at each probe for the folded revolution are positioned at the exact same position

as the ones displayed for the referenced revolution (i.e. Rev No 1).

Clearly displayed on Figure 3.10, are the two theoretical steady state offsets for the revolution

No 1 and No 2. The fitted theoretical integral engine order response is also displayed and

positioned at equal distance from the measured blade tip displacements, at each probe position.

Figure 3.10 – Steady state offsets displayed over one revolution


76

To demonstrate the advantages of this new integral engine order matrix-based model against

Russhard’s approach [9] for extracting the steady state offset values, the following example is

being used.

From Equation 3.1, the components directly linked to the extraction of the integral engine order

vibratory information can be isolated as:

3.32

Comparing Equations 3.24 and 3.32, the ‘ ’ and ‘ ’ terms are the parameters targeting the

steady state offset values. Therefore, based on three probe configuration with the extraction

process carried out over two revolutions, the following relationship can be established between

the two methods based on Equations 3.24 and 3.32:

3.33

Equation 3.33 can be re-written as follows:

3.34

Equation 3.34 demonstrates and validates the link between the new matrix-based model and

Russhard’s model for extracting integral engine order information. It also details one of the

improved features, which has been seamlessly incorporated in the new model and defined as

Feature No 3.


77

3.2.2.2 Feature No 3 – Zeroing of Synchronous Data per Revolution

Using Figure 3.10 as an example, Equation 3.34 clearly illustrates that the term ‘ ’ is equal to

zero because of the steady state offset values of the terms ‘ ’ and ‘ ’ being equal in amplitude

but opposite in sign.

However if the following assumptions are made:

3.35

with

3.36

then

3.37

With the assumptions made in Equations 3.35 and 3.36, Equation 3.37 clearly highlights one of

the new features introduced in the new integral engine order matrix based model; it extracts

from the measured blade tip displacements, an accurate steady state offset for each revolution.

Compared to the method developed by Russhard [9], the new model clearly demonstrates that

it doesn’t leave/introduce an average steady state offset error (see Equation 3.37).

The different processes required to analyse BTT data for integral engine order responses when

compared to previous methods have been covered and the new matrix model for integral

engine order frequency responses can be re-arranged and expressed as follows (see Equation

3.38).

3.38


78

The Equation 3.38 demonstrates that integral engine order frequency blade modal responses

can be extracted from a single step operation with improved features such as the extraction of

the steady offset values per revolution.

3.2.3 Non-Integral / Integral Engine Order Matrix-Based Model Displacement Interface

As mentioned earlier in Section 3.2.2, the new integral engine order matrix-based model

requires information from the non-integral engine order model to extract the synchronous blade

vibratory information.

For a resonance response at a non-integral engine order excitation, the measured blade tip

displacements at each probe for a selected number of revolutions are expressed as follows

based on Equation 3.12.

3.39

where


is the dynamic blade tip displacement at the revolution no. i (i = 1...m) at probe no. j ( j = 1...n ) for non-integral engine order response.

is the individual steady state position for an asynchronous modal frequency response for a particular blade at the revolution no. i (i = 1...m) at probe no. j ( j = 1...n ).


79

Using Equation 3.39, Equation 3.22 can be re-written as follows:

3.40

where

3.41

Equation 3.41 indicates that if a non-integral engine order response should become an integral,

when:

3.42

then

3.43


80

The information provided in Equation 3.43 demonstrates and provides the interface between the

new non-integral and integral engine order matrix-based models in terms of the blade tip

displacements to be used for the extraction of the blade synchronous vibratory information.

However, in a real case scenario, the ‘ ’ terms will never be equal to zero at the same time

when a non-integral engine order response becomes integral. The reason being is that the

measured blade tip amplitudes at each probe and at each revolution contain some residual

displacements (see Equations 3.8 and 3.21). Hence the ‘ ’ and ‘ ’ are not equal to zero,

except for a perfect vibratory response.

Therefore, to provide displacement information for each probe linked at each revolution to the

new synchronous matrix-based model (see Equation 3.38), the interface between the new non-

integral and integral engine order matrix-based models must be defined as follows:

3.44

where is the interface matrix providing the displacement for individual probes at each selected

revolution when a non-integral engine order response becomes integral.

Therefore, the Equations 3.25 can be expressed in a matrix form as follow:

3.45


81

3.3 Multiple Simultaneous Frequency Responses

For new civil and military engine development programs, the aero-thermo-mechanical limits are

being pushed continuously to improve performance and efficiency. Sometimes, despite all the

efforts being undertaken at the design phase to predict frequencies and stress distributions

associated to particular mode-shapes at particular engine conditions to maintain the mechanical

integrity of blades, high vibration amplitudes cannot always be attributed to engine orders.

Unpredicted unsteady aerodynamics forces [36] caused by non-uniform pressure fields due to

the wakes of upstream and potentially downstream vanes or further unsymmetrical flow

conditions, can excite blades to respond and to reach unacceptable high vibrations levels.

The BTT travelling wave plot (see Figure 3.11) highlights integral and non-integral engine order

blade events. By observing over time the displacements of all the blades recorded by a single

probe, the travelling plot creates a Fast Fourier Transform (FFT) graphical representation of the

rotor blade response. Each FFT requires a number of revolutions and through utilising a moving

window (step by one revolution), a one-revolution resolution can be achieved. The FFT bin

represents the engine order (EO) plus nodal diameter (ND) (i.e. Y-axis) and the X-axis is the

number of FTT performed (i.e. number of revolutions or time).

Y-a

xis

: N

oda

l D

iam

ete

r +

Engin

e O

rder

X-axis: Number of revolution (i.e. Time)

Figure 3.11 – Single Probe BTT Travelling Wave Plot


82

Using Russhard’s algorithms [9], single and/or multiple synchronous and/or asynchronous

events (see Figure 3.11) are identified, leading to the extraction of engine order plus nodal

diameter, probe phase difference and rotor speed for each of the targeted responses.

Therefore the new analysis process needs to be able to extract the vibratory characteristics of

every single response.

3.3.1 Multiple Non-Integral Engine Order Responses

For extracting multiple simultaneous non-integral engine order vibratory activities, a new matrix-

based model built on the following equations, has been developed using the model developed

in Section 3.2.1.

3.46

3.47

3.48

where


is the extracted probe displacement for the asynchronous modal

frequency response no. r (r = 1...p) at the revolution no. i (i = 1...m) for a particular blade at probe no. j.


are constants from which the amplitude and phase of the asynchronous modal frequency response no. r (r = 1...p) for a particular blade can be extracted.

is the steady state position for the combined asynchronous modal frequency responses for a particular blade at probe no. j ( j = 1...n ).

is the fitted engine order excitation for the asynchronous modal

frequency response no. r (r = 1...p) (see Equation 3.18).


83


is the angular circumferential probe position offset for the fitted

engine order for the asynchronous modal frequency response no. r (r = 1...p).

is the corrected circumferential angular position of probe j ( j = 1...n )

at the revolution no. i (i = 1...m) for the asynchronous modal frequency response no. r (r = 1...p).



3.49

where

3.50

3.51

3.52

3.53

with


84

3.54

3.55

3.3.2 Multiple Integral Engine Order Responses

Based on the same principles developed for the Single Non-Integral & Integral Engine Order

Response Matrix-Based Models (see Sections 3.2.1 and 3.2.2) and derived from the Equation

3.49, the matrix-based model for multiple, simultaneous integral engine order frequency

responses is expressed in the Equations 3.56 to 3.58.

3.56

3.57

3.58

where

is the extracted probe displacement for the synchronous modal

frequency response no. r (r = 1...p) at the revolution no. i (i = 1...m) for a particular blade at probe no. j.


85


are constants from which the amplitude and phase of the synchronous modal frequency response no. r (r = 1...p) for a particular blade can be extracted.

is the steady state position for the combined synchronous modal frequency responses for a particular blade at the revolution no. i (i = 1...m).

is the fitted engine order excitation for the synchronous modal




engine order for the synchronous modal frequency response no. r (r = 1...p).


at the revolution no. i (i = 1...m) for the synchronous modal frequency response no. r (r = 1...p).

Therefore, for m revolutions and for an n probe configuration, Equations 3.56 to 3.58 can be


3.59

where

3.60

3.61


86

3.62

3.63

with

3.64

3.65

3.3.3 Conclusions to Section 3.3

The previous two sections (3.3.1 and 3.3.2) have provided two matrix-based models for

multiple, simultaneous non-integral and integral engine order frequency responses (see

Equations 3.49 and 3.59). Showing many similarities, the main noticeable difference regards the

extraction process of the steady state offset for asynchronous and synchronous responses.

The and matrices (see Equations 3.55 and 3.65) show those differences which have

previously been discussed in Sections 3.2.1 and 3.2.2.


87

The interface linking the non-integral / integral engine order matrix-based models in terms of

displacements at each probe for each revolution remains the same as the one described in

Section 3.2.3, leading to Equation 3.56 to be expressed as in Equation 3.66.

3.66

3.4 Quantitative and Qualitative Improvements of New Filtering Techniques

To demonstrate the quantitative and qualitative improvements of the two new filtering

techniques for single non-integral and integral engine order responses against the processes

developed by Russhard [9], a comparative analysis was carried out between the two methods

based on a number of theoretical test cases.

The results are presented in sections 3.4.1 and 3.4.2 for single non-integral and integral engine

order responses respectively. The parameters used to build each theoretical test case are

described below:

Targeted engine order responses:

Single non-integral engine order response = 3.16

Single integral engine order response = 3.0

Targeted blade tip amplitudes:

From 0.02 to 0.10 mm peak

With increment of 0.02 mm peak

Number of iterations:

100

Number of revolutions used for averaging:

From 2 to 10 revolutions

Introduced random background probe noise levels

From 0.01 to 0.10 mm peak

With increment of 0.01 mm peak


88

Sections 3.4.1 and 3.4.2 provide comparisons between the tip amplitudes extracted by

Russhard’s method and the new models for different numbers of probes, targeted amplitudes,

utilised number of revolutions and introduced background noise levels.

To compare the modal blade tip displacements extracted using the newly developed matrix-

based models (i.e. AABM and SABM) with the previous validated techniques [9], the

Confidence Interval (CI) statistical function has been used with a 95% confidence level as per

previous research work [4] [9]. Note, the CI function indicates that there is a 95% chance of

obtaining results within the bounds at the either side of the calculated mean

To assess uncertainties between the modal blade tip displacements extracted using the newly

developed matrix-based models (i.e. AABM and SABM) against previous validated techniques

[9], the “Confidence Interval” statistical function (CI) has been used. By keeping a 95% level of

confidence as per previous research work [4] [9], the selected level of confidence will determine

the bounds capturing the true value for 95% of the occurrences [37]. For example, a 95% level

of confidence covers 95% of the normal distribution with the probability of observing a value

outside of this area being less than 0.05 (i.e. probability of 0.025 in each tail of the distribution –

see Figure 3.12).

Figure 3.12 – Definition of Level of Confidence (LC)


89

3.4.1 Single Non-Integral Engine Order Response Matrix-Based Model

3.4.1.1 Case Study No 1 – Targeted non-integral engine order amplitude of 0.04 mm

peak

The plots displayed in Figure 3.13 provide mean extracted values from one hundred iterations

for each of the background probe noise bands (10 in totals) and for each selected number of

revolutions used to carry out the AABM averaging process. It should be highlighted that

Russhard’s filtering and processing techniques [9] are based on forty averaged revolutions and

one revolution respectively by default, for non-integral engine order responses.

In Figure 3.14, the 95% confidence interval mean values for both techniques are being provided

for each background probe noise band from one hundred iterations and for each averaging

revolution number selected for the AABM process.

The 95% Confidence Interval (CI) for mean differences between the ‘AABM / Russhard’

extracted amplitudes and the targeted blade tip amplitude are displayed in Figure 3.15.

The Figure 3.16 displays the absolute mean errors between the extracted and targeted blade tip

amplitudes and, for both methods their 95% CI for mean errors in Figure 3.17.

Finally, the variations between the 95% Confidence Interval for mean differences and for mean

errors for a 0.04 mm peak targeted amplitude for both techniques are displayed in Figure 3.18.


90

Figure 3.13 – Extracted amplitudes using AABM & Russhard’s filtering techniques

for a 0.04 mm peak targeted amplitude


91

Figure 3.14 – 95% CI mean Values for AABM and Russhard’s filtering techniques


Extracted from the information displayed in Figure 3.13, the following qualitative improvements

can be associated to the new AABM filtering technique when compared to the filtering and

processing methods of Russhard as shown in Figure 3.14. The new AABM processing method

shows:

1. A linear rising variation with a reducing gradient of the 95% CI mean values with the

increasing background probe noise levels and with the increasing number of

averaging revolutions,


92

2. An exponential decay of the calculated 95% CI mean values for each of the

selected background probe noise levels based on the increasing numbers of

revolutions to carry out the averaging.

Figure 3.15 – 95% CI mean differences between the ‘AABM / Russhard’ extracted amplitudes


From a quantitative point of view, Figure 3.15 clearly demonstrates that the AABM zeroing and

processing scatter in terms of its 95% CI for mean amplitude is lower than the techniques

developed by Russhard when using:

o 3 averaging revolutions for the background probe noise levels up to 0.02

mm peak,


mm peak,

o 5 averaging revolutions for all the selected background probe noise levels.


93

Figure 3.16 – Absolute mean errors for a 0.04 mm

peak targeted amplitude


94

Figure 3.17 – 95% CI mean error values for a 0.04 mm



95

Figure 3.18 - 95% CI mean differences between the extracted AABM and Russhard amplitudes


Based on the information displayed in Figure 3.16 and Figure 3.17, Figure 3.18 provides a

qualitative assessment between the two methods against predicted amplitude of 0.04 mm peak.

From five averaging revolutions and above and for all the background probe noise bands, the

95% CI for absolute mean associated to the AABM is at least 5.4% better with an uncertainty

reduced by +/- 1.5% when compared to Russhard’s method. Note that, for a background probe

noise band of 0.01 mm peak, the 95% CI for absolute mean differences associated to the

AABM techniques has been measured to be at least 28% better with an uncertainty reduced by

7% than Russhard’s method.


96

3.4.1.2 Case Study No 2 – Targeted non-integral engine order amplitudes of 0.02 and

0.04 mm peak

Extracted amplitudes for targeted signals of 0.02 and 0.04 mm peak using the new AABM

filtering and processing method have been assessed against the numbers of averaging

revolutions selected and against the different bands of background probe noise.

Figure 3.19 shows that the levels of absolute mean errors for each background probe noise

band have doubled from three averaging revolutions and above. Those increased levels of

errors are in line with the ratio of the two targeted amplitudes. These observations can also be

applied to the extracted errors for background noise bands of 0.01 to 0.08 mm peak based on a

two averaging revolution.

However, for the background noise bands above 0.08 mm peak, the distribution pattern of

absolute mean errors is no more comparable because of the exponential increase of the

absolute mean errors associated with the 0.02 mm peak targeted amplitude.

Displayed in Figure 3.20, the 95% CI for absolute mean errors show that the uncertainties

associated with the extracted amplitudes for both targeted amplitudes using the AABM method

is consistent for all the numbers of averaging revolutions and background probe noise bands

selected.

Concurring with the previous observations made on Figure 3.15, Figure 3.20 shows

improvements of the AABM technique when compared to Russhard’s one for smaller targeted

amplitudes with higher signal to noise ratios. In fact, Figure 3.21 clearly demonstrates that for

targeted amplitude of 0.02 mm peak, the AABM zeroing and processing scatter in terms of its

95% CI for mean amplitude is lower than the techniques developed by Russhard when using:


mm peak,


mm peak,



97

Figure 3.19 - Absolute mean errors for targeted amplitudes

of 0.02 and 0.04 mm peak


98

Figure 3.20 – 95% CI for Absolute Mean errors for targeted amplitudes



99

Figure 3.21 – 95% CI mean differences between the ‘AABM / Russhard’ extracted amplitudes


3.4.1.3 Case Study No 3 – Targeted non-integral engine order amplitudes with five

averaging revolutions

The previous two case studies have shown that if five revolutions are selected to carry out the

averaging process, then the mean errors and associated uncertainties for the AABM technique

are lower levels than the ones extracted using Russhard’s techniques.

For this third case study, the AABM technique has been assessed with the number of averaging

revolutions set to five, against variable targeted amplitudes (i.e. from 0.02 to 0.10 mm peak with

increment of 0.02 mm peak) and variable background noise levels.

Figure 3.22 and Figure 3.23 display clearly that as the amplitudes of the targeted signal

increase, the absolute mean errors and uncertainties (i.e. 95% CI for absolute mean error)

show:


100

1. A linear rising variation with a reducing gradient for each targeted amplitude due to

the increasing background probe noise levels

2. An exponential decay for each of the selected background probe noise levels as

targeted amplitude increases.


of 0.02 and 0.04 mm peak using AABM process


101


of 0.02 and 0.04 mm peak using AABM process

3.4.1.4 Conclusions to 3.4.1

The comparative analysis between the new AABM and Russhard techniques for non-integral

engine order responses has highlighted some clear improvements from a qualitative and

quantitative point of view.

From a qualitative point of view, the statistical analysis of the extracted information has shown

that the usage of the new AABM technique has lowered the absolute mean errors and

uncertainties when compared to the ones extracted using Russhard’s methodology, for all the

targeted amplitudes and background probe noise levels, as long as the minimum number of

revolutions to carry out the averaging process is equal to or greater than five.

From a quantitative point of view, despite linear rising variations with reducing gradients for

each of the targeted amplitudes, the absolute mean errors and uncertainties have been halved

when compared to Russhard’s process, as long as the minimum number of revolutions to carry

out the averaging process is equal to or greater than five. Indeed, the extracted mean errors


102

and uncertainties when using the old method have shown a continuous and linear rise with the

increasing background probe noise levels.

3.4.2 Single Integral Engine Order Response Matrix-Based Model

3.4.2.1 Case Study No 1 – Targeted integral engine order amplitude of 0.04 mm peak

Using the analysis model for synchronous responses defined in Section 3.2.2, a comparative

analysis similar to the one previously described for non-integral engine order responses (see

Section 3.4.1) was carried out. The statistical analysis results are displayed in Figure 3.25 to

Figure 3.34.

The plots displayed in Figure 3.24 provide mean extracted values for each of the background

probe noise bands based on one hundred iterations and for each selected number of

revolutions used to carry out the SABM averaging process. Note that for synchronous

responses, Russhard’s processing technique is based on a single revolution.

In Figure 3.25, the 95% confidence interval mean values for both techniques are being provided

for each background probe noise band based on one hundred iterations and for each averaging

revolution number selected for the SABM process.

The 95% Confidence Interval for mean differences between the ‘SABM / Russhard’ extracted

amplitudes and the targeted blade tip amplitude are displayed in Figure 3.26.

Figure 3.27 displays the absolute mean errors between the extracted and targeted blade tip

amplitudes and, for both methods their 95% CI for mean errors in Figure 3.28.

Finally, the variations between the 95% Confidence Interval for mean differences and for mean

errors for a 0.04 mm peak targeted amplitude for both techniques are displayed in Figure 3.29.


103

Figure 3.24 – Extracted amplitudes using SABM & Russhard’s filtering techniques



104

Figure 3.25 – 95% CI mean Values for SABM and Russhard’s filtering techniques


Extracted from the information displayed in Figure 3.24, the following qualitative improvements

can be associated to the new SABM filtering technique when compared to Russhard‘s method

as shown in Figure 3.25. The new SABM processing method shows:

1. A linear rising variation with a slight reducing gradient of the 95% CI mean values

with the increasing background probe noise levels and with the increasing number

of averaging revolutions,


105

2. An exponential decay of the calculated 95% CI mean values for each of the

selected background probe noise levels based on the increasing numbers of

revolutions to carry out the averaging.

Figure 3.26 – 95% CI mean differences between the ‘SABM / Russhard’ extracted amplitudes


From a quantitative point of view, Figure 3.25 clearly demonstrates that the SABM filtering and

processing scatter in terms of its 95% CI for mean amplitude for synchronous responses is

lower than Russhard’s process when using:

o 2 averaging revolutions for the background probe noise levels up to 0.02 mm peak,





106

Figure 3.27 – Absolute mean errors for a 0.04 mm



107

Figure 3.28 – 95% CI mean error values for a 0.04 mm



108

Figure 3.29 - 95% CI mean differences between the extracted SABM and Russhard amplitudes


Based on the information displayed Figure 3.27 and Figure 3.28, Figure 3.29 provides a

qualitative assessment between the two methods against predicted amplitude of 0.04 mm peak.

From five averaging revolutions and above and for all the background probe noise bands, the

95% CI for absolute mean associated to the SABM is at least 2.2% better with an uncertainty

reduced by +/- 0.8% when compared to Russhard method. Note that for a background probe

noise band of 0.01 mm peak, the 95% CI for absolute mean differences associated to the

SABM techniques has been measured to be at least 35% better with an uncertainty reduced by

8 % than the displacements extracted using the previous methods.


109

3.4.2.2 Case Study No 2 – Targeted integral engine order amplitudes of 0.02 and 0.04

mm peak using SABM

Extracted amplitudes for targeted signals of 0.02 and 0.04 mm peak using the new SABM

filtering and processing method for synchronous responses have been assessed against the

numbers of averaging revolutions selected and against the different bands of background probe

noise.

Figure 3.30 shows that the levels of absolute mean errors associated to the lower targeted

synchronous amplitude for each of the background probe noise bands are one half higher or

more than the 0.04 mm peak targeted amplitude, whatever the selected number of averaging

revolutions. As shown in Figure 3.31, those observations can be applied to the 95% CI for

absolute mean errors extracted for each background probe noise band and selected number of

averaging revolutions.

Concurring with the previous observations made on Figure 3.26, Figure 3.31 shows

improvements of the SABM technique when compared to Russhard’s one for smaller targeted

amplitudes with higher signal to noise ratios.

In fact, Figure 3.32 clearly demonstrates that for targeted amplitude of 0.02 mm peak, the

SABM scatter in terms of its 95% CI for mean amplitude is lower than the techniques developed

by Russhard when using:






110

Figure 3.30 - Absolute mean errors for targeted amplitudes



111




112

Figure 3.32 – 95% CI mean differences between the ‘SABM / Russhard’ extracted amplitudes


3.4.2.3 Case Study No 3 – Targeted integral engine order amplitudes with five averaging

revolutions

The previous two case studies have shown (as well as the ones described in Section 3.4.1 for

non-integral engine order responses) that if five revolutions are selected to carry out the

averaging process, then the mean errors and associated uncertainties for the SABM technique

are lower levels than the ones extracted using Russhard’s techniques.

For this third case study, the SABM technique has been assessed with the number of averaging

revolutions set to five, against variable targeted synchronous amplitudes (i.e. from 0.02 to 0.10

mm peak with increment of 0.02 mm peak) with variable background noise levels.

Figure 3.33 and Figure 3.34 display clearly that as the amplitudes of the targeted signal

increase, the absolute mean errors and uncertainties (i.e. 95% CI for absolute mean error)

show:


113

1. A linear rising variation with increasing background probe noise levels with a

reducing gradient as the targeted amplitude increases.

2. An exponential decay for each of the selected background probe noise levels as

targeted amplitude increases.

Note that the linear variation described above is not defined as well as for the lowest of the

targeted amplitudes. This is noticeable with the increasing background probe noise levels (i.e.

high signal to noise ratio) and with the reported high level of absolute mean errors for this

amplitude.


of 0.02 and 0.04 mm peak using SABM process


114


of 0.02 and 0.04 mm peak using SABM process

3.4.2.4 Conclusions to 3.4.2

The comparative analysis between the new ABM and Russhard techniques for integral engine

order responses has highlighted some clear improvements from a qualitative and quantitative

point of view.

From a qualitative point of view, the statistical analysis of the extracted information has shown

that the usage of the new SABM technique has again lower the absolute mean errors and

uncertainties when compared to the ones extracted using Russhard’s methodology.

This is the case as long as the minimum number of revolutions to carry out the averaging

process is equal to or greater than five for all the targeted amplitudes and background probe

noise levels.

From a quantitative point of view, despite linear rising variations with reducing gradients for

each of the targeted amplitudes, the absolute mean errors and uncertainties have been reduced

by at least two thirds when compared to Russhard’s process, as long as the minimum number

of revolutions to carry out the averaging process is also equal to or greater than five.


115

Indeed, the extracted mean errors and uncertainties when using the old method have shown a

continuous and linear rise with the increasing background probe noise levels.

3.5 New Tracking Process for Extracting Blade Modal Amplitude Responses

Using the analysis techniques developed by Russhard, three compulsory preparatory steps

(see Section 3.1, Figure 3.1) are required before extracting the blade tip amplitudes linked to

asynchronous or synchronous activities:

o Generation of the blade activity mask

o Application of the noise filter removal

o Removal of the probe steady state offset

With the ABM models developed for asynchronous and synchronous activities, these three

steps are no longer required. Indeed, by using the predicted Finite Element information (i.e.

predicted modal frequency responses vs. rotational speeds, see Figure 3.35), the flow diagram

displayed as per Figure 3.36 can be applied to extract blade tip amplitudes for asynchronous

and synchronous activities at the same time.

Figure 3.35 – Finite Element Predictions


116

Figure 3.36 – New Tracking Method Process

The above flow diagram describes and provides an automated extraction process based solely

on FEM predictions. In this scenario, the process is aiming at a single frequency per mode at

each targeted rotational speed.

Forced vibration of gas turbine turbo machinery blades and vanes is typically caused by flow

disturbances which are introduced by nearby obstructions, such as other blade rows, struts, etc.


117

For a tuned system, aliasing does not affect the frequency of excitation but it does affect the

nodal diameter that the rotor ‘feels’. For a bladed disc (or blisc), a force is only applied to the

rotor through the blades. Because there are a finite number of blades, engine order excitation

greater than half the number of blades will be aliased to lower values through spatial aliasing.

However, a bladed disc may be mistuned by small variations in frequency of individual blades.

This causes a significant change in the structure such that the vibration modes are no longer a

set of individual nodal diameter modes [38]. The modes of a mistuned system contain a

contribution from many nodal diameters and therefore many modes can be excited by a single

nodal diameter excitation.

Therefore, instead of tracking a single blade mode frequency, a frequency band defined by the

FE cyclic symmetric analyses will be tracked.

The best BTT frequency fit for each blade is extracted based on an incremental frequency (i.e.

incremental engine order) located between the lower and upper frequencies of the modal

frequency band of the FE cyclic symmetric analyses.

For the new tracking method, the incremental frequency value is defined by the user and the

value can be fixed or modal frequency dependent. This is a clear improvement in comparison

with the previous method [9] regarding the accuracy of the extracted modal frequencies. Indeed,

for a targeted blade mode frequency, the incremental search was based on a tenth of an engine

order whatever the rotational speed of the engine. For example, if the rotational speed of the

engine is equal to 1000 RPM, then the incremental frequency value is set to 1.6 Hz and if the

engine is rotating at 10000 RPM, then the incremental value is 10 times higher.

Using the new tracking method, the BTT analysis can be compared to the strain gauge analysis

by matching the frequency analysis bin width instead of the number of revolutions [9]. Indeed,

Russhard used the equation proposed by Garcia and Knappett [39] based upon their

experience with strain gauge measurements to provide a new method for averaging BTT data.

Since the new ABM models for asynchronous and synchronous responses have already built-in

averaging methods, the incremental frequency approach is another additional improvement for

producing data which can be directly compared and in a more accurate manner to strain gauge

processed output.


118

3.6 Nodal Diameter Extraction Method

Compressor and turbine blades have a number of natural modes. The modes are characterised

by their mode shapes (i.e. displacement of the vibrating blade) and their nodal diameters,

forming a circumferential amplitude distribution which rotates on the rotor. The number of nodal

diameters of a mode (ND) indicates the number of diameter lines that go through zero

displacement. For example, Figure 3.37 shows the out-of-plane displacements of a two nodal

diameter pattern (i.e. 2 ND).

Figure 3.37 – Two Nodal Diameter Pattern

The maximum number of nodal diameters ( ) is defined by the number of blades ( ),

using the following equations:

For even number of blades,

3.67

For odd number of blades ( ),


119

3.68

Differences between integral and non-integral engine order responses exist; hence the

knowledge of these travelling waves in the rotating and static frames is important to assess the

differences in the measurement results.

The differences between synchronous and asynchronous resonances can be associated to the

speed of the travelling waves in the static frame of reference.

For synchronous resonances, the sine wave forming the circumferential amplitude distributions

travels at the same speed as the rotational speed of the rotor and in the opposite direction (i.e.

backwards). Hence, in the static frame of reference, the measured phase of the targeted

vibration signal at each probe does not change with time.

For non-integral engine order responses, the sine wave forming the circumferential amplitude

distributions does not travel at the same speed as the rotational speed of the rotor. Hence, this

implies that in the static frame of reference:

1. The measured phase of the targeted vibration signal at each probe changes with

time,

2. The measured blade tip displacements and the proportion of the amplitudes at each

probe are not consistent.

During blade vibrations, the regions of displacement including the nodal diameters move around

the rotor circumference and the combined circumferential amplitude patterns are observed by

each individual probe mounted on the rotor casing.

Hence, the extraction of nodal diameter pattern for each vibratory response to assess the

blade’s failure position which is dependent on the mode shape is very important.


120

Characterised by its frequency, the speed of a travelling wave can be converted from a static

frame of reference to a rotating frame of reference and vice versa by using the following

equation:

3.69

where

is the frequency (i.e. speed) of the travelling wave in the rotating frame of reference.

is the frequency (i.e. speed) of the travelling wave in the static frame of reference.

The method developed by Russhard [9] requires the extraction of the frequency (FS) of the

travelling wave in the static frame of reference in order to calculate the frequency (FR) of the

travelling wave in the rotating frame of reference (i.e. blade frequency).

To do so and based on the method developed by Chi and Watkins [40], the extraction of the

nodal diameter content is carried out by observing the vibration from two different angular

positions (i.e. circumferential probe positions) and using Equation 3.70.

3.70

where

is the phase difference of the observed frequency at the two probes.

is the circumferential angular separation of the two selected probes.

To determine the travelling wave and its phase, a Fourier transform in the time domain of a two

probe data set can be performed per revolution as shown in Figure 3.38.


121

Figure 3.38 – Static frame of reference FFT performed using a single probe

Note that the coordinates of the x-axis are defined as ‘EO + ND’ with a maximum x-axis range

defined as per Equations 3.67 and 3.68.

By performing a cross spectrum analysis between the two selected probes, the phase ‘ ’ can

be extracted at a selected ‘EO + ND’ peak response. Then a blade frequency can be calculated

using Equation 3.70 and Equation 3.69. Then using Equation 3.1 after having performed the

BTT Six Step Process Data Preparation described in Section 3.1, the BTT analysis process can

be performed.

One issue associated with the above process is the uncertainty associated to the determination

of the ND content. If the phase ‘ ’ is wrongly determined, then the ND content of the targeted

vibratory response would be incorrect which will lead to an inaccurate assessment of the

reported amplitude of each blade, of the circumferential amplitude distribution and of the mode

shape.

By performing small increments of the engine order using the new algorithms described in

Sections 3.2 and 3.3, the issue linked to Russhard’s method for extracting the phase ‘ ’ does


122

no longer matter since the best fitted frequency (FR) for the travelling wave in the rotating frame

of reference has already been extracted without the requirement of the nodal diameter content

of the targeted vibratory phenomena.

Using the equation 3.69, the best fitted frequency (FR) and the information available using the

static frame of reference FFT performed using a single, the nodal diameter content can be

extracted by solving Equation 3.71.

3.71

An assurance criterion for the extracted nodal diameter (NDac) can be inferred by using

Equation 3.72.

3.72

Equation 3.72 demonstrates that an assurance criterion of 1 means a hundred percent level of

confidence in the extracted value of the nodal diameter content for the targeted response.


123

3.7 Real-Time Analysis Improvements

The improvements associated to the real time data analysis when compared to the process

defined by Russhard [9], are clear due to the new ABM models (see Sections 3.2 and 3.3).

Indeed, using the real-time processing techniques developed by Russhard, a minimum of thirty

two revolutions of the rotor is required.

At the time, Russhard reported that the problem associated with the real-time integral engine

order response monitoring was the difficulty of removing the steady state displacement errors in

the probes whilst leaving the required steady state data intact. By developing a new method for

real-time monitoring analysis using only thirty two revolutions of the rotor, Russhard claimed that

the latency was typically reduced to less than 0.25 seconds.

Demonstrated in Section 3.4 and based on all the test cases studied (i.e. targeted amplitudes

vs. background noise levels), the minimum required number of revolutions has been defined to

5 revolutions of the rotor.

Hence, the problem described earlier by Russhard regarding the extraction of the individual

probe steady states has therefore been improved by at least a factor of 6 (i.e. latency of the

measurement reduced to less than 0.042 seconds).

In addition to the improved latency, the uncertainty and signal-to-noise ratio work described in

Chapter 5 can be used real-time instead of basing uncertainty on some off-line background

work as per Russhard’s real-time method.


124


The Blade Tip Timing technology has been previously limited to generating off-line and real-time

results with the difficulty of removing accurately the steady state displacement errors in the

probes whilst leaving the required steady state data intact.

Methods and algorithms have been developed in the past to do so by averaging the collected

probe data over a number of revolutions of the rotor, with two different values for the off-line and

real-time analysis (i.e. 40 and 32 revolutions respectively).

The problems associated with the removal of the probe steady state displacement data has now

been removed by integrating the three different processes into the new developed AABM

models for asynchronous and synchronous responses.

This chapter has detailed and demonstrated the clear advantages associated to these two

models for asynchronous and synchronous responses and they are:

1. Seamless automated averaging build-in matrix technique,

2. Frequency-domain adaptive filter,

3. Qualitative and quantitative improvements when compared to the Russhard’s validated

techniques [9], currently in use at Rolls-Royce plc,

4. Nodal diameter information no more required before the extraction of non-integral

engine order responses.

5. Reduction of the number of preparatory steps for processing the data, leading to speed

and efficiency improvements,

6. Reduction of the processing latency for real-time monitoring.

Chapter 4 Adapting BTT for Equally Probe Spacing Constraints

125


To position optical probes circumferentially on a compressor casing, Finite Element information

about the expected blade excitation orders is necessary. Based on an iterative process, a

number of solutions (i.e. circumferential probe locations) can be generated based on targeted

engine orders, number of probes and the exclusion areas.

For Turbine applications, the maximum number of probes is governed by the level of distortion,

the tip clearance losses, the predicted life of the component, the inter-segment leakages.

The schematic in Figure 4.1 displays the layout of a segment, a High Pressure Turbine (HPT)

blade and its fence for the BTT measurements, HP and IP Nozzle Guide Vanes (NGV).

Figure 4.1 – HPT Blade and Segment

The optimal location for the probe is at the mid-arc point of the segment since this is the point of

lowest thermal distortion, as shown by a Finite Element analysis [41] at maximum Turbine Entry

Temperature (TET), see Figure 4.2. The results displayed in Figure 4.2 show that the smallest

segment distortion in terms of displacements is located at the mid-arc point (i.e. Point 1 - dark

blue colour), with the maximum displacement at Point 2 (i.e. red colour). By positioning probes


126

at the lowest distortion point, the measurement errors due to the temperature gradient effects

are therefore minimised.

Figure 4.2 – HPT Segment at Maximum TET

With current BTT analysis techniques, the extraction of the blade tip amplitudes for engine

orders where their cycles are a multiple of the angular sector of one segment is impossible,

hence limiting severely the implementation of the BTT technology into turbine applications.

This chapter details the different issues linked to the current BTT analysis techniques based on

an Equally Spaced Probe (ESP) configuration, followed by a description of a new processing

technique which enables an accurate extraction of the turbine blade tip amplitudes.

4.1 Processing Issues Linked To Equally Spaced Probe Configuration

To highlight the processing issues linked to an ESP configuration when using the BTT analysis

technique developed so far today, a 10 engine order response over one revolution with zero

offset is displayed in Figure 4.3 based on the circumferential probe angles defined in Section

3.2.1 and with the number of segments equal to 20.


127

Figure 4.3 – ESP Configuration – 10EO Signal

Based on Figure 4.3, it is clear that a unique sine wave in terms of phase, and hence amplitude,

cannot be defined through the given data points. The displayed amplitudes in Figure 4.3 are

calculated from raw TOA data (see Section 3.1.2) and hence are not necessarily the maximum

tip displacements for the targeted modal response (i.e. 10EO). This is because if the phase is

not known to be defined correctly, neither is the targeted modal blade tip maximum amplitude

as shown in Figure 4.4. Therefore, the corresponding stress will be calculated incorrectly

leading to an erroneous assessment of the component life.


128

Figure 4.4 – ESP Configuration – 10EO Signals with two different choices of phase

By assessing the condition number based on the model developed by Russhard [9], the

processing issues detailed above can be highlighted at a very early stage. The matrix condition

number is the ratio of the largest to the smallest singular value. A large condition number means

that the solution is sensitive to small changes in blade tip displacement, leading to numerical

issues when calculating the solution. Russhard [9] stated that a well-conditioned matrix should

have a condition number in between 1 and 10.

Using Russhard’s synchronous response model (see Section 3.1) and the 8 probe configuration

(see Section 3.2.1) with a fitted engine order of 10, the matrix can be written as:

=

The singular values, the square roots of the eigenvalues of the MTM, where M

T is the transpose,

are equal to:


129

2.828

2.828

0

The ratio of the largest to the smallest singular value gives therefore a condition number of

infinity. This high number defines an ill-conditioned matrix.

In summary, the condition of the problem described above is governed by two parameters only:

The circumferential angular probe positions

The targeted engine order.

Based on the new developed matrix-based models (see Sections 3.3.1 and 3.3.2), a novel

analysis technique has been developed which removes these constraints which are mostly

linked to Turbine applications.

The new technique runs a pre-analysis process to find out and to provide a well-conditioned

matrix by reducing the condition number to its lowest value by:

1) Introducing a virtual engine order response to the measured probe displacements.

2) Removing a number of probes from the original configuration and replacing them by an

equal number of virtual probe(s).

The following sections provide a description of the processes for the virtual probe and engine

order optimisation, for the blade tip amplitude extraction and for the verification and validation of

the assumptions.


130

4.2 Virtual Probe & Engine Order Optimisation Process

The overall virtual probe and engine order optimisation process which includes the selection of

the best virtual probe position and the best virtual engine order is summarised by the following

flowchart.

Step No 1

Step No 2

Step No 3

Step No 4

Figure 4.5 – Overall Virtual Probe and EO Optimisation Process

The notion of probe permutation for the virtual optimisation process is the act of permuting a

fixed number of probes from a given set of probes. Also known as sequences without repetition,

the total number of permutations is given by:

4.1

It is noted that .

Select the best virtual probe position and the best virtual engine order from one of

the probe permutations

Add virtual engine order amplitude to each probe from the chosen original probe permutation and to the virtual

probe

Extract the measured and the virtual EO information

Verify & validate the virtual assumptions


131

where

is the number of probes in the original probe configuration.

is a fixed number of probes chosen from the original probe configuration.

is a number of virtual probes.

However, before starting the selection process for the best virtual engine order(s) to remove the

obstacles linked to an equally spaced probe configuration, it is necessary to establish the new

virtual matrix-based models (i.e. for integral and non-integral engine order responses). Those

two new models will define the best suited virtual engine order(s) based on their condition

number(s).

4.2.1 Multiple Simultaneous Non-Integral Engine Order Virtual Matrix Model

Based on the same principles developed for the Multiple Non-Integral Engine Order Response

Matrix-Based models (see Section 3.3.1), the virtual matrix-based model for multiple,

simultaneous integral engine order frequency responses is also derived from the Equation 3.49

for simultaneous non-integral engine order frequency responses (see Equations 3.56 to 3.58).

4.2

where

4.3

4.4

4.5

4.6

4.7


132

and

is the measured blade tip displacement at the revolution no. i (i = 1...m) for a particular blade at probe no. q (q = 1...n) from the best permuted probe selection.

is the added blade tip displacement for the virtual modal frequency

response no. u (u = 1...v) at the revolution no. i (i = 1...m) for a particular blade at probe no. q (q = 1...n) from the best permuted probe selection.

is a user-defined value for the blade tip amplitudes for a virtual

engine order response no. u (u = 1...v).

is the extracted displacement for the asynchronous modal

frequency response no. r (r = 1...k) at the revolution no. i (i = 1...m) for a particular blade at probe no. q (q = 1...n) from the best permuted probe selection.

is the extracted virtual displacement for the virtual modal frequency response no. u (u = 1...v) at the revolution no. i (i = 1...m) for a particular blade at probe no. q (q = 1...n) from the best permuted probe selection.

is the steady state position for an asynchronous modal frequency response for a particular blade at probe no. j ( j = 1...n ).

is the residual displacement term at the revolution no. i (i = 1...m) at probe no. q (q = 1...n) from the best permuted probe selection.

is the corrected circumferential angular position of the probe q (q =

1...n) from the best permuted probe selection at the revolution no. i (i = 1...m) for the asynchronous modal frequency response no. r (r = 1...k).


1...n) from the best permuted probe selection at the revolution no. i (i = 1...m) for the virtual modal frequency response no. u (u = 1...v).

is the angular circumferential position of probe q (q= 1...n ) from the best permuted probe selection.


engine order for the virtual asynchronous modal frequency response no. u (u = 1...v).


133

Based on m revolutions with an original configuration of n probes, with ‘p’ targeted non-integral

engine order responses and ‘v’ virtual engine order responses, Equations 4.2 to 4.7 can be


4.8

where

4.9

4.10

4.11

4.12


134

4.13

4.14

with

4.15

4.16


135

4.17

The matrix shown in Equation 4.15 displays a few more terms than the ones described in

Equation 4.16. The to additional components are the predicted measured blade tip

displacements at each of the virtual probe positions, which are unknown. To extract all the

components related to the measured and virtual information in a single pass process, Equations

4.9, 4.13 and 4.17 need to be altered. Those modifications are displayed in Equations 4.18 to

4.20.

4.18

4.19


136

4.20

Note that the to terms in Equation 4.19 represent the averaged predicted measured

blade tip amplitudes for each of the to terms (see Equation 4.9) at each virtual

probe position processed over m revolutions.

Having fully defined the virtual based model for multiple simultaneous non-integral engine order

responses, the following step of the process is to find out what are the best suited virtual engine

order(s) and virtual probe position(s) for the targeted engine order(s) (see Section 4.3).

4.2.2 Multiple Simultaneous Integral Engine Order Virtual Matrix Model

The previous section has successfully defined a virtual matrix-based model for multiple

simultaneous non-integral engine order frequency responses to deal with the processing issues

related to ESP configurations. However, if the targeted engine orders are integral, then a new

model needs to be defined. Indeed, the techniques previously developed for extracting the

probe offsets (see Equations 4.19 and 4.20) cannot be used for the following reasons.

For multiple simultaneous integral engine order frequency responses, the measured blade tip

displacements are equal in amplitude (see Figure 3.10 as an example) at each probe over a

selected number of revolutions. Therefore, the introduction of virtual engine order

displacements to measured BTT data, which in most cases will be non-integral to lower the

condition number, must preserve the built-in characteristics of the targeted engine order

frequency responses (i.e. steady state position). Based on the virtual model previously


137

developed for asynchronous responses (see 4.2 to 4.7) and on the matrix-based model

developed for multiple simultaneous integral engine order responses (see Section 3.3.2), a new

virtual matrix-based model for multiple simultaneous integral engine order responses has been

developed.

4.21

4.22

4.23

4.24

4.25

4.26

where

is the measured blade tip displacement at the revolution no. i (i = 1...m) for a particular blade at probe no. q (q = 1...n) from the best permuted probe selection.

is the added blade tip displacement for the virtual modal frequency

response no. u (u = 1...v) at the revolution no. i (i = 1...m) for a particular blade at probe no. q (q = 1...n) from the best permuted probe selection.



is the extracted displacement for the asynchronous modal

frequency response no. r (r = 1...p) at the revolution no. i (i = 1...m) for a particular blade at probe no. q (q = 1...n) from the best permuted probe selection.

is the extracted virtual displacement for the virtual modal frequency response no. u (u = 1...v) at the revolution no. i (i = 1...m) for a particular blade at probe no. q (q = 1...n) from the best permuted probe selection.


138


is the residual displacement term at the revolution no. i (i = 1...m) at probe no. q (q = 1...n) from the best permuted probe selection.


1...n) from the best permuted probe selection at the revolution no. i (i = 1...m) for the asynchronous modal frequency response no. r (r = 1...k).


1...n) from the best permuted probe selection for the virtual modal frequency response no. u (u = 1...v).

is the angular circumferential position of probe q (q= 1...n) from the best permuted probe selection.

Based on m revolutions with an original configuration of n probes, with ‘p’ targeted integral

engine order responses and ‘v’ virtual engine order responses, Equations 4.21 to 4.26 can be


4.27

where

4.28


139

4.29

4.30

4.31

4.32

4.33


140

with

4.34

4.35

4.36


141

Note that the to terms in Equation 4.32 represent the averaged predicted measured

blade tip amplitudes for each of the to terms (see Equation 4.9) at each virtual probe

position processed over m revolutions.

Having fully defined the virtual based model for multiple simultaneous integral engine order

responses, the following step of the process is to find out what are the best suited virtual engine

order(s) and virtual probe position(s) for the targeted engine order(s) (see Section 4.3).

4.3 Virtual Optimisation Process - Theoretical Example

The following sections will provide more specific details about each of the four different steps of

the optimisation process based on a theoretical example.

4.3.1 Step No 1 - Selection of Best Virtual Engine Order and Virtual Probe Position

Based on a three-stage iterative process (probe permutation(s), virtual engine order(s) and

virtual probe position(s)), the virtual matrix-based model is declared optimised depending on the

extracted value of its condition number for a specific targeted engine order. If a condition

number is found to be less than 10 (Russhard [9]) then the optimisation process will be

considered successful and stopped.

To limit the number of iterations during the optimisation process, the following boundaries are

being set up by default:

1) The value of the virtual engine order should not exceed 20 starting from 1 with an

increment of 0.1.

2) The circumferential angular virtual probe position can be selected between 0 and 359.9

degrees with an increment of 0.1.

To demonstrate the effectiveness of the virtual matrix-based model to extract the vibratory

information of a targeted integral engine order response with an equally spaced probe


142

configuration, the example introduced in Section 4.1 (see Figure 4.3 and Table 4.1) is being re-

assessed based on the boundaries defined above. It is noted that the effect of noise is not

included. The process will be applied on real data later in Chapter 6. For illustrative purpose,

1mm peak blade tip amplitude has been used.

Using the information provided earlier and described in Figure 4.3, the condition number (ratio

of the largest to the smallest singular values) extracted from Russhard’s model [9], was

calculated to be infinity for a targeted engine order of 10.

By means of Equation 4.27 and based on the three-stage iterative process, the lowest condition

number extracted for a single virtual engine order and a single virtual probe position from the

following selected iterative information has been found to be equal to 9.294.

The optimisation process has defined Probe 3 of the original ESP configuration to be removed

(see Table 4.1, parameter ) and has defined that:

1. The virtual probe should be positioned at a circumferential angular position of 44.6

degrees (see Table 4.2, parameter )

2. The virtual engine order should be equal to 17.7 (see Table 4.2, parameter ).

8.74 170 74 188 74 206.74

224.74 242.74 296.74 314.74

Table 4.1 - Original Equally Spaced Probe Configuration

8.74

44.6 170.74

206.74

224.74

242.74 296.74

314.74

Table 4.2 – Permuted Configuration with Virtual Probe and Virtual Engine Order


143

Note that in this example, no threshold was set for the condition number to stop the iterative

process.

4.3.2 Step No 2 - Combined Probe Virtual and Measured Displacements

The following step of the process after having defined the best virtual engine order(s) and the

best virtual probe circumferential angular position(s) is to calculate the virtual tip displacement

at each probe angle from the best permuted probe selection using Equations 4.3 or 4.22 and

the information displayed in Table 4.3. Table 4.4 provides the displacements of the targeted

engine order response at each revolution including DC offsets.

By calculating the virtual displacements at each probe using Equation 4.22 in this case since

the targeted engine order is 10, and by adding them to their corresponding measured blade tip

displacements using Equation 4.18 or 4.28, the combined displacements as shown in Table 4.5

can now be extracted using the equally spaced probe model defined in Equation 4.27.

Amplitude

Targeted EO amplitude (mm 0-peak) 1.00

Virtual EO amplitude (mm 0-peak) 1.00

DC Offset Rev No 1 (mm) 0.10

DC Offset Rev No 2 (mm) -0.20

Table 4.3 – ESP General Information


144

Rev

No

Probe

No

Probe Position

(deg)

Targeted EO

Amplitude

(mm)

DC Offset

(mm)

Combined

Displacement

(mm)

1 1 8.74 +0.999 0.10 +1.099

1 2 170.74 -0.999 0.10 -0.899

1 3 188.74 +0.999 0.10 +1.099

1 4 206.74 -0.999 0.10 -0.899

1 5 224.74 +0.999 0.10 +1.099

1 6 242.74 -0.999 0.10 -0.899

1 7 296.74 +0.999 0.10 +1.099

1 8 314.74 -0.999 0.10 -0.899

2 1 368.74 +0.999 -0.20 +0.799

2 2 530.74 -0.999 -0.20 -1.199

2 3 548.74 +0.999 -0.20 +0.799

2 4 566.74 -0.999 -0.20 -1.199

2 5 584.74 +0.999 -0.20 +0.799

2 6 602.74 -0.999 -0.20 -1.199

2 7 656.74 +0.999 -0.20 +0.799

2 8 674.74 -0.999 -0.20 -1.199

Table 4.4 – Targeted EO Information

It is noted that the two rows shaded in an orange colour, defined the measured blade tip

displacement at Probe No 3 of the original equally spaced probe configuration (see Table 4.1),

from which the optimisation process has removed (See Section 4.3.1).

However, the green shaded rows in Table 4.5, define the information associated with added

virtual probe.


145

Rev

No

New

Probe

No

New Probe

Position

(deg)

Targeted

EO

Amplitude

(mm)

Virtual

EO

Amplitude

(mm)

DC

Offset

(mm)

Combined

Displacement

(mm)

1 1 8.74 +0.999 +0.427 0.1 1.526

1 2 44.6 ? +0.936 ? ? + (0.936) + ?

1 3 170.74 -0.999 +0.614 0.1 -0.285

1 4 206.74 -0.999 +0.860 0.1 -0.039

1 5 224.74 +0.999 +0.307 0.1 1.406

1 6 242.74 -0.999 -0.399 0.1 -1.298

1 7 296.74 +0.999 -0.534 0.1 0.565

1 8 314.74 -0.999 +0.158 0.1 -0.741

2 1 368.74 +0.999 +0.728 -0.2 1.527

2 2 404.60 ? -0.624 ? ? + (-0.624) + ?

2 3 530.74 -0.999 +0.561 -0.2 -0.638

2 4 566.74 -0.999 -0.751 -0.2 -1.950

2 5 584.74 +0.999 -1.000 -0.2 -0.201

2 6 602.74 -0.999 -0.749 -0.2 -1.948

2 7 656.74 +0.999 +0.969 -0.2 1.768

2 8 674.74 -0.999 +0.890 -0.2 -0.309

Table 4.5 – Targeted + Virtual EO & DC Information

With the removal of the mathematical restrictions associated to the original equally spaced

probe configuration (see Section 4.1) by adding virtual information to the targeted engine order

responses as shown on Figure 4.6, the extraction process can now be performed (see Section

4.3.3). Figure 4.6 clearly highlights the effects of the virtual information when compared to the

original targeted engine order responses displayed in Figure 4.3.


146

Figure 4.6 – ESP Configuration – Targeted 10EO + 17.7EO Virtual Signals

4.3.3 Step No 3 - Extraction of Targeted and Virtual Vibratory Information

To extract the coefficients defined in Equations 4.30, 4.31 and, 4.32, Equation 4.27 must be

transformed as shown in Equation 4.37.

4.37

Based on Singular Value Decomposition, the matrix can be factored as:

4.38


147

where U is an m × m orthogonal matrix whose columns are the eigenvectors of , V is a n ×

n orthogonal matrix whose columns are the eigenvectors of , and is a m × n matrix of the

form:

4.39

where the 0’s denote appropriately sized zero matrices and the diagonal matrix in the top left

hand corner is composed of the singular values of A, which are the positive square roots of the

non-zero eigenvalues of ,, 1 ≥ 2... ≥ r ≥ 0 where r = rank( ) Problems arise when one of

the ’s is so small that its value is dominated by round-off error. The more the ’s are affected

by this issue, the more badly conditioned A is.

The extractions of the coefficients are performed by computing the Moore-

Penrose inverse of Equation 4.37:

4.40

where

4.41

Using the information of the ESP example detailed in Section 4.1 and the combined

displacements displayed in Table 4.5, the ESP coefficients are calculated to be equal to:


148

=

4.42


149

4.3.4 Step No 4 - Verification and Confirmation of Assumptions

The calculated vibratory information (see Equation 4.42) for the targeted and the virtual

responses requires some levels of verification and validation. Since the extraction of this ESP

information has been made possible thanks to the introduction of some elements which were

not part of the original captured information, a level of confidence is required and needed about

the extraction process by assessing the levels of uncertainty [42].

The verification process is based solely on information linked to the virtual elements. A Factor of

Validity (FoV), equal to the square root of the sum of the squares of each individual normalised

virtual engine order amplitude error can be extracted as per Equation 4.43.

4.43

where

is the calculated virtual coefficient of the sine term of a virtual engine order response no. u (u = 1...v).

is the calculated virtual coefficient of the cosine term of a virtual engine order response no. u (u = 1...v).



The factor provides a level of confidence about the blade tip amplitude extraction process with

the introduction of the virtual information into the original data. A confidence level of one

hundred percent in extracting the right virtual engine order amplitude(s) will be associated to a

FoV equal to one.

Using the extracted information as per Equation 4.42, the FoV is defined as:


150

4.44

As described in Section 4.2, the virtual probe and virtual engine order optimisation process is

based on removing a number of probes and replacing them with virtual probes in order to

improve the condition number. Hence, the information collected at these unused original probe

positions can now be assessed against the theoretical blade tip amplitudes (Equation 4.37).

Hence, the following step is to provide a Factor of Conformity (FoC) to assess the calculated

blade amplitude against the original measured blade tip displacements at the unused probe

position(s).

A factor of conformity for each of the unused probe positions defined by the index t and equal to

the square root of the sum of the squares of the normalised calculated amplitude errors at each

probe t at each revolution can be extracted using Equation 4.45 for non-integral engine order

responses or Equation 4.46 for integral engine order responses.

4.45

4.46

is the calculated displacement for the asynchronous modal

frequency response no. r (r = 1...k) at the revolution no. i (i = 1...m) for a particular blade at the unused probe no. t.

is the calculated displacement for the synchronous modal frequency response no. r (r = 1...k) at the revolution no. i (i = 1...m) for a particular blade at the unused probe no. t.


151

is the measured blade tip displacement at the revolution no. i (i = 1...m) for a particular blade at an unused probe no. t.

is the steady state position for the combined asynchronous modal frequency responses for a particular blade at the revolution no. i (i = 1...m).


The factor provides a level of confidence about the blade tip amplitude extraction process using

the introduction of the virtual information into the original data. A confidence level of one

hundred percent in extracting the measured engine order amplitude(s) will be associated to a

FoC equal to one.

Using the information displayed in Table 4.4 and Equation 4.23, the factor of conformity for the

targeted synchronous response can be calculated as shown below for the unused probe no. 3

of the original probe configuration defined in Section 4.3.

4.47

Using the test case information defined in Section 4.3, the new ESP algorithms have allowed

the extraction of the targeted blade tip amplitudes with a factor of validity of 0.973 and a factor

of conformity equal to 0.983.

The differences between the two factors to one are linked with DC offsets between the two

successive revolutions. To show the effects of smaller targeted amplitudes and DC offsets

values of the extracted ESP coefficients, Test cases were run and are summarised in Table 4.6.


152

Engine Order Amplitude (mm 0-peak)

Targeted 1.00 1.00 1.00 0.50 0.04 0.04 0.02

Virtual 1.00 1.00 1.00 1.00 0.5 0.1 0.1

DC Offset (mm)

Rev No 1 0.10 0.01 0.00 0.01 0.01 0.01 0.01

Rev No 2 -0.20 -0.02 0.00 -0.02 -0.02 -0.02 -0.01

Extracted ESP Coefficients

s1,1 +0.999 +0.999 +0.999 +0.500 +0.040 +0.040 +0.020

s1,2 +0.022 +0.021 +0.021 +0.011 +0.001 +0.001 +0.000

v1,1 +0.973 +0.997 +1.000 +0.997 +0.497 +0.097 +0.098

v1,2 +0.004 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000

c1 +0.090 +0.009 +0.000 +0.009 +0.009 +0.009 +0.009

c2 -0.182 -0.018 +0.000 -0.018 -0.018 -0.018 -0.009

c3 +0.951 +0.993 +0.998 +0.494 +0.035 +0.035 +0.020

ESP Factors

FoV 0.973 0.997 1.000 0.997 0.994 0.973 0.982

FoC 0.983 0.998 1.000 0.997 0.934 0.934 0.913

Table 4.6 – Summarised ESP Test Cases

Table 4.6 shows that for smaller DC offset values, the ESP factors are closer to unity as

expected and there are no issues with the new ESP algorithms in regard to the extraction of

smaller targeted displacements.


The introduction of virtual probe and engine order information to existing equally spaced probe

configurations and recorded blade tip displacements has enabled the development and the


153

verification of new analysis techniques for multiple and simultaneous non-integral / integral

engine order frequency responses.

The new BTT algorithms have successfully bypassed any of the previous analysis restrictions

imposed on targeted engine orders where their cycles are a multiple of the angular sector of

one segment.

By following the four-step optimisation process defined in the above sections, the extracted

vibratory information for the targeted and virtual blade tip amplitudes can also be verified and

confirmed thanks to two different factors; one verifying the virtual assumptions (FoV) and the

other one validating the measured blade tip displacements (FoC).

Chapter 5 BTT Signal Noise to Ratio & Uncertainties

154

Chapter 5 BTT Signal to Noise Ratio & Uncertainties

From a Blade Tip Timing point of view, blade tip amplitude reported on its own is misleading in

that it is an extracted value (i.e. the result of the BTT processing of raw probe data) and its

value will inevitably be different to some extent from the actual (“true”) amplitude. This

discrepancy is regarded as “the measurement error” of the BTT process.

The research undertaken by Russhard [9] in this domain has highlighted that:

a. The measurement uncertainty is lowest when the condition number of the BTT

matrix(see Equations 3.11 or 3.25 for single asynchronous or synchronous response),

is minimised,

b. Using six probes or more, resulted in substantially lower errors when the amplitude of

the resonance is small,

c. Comparing simulated data with real data, greater measurement errors are encountered

when working with the latter.

Because the true value of the amplitude is never precisely known, neither is the measurement

error. A statement of uncertainty is therefore required to indicate how large the measurement

error might be. Measurement error can be of two main types, resulting in distinct associated

uncertainty statements:

a. random errors or noise: errors that change randomly each time an experiment is

repeated, necessitating a precision statement.

b. systematic errors linked to something repeatedly “wrong” with the measurement (i.e. the

raw data and/or BTT processing), necessitating an accuracy statement.

This chapter first provides a method to quantify the overall uncertainty (due to both above types

of error) in the extraction of blade tip amplitudes for integral and non-integral engine order

responses. The uncertainties due to each of the above error types are then developed. It is


155

important to note that the novelty of these techniques is that the uncertainty is quantified solely

on the basis of the measured raw blade tip displacements at each revolution of the rotor. These

techniques hence overcome the disadvantages of current uncertainty techniques [9], whose

dependency on theoretical data records and associated disadvantages were discussed in

Chapter 2. The latter part of the chapter uses simulated data as the “raw measurements” at the

probes to validate the novel techniques in two ways: (i) comparing the processed BTT results

and the true data input; (ii) comparing the novel uncertainty techniques with Russhard’s [9].

5.1 Extraction of Residual Blade Tip Displacements

5.1.1 Asynchronous (non-integral) residual blade tip displacements

Based on the multiple non-integral engine order matrix based model defined in Equations 3.46

and 3.47, the asynchronous residual blade tip displacements can be isolated and quantified in

terms at each probe and for each selected revolution (see Equation 5.1).

5.1

where

is the residual displacement term at the revolution no. i (i = 1...m) at probe no. j ( j = 1...n ).


are constants from which the amplitude and phase of the asynchronous modal frequency response no. r (r = 1...p) for a particular blade can be extracted.

is the fitted engine order excitation for the asynchronous modal



at the revolution no. i (i = 1...m) for the asynchronous modal frequency response no. r (r = 1...p).


156

is the steady state position for the combined asynchronous modal frequency responses for a particular blade at probe no. j ( j = 1...n ).

5.1.2 Extraction of the synchronous (integral) residual blade tip displacements

Based on the multiple integral engine order matrix based model defined in Equations 3.56 and

3.57, the synchronous residual blade tip displacements can be isolated and quantified in terms

of the residual blade tip displacements at each probe and for each selected revolution (see

Equation 5.2).

5.2

where



are constants from which the amplitude and phase of the synchronous no. r (r = 1...p) for a particular blade can be extracted.

is the fitted engine order excitation for the synchronous modal



at the revolution no. i (i = 1...m) for the synchronous modal frequency response no. r (r = 1...p).



157

5.2 Blade Tip Timing Uncertainty Model

The extraction of the levels of uncertainty carried out by previous researchers solely based on

condition numbers was misleading and did not take fully into account the influence of the signal

to noise ratio [35]. Because of the random nature of blade vibrations, it is unlikely that two

samples (i.e. two revolutions) from a given population (i.e. measured displacements at each

probe) will yield identical confidence intervals. However, if this sample is repeated many times,

a certain percentage of the resulting intervals would contain the unknown population parameter

(i.e. noise).

Since random and systematic errors are statistically independent, a BTT uncertainty model [43]

can be defined as per Equation 5.3.

5.3

where

is the overall measurement uncertainty associated to a modal frequency response no. r (r = 1...p) for a particular blade at the revolution.

is the random measurement uncertainty associated to a modal

frequency response no. r (r = 1...p) for a particular blade at the revolution.

is the systematic measurement uncertainty attributed to a modal frequency response no. r (r = 1...p) for a particular blade at the revolution.

The uncertainty in the measurement of a variable is related to the standard deviation of the

distribution of measurements of the variable for a given sample.

In regards to blade tip timing, the errors associated with the reported levels of uncertainty are

very important since the sample size can be variable (i.e. dependent on the selected number of

probes and revolutions). By introducing the Student’s t-distribution [44], the estimated standard

deviation from the mean can be linked with a confidence level to adjust for the unknown

variance introduced by small sample sizes.


158

Based on the uncertainty model defined in Equation 5.3, the overall measurement uncertainty

for a particular blade at the revolution using the Student’s t-distribution is defined as:

For an asynchronous modal frequency response,

5.4

For a synchronous modal frequency response,

5.5

with

5.6

where

is the overall fractional measurement uncertainty associated to the tip displacement of the targeted asynchronous modal frequency response no. r, extracted for a particular blade at a revolution.

is the overall fractional measurement uncertainty associated to the tip displacement of the targeted synchronous modal frequency response no. r, extracted for a particular blade at a revolution.

is the selected t-value for a confidence level of 99.9%. This value will be determined by the sample size which is defined by the selected number of revolutions, m, by the number of probes, n.

is the sample standard deviation of the residual displacement terms.

are constants from which the amplitude of the asynchronous modal frequency response no. r, for a particular blade can be extracted.




159

is the mean value of the residual displacement terms between the revolutions no. i (i = 1 to m) at for the probes no. j ( j = 1 to n ).

is the sample size defined by the number of selected revolutions and the number of probes (i.e. m * n).

Based on Equation 5.3, it is clear that a high confidence level must be set for the assessment of

the overall measurement uncertainty since it regroups the random and the systematic

measurement uncertainties. Hence, a confidence level of 99.9% (i.e. ) is used to indicate the

reliability of the estimate leaving only 5x10-2

% in each tail of the area of the normal distribution

curve.

To compute the overall measurement uncertainty using Equations 5.4 and 5.5 for non-integral

and integral engine order responses respectively is straight forward using the Student’s t-

distribution based on a confidence level of 99.9%. The difficult part of the process is the

quantification of each of measurement uncertainty parameters defined in the BTT uncertainty

model (i.e. the random measurement uncertainty and systematic measurement uncertainty).

The quantification of the random and systematic measurement uncertainty values need to be

carried out in two stages:

1. Quantification of the systematic measurement uncertainty,

2. Quantification of the random measurement uncertainty based on the extracted overall

and the systematic uncertainty values.

5.3 Quantification of the Systematic Measurement Error Uncertainty

Based on the same concept as the overall measurement uncertainty, the quantification of the

fractional systematic measurement uncertainty associated with an extracted blade tip

displacement at a given revolution of the rotor can be extracted as shown in Equation 5.7 for an

asynchronous response and in Equation 5.8 for a synchronous response.


160

5.7

5.8

with

5.9

where

is the fractional systematic measurement uncertainty associated to the tip displacement of the targeted asynchronous modal frequency response no. r, extracted for a particular blade at a revolution.

is the fractional systematic measurement uncertainty associated to the tip displacement of the targeted synchronous modal frequency response no. r, extracted for a particular blade at a revolution.

is the selected t-value associated to a level on confidence (to be defined), for m revolutions and for a n probe configuration.

is the sample standard deviation of the residual displacement terms.

are constants from which the amplitude of the asynchronous modal frequency response no. r, for a particular blade can be extracted.



is the mean value of the residual displacement terms between the revolutions no. i (i = 1 to m) at for the probes no. j ( j = 1 to n ).

is the sample size defined by the number of selected revolutions and the number of probes (i.e. m * n).


161

In order to calculate fractional measurement uncertainty for asynchronous or synchronous

modal response, a level of confidence is required to define a t-value of the Student’s t-

distribution. Section 5.5 will provide the necessary evidence of the best suited level of

confidence.

5.4 Quantification of the Random Measurement Error Uncertainty

Using the uncertainty model defined in Equation 5.3, the quantification of the random

measurement uncertainty can now be calculated as per Equation 5.10.

5.10

Hence, based on Equation 5.10, the signal-to-noise ratio, a comparison of the level of desired

signal to the level of background noise by definition, for a particular blade at a revolution is

defined:

For an asynchronous modal frequency response,

5.11

For a synchronous modal frequency response,

5.12

5.5 Verification of Noise and Uncertainty Extraction Methods

To validate the extraction of the systematic and random measurement associated with a single

or combined modal frequency response(s), the section provides:

a) A comparative analysis between processed data and theoretical inputs,

b) A justification for selecting a confidence level of 90.0% to extract the systematic

measurement uncertainty (see Equations 5.7 and 5.8),


162

c) A comparative analysis between the extractions of uncertainty based on condition

numbers (Russhard [9]) and on the method developed in Section 5.5.4.

Based on simulated data, the validation has been performed by using a series of test cases to

take into account different parameters (see Table 5.1) which may impact on the final targeted

deliverables.

Number of iterations:

o 100

Targeted combined non-integral engine order responses:

o Mode 1 = 2.5

o Mode 2 = 3.5

Targeted blade tip amplitudes:

o Mode 1 = 0.04 mm peak

o Mode 2 = 0.5 mm peak

Confidence Intervals (%)

o 99.9, 99.7, 99.5, 99%, 98%, 95%, 90%, 80%, 70%, 60%, 50%

Maximum random background probe noise levels based on 0.1 mm peak

o 100%, 75%, 50%, 25%, 10%, 5%

Probe DC Offset

o 0.3 mm peak (± 1%)

Number of revolutions used for averaging

o 5 to 10 revolutions

Number of Probes

o 4 Probes - Circumferential Probe Angles (deg)

188.74, 206.74, 296.74, 314.74


170.74, 188.74, 242.74, 252.74, 296.74, 314.74


8.74, 170.74, 188.74, 206.74, 242.74, 252.74, 296.74, 314.74

Table 5.1 – Simulated SNR and Uncertainty Parameters


163

The validation of the SNR and uncertainty extraction algorithms is based on comparing two

analysis methods, identified as follows:

Method 1: where the output parameters (i.e. targeted blade tip amplitude, random

noise displacement at each probe and at each revolution and prove DC offset) are

equal to the input parameters (i.e. no data processing has been carried out).

Method 2: where the output parameters have been extracted from the processed

simulated data based on the parameters listed in Table 5.1 using the BTT

processing techniques described in Section 3.2.

Finally, a comparative analysis is carried out to estimate the differences, if any between the

uncertainty levels extracted using the new method described in this chapter and the method

described by Russhard [9] using matrix condition numbers.

5.5.1 Probe Selection

To assess the effects of the number of probes on the measurement uncertainty, three BTT

probe configurations (i.e. number of probes and locations) have been carefully selected using

the condition numbers,

Figure 5.1 provides a summary graphical display of the extracted condition numbers for each

probe configuration defined in Table 5.1 and by taking also into account the selected number of

revolutions used for carrying out the averaging process (see Section 4.1). The bar graph (see

Figure 5.1) displays the minimum, average and maximum values of all the extracted condition

numbers for ‘8 Probes’, ‘6 Probes’ and ‘4 Probes’ configurations.


164

Figure 5.1 – Condition Numbers

By assessing all the possible probe permutations for each probe configurations, the differences

have been kept to the minimum. Those small differences in condition numbers describing the

sensitivity of the matrix to numerical operations will be assessed in Section 5.5.4.

5.5.2 Uncertainty Levels vs. Confidence Intervals

Based on a series of statistical analyses, Figure 5.2, Figure 5.3 and Figure 5.4 provide three

plots (i.e. configurations for 8 probes, 6 probes and 4 probes) which summarise the differences

between Method 1 and Method 2 in absolute fractional uncertainty for a targeted blade tip

amplitude of 0.04 mm peak for different noise levels and confidence intervals.

Figure 5.5, Figure 5.6 and Figure 5.7 provide the same information as the previous three figures

for targeted blade tip amplitude of 0.5 mm peak.

Using the information displayed in these six plots, the following observations can be made:

1. For each targeted blade tip amplitude and selected probe configuration, the

extracted differences of uncertainty between the two methods show an exponential


165

decay with the decreasing levels of noise and for each selected confidence interval

level,

2. By considering the different levels of noise, the confidence interval level of 90%

provides in most of the test cases, the lowest absolute differences in uncertainty

levels across the three different probe configurations and for the two targeted blade

tip amplitudes.

Figure 5.2

0.04 mm peak Targeted Amplitude – Fractional Uncertainty Differences - 8 Probes


166

Figure 5.3


Figure 5.4



167

Figure 5.5


Figure 5.6



168

Figure 5.7


Figure 5.8 provides summary plots of the extracted levels of uncertainty for each of the three

probe configurations and for both methods based on a 90% confidence interval. On the left

hand side, details for blade tip amplitude targeted at 0.04 mm peak are provided and on the

right hand side for blade tip amplitude targeted at 0.5 mm peak.


169

Figure 5.8 - Fractional Uncertainty Differences Method 1 vs. 90% CI Method 2

5.5.3 Uncertainty Levels vs. Number of Averaging Revolutions

To carry out the automated averaging matrix process described in Section 3.4, the number of

revolutions can be increased or decreased. This is therefore an important parameter to be

assessed when dealing with Blade Tip Timing measurement uncertainties.


170

Figure 5.9 provides six plots summarising the extracted levels of uncertainty for each targeted

level of noise and for both targeted blade tip amplitudes (i.e. 0.04 mm peak Mode 1 on the left

hand side and 0.5 mm peak for Mode 2 on the right hand side) using five different numbers of

revolution for carrying out the averaging process. This assessment has been carried out using 5

to 10 revolutions (see Table 5.1).

The analysis of the extracted measurement uncertainty with a confidence level set at 90% (see

Section 5.5.2) shows clearly that for both targeted blade tip amplitudes:

1. The extracted levels of uncertainty decrease at the different targeted noise levels

when the number of revolutions to carry out the averaging process increases,

2. For the three probe configurations, the extracted fractional uncertainties show an

exponential decay with the decreasing levels of noise


171

Figure 5.9 – 90% CI Fractional Uncertainty Differences at Averaging Revolution Number

Figure 5.10 provides a set of three values for each targeted probe noise level (i.e. one for each

probe configuration) which indicates the difference in uncertainty levels between the different

numbers of revolution used to carry out the averaging process.


172

Figure 5.10 - 90% CI for Fractional Uncertainty Differences

at Averaging Revolution Numbers

The maximum extracted fractional uncertainties show a decaying pattern as the random noise

decreases with the maximum differences of uncertainty between the different probe

configurations being less than 3.92% and 0.17% for the 0.04 and the 0.5 mm peak targeted

amplitudes respectively (see Table 5.2).

Mode 1 Targeted Amplitude Mode 2 Targeted Amplitude

Noise Level Maximum differences in fractional uncertainty (%)

100% 3.92 0.17

75% 4.05 0.11

50% 0.75 0.06

25% 0.68 0.03

10% 0.13 0.01

5% 0.07 0.01

Table 5.2 – Maximum differences in fractional uncertainty


173

5.5.4 Uncertainty Levels vs. Matrix Condition Numbers

Mentioned earlier in this chapter, the condition number is a figure that indicates the sensitivity of

the matrix to numerical operations. The work carried out by Russhard [9] clearly highlighted its

effects on the extracted blade tip amplitudes (i.e. extracted uncertainty levels) based on

simulated data. It also demonstrated that low condition number resulted in lower uncertainty

levels and vice versa.

Based on the work carried out by Judd [45], the matrix sensitivity M to numerical operations for

each of the reported blade tip amplitude(s) can be bounded using Equation 5.13.

5.13

where

o For asynchronous responses (see Section 3.3.1 for the definition of and )

5.14

o For synchronous responses (see Section 3.3.2 for the definition of and )

5.15

o , is the norm of the vector defining the residual displacement terms at the

revolution no. i (i = 1...m) at probe no. j ( j = 1...n ), see Equation 5.1 for

synchronous responses and see Equation 5.2 for asynchronous responses,

o , is the norm of the vector defining the measured blade tip displacements at

the revolution no. i (i = 1...m) at probe no. j ( j = 1...n ).

o cond, uses the SVD function (see Section 4.1) to return the ratio of the largest

singular value of M to the smallest.

Figure 5.11 provides fractional uncertainty values associated with the singular value

decomposition of the BTT matrices (Equations 5.14 and 5.15 for asynchronous and


174

synchronous responses respectively) for each of the three BTT configurations, using five

different numbers of revolutions to carry out the averaging process.

Figure 5.11 – SVD Fractional Uncertainties

The lower and upper fractional uncertainty levels displayed in

Figure 5.11 are consistent for the three BTT configurations, as expected based on Equation

5.13. By keeping the differences between the condition numbers to a minimum for each of the

three probe configurations (see Figure 5.1), the variations between the computed levels of

uncertainty for each targeted noise level are minimised, as shown in Figure 5.12.


175

Figure 5.12 – Maximum SVD Fractional Uncertainty Differences

Based on the above test cases, the maximum computed scatter (i.e. 0.13%) is linked with the

four probe configuration at 100% input noise level based on a 0.1 mm peak. The effects of the

number of probes on the SVD fractional uncertainties are therefore negligible if the differences

between condition numbers are kept as low as possible.


176

5.5.5 Signal to Noise Ratio

With the evidence provided in Sections 5.5.1 to 5.5.4 demonstrating the use of a 90%

confidence interval for extracting the BTT measurement uncertainties, the quantification of the

noise levels can now be assessed by applying the equations defined in Section 5.4.

Figure 5.13 provides Signal-to-Noise Ratio theoretical and computed values (i.e. for Method 1

and Method 2 respectively) for each of the input random noise levels (100%, 75%, 50%, 25%

10% and 5% based on a 0.1mm peak amplitude) and for each of the BTT probe configurations

for a targeted blade tip amplitude of 0.04 mm peak (i.e. Mode 1).

Figure 5.14 provides SNR theoretical and computed values (i.e. for Method 1 and Method 2

respectively) for each of the input random noise levels (100%, 75%, 50%, 25% 10% and 5%

based on a 0.1mm peak amplitude) and for each of the BTT probe configurations for a targeted

blade tip amplitude of 0.5 mm peak (i.e. Mode 2).

The extracted SNRs provide clear evidence as expected that while the input random noise

decreases, the signal to noise ratio for each probe configuration increases.

To assess further the extracted signal to noise ratios displayed in Figure 5.13 and Figure 5.14

for Mode 1 and Mode 2 respectively, absolute differences between the two methods (i.e.

theoretical and computed information) have been calculated. Based on the data displayed in

Figure 5.15 and Figure 5.16, the absolute mean difference between all the reported SNRs (i.e.

between the two targeted tip amplitudes for all the configurations and random noise levels) is in

the order of 1.1dB with a maximum mean difference of 1.4dB.

For all the probe configurations, there is a clear increase in the differences between the

reported theoretical and calculated SNRs for the 5% noise level (see Figure 5.15 and Figure

5.16). This is explained by the fact that the reported systematic measurement uncertainties are

lower than the theoretical ones as displayed in Figure 5.8.


177

Figure 5.13 - Extracted Signal / Noise Ratios for

BTT Mode 1

Figure 5.14 - Extracted Signal / Noise Ratios for

BTT Mode 2


178

Figure 5.15 – Differences in Theoretical and Computed SNRs for BTT Mode 1

Figure 5.16 – Differences in Theoretical and Computed SNRs for BTT Mode 2


The new matrix based models for integral and non-integral engine order responses have

provided new capabilities to extract seamlessly the residual blade tip displacements for targeted

modal responses from the raw data.

By capturing residual blade tip displacements, new processing techniques have been

developed from which measurement uncertainties and signal-to-noise ratios can be associated

with each of the extracted blade tip amplitudes. Validation studies have confirmed the reliability

of these methods.


179

The verification of the new processing methods has shown that:

o The extraction of the levels of uncertainty carried out by previous researchers solely

based on condition numbers was misleading and did not take fully into account the

influence of the signal-to-noise ratio,

o The extraction of the measurement uncertainties should be carried out using a

90.0% confidence level,

o When targeting lower blade tip displacements (i.e. based on the Finite Element

Model predictions), the levels of accuracy in the delivery of the systematic

measurement uncertainties improve with increasing number of probes mounted

circumferentially on the casing.

Chapter 6 Validation Of Improved BTT Capabilities

180

Chapter 6 Validation of Improved BTT Capabilities

Following the mathematical description and verification of the new processing techniques using

simulated data in Chapter 3, Chapter 4 and Chapter 5, the validation of the improved BTT

capabilities are carried out in this chapter.

Using Blade Tip Timing data recorded from two engine tests for High Pressure Compressor

(HPC) blades [46] [47] and Low Pressure Turbine (LPT) blades on a mechanical spinning test

rig in vacuum [48], each of the following responses will be analysed using the new processing

capabilities:

1. Single and multiple non-integral engine order blade responses. Described in

Sections 3.2.1 and 3.3.1, the analysis techniques are validated in Sections 6.1.1

and 6.1.2).

2. Single integral engine order blade response. Exposed in Section 3.2.2, the

technique is validated in Section 6.2.1.

3. Equally Spaced Probe (ESP) integral engine order blade response. The novel

technique described in Section 4.2.2 is validated in Section 6.2.2 using the multiple

integral engine order matrix based model.

4. Signal/Noise ratio and uncertainty measurements. Exposed in Chapter 5, the

techniques are validated in Section 6.3.

The processed data using the new analysis techniques are compared and assessed against the

processed information using the two validated Rolls-Royce’s proprietary tools:

1. BTT Replay.

2. Batch Processor (BP).


181

The BTT Replay tool was first developed based on the techniques developed by Russhard [9].

Since then, an automated version called BTT Batch Processor has been developed and

released to minimise user’s input (e.g. linked with component FEM information) and to reduce

the processing time. Therefore both processing tools have been used for the validation of the

new techniques depending on the levels of information available at the time.

Unfortunately, the High Pressure Turbine engine test targeted for the validation of the new

techniques has failed to deliver results from any of the planned experiments. Hence, other BTT

engine tests have been sourced using the same optical hardware, to validate the novel

techniques described in the previous chapters.

6.1 Validation for Non-Integral Engine Order Blade Tip Activities

6.1.1 Single Asynchronous Compressor Blade Response

Using the novel Asynchronous Averaging Built-in Matrix model presented in Section 3.2.1, the

vibratory information of the targeted non-integral engine order blade response highlighted in

Figure 6.1 was extracted using the predicted FEM blade modal frequencies defined in Figure

6.2.

Y-a

xis

: N

oda

l D

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X-axis : Revolution Number (i.e Time)

Figure 6.1 – BTT Travelling Plot of Targeted Asynchronous Blade Response

Targeted Asynchronous Response


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Figure 6.2 – FEM Predicted Frequency Response

The frequency band displayed on Figure 6.2 defines the lower and upper FEM predicted

frequencies for a targeted modal frequency response against speed. This bandwidth is

determined by the predicted changes in modal frequency due to increasing nodal diameters.

Each dotted line starting from zero RPM and with a different gradient defines an engine order

(e.g. in this case, engine orders plotted are between 1 and 12).

Based on an incremental frequency approach at each of the targeted revolutions of the engine,

the BTT AABM processing techniques have been applied to assess the best fitted engine order

excitation (see Equation 3.9).

Figure 6.3 provides a comparison of the two processing techniques for the best fitted engine

orders (EO) for the targeted asynchronous event highlighted in Figure 6.1.

Predicted modal frequency band


183

Figure 6.3 – Single Asynchronous Engine Order – BTT Replay vs. AABM

Figure 6.3 displays clearly an engine order incremental value of ‘0.1’ from the BTT Replay

analysis in contrast with the AABM processing techniques, where an incremental frequency

value of 1Hz was set in this occasion (i.e. delivering a more refined engine order tracking

response). The extracted engine orders for this targeted asynchronous response are contained

between 3 and 2.5 EOs, which relates to a rotational speed of 5880 and 8833 RPM (see Figure

6.2).

Using the rotational speed of the engine at each revolution, the information displayed in Figure

6.3 can be converted into the frequency domain as shown in Figure 6.4.

Figure 6.4 – Single Asynchronous Frequency – BTT Replay vs. AABM

The information displays in Figure 6.4 shows that the two processes agree well for a low

frequency modal response.


184

Figure 6.5 provides a comparison of the computed coherence values of the two processing

methods, where both methods are showing a good level of correlation during the asynchronous

blade response.

The coherence plot also highlights that the BTT Replay method provides higher coherence

values than the AABM new processing techniques; this is explained by the fact the BTT Replay

correlation technique is based on filtered data (i.e. Russhard’s steps 4 and 5 - see Section 3.1,

[9]) against the AABM technique which correlates the extracted responses using un-filtered

data.

Figure 6.5 – Single Asynchronous Coherence – BTT Replay vs. AABM

Last but not least is the comparison of the extracted blade tip amplitudes between the two

processing techniques (see Figure 6.6), showing that the AABM process defined by Equation

3.17 extracts a “cleaner” response of the blade tip activities than BTT Replay.

The extraction of the blade tip amplitudes using the AABM process is reporting some high peak-

peak amplitudes which are not observed when using the BTT Replay tool. Those differences

highlight the effects of filtering techniques applied on the raw data prior the analysis (see

Section 3.1.5).


185

Figure 6.6 – Single Asynchronous Amplitude – BTT Replay vs. AABM

The differences in the reported amplitudes between the BTT Replay and the AABM processed

data for targeted asynchronous vibratory response are shown in Figure 6.7 and from a

percentage point of view, in Figure 6.8.

Figure 6.7 – BTT Replay vs. AABM Differences in Amplitude (mm)


186

Figure 6.8 – BTT Replay vs. AABM Differences in Amplitude (%)

From the information displayed in Figure 6.7, a statistical analysis was carried out and the

results are displayed in Figure 6.9.

Figure 6.9 – Statistical Analysis of BTT Replay vs. AABM Differences in Amplitude


187

Based on a 95% confidence interval for mean, a statistical assessment of the overall differences

in amplitude between the two methods shows a bias error of 0.017 mm with an uncertainty of ±

5.6x10-3

mm.

The reported differences between the two processing techniques (see Figure 6.7) during the

built-up of the non-integral engine response (i.e. from 35 to 60 seconds) are higher than the

differences reported for the rest of asynchronous response (i.e. from 60 to 90 seconds).

For that reason, the initial statistical analysis was repeated to take into account those two

variations and it shows:

From 35 to 60 seconds, the bias error is 0.018 mm with an uncertainty of 0.012 mm

(see Figure 6.9),

From 60 to 90 seconds, the bias error is 0.017 mm with an uncertainty of 4.6x10-3

mm (see Figure 6.10).

The above statistical analyses imply there is a constant bias error between the two analysis

methods (i.e. 0.018 mm) and an increased variation during the built-up of the non-integral

engine order response.

One of the obvious factors is a better zeroing algorithm built in the AABM process when

compared to the BTT Replay 40 averaged revolutions techniques. One of the main factors

which will be discussed in Appendix E, is the axial shift of the blade during resonances which is

not taken into consideration and measured today by the BTT analysis tools.


188

Figure 6.10 – Statistical Analysis of Differences in Amplitude between 35 to 60 sec

Figure 6.11 – Statistical Analysis of Differences in Amplitude between 60 to 90 sec


189

As mentioned in the discussion of Figure 6.5, the AABM computed levels of coherence are

based on unfiltered data, leading to lower coherence values when compared to previous

analysis process. However, by doing so, it enables the new Asynchronous Averaging Built-in

Matrix process to provide accurate measurements of the residual blade tip amplitudes (see

Equation 5.1) which can be used to determine the signal-to-noise ratio of the system as defined

in Section 5.4.

Figure 6.12 – Single Asynchronous SNR – BTT Replay vs. AABM

Figure 6.12 provides the computed SNR of the asynchronous response based solely on raw

BTT data, a new feature which was not delivered by the previous researchers.

With a confidence interval of 90%, the residual and extracted blade tip amplitudes,

measurement uncertainties (see Section 5.3) can also be extracted using Equation 5.7. Figure

6.13 displays the computed measurement uncertainties associated to the targeted non-integral

engine order blade response.


190

Figure 6.13 – Single Asynchronous Uncertainty – BTT Replay vs. AABM

The signal-to-noise ratios and measurement uncertainties highlight the benefits of the new

AABM processing techniques in carrying out simultaneously the filtering and the processing of

the BTT data by using fewer revolutions than the previous reported techniques.

Indeed, Figure 6.13 demonstrates that while the levels of uncertainty increase, the reported

levels of the SNR and coherence decrease, with an increasing spread of the extracted engine

order (see Figure 6.3), and vice versa when the reported levels of uncertainty decrease.

Note that BTT Replay based on Russhard’s work [9] does not have the capability to report SNR

and measurement uncertainty for a tracked frequency response; hence displaying a zero entity

for both responses (see Figure 6.12 and Figure 6.13).

However, the reported processed data using the BTT Replay tool do not provide such evidence

and the only sign showing increased levels of uncertainty is the spread of the reported

coherence values for each of the blade tip amplitudes.


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6.1.2 Multiple Asynchronous Compressor Blade Responses

The validation of the new AABM based model for multiple asynchronous responses (see

Section 3.3.1) has been carried out by comparing the processed HPC BTT blade data to the

BTT Batch Processor processed results, an automated version of the BTT Replay tool. The two

simultaneous non-integral engine order blade vibratory responses shown in Figure 6.14were

targeted using the FEM information described in Figure 6.14.

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Figure 6.14 – BTT Travelling Plot of Two Simultaneous Asynchronous Blade Responses

Figure 6.15 – FEM Predicted Frequency Responses

Asynchronous Mode ‘A’ Response

Asynchronous Mode ‘B’ Response

Asynchronous Mode ‘A’ Response

Asynchronous Mode ‘B’ Response


192


frequencies for a targeted modal A and B frequency responses against speed. Each dotted line

starting from zero RPM and with a different gradient defines engine orders (e.g. in this case,

engine orders plotted are between 1 and 15).

The analysis of the BTT data using the AABM and Batch Processor processing techniques was

successfully carried out and both sets of extracted information were plotted. Further

comparative results including the ones discussed in this section are available in Appendix A.

The Batch Processor processed information highlights some of the settings used for the

extraction of the vibratory blade responses. The Mode ‘A’ engine order incremental value was

set to 0.1 EO as shown in Figure 6.16 and it was set at 0.05 EO for Mode ‘B’ (see Figure 6.17).

Figure 6.16 – Asynchronous Mode ‘A’ Engine Order – Batch Processor vs. AABM

Figure 6.17 – Asynchronous Mode ‘B’ Engine Order – Batch Processor vs. AABM


193

The reduced Mode ‘B’ incremental engine order provides a better match to the AABM extracted

EO responses (see Figure 6.17) than the Mode ‘A’ (see Figure 6.16). The differences in

amplitude for both targeted asynchronous vibratory responses between the Batch Processor

and the AABM processed data are shown in Figure 6.18 and Figure 6.19 for Modes ‘A’ and ’B’

respectively. From a percentage point of view, the differences are displayed in Figure 6.20 and

Figure 6.21 for Modes ‘A’ and ’B’ respectively.

Figure 6.18 – BP vs. AABM Mode ‘A’ Differences in Amplitude (mm)

Figure 6.19 – BP vs. AABM Mode ‘B’ Differences in Amplitude (mm)


194

Figure 6.20 – BP vs. AABM Mode ‘A’ Differences in Amplitude (%)

Figure 6.21 – BP vs. AABM Mode ‘B’ Differences in Amplitude (%)

From the information displayed in Figure 6.18 and Figure 6.19, a statistical analysis was carried

out and the results are displayed in Figure 6.22 and Figure 6.23.


195

Figure 6.22 – Statistical Analysis of BP vs. AABM Mode ‘A’ Differences in Amplitude

Figure 6.23 – Statistical Analysis of BP vs. AABM Mode ‘B’ Differences in Amplitude


196

Based on a 95% confidence interval for mean, the statistical analyses of differences in

amplitude between the two processing methods yields the following figures:

For Mode ‘A’, a bias error of 0.12 mm and an uncertainty of ±1.3x10-2

mm.

For Mode ‘B’, a bias error of 0.13 mm and an uncertainty of ±1.28x10-2

mm.

The above two statistical analyses demonstrate that the Mode ‘B’ refined engine order

incremental value does not reduce the levels of uncertainty between the two processing

techniques (i.e. about ±1.3x10-2

mm) when compared to the one from Mode ‘A’. The analysis

shows also that the extracted blade tip amplitudes using the AABM methods provides higher

amplitude than the Batch Processor processed data by 0.13 mm.

The AABM process provided better coherence levels than the Batch Processor as shown in

Figure 6.24, which implies a better zeroing technique from the asynchronous averaging built-in

matrix model, using only five revolutions and an incremental value of 1Hz.

Figure 6.24 – Asynchronous Mode ‘A’ and ‘B’ Coherence – Batch Processor vs. AABM


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6.2 Validation for Integral Engine Order Blade Tip Activities

6.2.1 Single Synchronous Compressor Blade Response

Using the novel Synchronous Averaging Built-in Matrix model (SABM) described in Section

3.2.2 and the predicted FEM blade frequency responses defined in Figure 6.25 , the vibratory

information of the targeted integral engine order blade response highlighted in Figure 6.26 was

processed.

Figure 6.25 – FEM Predicted Frequency Response


frequencies for four modal frequency responses against speed. In this occasion, only one

engine order has been displayed, the 48th engine order which crosses our targeted modal

response.

Targeted Synchronous Response


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Figure 6.26 – BTT Travelling Plot of Targeted Synchronous Blade Response

The analysis of the BTT data using the SABM and BTT Replay processing techniques was

successfully carried out. Further comparative results including the ones discussed in this

section are available in Appendix B.

Based on an incremental frequency approach (i.e. 1Hz increment) for each of the targeted

revolutions of the engine, the new SABM processing techniques was applied to extract a

synchronous blade response at a 48th engine order excitation (see Figure 6.27). For the engine

order frequency responses, the extracted values are displayed in Figure 6.28.

Figure 6.27 – Synchronous Engine Order – BTT Replay vs. SABM

Targeted Synchronous Response


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Figure 6.28 – Synchronous Frequency – BTT Replay vs. SABM

Using five revolutions to carry out the analysis using the SABM model, the extracted amplitudes

are plotted against the amplitudes processed with the validated BTT Replay tool (see Figure

6.29). The differences in amplitude for the targeted synchronous vibratory response between

BTT Replay and the AABM processed data are shown in Figure 6.30.

Figure 6.29 – Synchronous Amplitude – BTT Replay vs. SABM

Based on a 95% confidence interval for mean, the differences in amplitude between the two

processing methods are a bias error of -2.8x10-4

mm and an uncertainty of ±3.1x10-3

mm. At

resonance, the BTT Replay amplitude is 6.3E-2mm lower that the extracted SABM amplitude.

The main reason for those differences in amplitude at resonance is linked to the number of

revolutions used to carry out the “zeroing” of the data.


200

Figure 6.30 – Replay vs. 5 Revs SABM - Synchronous Amplitude Differences

In fact, Figure 6.30 is showing an interesting processing feature between the two processing

methods - prior to the resonance, the differences in amplitude are mainly positive and post-

resonance, the differences in amplitude are mainly negative. This feature is caused by the mask

generation (see Section 3.1.4) (i.e. where resonances are detected, the average values at the

beginning and at the end of the resonance period for each probe are used to generate a linear

interpolation of values for the zero to be applied during resonance [9]). For the SABM process,

those average values are not required since the linear interpolation is carried by default by the

AABM model, and in this case over five revolutions.


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6.2.2 Validation of Equally Spaced Probe Method

In Chapter 4, processing issues governed by the circumferential angular probe positions and by

the targeted engine orders based on Equally Spaced Probe (ESP) configurations were

highlighted for BTT Turbine applications.

Based on the new developed matrix-based models (see Sections 3.3.1 and 3.3.2), the novel

ESP processing technique of Chapter 4 has removed those constraints by running a pre-

analysis process that provided a well-conditioned matrix (i.e. of reduced condition number)

through the following strategy:

1) Removing a number of probes from the original configuration and replacing it by virtual

probe(s).

2) Introducing a virtual engine order response to the measured probe displacements.

For the validation of this new ESP processing technique, it was intended to use data from a BTT

High Pressure Turbine engine test experiment with equally spaced probes. Unfortunately, the

engine test did not deliver any of the planned experiments.

Today, access to ESP BTT data is difficult since it is no longer the preferred circumferential

probe distribution. Due to the lack of other ESP data, HPC data already used for the validation

of the SABM model for a single response (see Section 6.2.1) will again be used for validating

the new ESP algorithm since it is the ESP method that is being validated. Also, at the same

time, to validate the SABM model for multiple synchronous responses (see Section 3.3.2), an

incremental engine order of one was set for the optimisation of the virtual parameters (see

Section 6.2.2.1).

The following sections describe the selection process of the virtual engine order response, the

virtual probe position and finally the validation of the multiple SABM model based on the ESP

developed technique. Further comparative results including the ones discussed in this section

are available in Appendix C.


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6.2.2.1 Optimisation of the virtual parameters

To compare the two processing methods described in Chapter 3 and Chapter 4, the BTT

configuration parameters linked to the single BTT synchronous compressor blade responses

(see Section 6.2.1) have been optimised using the process described in Section 4.3.1.

Based on the original probe positions (see Table 6.1) and on a targeted 48th engine order

response (see Figure 6.25) with an incremental value of one for the virtual engine order and

with an incremental value of 0.1 degree for the virtual probe angle over five revolutions, the new

configuration parameters displayed in Table 6.2 have been extracted as the results of the virtual

optimisation process. Probe No 4 has been removed from the original configuration and has

been replaced with a virtual probe at a circumferential angular position of 73.0 degrees.

Probe No 1 2 3 4 5 6 7 8

Angle (deg) 18.9 46.9 67.5 88.3 94.5 105.5 111.7 177.5

Table 6.1 – Original Probe Configuration Parameters

Probe No 1 2 3 Virtual 4 5 6 8

Angle (deg) 18.9 46.9 67.5 73.0 94.5 105.5 111.7 177.5

Virtual EO 3.0

Virtual Amplitude

(mm peak) 0.5

Table 6.2 – New BTT Configuration Parameters

By adding a single virtual response to the original measured data, the extracted condition

number based on the information displayed in Table 6.2 has increased to 3.28 from its original

condition number of 1.97 based on the information displayed in Table 6.1; still within the limits

defined by Russhard [9].


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To demonstrate that the introduction of virtual parameters do not alter the recorded blade

responses, a comparison of the processed data between the SABM model and an SABM model

incorporating optimised virtual parameters (SABM~Virtual) validates the latter processing

technique in Section 6.2.2.2.

6.2.2.2 Comparison of SABM Model with SABM~Virtual Model

The synchronous response displayed in Figure 6.26 has been processed once more using the

SABM~Virtual model. The extracted blade tip amplitudes of the targeted response are displayed

in Figure 6.31 alongside the extracted SABM blade tip amplitudes (see Section 6.2.1).

At the start and at the end of the synchronous response, both processing techniques show

similar blade tip amplitudes. In between, the AABM~Virtual model displays higher blade tip

deflections than the SABM processed data.

Figure 6.31 – Blade Tip Amplitude of Targeted Response – SABM vs. SABM~Virtual

The differences in blade tip amplitudes between the two processing models are displayed in

Figure 6.32.


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Figure 6.32 – SABM vs. SABM~Virtual Differences in Targeted Response

At the maximum reported SABM blade tip amplitude (i.e. at resonance), the absolute difference

between the two processing techniques is less than 8.2.8x10-3

mm, with the SABM~Virtual

model giving a higher amplitude. Based on a 95% confidence interval for mean, the differences

in amplitude between the two processing methods are a bias error of 1.0x10-2

mm and an

uncertainty of ±2.8x10-3

mm.

Figure 6.33 and Figure 6.34 display the extracted engine order and frequency of the targeted

synchronous blade response for both processing models (i.e. SABM and SABM~Virtual).

Figure 6.33 – Targeted Synchronous Engine Orders – SABM vs. SABM~Virtual


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Figure 6.34 – Targeted Synchronous Frequencies – SABM vs. SABM~Virtual

The levels of coherence extracted using both processing techniques are displayed in Figure

6.35 and for the levels of uncertainty associated with the targeted response in Figure 6.36.

Figure 6.35 – Synchronous Coherences – SABM vs. SABM~Virtual

Figure 6.36 – Targeted Synchronous Uncertainties – SABM vs. SABM~Virtual


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For both processing models, the differences in terms of the extracted coherence and

uncertainty levels are less than 1% at the SABM resonance point.

Based on Equations 4.43 and 4.46, the factors of validity and conformity at each revolution have

been processed (see Figure 6.37). Extracted values of 0.99 and 0.93 for the FoV and FoC

respectively have been calculated at the SABM resonance point.

Figure 6.37 – FoV and FoC – SABM~Virtual

At the SABM resonance point, the factor of validity indicates a 1% discrepancy at the virtual

probe position between the extracted and the theoretical virtual amplitudes. For the factor of

conformity, a 2.3% discrepancy has been encountered when compared to the measured raw

displacement at the unused probe position. Note that the SABM measurement uncertainty at

the resonance point is processed at 4.5% (see Figure 6.36) using Equation 5.8 (i.e. all the

probes data points over five revolutions).

Figure 6.38 – Targeted Synchronous Uncertainties – SABM vs. SABM~Virtual


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6.3 Validation for Signal to Noise Ratio and Uncertainty Measurements

The validation of the signal-to-noise ratio and uncertainty algorithms described in Chapter 5 is

carried out using time-of-arrival blade data of Low Pressure Turbine (LPT) blades recorded on a

mechanical rig, in vacuum under rotation. The main reasons for using such data are as follows:

1. The input forced excitation to the rotor blade is known and controlled.

2. The aerodynamic loads on the blades in a vacuum environment are

minimised.

Using the validated BTT Replay tool, where the task of zeroing the raw BTT data (see Sections

3.1.5 and 3.1.6) can be turned on/off, does provide the right conditions and parameters to

assess the validity of the two new techniques.

To validate the above two new techniques, the raw BTT data files are processed using three

different methods, which are:

1. The AABM / SABM process,

2. BTT Replay with the zeroing process deactivated,

3. BTT Replay with the zeroing process activated.

Each of the tests performed on this rig to assess its mechanical behaviours was part of a

controlled experiment and on this occasion, the characterisation of the rotor forced response

subject to a 12 engine order excitation was performed.

Using the AABM/SABM models and two BTT Replay processing techniques, the analysis of the

BTT data was successfully carried out. Further comparative results including the ones

discussed in this section are available in Appendix D.

Figure 6.39 and Figure 6.40 provide comparative displays of the extracted blade tip amplitudes

subject to the synchronous source of excitation (i.e. 12 engine order forced excitation). Despite


208

looking very similar in amplitudes, differences can be observed and Figure 6.41 provides a

display of the scatters between the zeroed and non-zeroed data.

Figure 6.39 – Synchronous Amplitude – Non-Zeroing BTT Replay vs. SABM

Figure 6.40 – Synchronous Amplitude – Zeroing BTT Replay vs. SABM


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Figure 6.41 – BTT Replay Zeroing vs. Non-Zeroing Amplitude Differences

Since the differences in amplitude displayed in Figure 6.41 are linked to the filtered noise and

probed steady state offset, the uncertainty based on the two BTT Replay processed data can be

extracted using Equation 6.1.

6.1

The calculated BTT Replay and SABM processed levels of uncertainty displayed in Figure 6.42

demonstrate that the algorithm developed in Section 5.3 for extracting the levels of uncertainty

based solely on BTT data is valid as shown for the resonance point indicated.

Figure 6.42 – Synchronous Uncertainty Comparison - BTT Replay vs. SABM

The differences in the levels of uncertainty prior and post resonance (see Figure 6.41) are

linked to the features described at the end of Section 6.2.1 (i.e. BTT Replay linear interpolation

across the resonance and number of revolutions used to carry out the averaging).


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The validation of the uncertainty measurement process based on the information displayed in

Figure 6.42 leads to the validation of the signal-to-noise ratio equation defined in Section 5.4.

Figure 6.43 – SABM SNR Extracted Information

To summarise the above information, the maximum extracted blade tip amplitude at resonance

is 0.13 mm peak-peak with a measurement uncertainty of 5.12% and with a signal-to-noise ratio

of 47.2 dB.


The verification of the new automated matrix models for integral and non-integral engine order

responses in Chapter 3, Chapter 4 and Chapter 5 against theoretical models provided clear

evidence of improvements against validated analysis tools and especially in terms of the new

integrated data zeroing techniques.

Using real engine test data for integral and non-integral engine order responses during single

and multiple resonances, the new analysis techniques (i.e. AABM, SABM) have been

successfully endorsed against validated analysis tools (i.e. BTT Replay and Batch Processor)

and showed some clear improvement such as the removal of the pre-post resonance linear

interpolation.

The new analysis technique which removes some of the constraints linked to an equally spaced

probe configuration by introducing virtual response into the recorded raw has been successfully

validated using real engine test data. Despite using a non-equally spaced probe configuration to


211

validate the ESP processing technique, there are no foreseen issues for the use of this novel

technique especially designed for equally spaced probes.

Finally, the method developed based on the AABM and SABM models to extract the levels of

uncertainty and signal-to-noise ratio using time-of-arrival blade data of Low Pressure Turbine

(LPT) blades recorded on a mechanical rig, in vacuum under rotation has been successfully

validated and linked to a confidence level of 90%.

Chapter 7 Method for Extracting BTT Axial Displacement & Untwist

212


From an acquisition point of view, the recording of compressor and/or turbine blade time of

arrivals (TOA) is not an issue as long as the hardware requirements are met (i.e. probe,

acquisition card clock speed) [9].

Compressor Blade Shrouded Turbine Blade

Figure 7.1 - Compressor Blade Tip vs. Turbine Blade Tips

The complexity of the shrouded turbine blade tip (circled in red) when compared to compressor

blade tip (red arrow) is shown in Figure 7.1 and at the same time highlighting a number of

detectable features from a BTT point of view. Because of the circumferential constraints

imposed on the BTT probe positions on turbine casing (see Chapter 4), the recording of

additional TOA data point per blade per revolution is important in order to extract for example,

the BTT axial displacement and untwist parameters.

This appendix addresses methods for extracting the turbine blade axial displacement and

untwist based on BTT time-of-arrival data points. The information given in this appendix is

protected by Patent GB1309624.3.


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7.1 BTT Blade Axial Displacement

To reduce FEM uncertainties during a model validation when using extracted BTT information,

the blade tip axial measurement positions (i.e. displacement) need to be computed and can be

extracted using the recorded TOAs.

Denton [49] provides a definition of the true lean and the true sweep of a blade as shown on

Figure 7.2:

Lean is defined as a blade displacement perpendicular to the local chord line,

Sweep is defined to the moving the sections along the chord line

Figure 7.2 - Definition of Blade Lean and Blade Sweep [49]


214

However, from a BTT point of view, the true lean and the true sweep displacements need to be

converted as BTT measurable displacements (see Figure 7.3) using the blade stagger angle

[50].

Figure 7.3 - Definition of BTT Axial and Radial Displacements

Strain gauge measurements on compressor and turbine blades provide stress engineers with

strain information at known positions on the blade. In regards to Blade Tip Timing, the axial

blade tip measurement positions at each revolution are different (see Figure 7.3) due to:

Blade mode shape response

Shaft/case thermal growth

Bearing movement

Non-uniformed gas loading

Centrifugal loading (i.e. blade untwist, blade lean)

Hence, to correlate the BTT analysis results to FEM predictions, the extraction of the blade tip

axial measurement positions (i.e. BTT sweep displacement) from the recorded TOA data is

crucial.


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7.2 Turbine Blade Axial Shift & Untwist

7.2.1 BTT Turbine Data Blade Acquisition

In comparison with compressor blades, where a single TOA data point per blade per revolution

is captured, four TOA data points for shrouded turbine blades (see Figure 7.4) is recorded per

blade per revolution.

Figure 7.4 - Definition of Shrouded Turbine Blade TOA Data points

Where each TOA data point (e.g. “t101” see Figure 7.4) is associated to an identifier built from a

combination of the parameters i, j and k where:

“i” represents the Blade Nº,

“j” represents the revolution Nº,

“k” represent the TOA value Nº.

HPT Blade Top View


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7.2.2 BTT Turbine Axial Displacement and Untwist

To carry out the extraction of the axial displacements and untwist values at each revolution for

each turbine blade, some information which is logged automatically at the final stage of the

manufacturing verification process for each blade is required and shown in Figure 7.5, are:

dF1, is the width of the HPT blade Fence 1,

dF2, is the width of the HPT blade Fence 2,

101, is the static angular sector of the Fence 1 and the Blade Frame of

Reference,

101, is the static angular sector of the Fence 2 and the Blade Frame of

Reference.

The angle with their identifier (e.g. on Figure 7.5) is built from a combination of parameters

i, j and m where:

“i” represents the blade Nº,

“j” represents the revolution Nº,

“m” represents the probe No.


217

Figure 7.5 - Shrouded Turbine Blade Tip Manufacturing Information

Figure 7.6 provides a description of the blade tip axial displacement parameter bax

, in reference

to the static Fence 1 / Fence 2 midpoint and the following equations can be extracted from:

7.1

7.2

7.3

7.4

HPT Blade Top View


218

Figure 7.6 - Definition of Shrouded Turbine Blade Tip Axial Displacement


219

The untwist value for every blade at every revolution and at each circumferential

measurement casing position (i.e. at each probe) can then be extracted using Equations 7.1 to

7.4 as shown in Equation 7.5.

7.5

Using the zoomed information shown in Figure 7.7, the blade axial displacement bax

, can be

extracted using Equation 7.6:

7.6

where

7.7

with

7.8

7.9

7.10

7.11


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Figure 7.7 - Zoomed Definition of Shrouded Turbine Blade Tip Axial Displacement

By combining the Equations 7.6 to 7.11 into Equation 7.5, the blade axial displacement at

revolution Nº1 for blade No 1 at probe N

o 1 is defined as:

7.12

7.3 Conclusions of Chapter 7

Using blade information logged at the final stage of the manufacturing verification process and

the time-of-arrival data points recorded at each fence, the blade axial displacement (i.e. BTT

sweep) and blade untwist can be successfully extracted using Equation 7.12. These two new


221

parameters can be processed if required for each rotating component at each revolution and for

each probe.

A significant improvement to the actual BTT processing capabilities, the new technique enables

to extract the blade position in the axial direction of the engine during the acquisition of the TOA

data points, an important and essential piece of information for the stress engineers when

carrying out a FEM / BTT correlation.

Chapter 8 Commercial Aspects & Context of the Research Work

222


“Trusted to deliver excellence”, Rolls-Royce plc [51] provides solutions for its customers in civil

and defence aerospace, marine and energy markets by relying on skilled people to deliver value

by following business processes effectively and reliably.

Being a global company, Rolls-Royce’s business model is built on five key activities:

1. Invest in leading technologies and skilled people,

2. Develop world-class products,

3. Manufacture efficiently,

4. Develop close customer relationships globally,

5. Provide services that add value.

In 2012, the net Research and Development (R&D) expenditure was estimated at about five

percent of the underlying revenue [51] in products across the four major segments (i.e. civil,

defence, marine and energy).

Highlighted in Chapter 1 and based on the approach of ‘invest once use many times’, simulation

tools, as an example, have become the driving force in the design of blades for gas turbines.

Similarly, the same concepts of efficiency and ’invest once use many times’, has led to the

requirement of a cost effective blade vibration measurement and analysis system; Blade Tip

Timing.

Successfully deployed for the certification of Rolls-Royce Trent XWB compressor blades in

2011, the techniques and methods generated by Russhard [9] were first independently peer

reviewed by Prof. N. A. Cumpsty [52] for a prototype Blade Heath Monitoring (BHM) system;

achieving a rating of five out of five for its engineering excellence, engineering output and

quality of research.

In Recent years, BTT applications for gas turbine engines have brought worldwide interest,

leading to the International Society of Automation (ISA) [53] to set up a BTT subcommittee


223

(ISA107.1) with the scope to standardise the BTT application including the acquisition and data

processing.

8.1 Cost Reduction Benefits associated with BTT

Over the past few years, Blade Tip Timing systems have demonstrated some significant

technical advantages and substantial financial benefits in comparison with the limited life

expectancy of strain gauges in hostile environments, the wear of slip-rings, the failure of

telemetry systems due to temperature and the embedded electronic system fatigue.

The implementation of the BTT technology for engine test experiments provides tip

displacements for “All The Blades, All The Time”) with no change required for the blade design

(i.e. non-intrusive measurement - see Chapter 1), except for the casing where the installation of

the probes is required.

With Commercial Off The Shelf (COST) acquisition components and Rolls-Royce’s global vision

to standardise test equipment, non-intrusive measurement systems have led to substantial cost

savings for the overall test experiments. For example, the overall cost (i.e. hardware and labour)

for a large IPC telemetry system in 2010 was estimated at just under half a million pounds

compared to £24K for a 10 channel acquisition BTT system [9] with £15K per probe. Note that

the cost of a probe includes the casing modification/rework and its installation. In addition, the

overall expenditures could be further reduced with the Turbine Blade Tip Timing algorithms for

Equally Spaced Probe constraints. Indeed, with the implementation of the virtual probe(s) (see

Chapter 4), experimental cost could be further reduced.

To develop world class products and to manufacture them efficiently (two of the five key

activities of Rolls-Royce’s business model), lead time for engine development testing is also an

important parameter in addition to the cost saving activities described above. Indeed,

unexpected engine strip-down for unforeseen activities can be further delayed when using strain

gauge telemetry systems due to the complicated instrumentation. Note that engine rebuild cost

could be in excess of £1million per test campaign [8] which could be significantly reduced by the

simpler instrumentation methodology utilised by the non-intrusive BTT measurement system.


224

8.2 Rolls-Royce’s BTT Strategy

In the foreseeable future, the usage of strain gauges for turbine test experiments will be revoked

due to a 20% increase of the HPT blade surrounding temperature. By gaining Technology

Readiness Level 4 (see Section 1.2.2), Rolls-Royce has funded a programme of work for the

validation of Blade Tip Timing Turbine until 2020 to assure that:

1. All the measurements are delivered with the Blade Tip Timing technology to meet the

higher temperature design constraints.

2. The implementation of the developed techniques into Rolls-Royce BTT tools meet

European Aviation Safety Agency (EASA) requirements for the certification of HPT

engine blades by 2018.

To achieve Technology Readiness Level 6 for the BTT Turbine technology, the Environmental

Friendly Engine (EFE) programme [54] led by Rolls-Royce is the right test vehicle to utilise.

Indeed, to deliver and maintain the Strategic Research Agenda (SRA) defined by the Advisory

Council for Aeronautics Research in Europe (ACARE) [55], the EFE programme targets three

areas of the 2020 ACARE environmental goals: reducing CO2, NOx and noise. High turbine

entry temperatures are required to improve turbine efficiency and low emissions lean burn

combustion.

The Blade Tip Timing system provides the necessary measurement requirements in the high

temperature turbine environment that EFE must generate to achieve those deliverables.

Chapter 9 Conclusions & Future Work

225


9.1 Conclusions

For the past few years, Rolls-Royce has embraced Blade Tip Timing as a mainstream

measurement technology to support Finite Element predictions for the certification of rotary

compressor components. After many failed attempts in understanding the content of the Time-

Of-Arrival data, Russhard’s decomposition and understanding of the probe signals provided a

major step forward in assessing the dynamic behaviour of blades under vibration from a BTT

perspective.

Since recognising that all probes have different steady state offsets, this present thesis has

generated two new matrix-based models for carrying out the extraction of blade tip amplitudes

for non-integral and/or integral engine order response(s). Indeed, Chapter 3 described and

verified Averaging Built-in Matrix (ABM) models for both asynchronous and synchronous

responses using simulated data. One of the advantages of the new models is the removal of

Russhard’s forty revolution zeroing process. Purely based on the usage of matrices and with a

minimum of two successive revolutions, the best fit modal frequency responses are tracked to

deliver all the necessary vibratory information for each blade. This information includes steady

state offsets and residual displacement terms at each probe. In addition, the new extraction

process based on the ABM models has eliminated both the need for generating a blade activity

mask and for applying a noise filter.

With the current BTT analysis techniques, it is impossible to extract the blade tip amplitudes for

engine orders where their cycles are a multiple of the angular sector of one segment. This

severely limits the implementation of BTT technology into Turbine applications. Probe positions

in turbine applications are defined by the number of segments. Previous attempts in solving the

problem with a small number of Equally Spaced Probes (ESP) have failed and held back the

development of Blade Tip Timing. Previous analysis methods imposed restrictions on targeted

engine orders where their cycles are a multiple of the angular sector of one segment. By adding

virtual information to existing ESP configurations and recorded blade tip displacements, as

demonstrated in Chapter 4, new BTT algorithms based on the ABM models have successfully

bypassed many of these restrictions.


226

Often overlooked, measurement uncertainty and Signal-to-Noise Ratios (SNRs) are vital pieces

of information to correctly assess the validity of the extracted vibratory information. In Chapter 5,

the advantages of the new processing capabilities based upon the residual displacement terms

at each probe are defined. These definitions were made by assessing uncertainty from

measured BTT data as opposed to uncertainty from processing theoretical simulations. This has

the added bonus of considering the effects of noise associated with the targeted component

which was not considered with previous methods.

Leading to four patent applications, the outputs from the new processes have been thoroughly

compared against those from certified BTT analysis tools. Validation work has been detailed in

Chapter 6 for the new asynchronous and synchronous models for single and multiple

responses, including ESP configurations. Each of the above listed improvements was confirmed

using SNRs and measurement uncertainties based on real engine test data.

Finally, to determine untwist values and BTT axial displacements for shrouded turbine blades,

algorithms have been developed in Chapter 7 based solely on recorded raw BTT time-of-arrival

data points. There are critical parameters when assessing the blade tip displacements against

FEM predictions. Unfortunately, the limitations of the test facilities could not validate these

methods.

9.2 Future Work

In 2010, Rolls-Royce’s strategy for carrying out the certification of its latest Trent engine relied

upon BTT technology and AU3D modelling, leading to a successful programme. To reach the

same levels of success as for compressor blades and a cost effective method for validating

turbine blade simulations, the following activities should be investigated for further

improvements.

o High Pressure Turbine Engine Test

To reach Technology Readiness Level of 6, the BTT techniques developed in this

research work must be validated on a full system / subsystem in a relevant

environment. In addition, the engine test will also validate the method for extracting

BTT axial displacement and untwist for turbines described in Chapter 7.


227

o BTT Processing Techniques

a. To find out the optimum number of virtual probes for both types of response

(i.e. asynchronous and synchronous).

b. To investigate an alternative computational process to Singular Value

Decomposition, in order to speed up convergence to the best engine order fit(s)

for the targeted modal response(s).

c. To extract vibratory blade information for single/multiple integral and non-

integral engine order responses based on an automated single pass analysis.

d. To develop a process to extract shaft torsional vibratory information using the

raw BTT time-of-arrival data.

o BTT Test Facility Laboratory

To characterise turbine blade vibration response(s) and finite element prediction

validation, some hardware has been set up as part of this project in the BTT Test

Facility Laboratory at the University of Manchester. Appendix E exhibits some of the

hardware positioned on an isolated vibration table inside a sound booth. The main

systems are two sources of excitation (i.e. Electromagnetic (EM) shaker and

chopped air jet exciter), one dynamic strain gauge measurement system and two

firewire cameras.

These resources will form the basis of a future project which will integrate the above

contributions with the test facility to create an end-to-end verification of this

improved BTT methodology for turbine blade applications. Some of the activities will

be based on:

a. Carrying out BTT FEM validation using a parametric model of the specimen.

b. Correlating BTT measurement vs. Parametric FEM predictions vs. Strain

Gauges.


228

c. Assessing the propagation of uncertainty between:

o BTT measurements vs. Validated FEM

o BTT Measurements and SG Measurements vs. Validated FEM

9.3 Closing Remarks

The overall objectives of this research work were to improve the current validated Rolls-Royce

BTT extractions techniques and to validate the improved extraction using simulated and real

data in order to bring the Turbine BTT technology to a Technology Readiness Level of 4.

Indeed, if successful, the benefits of applying BTT to the turbine section of the aero engine are

even more bountiful than for the compressor section. This is in no small part due to the fact that

for high-pressure turbine blades, strain gauge mortality is extremely high and re-test costs are

prohibitive. It is now believed that the proposed ABM models combined with novel validated

techniques satisfy the above objectives.

Whilst an engine test is still required to bring the novel BTT techniques to a Technology

Readiness Level of 6, this research work has successfully provided novel methods to extract

information on the vibration behaviour of High Pressure Turbine blade applications. This work

has successfully brought forward BTT techniques in overcoming previous analysis restrictions

through the use of virtual parameters and by providing Rolls-Royce with a capable methodology

to assess the accuracy of the extracted information.

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Appendices

235

Appendices

Appendix A

236

A Multiple Asynchronous Compressor Blade Response Comparative Displays

Figure A1 – Asynchronous Mode ‘A’ Amplitude – Batch Processor vs. AABM

Figure A2 – Asynchronous Mode ‘A’ Engine Order – Batch Processor vs. AABM

Appendix A

237

Figure A3 – Asynchronous Mode ‘A’ Frequency – Batch Processor vs. AABM

Figure A4 – Asynchronous Mode ‘B’ Amplitude – Batch Processor vs. AABM

Figure A5 – Asynchronous Mode ‘B’ Engine Order – Batch Processor vs. AABM

Appendix A

238

Figure A6 – Asynchronous Mode ‘B’ Frequency – Batch Processor vs. AABM

Figure A7 – Asynchronous Mode ‘A’ and ‘B’ Coherence – Batch Processor vs. AABM

Figure A8 – AABM Asynchronous Modes ‘A’ SNR

Appendix A

239

Figure A9 – AABM Asynchronous Modes ‘B’ SNR

Figure A10 – Asynchronous Mode ‘A’ Uncertainty – Batch Processor vs. AABM

Figure A11 – Asynchronous Mode ‘B’ Uncertainty – Batch Processor vs. AABM

Appendix B

240

B Single Synchronous Compressor Blade Response Comparative Displays

Figure B1 - Synchronous Amplitude – BTT Replay vs. SABM

Figure B2 - Synchronous Engine Order – BTT Replay vs. SABM

Appendix B

241

Figure B3 - Synchronous Frequency – BTT Replay vs. SABM

Figure B4 - Synchronous Coherence – BTT Replay vs. SABM

Figure B5 - Synchronous SNR – BTT Replay vs. SABM

Appendix B

242

Figure B6 - Synchronous Uncertainty – BTT Replay vs. SABM

Appendix C

243

C Multiple Synchronous Compressor Blade Response Comparative Displays

Figure C1 - Targeted Synchronous Amplitudes – SABM vs. SABM~Virtual

Figure C2 - Targeted Synchronous Engine Orders – SABM vs. SABM~Virtual

Figure C3 - Targeted Synchronous Frequencies – SABM vs. SABM~Virtual

Appendix C

244

Figure C4 - Synchronous Coherences – SABM vs. SABM~Virtual

Figure C5 - Synchronous SNRs – SABM vs. SABM~Virtual

Figure C6 - Targeted Synchronous Uncertainties – SABM vs. SABM~Virtual

Appendix C

245

Figure C7 - Virtual Synchronous Amplitude Response

Figure C8 - Virtual Synchronous Frequency Response

Figure C9 - Virtual Synchronous Engine Order Response

Appendix C

246

Figure C10 - Virtual Uncertainty Response

Figure C11 - Virtual SNR Response

Figure C12 - FoV and FoC – SABM~Virtual

Appendix D

247

D SNR and Uncertainty Blade Response Comparative Displays

Figure D1 - Synchronous Amplitude – Non-Zeroing BTT Replay vs. SABM

Figure D2 - Synchronous Engine Order – Non-Zeroing BTT Replay vs. SABM

Figure D3 - Synchronous Frequency – Non-Zeroing BTT Replay vs. SABM

Appendix D

248

Figure D4 - Synchronous Coherence – Non-Zeroing BTT Replay vs. SABM

Figure D5 - SABM Synchronous SNR

Figure D6 - SABM Synchronous Uncertainty

Appendix D

249

Figure D7 - Synchronous Amplitude – Zeroing BTT Replay vs. SABM

Figure D8 - Synchronous Engine Order – Zeroing BTT Replay vs. SABM

Figure D9 - Synchronous Frequency – Zeroing BTT Replay vs. SABM

Appendix D

250

Figure D10 - Synchronous Coherence – Zeroing BTT Replay vs. SABM

Figure D11 - SABM Synchronous SNR

Figure D12 - SABM Synchronous Uncertainty

Appendix D

251

Figure D13 - Synchronous Uncertainty Comparison - BTT Replay vs. SABM

Appendix E

252

E BTT Test Facility Laboratory – University of Manchester

Figure E1 – Test Facility Laboratory Hardware

Figure E2 – HPT Blade and Mass Block

Appendix E

253

Figure E3 – Chopped Air Jet Exciter