VIBRATION DIAGNOSIS OF BLADES OF ROTATING MACHINES

VIBRATION DIAGNOSIS OF BLADES OF ROTATING

MACHINES

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

Doctor of Philosophy

in the Faculty of Engineering and Physical Sciences

2015

AHMED GUBRAN

SCHOOL OF MECHANICAL, AEROSPACE AND CIVIL

ENGINEERING

TABLE OF CONTENTS

2

TABLE OF CONTENTS

TABLE OF CONTENTS ........................................................................................................... 2 List of Figures ............................................................................................................................... 5

List of Tables .............................................................................................................................. 11

List of Nomenclatures ................................................................................................................. 13

List of Abbreviations .................................................................................................................. 15

ABSTRACT ............................................................................................................................... 17

DECLARATION....................................................................................................................... 18

COPYRIGHT STATEMENT .................................................................................................. 19

ACKNOWLEDGEMENTS ..................................................................................................... 20

DEDICATION........................................................................................................................... 21

CHAPTER 1 INTRODUCTION ...................................................................................... 22

1.1 General Introduction ....................................................................................................... 22

1.2 Motivation ......................................................................................................................... 28

1.3 Objective ........................................................................................................................... 29

1.4 Thesis outline .................................................................................................................... 29

1.5 Research contribution ...................................................................................................... 31

1.6 Publications ....................................................................................................................... 31 1.6.1 Journal publications ................................................................................................... 31

1.6.2 Conferences publications ........................................................................................... 31

CHAPTER 2 LITERATURE REVIEW .......................................................................... 33

2.1 Introduction ...................................................................................................................... 33

2.2 Condition monitoring in rotating machines ................................................................... 33

2.3 Vibration-based fault diagnosis ...................................................................................... 34

2.4 Blades Vibration ............................................................................................................... 35

2.5 Blade failure modes .......................................................................................................... 37 2.5.1 Blades with mistuned effects ..................................................................................... 37

2.5.2 Blade root looseness .................................................................................................. 38

2.5.3 Cracks on blades ........................................................................................................ 39

2.5.4 Blade flutter ............................................................................................................... 40

2.5.5 Blade rubbing ............................................................................................................ 40

2.5.6 Blade fatigue .............................................................................................................. 41

2.6 Blade vibration measurements ........................................................................................ 43 2.6.1 Strain gauge ............................................................................................................... 43

2.6.2 Blade tip timing (BTT) .............................................................................................. 46

2.6.3 Torsional vibration .................................................................................................... 49

2.6.4 On-bearing vibration (OBV) ..................................................................................... 51

2.6.5 On-casing vibration (OCV) ....................................................................................... 51

2.7 Signal processing techniques ........................................................................................... 52 2.7.1 Time domain analysis ................................................................................................ 52

2.7.2 Frequency domain analysis ....................................................................................... 53

2.7.3 Short time Fourier transform (STFT) ........................................................................ 53

2.7.4 Instantaneous angular speed (IAS) ............................................................................ 53

2.7.5 Order tracking analysis (OTA) .................................................................................. 54

2.7.6 Time synchronising averaging (TSA) ....................................................................... 54

2.8 Research plan to investigate blades’ health using alternative vibration measurements

............................................................................................................................................ 55

2.9 Summary ........................................................................................................................... 55

CHAPTER 3 RIG DESIGN AND EXPERIMENTAL SETUP ..................................... 57

3.1 Introduction ...................................................................................................................... 57

3.2 Finite element modelling .................................................................................................. 57

TABLE OF CONTENTS

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3.3 Primary design model ...................................................................................................... 58

3.4 Final optimised model ...................................................................................................... 63

3.5 Manufacturing of the experimental rig .......................................................................... 66 3.5.1 The experimental rig .................................................................................................. 66

3.5.2 Parts of the experimental rig ...................................................................................... 67

3.5.2.1 Motor ................................................................................................................ 67

3.5.2.2 Shaft .................................................................................................................. 68

3.5.2.3 Bladed disc ........................................................................................................ 68

3.5.2.4 Ball bearing ....................................................................................................... 70

3.5.2.5 Flexible coupling .............................................................................................. 71

3.5.2.6 Foundation table ............................................................................................... 72

3.5.2.7 Rig casing ......................................................................................................... 73

3.5.3 Instrumentation .......................................................................................................... 74

3.5.3.1 Incremental rotary encoder ............................................................................... 74

3.5.3.2 Optical tacho sensor .......................................................................................... 76

3.5.3.3 Tachometer screen ............................................................................................ 76

3.5.3.4 Speed controller ................................................................................................ 77

3.5.3.5 Data acquisition ................................................................................................ 78

3.5.3.6 Accelerometer ................................................................................................... 79

3.5.3.7 Signal conditioning unit .................................................................................... 79

3.5.3.8 Measurement scheme ........................................................................................ 80

3.6 Modal testing .................................................................................................................... 81 3.6.1 Long and short blades FRF ........................................................................................ 82

3.7 Summary ........................................................................................................................... 85

CHAPTER 4 BLADE DIAGNOSIS USING ON-BEARING VIBRATION (OBV) .... 86

4.1 Introduction ...................................................................................................................... 86

4.2 Blade faults simulation..................................................................................................... 86 4.2.1 Healthy with mistuned effect ..................................................................................... 88

4.2.2 Root looseness ........................................................................................................... 88

4.2.3 Crack simulation ........................................................................................................ 89

4.3 Computation of engine order tracking (EOT) ............................................................... 93

4.4 Long blades experiments and data analysis ................................................................... 98 4.4.1 Data analysis .............................................................................................................. 98

4.4.2 Observations and results .......................................................................................... 100

4.5 Short blades experiments and data analysis ................................................................ 104 4.5.1 Experimental setup .................................................................................................. 104

4.5.2 Data analysis ............................................................................................................ 104


4.6 Summary ......................................................................................................................... 109

CHAPTER 5 BLADE DIAGNOSIS USING ON-CASING VIBRATION (OCV) ..... 110

5.1 Introduction .................................................................................................................... 110

5.2 Experiments on short blades ......................................................................................... 110 5.2.1 Data analysis ............................................................................................................ 110


5.3 Summary ......................................................................................................................... 117

CHAPTER 6 BLADE DIAGNOSIS USING SHAFT TORSIONAL VIBRATION

(IAS) .................................................................................................................... 118

6.1 Introduction .................................................................................................................... 118

6.2 Instantaneous angular speed (IAS) measurement method ......................................... 118

6.3 Experiments conducted .................................................................................................. 121

6.4 Data analysis ................................................................................................................... 122

6.5 Results of the experiments on long blades .................................................................... 124

6.6 Results of the experiments on short blades .................................................................. 135

TABLE OF CONTENTS

4

6.7 Observations and results ............................................................................................... 137

6.8 Summary ......................................................................................................................... 138

CHAPTER 7 COMPARATIVE STUDY BETWEEN OBV, OCV AND IAS

METHODS .................................................................................................................... 140

7.1 Introduction .................................................................................................................... 140

7.2 Results and observations ............................................................................................... 144 7.2.1 Comparison of the three measurements for monitoring short blades ...................... 144

7.2.2 Comparison of the two measurements for monitoring long blades ......................... 145

7.2.3 Final conclusion ....................................................................................................... 145

7.3 Summary ......................................................................................................................... 146

CHAPTER 8 DEVELOPMENT OF POLAR PLOT PRESENTATION (P3)

METHOD .................................................................................................................... 147

8.1 Introduction .................................................................................................................... 147

8.2 Signal processing concept developed ............................................................................ 147 8.2.1 Filter for each blade resonance related to the engine orders.................................... 147

8.2.2 Combining engine orders......................................................................................... 148

8.2.3 Time synchronous averaging for each engine order related to blade resonance ..... 148

8.3 Polar plot ......................................................................................................................... 149 8.3.1 Polar plot diagnosis approach .................................................................................. 149

8.4 Polar plot presentation (P3) for long blades ................................................................ 151 8.4.1 Encoder data analysis .............................................................................................. 152

8.4.2 Encoder data observations and discussion ............................................................... 158

8.4.3 On-bearing data analysis ......................................................................................... 158

8.4.4 On-bearing data observations and discussion .......................................................... 163

8.5 Polar plot presentation (P3) for short blades ............................................................... 163 8.5.1 Encoder data ............................................................................................................ 164

8.5.2 Encoder data observations and discussion ............................................................... 169

8.5.3 On-bearing data analysis ......................................................................................... 169

8.5.4 On-bearing data observations and discussion .......................................................... 174

8.5.5 On-casing data analysis ........................................................................................... 175

8.5.6 On-casing data observations and discussion............................................................ 182

8.6 Summary ......................................................................................................................... 183

CHAPTER 9 MATHEMATICAL MODEL .................................................................. 184

9.1 Introduction .................................................................................................................... 184

9.2 Simple mathematical model .......................................................................................... 184

9.3 Crack simulation ............................................................................................................ 185

9.4 Equation of motion ......................................................................................................... 186 9.4.1 Shaft forces components .......................................................................................... 186

9.4.2 Blades forces components ....................................................................................... 188

9.4.3 The unbalancing disc force components.................................................................. 188

9.5 Dynamic equations of the mathematical model ........................................................... 189 9.5.1 Derivation of the matrices system ........................................................................... 190

9.6 Results and observations ............................................................................................... 197

9.7 Summary ......................................................................................................................... 201

CHAPTER 10 CONCLUSIONS AND FUTURE WORK ............................................. 203

10.1 Overview ......................................................................................................................... 203

10.2 Review of project objectives, achievements and contributions .................................. 204

10.3 Overall conclusion .......................................................................................................... 207

10.4 Novel features ................................................................................................................. 207

10.5 Future work .................................................................................................................... 208

APPENDICES ......................................................................................................................... 209

REFERENCES ........................................................................................................................ 219

LIST OF FIGURES

5

LIST OF FIGURES

Figure ‎1.1: Typical photograph of low pressure steam turbine rotor with bladed disc stages [2]

............................................................................................................................................ 23

Figure ‎1.2 : Turbofan engine, Rolls-Royce Trent-900 [3] .......................................................... 24

Figure ‎1.3: General usage of various techniques in the machinery condition monitoring [1] .... 24

Figure ‎1.4: Typical turbo-machinery rotating components [7] ................................................... 25

Figure ‎1.5 : Blade faults due to various operation conditions: (a) crack in steam turbine

blades[8], (b) Pitting and corrosion in steam turbine blades [9], (c) erosion in steam turbine

blades [10], (d) corrosion in steam turbine blades [11], (e) rubbing in tip of turbine blades

[12], (f) blades failure due to deficit in thermal compensation [13] ................................... 27

Figure ‎1.6: The complex shape of turbo-machinery blade: (a) front view, (b) back view [14] .. 28

Figure ‎2.1: A schematic of vibration condition monitoring transducers system on turbo-

generator set [20] ................................................................................................................ 35

Figure ‎2.2: A turbo-generator: a steam turbine bladed system [29]. .......................................... 36

Figure ‎2.3: Blade failure of a gas turbine due to blade root looseness (adapted from Hee et al.,

2014) [31] ........................................................................................................................... 38

Figure ‎2.4: A typical crack on a blade in a steam turbine (adapted from Hahn and Sinha, 2015)

[42] ...................................................................................................................................... 39

Figure ‎2.5: Blade failure in a gas turbine due to rubbing (adapted from Hee et al., 2014) [31] . 41

Figure ‎2.6: Failure mode distribution in jet engines (adapted from Cowles, 1989) [56] ............ 42

Figure ‎2.7: Distribution of HCF on jet engine components (adapted from Cowles, 1989) [56] 42

Figure ‎2.8: Foil strain gauges: (a) schematic of foil gauge (reproduced from Russhard, 2015)

[59] (b) sensor attached on the object [65] ......................................................................... 45

Figure ‎2.9: Typical mounting of strain gauges: (a) on bladed discs, (b) on blades (a and b

reproduced from Russhard, 2015) [59], and (c) on a steam turbine blade (Reproduced from

Hahn and Sinha, 2013) [66] ................................................................................................ 45

Figure ‎2.10: Schematic of a two-coil inductive sensor for blade tip clearance measurement

(Reproduced from Li et al., 2014) [76] ............................................................................... 47

Figure ‎2.11: Non-contact blade vibration tip timing measurement system (Reproduced from

Tamura et al., 2014) [77] .................................................................................................... 47

Figure ‎2.12: Typical mounting of BTT probes system on a turbine casing for BHM of last stage

blades (Hahn and Sinha, 2013) [66].................................................................................... 48

Figure ‎2.13: Frequency spectrum of measured torsional vibration signal: (a) healthy tuned

blades, (b) one faulty blade (mistuned) (adapted from Maynard et al., 2000) [94] ............ 50

Figure ‎3.1: Typical FE mesh for the shaft-disc-blades model: (a) side view, (b) front view ..... 59

Figure ‎3.2: Typical FE mesh for shaft-disc-blades with blade tip mass model: (a) side-view with

bearings location, (b) front view ......................................................................................... 60

Figure ‎3.3: Cylindrical blades: (a) blade with blade tip mass, (b) blade without blade tip mass,

(c) crack on blade 20% of blade diameter ........................................................................... 61

Figure ‎3.4: Experimental rig with cylindrical blades .................................................................. 62

Figure ‎3.5: Blade fault diagnosis using cylindrical blades: (a) on test rig, (b) bladed disc [90] . 62

Figure ‎3.6: Five magnets with an attached ring opposite the cylindrical blades ........................ 63

Figure ‎3.7: FE model of long blades’‎first‎natural‎frequency‎with‎matched‎mode‎shape........... 65

Figure ‎3.8:‎FEM‎of‎short‎blades’‎first‎natural‎frequency‎with‎matched‎mode‎shape ................. 65

Figure ‎3.9: Photograph of the experimental rig with rectangular blades .................................... 66

Figure ‎3.10: Electrical motor ...................................................................................................... 68

Figure ‎3.11: Bladed discs: (a) Long blades, (b) Short blades ..................................................... 69

Figure ‎3.12: Photograph of a long blade and a short blade ......................................................... 70

Figure ‎3.13: Pedestal ball bearing unit........................................................................................ 70

Figure ‎3.14: Flexible coupling: (a) integral clamp attachment methods, (b) Unequal diameter

LIST OF FIGURES

6

shafts [125].......................................................................................................................... 71

Figure ‎3.15: Flexible coupling installation with the motor shaft and the end of the rotor .......... 72

Figure ‎3.16: Rig foundation table ............................................................................................... 73

Figure ‎3.17: Rig safety cover with (a) Side monitoring windows, (b) Top monitoring windows,

(c) Electrical safety switch .................................................................................................. 74

Figure ‎3.18: Location of encoder at the end of the rotor ............................................................ 75

Figure ‎3.19: Rotary shaft encoder ............................................................................................... 75

Figure ‎3.20: Optical tacho sensor ............................................................................................... 76

Figure ‎3.21: Tachometer screen .................................................................................................. 77

Figure ‎3.22: Speed controller ...................................................................................................... 78

Figure ‎3.23: National Instruments NI USB-6221 board ............................................................. 78

Figure ‎3.24: Accelerometer ........................................................................................................ 79

Figure ‎3.25: Front and back panel of 4-Channel signal conditioner PCB Piezotronics, 482C ... 79

Figure ‎3.26: Schematic diagram of the rig data acquisition system ........................................... 81

Figure ‎3.27: Schematic diagram of blades modal testing ........................................................... 83

Figure ‎3.28: Photograph of modal testing setup ......................................................................... 83

Figure ‎3.29: Typical FRF plots for a long blade (blade 4) first natural frequency at 127.50 Hz:

(a) Amplitude, (b) Phase, (c) Imaginary part ...................................................................... 84

Figure ‎3.30: Typical FRF plots for a short blade (blade 8) first natural frequency at 234.90 Hz:

(a) Amplitude, (b) Phase, (c) Imaginary part ...................................................................... 84

Figure ‎4.1: Schematic diagram of the blade positions with respect to the tacho sensor ............. 88

Figure ‎4.2: Simulation of long blade root looseness fault .......................................................... 89

Figure ‎4.3: Long blade crack simulation: (a) front side of a crack, (b) back side of a crack, (c) a

very thin metal sheet in the crack, and (d) cracked blade location on the bladed disc on the

rig ........................................................................................................................................ 90

Figure ‎4.4: Short blade crack simulation: (a) crack dimensions, (b) cracked blade with shim

location on the bladed disc on the rig, (c) shim on crack adhesive side and (d) shim on

crack non-adhesive side ...................................................................................................... 90

Figure ‎4.5: Cracks on the blades at different locations: (a) long blades (b) short blades ........... 91

Figure ‎4.6: Crack on one long blade on the bladed disc ............................................................. 92

Figure ‎4.7: Crack on two short blades on the bladed disc .......................................................... 92

Figure ‎4.8: Tachometer signals: (a) rotating shaft speed, (b) blades EO1 of run-up speed (1X),

and (c) zoom view of (a) ..................................................................................................... 94

Figure ‎4.9: Measured vibration signal: (a) acceleration raw signal and (b) zoomed view of (a) 95

Figure ‎4.10: Typical contour plot of speed orders for on-bearing vibration response in horizontal

direction .............................................................................................................................. 96

Figure ‎4.11: Typical measured on-bearing vibration data for engine order spectra of EO5 of

healthy blades...................................................................................................................... 97

Figure ‎4.12: Accelerometer location in relation to the on bearing pedestals in the vertical and

horizontal directions ............................................................................................................ 99

Figure ‎4.13:‎Typical‎amplitude‎spectrum‎for‎long‎blades ........................................................... 99

Figure ‎4.14: Measured‎on-bearing‎acceleration‎data‎for‎engine‎order spectra of EO5 for healthy

blades with mistuned effects (Case 1)............................................................................... 101

Figure ‎4.15: Measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎spectra of EO5 for blade

looseness (Case2 (ii): Blade no. 5) .................................................................................... 101

Figure ‎4.16: Measured‎ on-bearing‎ acceleration‎ data‎ for‎ engine‎ order spectra of EO5 for two

cracked blades (Case3 (ii): Blades no. 2 and 4) ................................................................ 102

Figure ‎4.17: Measured‎ on-bearing‎ acceleration‎ data‎ for‎ engine‎ order‎ spectra of EO10 for

healthy blades (Case1) ...................................................................................................... 102

Figure ‎4.18: Measured‎on-bearing‎acceleration‎data‎for‎engine‎order spectra of EO10 for blade

looseness (Case 2 (ii): Blade no. 5) ................................................................................... 103

Figure ‎4.19: Measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎spectra of EO10 for two

LIST OF FIGURES

7

cracked blades (Case 3 (ii): Blade no. 2 and 4) ................................................................ 103

Figure ‎4.20: Typical measured on-bearing acceleration signals at machine run-up from 600 to

1800 rpm ........................................................................................................................... 104

Figure ‎4.21:‎ Measured‎ on-bearing‎ acceleration‎ data‎ for‎ engine‎ order‎ spectra‎ of‎ EO10‎ for‎

healthy‎blades‎with‎mistuned‎effects‎(Case 1) .................................................................. 106

Figure ‎4.22:‎Case3 (i): measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎spectra‎of‎EO10‎

for‎one‎cracked‎blade‎(Case 3 (i): Blade no. 4)................................................................. 106

Figure ‎4.23:‎Measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎ spectra‎of‎EO10‎ for‎ two‎

cracked‎blades‎(Case 3 (ii): Blades no. 2 and 4) ............................................................... 107

Figure ‎4.24:‎ Measured‎ on-bearing‎ acceleration‎ data‎ for‎ engine‎ order‎ spectra‎ of‎ EO20‎ for‎

healthy‎blades‎with‎mistuned‎effects‎(Case 1) .................................................................. 107

Figure ‎4.25:‎Case3 (i): measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎spectra‎of‎EO20‎

for‎one‎cracked‎blade‎(Case 3 (i): Blade no. 4)................................................................. 108

Figure ‎4.26: Measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎ spectra‎of‎EO20‎ for‎ two‎

cracked‎blades‎(Case 3 (ii): Blades no. 2 and 4) ............................................................... 108

Figure ‎5.1:‎A‎schematic‎of‎on-casing‎measurement‎setup:‎(a)‎side‎view‎and‎(b)‎top‎view‎of‎the‎

rig ...................................................................................................................................... 111

Figure ‎5.2:‎On-casing‎measurement‎setup:‎ (a)‎top‎view‎of‎rig‎showing‎ the‎blades‎and‎the‎on-

casing‎accelerometer‎(b)‎rig‎backside‎casing .................................................................... 112

Figure ‎5.3: Typical on-casing measured acceleration data during machine run-up speed (600 to

1800 rpm) .......................................................................................................................... 113

Figure ‎5.4: On-casing measured acceleration data for engine order EO10 spectra for healthy


Figure ‎5.5: On-casing measured acceleration data for engine order EO10 spectra for a crack on

one blade (Case 3(i)) ......................................................................................................... 115

Figure ‎5.6: On-casing measured acceleration data for engine order EO10 spectra for cracks on

two blades (Case 3(ii)) ...................................................................................................... 115

Figure ‎5.7: On-casing measured acceleration data for engine order EO20 spectra for healthy


Figure ‎5.8: On-casing measured acceleration data for engine order EO20 spectra for a crack on

one blade (Case 3(i)) ......................................................................................................... 116

Figure ‎5.9: On-casing measured acceleration data for engine order EO20 spectra for cracks on

two blades (Case 3(ii)) ...................................................................................................... 117

Figure ‎6.1: Schematic of the encoder pulse train ...................................................................... 119

Figure ‎6.2: Measured encoder pulse train of the rotating shaft ................................................. 119

Figure ‎6.3: Ideal shaft IAS showing a constant shaft speed without torsion ............................ 121

Figure ‎6.4: Typical shaft IAS showing the possibility of shaft torsion .................................... 121

Figure ‎6.5: A typical rotor speed profile for the machine during run-up .................................. 122

Figure ‎6.6: Typical magnified measured encoder raw signals .................................................. 122

Figure ‎6.7: A typical IAS response at e.g. EO5 for Case 1: healthy blades illustrating frequency

modes ................................................................................................................................ 123

Figure ‎6.8: A typical IAS response at EO10 for short blades; Case 1: Healthy blades ............ 124

Figure ‎6.9: Measured encoder (IAS) data for engine order EO5 spectra for healthy blades (Case

1) ....................................................................................................................................... 125

Figure ‎6.10: Measured encoder (IAS) data for engine order EO5 spectra for blade root looseness

(Case 2(i): Blade no. 1) ..................................................................................................... 125

Figure ‎6.11: Measured encoder (IAS) data for engine order EO5 spectra for blade root looseness

(Case 2(ii): Blade no. 5) .................................................................................................... 126

Figure ‎6.12: Measured encoder (IAS) data for engine order EO5 spectra for a crack on one

blade (Case 3(i): Blades no. 4) .......................................................................................... 126

Figure ‎6.13: Measured encoder (IAS) data for engine order EO5 spectra for cracks on two

LIST OF FIGURES

8

blades (Case 3(ii): Blades no. 2 and 4) ............................................................................. 127


blade (Case 3(iii): Blade 2) ............................................................................................... 127


blade after 100 minutes of machine operation (Case 3(iv): Blade 4)................................ 128

Figure ‎6.16: Measured encoder (IAS) data for engine order EO10 spectra for healthy blades

(Case 1) ............................................................................................................................. 128

Figure ‎6.17: Measured encoder (IAS) data for engine order EO10 spectra for blade root

looseness (Case 2(i): Blade no. 1) ..................................................................................... 129


looseness (Case 2(ii): Blade no. 5) .................................................................................... 129


blade (Case 3(i): Blade no. 4) ........................................................................................... 130




blade (Case 3(iii): Blade no. 2) ......................................................................................... 131


blade after 100 minutes of machine operation (Case 3(iv): Blade no. 4).......................... 131


(Case 1) ............................................................................................................................. 132


looseness (Case 2(i): Blade no. 1) ..................................................................................... 132


looseness (Case 2(ii): Blade no. 5) .................................................................................... 133






blade (Case 3(iii): Blade no. 2) ......................................................................................... 134


blade after 100 minutes of machine operation (Case 3(iv): Blade no. 4).......................... 135


(Case 1) ............................................................................................................................. 136





Figure ‎7.1: A schematic flowchart for the processes that are followed to select the best

measurement for BHM of rotating machines .................................................................... 140

Figure ‎8.1 Typical sample of the polar plot presentation model ............................................... 150

Figure ‎8.2: Mean speed of EO5 for IAS data from healthy long blades ................................... 152

Figure ‎8.3: Polar plot of IAS measured data of EO5 for cases: (a) healthy blades, (b) blade root

looseness, (c) a crack on one blade and (d) cracks on two blades .................................... 153


looseness, (c) crack on one blade and (d) cracks on two blades ....................................... 154


looseness, (c) crack on one blade and (d) cracks on two blades ....................................... 155

Figure ‎8.6: Polar plot of IAS measured data of EO5+EO10 for cases: (a) healthy blades, (b)

blade root looseness, (c) crack on one blade and (d) cracks on two blades ...................... 156

LIST OF FIGURES

9

Figure ‎8.7: Polar plot of IAS measured data of EO5+EO10+EO15 for cases: (a) healthy blades,

(b) blade root looseness, (c) crack on one blade and (d) cracks on two blades ................ 157

Figure ‎8.8: Polar plot of acceleration (OBV) measured data of EO15 for cases: (a) healthy

blades, (b) blade root looseness, (c) crack on one blade and (d) cracks on two blades .... 159

Figure ‎8.9: Polar plot of acceleration (OBV) measured data of EO5+EO10 for cases: (a) healthy

blades, (b) blade root looseness, (c) crack on one blade and (d) cracks on two blades .... 160

Figure ‎8.10: Polar plot of acceleration (OBV) measured data of EO5+EO10+EO15 for cases: (a)

healthy blades, (b) blade root looseness, (c) crack on one blade and (d) cracks on two

blades ................................................................................................................................ 161

Figure ‎8.11: Polar plot of acceleration (OBV) measured data of EO10+EO20 for cases: (a)

healthy blades, (b) blade root looseness, (c) crack on one blade and (d) cracks on two

blades ................................................................................................................................ 162

Figure ‎8.12: Polar plot of IAS measured data of EO10 for cases: (a) healthy blades, (b) crack on

one blade and (c) cracks on two blades ............................................................................. 165

Figure ‎8.13: Polar plot of IAS measured data of EO20 for cases: (a) healthy blades, (b) crack on

one blade and (c) cracks on two blades ............................................................................. 166

Figure ‎8.14: Polar plot of IAS measured data of EO10 + EO20 for cases: (a) healthy blades, (b)

crack on one blade and (c) cracks on two blades .............................................................. 167

Figure ‎8.15: Polar plot of IAS measured data of EO10+EO30 for cases: (a) healthy blades, (b)

crack on one blade and (c) cracks on two blades .............................................................. 168


healthy blades, (b) crack on one blade and (c) cracks on two blades ............................... 170





Figure ‎8.19: Polar plot of acceleration (OBV) measured data of EO10+EO20+EO30 for cases:

(a) healthy blades, (b) crack on one blade and (c) cracks on two blades .......................... 173

Figure ‎8.20: Polar plot of acceleration (OCV) measured data of EO30 for cases: (a) healthy

blades, (b) crack on one blade and (c) cracks on two blades ............................................ 176

Figure ‎8.21: Polar plot of acceleration (OCV) measured data of EO10+EO30 for cases: (a)






Figure ‎8.24: Polar plot of acceleration (OCV) measured data of EO20+EO30+EO40 for cases:


Figure ‎8.25: Polar plot of acceleration (OCV) measured data of EO10+EO20+EO40 for cases:


Figure ‎9.1: Simplified rotor model with 8 blades ..................................................................... 185

Figure ‎9.2: Free body diagram for rotor forces ......................................................................... 187

Figure ‎9.3: Free body diagram of unbalanced mass disc forces in x-y plane ........................... 189

Figure ‎9.4: Typical acceleration run-up responses signal, (a) Healthy blades, (b) Crack on Blade

.......................................................................................................................................... 198

Figure ‎9.5: Typical contour plot of BR frequency (1xBR), (a) Healthy blades, (b) Crack on

Blade ................................................................................................................................. 199

Figure ‎9.6: Typical contour plot of BR frequency (2xBR), (a) Healthy blades, (b) Crack on

Blade ................................................................................................................................. 200

Figure ‎9.7: Typical estimated acceleration responses at EO5, (a) Healthy blades, (b) Crack on

Blade 2 .............................................................................................................................. 201

LIST OF FIGURES

10

Figure A 1: Combined curves of bearing measured acceleration data for long blades for engine

order EO5 spectra: Case (1) healthy blades, (2-ii) blade 5 root looseness, (3-ii) cracks on

blades 2 & 4 ...................................................................................................................... 209



blades 2 & 4 ...................................................................................................................... 210

Figure A 3: Combined curves of bearing measured acceleration data for short blades for engine

order EO10 spectra: Case (1) healthy blades, (3-i) crack on blade 4, (3-ii) cracks on

blades 2 & 4 ...................................................................................................................... 211

Figure A 4: Combined curves of bearing measured acceleration data of short blades for engine

order EO20 spectra for: Case (1) healthy blades, (3-i) crack on blade 4, (3-ii) cracks on

blades 2 & 4 ...................................................................................................................... 212

Figure B 1: Combined curves of casing measured acceleration data for short blades for engine


blades 2 & 4 ...................................................................................................................... 213



blades 2 & 4 ...................................................................................................................... 214

Figure C 1: Combined curves of measured encoder (IAS) data for engine order EO5 spectra:

Case (1) healthy blades, Case (2-i) blade 1 root looseness, Case (2-ii) blade 5 root

looseness, (3-i) crack on blade 4, (3-ii) cracks on blades 2 & 4, (3-iii) crack on blade 2, (3-

iv) crack on blade 4 after 100 minute of running .............................................................. 215









Figure C 4: Combined curves of measured encoder (IAS) data of short blades for engine order

EO10 spectra: Case (1) healthy blades, (3-i) crack on blade 4, (3-ii) cracks on blades 2 & 4

.......................................................................................................................................... 218

LIST OF TABLES

11

LIST OF TABLES

Table ‎3-1: Shaft-disk-blades model dimensions ......................................................................... 58

Table ‎3-2: Model properties and dimensions of the shaft-disc-blades system including design of

blade tip mass ...................................................................................................................... 60

Table ‎3-3: Shaft–disc–blade(s) data for long and short blades ................................................... 64

Table ‎3-4: Specification of the motor ......................................................................................... 67

Table ‎3-5: Specification of the encoder ...................................................................................... 75

Table ‎3-6: Specifications of the Tacho sensor ............................................................................ 76

Table ‎3-7: Specifications of the speed controller CL750 ........................................................... 77

Table ‎3-8: Experimentally identified long and short blades first natural frequency ................... 82

Table ‎4-1: Cases of blade faults conditions ................................................................................ 87

Table ‎7-1 : Comparison between the results of OBV, OCV and IAS for short blades ............. 141

Table ‎7-2: Comparison between the results of OBV and IAS for long blades ......................... 143

Table ‎7-3: Articles published related to this study in the research area of blade vibration fault

detection using different measurements ............................................................................ 146

Table ‎8-1: The numbers of single leaves and coupled leaves in the polar plot of EO5 for the four

cases of blade health conditions based on IAS data .......................................................... 153

Table ‎8-2: The numbers of single leaves and coupled leaves in the polar plot of EO10 for the

four cases of blades health conditions based on IAS data ................................................ 154


four cases of blades health conditions based on IAS data ................................................ 155

Table ‎8-4: The numbers of single leaves and coupled leaves in the polar plot of combination of

EO5+EO10 for the four cases of blades health conditions based on IAS data ................. 156


EO5+EO10+EO15 for the four cases of blades health conditions using IAS data ........... 157


four cases of blade health conditions using OBV data ..................................................... 159

Table ‎8-7: The numbers of single leaves and coupled leaves in the polar plot of a combination

of EO5+EO10 for the four cases of blade health conditions using OBV data .................. 160


EO5+EO10+EO15 for the four cases of blade health conditions using OBV data........... 161


EO10+EO20 for the four cases of blade health conditions using OBV data .................... 162


three cases of blade health conditions using IAS data ...................................................... 165


three cases of blade health conditions using IAS data ...................................................... 166


EO10+E20 for the three cases of blade health conditions using IAS data ........................ 167


EO10+E30 for the three cases of blade health conditions using IAS data ........................ 168


EO10+E20 for the three cases of blade health conditions using OBV data ...................... 170






LIST OF TABLES

12

EO10+EO20+E30 for the three cases of blade health conditions using OBV data .......... 173


three cases of blade health conditions using OCV data .................................................... 176


EO10+E30 for the three cases of blade health conditions using OCV data ...................... 177






EO20+EO30+E40 for the three cases of blade health conditions using OCV data .......... 180


EO10+EO20+E40 for the three cases of blade health conditions using OCV data .......... 181

Table ‎9-1: Rotor/ blade parameters used in the mathematical model ....................................... 185

Table ‎9-2: First mode shape frequencies for blades and shaft obtained using the mathematical

model ................................................................................................................................ 190

LIST OF NOMENCLATURES

13


E Young’s‎modulus

density (kg/m3)

Rpm revolution per minute

Rps revolution per second

M Mass

A Acceleration

F Force

K Stiffness

C Damping

mb blade mass

kb blade stiffness

cb blade damping

xb blade acceleration

xb blade velocity

xb blade displacement

mr rotor mass

kr rotor stiffness

cr rotor damping

xr rotor acceleration

xr rotor velocity

xr rotor displacement

mu unbalancing mass

R Radius

𝜔 angular velocity

Fimb imbalanced force

F frequency (Hz)

[M] mass matrix

[C] damping matrix

[K] stiffness matrix

{𝐹𝑢𝑛𝑏} unbalanced force vector

{X} acceleration vector


14

{X} velocity vector

{X} displacement vector

t time (s)

tv amplitude of signal (V)

x distance (m)

LIST OF ABBREVIATIONS

15


AC Alternating Current

BHM Blade Health Monitoring

BPF Blade Pass Frequency

BR Blade Resonance

BTT Blade Tip Time

CBM Condition Based Monitoring

CFD Computational Fluid Dynamics

CM Condition Monitoring

DC Direct Current

Di Inner Diameter

Do Outer Diameter

EO,‎EO’s Engine Order(s)

EOT Engine Order Tracking

FE Finite Element

FEA Finite Element Analysis

FEM Finite Element Modelling

FFT Fast Fourier Transform

FOD Foreign Object Damage

FRF Frequency Response Function

HCF High Cycle Fatigue

IAS Instantaneous Angular Speed

IRM Impulse-Response Modal

LCF Low Cycle Fatigue

LPT Low Pressure Turbine

MACE Mechanical, Aerospace and Civil Engineering

MW Mega Watt

MDOF Multi Degrees Of Freedom

NI National Instruments

OBV On-Bearing Vibration

OCV On-Casing Vibration

OT Order Tracking


16

OTA Order Tracking Analysis

P3 Polar Plot Presentation

PC Personal Computer

RPM Revaluation Per Minute

RPS Revolution Per Second

SDOF Single Degree Of Freedom

STFT Short Time Fourier Transform

TG Turbo-Generator

TOA Time of Arrival

TSA Time Synchronizing Averaging

ABSTRACT

17

ABSTRACT

Ahmed Gubran - Doctor of Philosophy

The University of Manchester – 09 February 2015

VIBRATION DIAGNOSIS OF BLADES OF ROTATING MACHINES

Rotating blades are considered to be the one of the most common cause of failures in

rotating machinery. Blade failure modes normally occur as a result of cracks due to

unexpected operating conditions, which are normally caused by accidents of foreign

objects damage, high cycle fatigue, blade rubbing, blade root looseness, and degradation

from erosion and corrosion. Thus, detection of blade faults has an important role in

reducing blade related failures and allowing repairs to be scheduled for the machinery.

This in turn will lead to reduction in maintenance costs and thus raise productivity and

safety aspects of operation. To maintain vital components of rotating machines, such as

blades, shafts, bearings and gear boxes, at optimal levels, detection of failures in such

components is important, because this will prevent any serious damage that could affect

performance.

This research study involves laboratory tests on a small rig with a bladed disc rotor that

applied vibration measurements and analysis for blade fault detection. Three

measurements: shaft torsional vibration, on-bearing vibration (OBV) and on-casing

vibration (OCV), are used. A small test rig of a single stage bladed disc holding 8-

blades was designed and manufactured, to carry out this research study to assess the

usefulness and capability of each vibration technique in detection of incipient defects

within machine blades.

A series of tests was conducted on a test rig for three different cases of blade health

conditions: (a) healthy blade(s) with mistuned effects, (b) blade root looseness and (c)

cracks in a blade on two different blade sizes (long and short blades) in order to

discover‎ changes‎ in‎ blades’‎ dynamic‎ behaviour during the machine running-up

operation. The data were collected using the three measurements during machine run-up

and‎then‎recorded.‎The‎measured‎vibration‎data‎were‎analysed‎by‎computing‎the‎blades’‎

resonance at different engine orders (EOs) related to the blade(s) resonance frequencies

and their higher harmonics, to understand the blade(s) dynamics behaviour for the cases

of healthy and faulty blade(s).

Data have been further processed using a polar plot presentation method which provides

clear results that can be used for monitoring blade integrity. To validate the obtained

experimental results, a simplified mathematical model was also developed. Finally, a

comparative study between three methods was undertaken to understand the relative

advantages and limitations in the blade heath monitoring.

Keywords: Blade vibration, Blade health monitoring, Shaft torsional vibration, On-

bearing vibration (OBV), On-casing vibration (OCV), Blade faults, Engine orders

(EOs), Polar plot presentation, Order tracking (OT).

DECLARATION

18

DECLARATION

I hereby declare that 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

19

COPYRIGHT STATEMENT

The following four notes on copyright and the ownership of intellectual property rights

must be included as written below:

i. The author of this thesis (including any appendices and/or schedules to this thesis)

owns certain copyright or related rights‎in‎it‎(the‎“Copyright”)‎and‎s/he‎has‎given‎The‎

University of Manchester certain rights to use such Copyright, including for

administrative purposes.

ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic

copy, may be made only in accordance with the Copyright, Designs and Patents Act

1988 (as amended) and regulations issued under it or, where appropriate, in accordance

with licensing agreements which the University has from time to time. This page must

form part of any such copies made.

iii. The ownership of certain Copyright, patents, designs, trade marks and other

intellectual‎ property‎ (the‎ “Intellectual‎ Property”)‎ and‎ any‎ reproductions‎ of‎ copyright‎

works‎ in‎ the‎ thesis,‎ for‎ example‎ graphs‎ and‎ tables‎ (“Reproductions”),‎which‎may‎ be‎

described in this thesis, may not be owned by the author and may be owned by third

parties. Such Intellectual Property and Reproductions cannot and must not be made

available for use without the prior written permission of the owner(s) of the relevant

Intellectual Property and/or Reproductions.

iv. Further information on the conditions under which disclosure, publication and

commercialisation of this thesis, the Copyright and any Intellectual Property and/or

Reproductions described in it may take place is available in the University IP Policy

(see http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=487), in any relevant

Thesis restriction declarations deposited in the University Library, The University

Library’s‎regulations‎(see‎http://www.manchester.ac.uk/library/aboutus/regulations) and

in‎The‎University’s‎policy on Presentation of Theses.

http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=487

http://www.manchester.ac.uk/library/aboutus/regulations

ACKNOWLEDGEMENNTS

20

ACKNOWLEDGEMENTS

First of all, my ultimate thanks are to Allah almighty who created me and gave me

strength and knowledge.

Also, I would like to express my appreciation and sincere gratitude to my supervisor,

Dr Jyoti K. Sinha, for his continuous support, supervision, and guidance over the entire

period of this research study.

I would also like to express my gratitude to the school of MACE postgraduate

programme administrator Ms Beverley Knight for her diligent and positive efforts in

ensuring my PhD runs smoothly.

My thanks go to the school technicians who have helped me to manufacture and

assemble the test rig and especially to the technical coordinators at the Pariser Building

workshop, Mr Paul Townsend and Mr Phil Oakes, for their assistance in preparing

the test rig manufacture.

Special thanks go also to my uncle Abdullah Jubran for his unlimited support and

encouragement, and also to my brothers, Mahmud and Abdulhameed, for all their

immense support and also to all my other brothers and sisters.

Specially and most importantly, I would like to thank my wife Aisha for her support,

patience, encouragement and sharing every moment throughout my PhD in great love

and support. Also, my thanks go to my beloved daughter Aziza and beloved sons

Abdurrahman and Abdullah.

I would also like to express my gratitude to all my friends and colleagues for making

these years in Manchester very special and extremely pleasant.

Finally, my special thanks are dedicated to the Libyan Government for granting me a

scholarship for my PhD study.

ACKNOWLEDGEMENNTS

21

DEDICATION

I dedicate this work to my mother (died 1987), my father (died 2007), my uncle

Abdullah, my wife, my kids and all my family members who encouraged me to

complete this PhD study.

CHAPTER 1 Ahmed. Gubran 2015, PhD Thesis, The University of Manchester, UK

22

CHAPTER 1

INTRODUCTION

1.1 General Introduction

Rotating machinery are commonly integrated with most vital industrial processes such

as power generation, aerospace, mining, food processing, etc. Figure 1.1 and 1.2 show

pictures of rotating machines in a steam turbine and an aero-engine respectively. These

industries face costly failures due to vibration problems in the rotating machinery which

at times result to huge annual financial losses to the companies, including safety

implications. Over the years, the need to eliminate costly (reduced throughput, safety,

environment, customer satisfaction, etc.) downtimes by companies has significantly

tilted attention towards effective machinery faults diagnosis and more proactive

maintenance techniques. A very prominent strategy that has gained significant attention

over the past decades is Condition-based Maintenance (CBM), which basically entails

studying and trending key operational parameters (such as vibration, pressure,

temperature, sound, etc.) of machines during day-to-day operations without necessarily

interrupting production activities. A very vital merit of CBM over other maintenance

strategies (e.g. run-to-failure or planned preventive maintenance) revolves around the

fact that emerging machine faults and abnormalities can be captured very early, before

such faults can lead to catastrophic failures, which in turn enhances the ability of

companies to improve the satisfaction of their companies. In order to adequately

harness all the benefits of a CBM system, it is very vital that this strategy is strictly

limited to the most critical equipment of any company.

During machinery faults diagnosis with CBM, various operating parameters are

captured and tracked, using different monitoring measurements. Amongst all the

conventional CBM techniques (e.g. vibration analysis, lube & wear debris analysis,

infrared thermography, acoustic emission, process monitoring, human senses, etc.),

vibration analysis is the most popular owing to the fact that it offers the longest lead

time to equipment failure. It represents up to 41% of CBM techniques used in rotating

machines monitoring as can be seen in the pie chart in Figure 1.3. The pie chart also


23

shows the usage percentages of other CBM techniques for monitoring rotating machines

[1].

Figure 1.1: Typical photograph of low pressure steam turbine rotor with bladed disc stages [2]

Bladed discs Main shaft

Blade

Disc


24

Figure 1.2 : Turbofan engine, Rolls-Royce Trent-900 [3]

Figure 1.3: General usage of various techniques in the machinery condition monitoring [1]

Vibration

41%

Tribology

12%

Thermography

5%

Ultrasonics

3%

Motor Analysis

11%

Electrical

Analysis

1%

Process

Parameters

25%

Airborne Noise

2%

Engine

casing

Compressor

blade stages

Exhaust

nozzle

discs

Turbine blade

stages

Fan

blades

Main

shaft


25

With vibration in rotating machines been recognized as a major cause of failure, the task

of faults diagnosis in rotating machines through the application of vibration analysis

primarily involves understanding the vibrational behavior of the machine during healthy

and suspected faulty conditions at pre-defined intervals, so as to capture irregularities in

performance, prior to failure. Research in condition monitoring resulted in developing

better diagnostic techniques which have benefited companies by allowing them to save

huge amounts of money [4].

A typical turbo-machinery is composed of shafts, bladed discs, bearings, sleeves,

couplings, gears, housing and foundation as shown in Figure 1.4. However, turbine

blades, which are key components of gas turbines, suffer high mechanical loading due

to extreme changes in both temperature and pressure, which have often been classified

as major sources of failures in many steam turbines and jet engines. Carter [5] reported

that turbine blade damage can also be caused by foreign object damage (FOD) or

torsion forces. Figure 1.5 shows blade failures due to impacts of varying environmental

conditions. The most common cause of failures in gas turbines and jet engines is related

to blade faults, which were reported to represent up to 42% of total gas turbine failures

[6].

Figure 1.4: Typical turbo-machinery rotating components [7]

Blade stages Bladed discs

Turbine

housing Shaft

Disc


26

The continuous need for enhanced performance of modern day industrial machines such

as turbines has led to complicated shapes of components such as blades (Figure 1.6),

which significantly increase the difficulty levels of their manufacture The operating

conditions of turbines expose these blades to extreme vibration excitation mechanisms,

thus making it sometimes difficult to measure performance. Despite the advances in

theory and technology of faults detection and diagnosis over the years, effective and

accurate measurement still poses some challenges, which in turn triggers the need for

further improvements on the understanding of blade vibration phenomenon. The lack of

full understanding of the mechanisms of vibration and the challenges associated with

direct measurements of blade vibration and its interaction with other components have

made the diagnostic process very difficult. This has however led to the application of

alternative approaches such as indirect measurement techniques for ascertaining the

vibration of machine components known to have strong dynamic interactions with the

blades.


27

(a)

(b)

(c)

(d)

(e)

(f)

Figure 1.5 : Blade faults due to various operation conditions: (a) crack in steam turbine

blades[8], (b) Pitting and corrosion in steam turbine blades [9], (c) erosion in steam

turbine blades [10], (d) corrosion in steam turbine blades [11], (e) rubbing in tip of

turbine blades [12], (f) blades failure due to deficit in thermal compensation [13]


28

Figure 1.6: The complex shape of turbo-machinery blade: (a) front view, (b) back view [14]

1.2 Motivation

Rotating machinery is widely used in modern industries and these machines are

complex and have several components that can potentially fail at any stage during

operation, especially under extreme conditions. Since blades represent the main parts

(core) of many industrial rotating machines (e.g. turbo-generators, induced draft fans,

compressors, pumps, etc.), there exists a pressing need to develop an effective and

robust CBM technique that will adequately simplify blade faults diagnosis, so as to

enhance the reliability of bladed rotating machines Nowadays, the most effective

approaches for diagnosing rotating machine faults is vibration based condition

monitoring. Hence, the motivation of this study is to investigate and proposed vibration

based faults diagnosis techniques that can simplify blade health monitoring (BHM),

without necessarily comprising the ability to detect faults early. Owing to the efficiency

gaps in the currently used BHM techniques, there is a significant need for more

effective, non-contact and non-destructive measurements to detect and diagnose blade

health conditions, using advanced signal processing methods. In order to achieve the

objectives of this research, three measurements were investigated, namely; shaft

torsional vibration based-on instantaneous angular speed (IAS), on-bearing vibration

(OBV) and on-casing vibration (OCV). The significance of this research lies in the

development of an advanced signal processing technique to develop a relatively easy

and more effective method for BHM.

(a) (b)


29

1.3 Objective

The objectives of the current research are as follows:

Objective 1: To design and manufacture a test rig suitable for simulating rotating

machine blades and to detect blade faults due to mistuned blades, blade root looseness

and blade cracks, using vibration based condition monitoring measurements.

Objective 2: To apply the proposed measurements of shaft torsional vibration, OBV

and OCV during rotating machine running-up and/or running-down in order to examine

their abilities to detect blade faults based on vibration signals.

Objective 3: To compare and analyse the results obtained using the three proposed

measurements, so as to deduce which measurement is the most useful for detecting and

diagnosing blade faults.

Objective 4: To select the best measurement in combination with a unique signal

processing method that will enhance the detection of blade mistuning effects, blade root

looseness and cracked blades.

Objective 5: To compare both theoretical and experimental observations, so as to better

understand blade vibration behaviour.

1.4 Thesis outline

This thesis consists of ten chapters, and the contents of each chapter are summarised as

follows:

Chapter 2 provides a review of the literature pertinent to this research. The chapter

reports earlier studies in the area of rotating machines condition monitoring, with

particular emphasis on blade vibration fault detection, using torsional vibration

measurement, on-bearing and on-casing vibration measurements. The chapter also

provides a highlight of some of the popularly applied blade vibration fault detection

measurements and blade failure modes.

Chapter 3 describes the experimental setup including rig design, rig construction and

the various sensors used in this research. Additionally, a description of the finite


30

element (FE) model for the entire rig and its rotating components (shaft-disc-blades)

using ABAQUS code is also provided, and modal analysis for shaft and blades.

Chapter 4 describes the experimental results and the corresponding discussions

relevant to the detection of blade faults (blade root looseness and cracked blade(s))

using the OBV measurement.

Chapter 5 describes the experimental results and corresponding discussion relevant to

the detection of blade faults (cracked blade(s)) using an OCV measurement, which was

based on using acceleration signals data on casing towards the rotating blades disc.

Chapter 6 describes the experimental results and the corresponding discussions

relevant to the detection of blade faults (blade root looseness and cracked blade(s))

using shaft torsional vibration measurement, which was based on the application of

incremental shaft encoder, through the application of IAS signals.

Chapter 7 describes a comparison of the results obtained from the application of all

three measurements (i.e. OBV, OCV and shaft torsional vibration based-on IAS), so as

to determine which of the measurements is the most suitable for BHM.

Chapter 8 discusses a polar plot method of the healthy and faulty blade conditions for

both long and short blades, using the diagnosis results from IAS signals, OBV and OCV

signals. It must be stated that this method is considered a novel technique for the

detection and diagnosis of blade health conditions.

Chapter 9 describes the mathematical model of a single staged bladed disc rotor with

eight blades, which was developed and simulated using transient vibration response

signals of rotating blades. The analytically and numerically modelled blade vibrations

were then verified using experimental data, so as to boost the confidence level of the

present study.

Chapter 10 presents a review of the objectives and achievements of the current

research, in addition to a comprehensive conclusion and areas of future endeavours.


31

1.5 Research contribution

The overall conclusion is about improved turbine blades’ condition monitoring

processes for steam turbines and aero-engines using vibration measurements of

torsional vibration based on IAS signals as the specific area in which a contribution to

knowledge is claimed. Also, measurements based on OBV and OCV developed in this

study are highlighted in order to be employed for BHM. The current research has

successfully developed and applied a new signal processing technique that is based on a

polar plot representation of frequency analysis, which can be useful for the diagnosis of

blade faults associated with rotating machines such as steam turbines, gas turbines, etc.

1.6 Publications

The findings of this research study were published in following international journals

and conferences.

1.6.1 Journal publications

1- Gubran A. A. and J. K. Sinha, Shaft instantaneous angular speed for blade vibration

in rotating machine. Mechanical Systems and Signal Processing, 2014. 44(1-2): p.

47-59. (Special Issue on Instantaneous Angular Speed (IAS) Processing and Angular

Applications).

2- Gubran A. A. and J. K. Sinha, A comparison of on-bearing and shaft torsional

vibration for blade vibration. SOP Transactions on Signal Processing, 2014. 1(1):

p.1-9.

1.6.2 Conferences publications

1- Gubran A. A. and J. K. Sinha, Blade vibration: A comparison of on bearing and shaft

torsional vibration. 11th International Conference on Vibration Problems ICOVP,

Lisbon, Portugal, 9-12th September 2013.


32

2- Gubran A. A. and J. K. Sinha, Comparison between long and short blade vibration

using shaft instantaneous angular speed in rotating machine. Proceedings for the

ASME: Turbine Technical Conference and Exposition, Dusseldorf, Germany, 16-

20th

June 2014.

3- Gubran A. A. and J. K. Sinha, Comparison of on-bearing and on-casing vibration for

blade vibration. 10th International Conference on Vibration Engineering and

Technology of Machinery VETOMAC-X, Manchester, UK, 9-11th September 2014.


33

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

This chapter presents a comprehensive literature review summarising the previous

published work in the area of blade vibration condition monitoring of rotating

machinery, as well as different measurement techniques commonly used for the

detection and diagnosis of blade(s) health conditions. The detection of blade faults is

not easy due to the lack of practical direct sensor on the blade during machine operation

to‎monitor‎ the‎ blade‎ health‎ condition.‎ The‎ diagnosis‎ of‎ rotating‎ blades’‎ conditions‎ is‎

usually conducted using indirect measurements such as vibration techniques which are

widely utilized in rotating machines.

2.2 Condition monitoring in rotating machines

Condition monitoring (CM) is the process of monitoring and observing the conditions

of machines during operation, so as to avoid failures and its consequences. CM often

involves the monitoring of various measured parameters associated with machine

mechanical conditions such as vibration, pressure, temperature, oil debris, and machine

performance in order to determine‎ the‎ machine’s‎ state‎ of health [15]. Machine

malfunction diagnosis using CM has developed over many years due to the increasing

need for running more efficient machines at higher speeds and long operation hours

with less shutdown time, less maintenance cost, high productivity and better safety

considerations. Hence, by applying CM to rotating machines, failures can be prevented

and machine stoppage for unscheduled maintenance can be minimised. Failure occurs

because of many factors (either one at a time or in combination), and these factors are

related to many parameters which may include mode and duration of operation.

Various parameters including vibration, noise, corrosion, fatigue, shock, heat, cold,

dust, humidity, oil debris, temperature, pressure, and speed are known to have a

negative impacts on the health of rotating machines [16]. The use of condition

monitoring allows for the effective scheduling of routine maintenance activities, so as to

prevent catastrophic failures and costly downtimes. Therefore, it has recently become


34

essential to monitor the conditions of turbo-machinery so as to ensure their long term

availability and reliability.

2.3 Vibration-based fault diagnosis

Vibration analysis is the most important and most commonly used method for the

detection and diagnosis of faults in rotating machines. It is very widely used in the

industry to detect, locate and diagnose most of the common types of faults in one or

more rotating machine components [17]. Any abnormal vibrations discovered in the

rotating machinery gives a first indication that the rotating components of the machine

are failing. The use of vibration analysis for the diagnosis of machine operating

conditions can be carried out by comparing the vibration signals generated by a machine

operating in healthy conditions with those generated under faulty conditions. By

comparing these vibration signals, machine failure can be detected early, and thus the

possibility of significant damage occurring during machine operation can be reduced or

even eliminated using a condition monitoring system. The procedure of monitoring

using vibration analysis is dependent on various steps, including the application of

advanced signal processing programmes, so as to enhance the accuracy and reliability of

the faults diagnosis process. In this research study, vibration measurement techniques

are applied for the purpose of detection and diagnosis of blade faults in rotating

machines based on a simple setup, low cost equipment and quality analysis of the

results. Many studies have reported the importance of using vibration measurement for

fault detection and diagnosis in machines, as part of preventive and predictive

maintenance strategies [17-22]. In particular, Atoui et al. [19] described the use of

vibration signals for the detection and diagnosis of unbalances in rotating machines.

Other studies [23] also stated that the most established diagnostic technique for

monitoring the health of rolling elements bearings in rotating machinery is vibration

monitoring. The process of vibration measurement for predictive and preventive

maintenance programmes consists of two main parts [18]: (a) picking up raw vibration

data through the aid of vibration sensors such as accelerometers, proximity probes,

velocity meters, optical sensors, etc., (b) processing of the measured vibration signal

either in the time or frequency domains, using different advanced signal processing

tools developed using software such as MATLAB, LABVIEW, etc.. Figure 2.1 shows a


35

schematic representation of a turbo-generator, with several sensors installed for

vibration based health monitoring.

Vibration analysis has become an important CM technique, used to reduce or eliminate

approximately 80% of rotating components problems, especially rotor-related faults

such as misalignment and unbalance [24]. The cost of implementing an effective

preventive and predictive maintenance strategy is well under the cost of machine failure

(including damaged machine components, downtime, personnel injuries, etc.) [18].

Figure 2.1: A schematic of vibration condition monitoring transducers system on turbo-

generator set [20]

2.4 Blades Vibration

Rotating blades are considered the component most likely to cause failures in rotating

machinery. Turbine blades are exposed to various high dynamic loads during machine

operation, received directly from the steam jet and converted into driving forces. These

loads include thermal, inertia and bending loads [25]. Blade failure modes normally

occur as a result of cracking, high cycle fatigue (HCF), blade rubbing, blade root

looseness, erosion, creep and corrosion. Therefore, early fault detection is important in

reducing blade related failures and hence there is a need for a reliable and simple blade

health monitoring (BHM) technique. Al-Bedoor et al., [21] reviewed the different

methods that have been attempted for blade vibration measurements up to the year


36

2002. In addition, Abdelrhman et al., [26] reviewed CM techniques used for the

detection and diagnosis of blade health conditions in rotating machines. In practice,

blade crack fault is not easily detectable, owing to the lack of specific crack detection

sensors, which in turn makes the application of indirect measurements such as vibration

analysis imperative. Blade health can be established by observing and comparing the

vibration levels at the blade natural frequency during normal and faulty operating

conditions [20]. Any significant changes in blade vibration amplitude or any shifts in

natural frequency should be investigated to prevent blade failure [20]. Blade vibration

can be classified based on two parameters, namely; the type of excitation force and the

way the excitation force affects the vibration [27]. Blade resonance vibration occurs

when the blade natural frequency matches an excitation frequency [27]. There are three

methods used for measuring blade vibration: (1) stationary testing, which measures

blades natural frequency in a static condition using instrumented impact hammer or a

loudspeaker, (2) rotational testing by measuring blades natural frequencies under the

influence of centrifugal forces, and (3) in-service testing by measuring blades natural

frequencies under operation conditions [28]. Typical steam turbine blades are shown in

Figure 2.2.

Figure 2.2: A turbo-generator: a steam turbine bladed system [29].

Shaft

Disc Blades Stages


37

2.5 Blade failure modes

Rotating blades are considered the most common cause of failure in rotating machinery.

Blade failures normally occur as a result of cracking, high cycle stress, blade rubbing,

blade root looseness, foreign object damage (FOD), erosion, creep, corrosion, etc. It is

known that turbines contain numerous moving and stationary components, with many

of these components been subjected to very strenuous conditions inside the turbine. In

addition to that, out of the components inside the turbine, blades are the most likely

components to cause failure in rotating machines. Blades are exposed to high

temperatures; high pressures and stresses; and vibration resulting from aerodynamic

forces and centrifugal loads. All these factors can lead to failures in blades, and as a

result to machine breakdown. The most frequent blade failure causes in turbo-machines

include cracking, high cycle stress, blade rubbing, flutter, blade fouling, blade root

looseness, degradation from erosion, corrosion, deformation, etc. Meher-Homji et al.,

[6] and Carter [5] provided comprehensive reviews of blade failure modes in rotating

machines. Blade related failures are the most common faults in gas turbines observed

from operational experiences [5, 30]. Hee et al. [31] provided a review of blade fault

classification and also presented an overview of blade fault detection and assessment

techniques in gas turbines. Rao et al. [32] also presented a comparison of different

cumulative damage theories for blade life estimation. Leong [33] presented the common

types of blade faults and the vibration based methods used for their detection, using

three case studies on blade faults in gas turbines. In this section, the main blade failure

modes commonly encountered in rotating machines are presented with particular

emphasis on blade faults such as mistuned effects, blade root looseness, cracks on

blade(s), flutter, rubbing and fatigue.

2.5.1 Blades with mistuned effects

Mistuning constitutes small variations from one blade to another, which often occurs

due‎ to‎ differences‎ between‎ blades’‎ geometric properties; manufacturing and fitting

imperfection. The existence of such imperfections and irregularities are often inherent in

the manufacturing and assembly process of bladed discs, which is near impossible to

avoid. Choi et al., [34] and Petrov and Ewins [35] indicated that blade mistuned effects

lead to a significant increase in blades resonant response amplitude, and hence are often


38

referred to as a source of HCF in gas turbine engines. Ewins [36] considered mistuning

effects of blades on the natural frequencies of the assembled bladed disc, through the

conduction of several modal tests on different blades, so as to determine the effects of

mistuning‎effects‎on‎the‎blades’‎natural‎frequencies.‎

2.5.2 Blade root looseness

Blade root looseness fault in rotating machines occurs as a result of excess dimensional

tolerance (i.e. the gap) between the blade root attachment and the disc supporting

structure. The stress on a blade root increases when the tolerance gap increases during

blade rotation due to centrifugal forces, which may eventually cause cracks on the blade

root. In addition, if the blades are not correctly mounted and assembled on the disc, then

the blade root may become loose, which may result to rubbing during machine

operation lead to failure. Bhat et al., [37] observed that some variations occur in turbine

blades’‎natural‎ frequencies‎due‎ to‎manufacturing‎ tolerances.‎Leong‎ and Hee [30] and

Lim and Leong [38] applied wavelet analysis for the detection and diagnosis of blade

root looseness during rotor coast-down. Figure 2.3 shows the case where the tolerance

gap between a blade root and disc is larger than normal; this case of blade root

looseness is a type of blade faults.

Figure 2.3: Blade failure of a gas turbine due to blade root looseness (adapted from Hee et al.,

2014) [31]

Tolerance gap larger

than normal


39

2.5.3 Cracks on blades

Another very common cause of blade failure is crack, which can lead to catastrophic

failures in rotating machinery [39, 40]. Cracks on blades can be related to a variety of

factors including; foreign object damage (FOD), manufacturing flaws, high or low cycle

fatigue, resonant fatigue and stress corrosion. In a comprehensive review conducted by

Carter [5], it was reported that the most common cause of cracks in gas turbine blades

results from torsional forces or FOD. In a survey conducted by Rao and Dutta [41], it

was highlighted that approximately 50% of turbine blades failures can be attributed to

fatigue, stress corrosion, crack and corrosion fatigue, while 40% of blade failure causes

are yet to be fully understood. Figure 2.4 shows a typical crack on steam turbine blade.

Figure 2.4: A typical crack on a blade in a steam turbine (adapted from Hahn and Sinha, 2015)

[42]

Crack


40

2.5.4 Blade flutter

Flutter phenomenon can be defined as self-excited and self-sustained vibration of

rotating‎machines’‎ blades,‎ owing‎ to‎ the‎ interactions‎ between‎ aerodynamic‎ forces‎ and‎

blade vibration displacements. However, the enhancement of blade designs through

rigorous theoretical simulation (including finite element modelling and computational

fluid dynamics) of blade performance under different conditions may help minimise or

eliminate the fluttering‎of‎ rotating‎machines’‎blades.‎Vedeneev et al. [43] described a

numerical method for identifying the emergence of flutter in compressor blades. Mazur

et al. [44] also investigated the failure of several blades at the last stage of a low

pressure (LP) turbine of two 660 MW units.

2.5.5 Blade rubbing

Blade rubbing is another significant cause of faults in turbo-machinery [45]. Blade

rubbing faults in gas turbines represent approximately 23% of total blade faults [46].

Blade tip rubbing occurs as a result of contact between the stationary (casing) and

rotating (blades) parts of the turbine, leading to blades tip wear or failure. The primary

reason for blade-to-casing rubbing is high lateral rotor vibration and displacement of the

rotor centre line due to rotor misalignment. In aero-engines for instance, there are many

other reasons for blade rubbing including the deformation of engine casing due to heavy

landing, leading to contact between the compressor blade tips and the casing. This can

also happen as a result of blade expansion due to high temperatures and tight clearances

between the blades and the casing, which is common in modern-day aircrafts as the gap

between blade tips and the engine casing is reduced. Many researchers investigated

blade rubbing faults [47-49], while others investigated blade rubbing detection in

rotating machines using vibration techniques [30,50, 51]. For example, Mba and Hall

[52] applied acoustic emissions for detecting rubbing in rotating machines. Figure 2.5

shows the picture of a failed rotating machine blade due to rubbing.


41

Figure 2.5: Blade failure in a gas turbine due to rubbing (adapted from Hee et al., 2014) [31]

2.5.6 Blade fatigue

The operation of rotating machines such as steam turbines under high temperature,

pressure and speed contributes significantly to blade fatigue failure, especially HCF

[53]. Blade fatigue faults are reported to contribute as much as 18.5% of all blade

failures in gas turbines [46]. Blade fatigue failures are often due to irregularities in

mechanical behaviour and manufacturing defects [54]. Blade fatigue failures can be

broadly classified into two groups;

(a) High cycle fatigue (HCF): This occurs infrequently in turbine blades unless when

initiated by other damage sources such as FOD or the occurrence of abnormal vibrations

in the engine, causing extensive bending of the blades [5]. Else, HCF can be caused by

aerodynamic excitation or blade self-exited vibration and flutter [55].

(b) low cycle fatigue (LCF): This is related to frequent start-up and shut-down operation

of the machine under high centrifugal stress imposed by high speed and thermal stress,

which eventually causes cracks to occur at several locations on the blades and bolt holes

or bores of the bladed discs [26]. Figures 2.6 and 2.7 show the distribution of failure

modes including HCF, LCF and other failures associated with different engine parts.


42

Figure 2.6: Failure mode distribution in jet engines (adapted from Cowles, 1989) [56]

Figure 2.7: Distribution of HCF on jet engine components (adapted from Cowles, 1989) [56]


43

In this research study, the chosen three types of blade failure modes are healthy with

mistuned effect, blade root looseness and crack(s) in blade(s) for the experimental tests.

This three failure modes are common in rotating machines according to the Figure 2.6.

From the pie chart percentages, failure modes that commonly cause cracks in the

rotating blades leading to blade failure are: HCF 24%, LCF 12%, corrosion 8%,

mechanical damage 12%, overstress 12%, and other types of fatigue 13%, which means

that a total of 71% of blade failure modes can result in crack in blades. Blade root

looseness occurs as a result of materials 7%, the manufacturing process 11%, thermal

stress 1%, and overstress 12%. Blade mistuning occurs as a result of materials 7%

and/or the manufacturing process 11%. By choosing these three common blade faults,

this research study will cover the most common types of blade failure modes in rotating

machines.

2.6 Blade vibration measurements

Although studies [57], have shown that blade vibration is a significant contributor to

most major and costly failures in rotating machine, especially considering the

challenges associated with acquiring measurements that will explain the condition of

bladed rotating machines during operation. There are many direct measurement

techniques for monitoring blade conditions in situ, including the use of strain gauges

attached directly to the blade; laser Doppler systems and optical methods. On the other

hand, indirect techniques such as vibration measurements involve picking up vibration

signals from the casing, bearing pedestals or the main rotor and then conducting

diagnosis through the application of techniques such as instantaneous angular speed

(IAS). Al-Bedoor [58] and Abdelrhman et al., [26] respectively provided extensive

reviews on the different approaches for measuring blade vibrations, as well as the

strengths of each technique.

2.6.1 Strain gauge

Strain gauge is a direct measurement tool and a conventional method widely used in

blade health monitoring for estimating the blade vibration properties. During blade

health monitoring, the strain gauge is often attached to one or more blades, so as to

measure blade deflection. The use of strain gauges offers the least intrusive amongst


44

direct measurement techniques. A typical strain gauge is shown in Figure 2.8. The

application of strain gauges for blade health monitoring has also been described by

several studies, for instance, Russhard [59] provided a review of the development of

strain gauges in monitoring blade vibration over four decades, while Knappett and

Garcia [60] described the measurement of blade strain during machine operation, which

can be eventually used for estimating the stress and possibly the prediction of residual

stress [61]. In a different study, the optimal placements of strain gauges for measuring

rotating blade vibration were investigated by Szwedowicz et al. [62]. Over the years, the

optimal method for collecting data was through a combination of strain gauges with

radio telemetry and slip rings [59]. The main strength of this method involves the ability

to measure blade vibration by installing strain gauges on individual blade surfaces as

well as on the bladed disc as shown in Figure 2.9 (a) and (b), which allows facilitates

the measurement of vibrations on individual blades and the bladed disc. Another merit

of this method is the ability to directly record continuous and high response data.

However, this method is also associated with some disadvantages, including the

mounting of the sensors on the external surfaces of the blade (i.e. the flow path), which

in turn exposes the sensors to harsh operating conditions (such as high temperatures and

centrifugal forces) that contribute to their short life span [58]. Additionally, it is difficult

to access and transmit the generated signals from strain gauges to the external

processing device, which is the reason for the incorporation of complex systems of slip

rings or radio telemetry [63], which eventually increase the overall cost blade CM [64].

The complex shapes of the blades sometimes make it difficult to locate suitable

mounting surfaces for the strain gauges.


45

Figure 2.8: Foil strain gauges: (a) schematic of foil gauge (reproduced from Russhard, 2015)

[59] (b) sensor attached on the object [65]

Figure 2.9: Typical mounting of strain gauges: (a) on bladed discs, (b) on blades (a and b

reproduced from Russhard, 2015) [59], and (c) on a steam turbine blade (Reproduced from

Hahn and Sinha, 2013) [66]

(a)

(c)

(b)


46

2.6.2 Blade tip timing (BTT)

Blade tip timing is a direct and non-contact measurement method. Blade tip sensors

(capacitance, optics, and eddy current) are commonly used for monitoring blades

parameters in steam and gas turbine engines [67], as well as for diagnosis and prediction

of blade conditions in rotating machines during operation. Some of the most commonly

used BTT sensing techniques for blade vibration monitoring include capacitive,

inductive, optical, microwave, infrared, eddy-current, pressure and acoustic based

sensors [68]. Many studies [53, 69-72] have investigated the use of BTT as a vibration

based fault detection in rotating blade assemblies, and it was observed to be a useful and

effective method for blade health monitoring by measuring blade parameters such as

natural frequency, time of arrival and angle of arrival, hence providing rich information

that enhance the detection of a variety of blade faults including blade rubbing, cracks,

bending and blade looseness. BTT works by using a number of capacitance or optical

probes mounted on the enclosure of each engine blade stage as shown in Figure 2.10,

and the minimal number of probes is one sensor per stage. These probes measure the

time when blades tip passes a probe. Figure 2.11 shows a typical BTT measurement

system consisting of four proximity probes and a shaft speed tachometer for measuring

engine driving shaft speed. The time of arrival (TOA) of the blade is compared to that

when no dynamic motion is applied. BTT has received considerable attention in recent

years as it is capable of identifying blades that exhibit high vibration [60, 73] and

therefore BTT is considered a promising approach for blade vibration monitoring [74,

75]. Using non-contact BTT systems makes it possible to measure blade(s) vibration

and to detect blade health conditions in turbo-machinery [75]. In general, capacitance or

optical probes have been used extensively for these reasons [64].


47

Figure 2.10: Schematic of a two-coil inductive sensor for blade tip clearance measurement

(Reproduced from Li et al., 2014) [76]

Figure 2.11: Non-contact blade vibration tip timing measurement system (Reproduced from

Tamura et al., 2014) [77]

BTT is suitable for early detection of blade rubbing in gas turbines which has already

provided good results [26]. However, BTT systems suffer from some drawbacks,


48

Owing to the fact that optical probes require frequent maintenance to keep the lenses

clean from fouling [64]. The weight of system unlikely to add to the weight of aero-

engines which is fitted on an operational engine, which in airplanes need to reduces the

weight BTT systems are also sensitive to resonance vibration [78], intrusive and can be

expensive methods. In addition, the measurement system is limited to the blade tip,

thereby allowing for measurements only when the blade tip passes the probes. However,

the probes are sometimes unable to detect deflection responses that do not provide

sufficient tip motion. Another disadvantage is that incorrect probe spacing and if the

number of probes not enough can lead to vibration frequency aliasing [79]. However,

the recent initiatives on the combination of stain gauges and BTT probes in a single

system offers the potentials to overcome some disadvantages and hence achieve better

results of blade monitoring. However, both BTT and strain measurement methods are

intrusive and exorbitant. Hence, there is a need for more reliable and simple but robust

methods to meet the requirements of BHM. Figure 2.12 shows a typical BTT system on

the casing of a last stage steam turbine.

Figure 2.12: Typical mounting of BTT probes system on a turbine casing for BHM of last stage

blades (Hahn and Sinha, 2013) [66]


49

2.6.3 Torsional vibration

Torsional vibration in rotating machines is defined as the oscillatory movement of a

rotor as it rotates, or an oscillatory angular motion causing twisting in the rotating shaft

[80]. Torsional vibration can also be viewed as the cyclic variation of shaft speed.

Torsional vibration in rotating machines can cause various failures such as gear-tooth

breakage, blade faults due to blade fatigue in steam turbines [81], and shaft cracks. Al-

Bedoor [82] and Yang and Huang [83, 84] investigated the coupling between shaft

torsion and blade bending vibrations using a theoretical model of shaft-disk-blades

assembly. The results showed that a blade vibration signature can be extracted from the

shaft torsional vibration. Also, Huang and Ho [85] and Al-Bedoor [86] described the

coupling between blade bending and shaft torsion vibration for shaft-disc-blades

systems. Due to the interactions of vibration signals between blade bending and shaft

torsional vibration, this characteristic can be used to investigate the changes in blade

frequency, and hence detect blade faults. Therefore, shaft torsional vibration can be

used as a diagnostic tool to detect rapid changes in blade natural frequencies coupled to

shaft torsional modes, which enhance blade faults diagnosis as shown in Figure 2.13 (a)

and (b). Rotating machine vibration signature can be extracted from measurements of

shaft torsional vibration and then used for diagnosing machine conditions. This

technique can be used to monitor the changes in shaft torsional vibration frequencies

which are associated with blades frequencies, allowing for the assessment of blade

crack propagation [87]. There is limited research conducted on investigating the ability

of shaft torsional vibration measurements to provide information on blade vibration.

However, there is a potential for a new approach of indirect measurement of blade

vibration by measuring rotor torsional vibration [57, 88]. Non-intrusive measurement of

shaft torsional vibration signals in rotating machines has been a subject of interest in

research [89-91]. Experiments showed that shaft torsional vibration data analysis can be

effective for the detection and diagnosis of blade cracks, based on the changes in blades

natural frequency [89, 90, 92, 93] as shown in Figure 2.13. The changes in blades

frequency can be identified as seen in Figure 2.13 (b) for faulty blades compared to

profiles of healthy blades shown in Figure 2.13 (a).


50

Figure 2.13: Frequency spectrum of measured torsional vibration signal: (a) healthy tuned

blades, (b) one faulty blade (mistuned) (adapted from Maynard et al., 2000) [94]

Maynard and Trethewey [91] conducted simple experimental tests to identify blade

cracks in gas turbines through the application of the shaft torsional vibration method.

Other studies by Al-Bedoor [95] and Maynard and Trethewey [96] also reported on

experimental tests conducted to extract blade vibration data from shaft torsional

(a)

(b)


51

vibration measurements. The results indicated that the blades’ frequency responses are

often reflected in the shaft torsional vibration signals. Another study [97] on blades and

shaft vibration monitoring involved the application of random vibration excitation on

blades to determine the natural frequencies and mode shapes, through finite element

(FE) modelling. The blades and shaft torsional vibrations were monitored through the

combination of strain gauges installed on the blades and shaft, as well as on-bearing

accelerometers. The results showed that blade vibrations were apparent in the shaft

torsional vibrations. Maynard and Trethewey [91] have also demonstrated the field

application of the use of torsional vibration for tracking cracks in the shaft and blades of

rotating machines. Analytical simulations [82, 85, 98] have also shown the potential of

shaft torsional vibration in CM of turbine blades.

2.6.4 On-bearing vibration (OBV)

On-bearing vibration measurement is an indirect technique used to capture vibration

signals from the bearing pedestals of rotating machines and then the signals are

analysed to identify the dynamic behaviour of the blade(s), which provides information

about the blade health during machine operation. OBV measurements are simple to

initiate, non-intrusive and non-expensive method used to investigate blade health

conditions. Vibration signals extracted obtained through OBV measurements contain

information of machine vibration responses, including blades responses, which makes it

a valuable method for understanding machine condition [66, 99]. Hahn and Sinha [42]

carried out vibration measurements on a steam turbine generator (TG) using

accelerometers installed on bearing pedestals. It is suggested that using OBV measured

data of transient machine operation (run-up and run-down) during normal conditions is

important to identify and diagnose machine faults [20]. Sinha et al., [100] recently

analysed the in-situ measured vibration data at the bearing pedestals during the steady

state and transient operation of steam turbines, so as to understand machine dynamics as

well as identifying the root causes of failure of the last stage blades of the LP turbines.

2.6.5 On-casing vibration (OCV)

On-casing vibration is also an indirect measurement method used to diagnose blade

health conditions. The method is based on measuring casing vibrations by extracting the

vibration response signals of rotating blades using accelerometers mounted on the


52

machine casing (i.e. at each rotating blade stage on the outside surface of the casing)

during machine operation. The pressure of air or steam generated from the flow as well

as‎ the‎movement‎of‎ rotating‎blade‎ tips‎often‎affect‎ the‎ inner‎surface‎of‎ the‎machine’s‎

casing, and this gives valuable information on the blade vibration behaviour. Hence,

comparing the dynamic behaviour of blade(s) for varying cases of blade health

conditions through the analysis of machine on-casing vibration data can be useful in

BHM. Mathioudakis et al. [101] investigated the relation between casing vibration

responses of industrial gas turbines and engine operating conditions. Rao and Dutta

[102, 103] also investigated the use of casing vibrations to diagnose and detect blade

vibrations by monitoring the changes of blade passing frequency (BPF) components.

BPF vibration amplitude was found to be extremely sensitive to blade conditions during

operation [102]. An experimental work was carried out to estimate blade natural

frequencies from casing vibrations using proximity probes, so as to detect blade health

condition [104]. In addition, analytical and FE model has been developed to detect

blade frequencies from on-casing vibration response [105]. A combination of an

experimental work with an analytical model was recently presented to estimate blade

natural frequencies from on-casing vibrations as well as to describe how the internal

pressure of a turbine affects the blades frequency [106, 107].

2.7 Signal processing techniques

The most common signal processing techniques used in this research study for analysis

of blade vibration data in order to diagnose and detect blade fault conditions are

described in the following sections with literature related to these techniques.

2.7.1 Time domain analysis

Time domain analysis is a simple method for analysing vibration signals, and it is

widely used in CM of machine parts conditions. The time domain is a plot of the

relation between signal amplitude and time. Depending on the type of the vibration

sensor, the vibration signal used in time domain analysis can be acceleration, velocity or

proximity. Time domain data can be used in the identification of rotor faults in rotating

machines and several studies reported reliable identification of such faults. Goldman

and Muszynska [108] and Lee and Han [109] presented effective rotor fault


53

identification methods that use orbit shape analysis. Moreover, Doguer and Strackeljian

[110] recently presented a new method that uses time domain data to identify bearing

faults in rotating machines.

2.7.2 Frequency domain analysis

Frequency domain analysis (e.g. fast Fourier transform, FFT) is a mathematical method

which converts signal data from time domain into frequency domain. Frequency domain

analysis is the most commonly used process for analysing vibration signals in rotating

equipment, and it represents a very useful method particularly during steady state

operation when the signal is stationary (i.e. frequency components not variable over

time). The main disadvantage of frequency domain analysis is featuring only frequency

information of signals and losing any time information as well as capturing only two-

dimensional information [111].

2.7.3 Short time Fourier transform (STFT)

Short time Fourier transform (STFT) analysis is a mothed capable of providing time and

frequency information when analysing vibration data in the same plot. It is applied by

dividing the time series signals into smaller segments (windows), then applying FFT to

all sections individually, followed by reassembling the data into a 2D function of time

and frequency, offering compromised information about both. The STFT plot normally

shows time, frequency and amplitude information in the form of either waterfall plots or

contour maps [112].

2.7.4 Instantaneous angular speed (IAS)

Shaft instantaneous angular speed (IAS) signals extracted from rotary encoder raw

signals are representative of shaft torsional vibrations. This method can be employed for

calculating the time interval changes between the successive pulses of the encoder. This

method is generally non-intrusive and non-exorbitant and is currently the focus of

research for different applications on various types of machines. Li et al. [113]

published a review of the methods employed for the measurement of IAS. IAS based

methods can be applied in fault diagnosis in rotating machines [114]. Examples of this

application include using torsional vibrations (IAS) for the identification of faulty


54

combustion cylinder(s) in diesel engines [115-119] by monitoring the crank shaft IAS

signals. Another example describes using IAS signals to detect gearbox defects [120].

The application of IAS has also triggered the understanding that transverse blade

vibration is often reflected in the shaft torsional vibration, owing to the coupling

between shaft torsional and blade bending vibrations. It was experimentally verified on

small rigs, and the mistuning effect on the blade natural frequency was also observed

[89, 90].

2.7.5 Order tracking analysis (OTA)

Order tracking techniques represent a mothed based upon FFT. The method requires a

time domain data with tachometer signals to accurately compute the frequency of the

order at every time point. This is carried out by re-sampling the vibration data at times

equal to phase increments, providing a constant angular frequency. This equal phase

spacing used to re-sample the signals is determined synchronously with reference to

tachometer signals. Using OTA allows the sampling rate of data to be synchronized

with the shaft rotation speed to confirm the sampling locations as constant angles of the

shaft. Therefore, even if the machinery speed changes during run-up or coast-down, the

sampling will still happen at the same shaft angle and the frequency component will be

presented as a function of the order of shaft speed. FFT is subsequently applied to the

data to transform into order domains presented as sine waves of the amplitude of the

order (spectrum order). The order-tracking technique has recently become an important

approach for diagnosing faults in rotating machinery [121].

2.7.6 Time synchronising averaging (TSA)

Time synchronous averaging (TSA) is a time domain analysis method used to remove

any signal components not related to shaft rotation rate, which can reduce the noise in

spectra of complex signals. TSA works by calculating spectra averaging of the data after

performing FFT on each signal sample. This method is done with respect to tachometer

signals obtained from shaft rotation speed. The main advantage of this method is the

removal of all non-synchronous parts of the signal and any random noise from the shaft,

blades and gears with a rotational period not matching the averaging period [122]. In

this study, TSA is used to exclude all vibration components from signals except the


55

events related to the shaft and blades, which can then be used for monitoring any

changes in the blade frequency region, thus detecting blade(s) faults.

2.8 Research plan to investigate blades’ health using alternative vibration

measurements

For monitoring the blade health in real time, it is very useful to obtain on-line blade

vibration information. Researchers are always looking for a reliable method with few

disadvantages to accomplish this target. However, from the previous studies, it was

shown that both BTT and strain measurement methods are intrusive and exorbitant

methods in addition to other disadvantages discussed in Sections 2.6.1 and 2.6.2. In

view of these complications, the need to explore more reliable, non-exorbitant, non-

contact, non-intrusive and simple but robust methods that will effectively satisfy the

requirements of BHM becomes imminent. Moreover, it may be advantageous to select a

method based on shaft torsional vibration using IAS encoder signals as an alternative to

previous methods discussed in the sections mentioned above. Other chosen methods are

the OBV and OCV measurements which are simple and non-exorbitant to use.

However, a comparison of the three methods is required in order to select which of

these methods is more reliable for BHM.

2.9 Summary

According to the literature, rotating blades are considered one of the most common

causes of failures in rotating machines such as turbo-generators. Blades are exposed to

high mechanical loading and stress due to the extreme changes in both temperature and

pressure. Therefore, the need for a reliable early fault detection tool is important to

reduce blade related failures, and hence increase operational safety, efficiency and

reliability. In this chapter, a comprehensive literature review is presented, summarising

the previous research works on diagnosis and detection of blade vibration health

conditions in rotating machinery. Firstly, the chapter provided a brief description of CM

approaches which are commonly used for faults diagnosis in rotating machines. Then, a

brief discussion on vibration-based fault diagnosis in rotating machines was provided.

An overview of earlier studies on blade vibration condition monitoring is provided with

some blade failure modes. Finally, various vibration measurements which are


56

commonly used to detect and diagnose blade health conditions in rotating machines are

presented, along with their advantages and disadvantages, in addition to the signal

processing techniques are used in this study. In summary, to identify which of these

methods is more effective for the purposes of this study with regards to the advantages

and disadvantages of measurements based on strain gauges and BTT, the last three

measurements, i.e. shaft torsional vibration based-on IAS, OBV and OCV, were

eventually selected.


57

CHAPTER 3

RIG DESIGN AND EXPERIMENTAL SETUP

3.1 Introduction

In this chapter, details of design and manufacture of the test rig are discussed. The rig is

designed to simulate rotating machine blades in order to detect blade faults due to blade

vibration problems. The test rig was designed to allow measurements of the torsional

shaft vibrations, on-bearing vibration (OBV) and on-casing vibration (OCV) for the

purpose of detecting blade health condition.

A detailed description of the design, including the full dimensions of the shaft-disc-

blades system, is given, based on the results of the modelling done by means of the

Finite Element model (FEM) using ABAQUS software [123]. The rig was

manufactured using the dimensions obtained in accordance with the FEM. The

experimental work for this research was conducted on the rotating shaft-disk-blade

assembly, which is located in the Dynamics Lab in the School of Mechanical,

Aerospace and Civil Engineering (MACE) at the University of Manchester. A full

description of all rig components, equipment and measurement devices used in the

construction of the test rig is also provided.

3.2 Finite element modelling

The modal analysis was carried out based on a FEM using an ABAQUS 6.10 software

package to simulate the shaft-disc-blades system in order to estimate the natural

frequencies and the mode shapes, with the aim of obtaining optimum dimensions for the

rig design from a suitable natural frequency for blades, which is obtained using a FEM.

With the created model, some random dimensions for the rotating parts of the shaft-

disc-blades system of the rig were chosen initially and then these dimensions were

modified until appropriate results of natural frequency with reasonable dimensions were

obtained. These optimised dimensions were used for the final design.

For the simulation of the shaft-disc-blades system using ABAQUS 6.10, the Element

C3D8R (8-node solid brick) was chosen for model analysis, which is suitable for


58

dynamic analysis of the solid parts as it is compatible with the shaft-disc-blades system.

For linear incompatible modes, the ABAQUS explicit module was used with a 3D

eight-node linear brick element with reduced integration and hourglass control (C3D8R)

for modelling the shaft-disc-blades [123].

3.3 Primary design model

In order to obtain optimum dimensions for the test rig design, random dimensions were

chosen for the shaft-disk-blades system as listed in Table 3.1, in which the simulated

blades were chosen to be cylindrical rods. The system was created using a FEM using

the ABAQUS package.

Table ‎3-1: Shaft-disk-blades model dimensions

Part Property Value

Shaft Material Steel (E = 210 GPa, = 7800 kg/m3)

Length 1000 mm

Diameter 20 mm

Disk Material Steel (E = 210 GPa, = 7800 kg/m3)

Width 20 mm

Outer Diameter Do 50 mm

Inner Diameter Di 20 mm

Blade X 8 Material Steel (E = 210 GPa, = 7800 kg/m3)

Length 120 mm

Diameter 10 mm

(E),‎Young’s‎modulus;‎(), density; E and are theoretical values

A view of a typical modelling mesh for the shaft-disc-blades system is shown in Figure

3.1.


59

(a)

(b)

Figure 3.1: Typical FE mesh for the shaft-disc-blades model: (a) side view, (b) front view

The simulation and optimisation of the shaft-disk-blades system is done by discretising

the body into sub-regions which are called elements. Each element in the model

represents a discrete portion of the physical structure, which is, in return, represented by

many interconnected elements; the type of element used in this model is C3D8R. The

support condition of the shaft was assigned using the BOUNDARY option available in

ABAQUS (SIMULIA, 2010d) by constraining and releasing the corresponding degrees

of freedom at each end of the shaft. In the present numerical model, fifty frequency

modes were computed which conforms to the experimental results.

The natural frequencies for shaft and blades were obtained. However, according to the

results obtained from the pre-design model of the system, the natural frequency value of

the blade bending was extremely high at 699.12 Hz, and the shaft bending natural

frequency value was particularly low at 33.894 Hz. On the other hand, real values of

low‎pressure‎turbine‎blades’‎frequency‎in‎steam‎turbines‎range‎between‎100‎and‎120‎Hz‎

[124]. For this reason, the model was modified to obtain more logical frequency values

for the blades and shaft close to the values observed for steam turbines in order to

achieve optimum design of the rig. The system design was modified by trying the

dimensions listed in Table 3.2, which are chosen related to shaft and blades natural

frequency from FEM.


60

Table 3-2: Model properties and dimensions of the shaft-disc-blades system including design of

blade tip mass

Part Property Value

Shaft Material Steel ( E=210 GPa, =7800 kg/m3)

Length 600 mm

Diameter 20 mm

Disk Material Steel ( E=210 GPa, =7800 kg/m3)

Width 20 mm



Blade X 8 Material Steel ( E=210 GPa, =7800 kg/m3)

Length 110 mm

Diameter 5 mm

Blade tip mass X 8 Material Steel ( E=210 GPa, =7800 kg/m3)

Width 10 mm



Mass 25 grams


The finite element (FE) optimisation model of the shaft-disk-blades system with blades

tip masses was simulated as shown in Figure 3.2, using ABAQUS 6.10.

Figure 3.2: Typical FE mesh for shaft-disc-blades with blade tip mass model: (a) side-view

with bearings location, (b) front view


61

The boundary conditions were applied on the model by assuming the bearing position

on‎ the‎shaft‎at‎different‎distances‎within‎65‎mm‎and‎55‎mm‎from‎the‎shaft’s‎ends,‎as‎

shown in Figure 3.2, which considers the system simply as a support beam; that is, with

no movement in two directions (X,Y).

According to the results obtained from the FEM, the natural frequency value of blade

bending decreased sharply to 92.911 Hz compared to the pre-design model, and the

shaft natural frequency also increased sharply to 129.57 Hz compared to the pre-design

model frequency value. The new natural frequency values for blade and shaft bending

were within reasonable parameters and they confirmed that the dimensions and

materials made an optimum design for the rotating parts in rig fabrication and

manufacture. Figure 3.3 shows cylindrical blades and Figure 3.4 shows a photograph of

a rig with cylindrical blades.

Figure 3.3: Cylindrical blades: (a) blade with blade tip mass, (b) blade without blade tip mass,

(c) crack on blade 20% of blade diameter


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Figure 3.4: Experimental rig with cylindrical blades

Note that for more self-excitation force to the blades during machine running, a mass is

added on the tip of each blade, as shown in Figures 3.3 and 3.4. More than one mass can

be added at the end of each blade. The main reason for choosing cylindrical blades in

the initial design rather than rectangular ones, which are more similar to real blades, is

that cylindrical blades can easily simulate mistuned blade(s) faults. The blades were

tuned to a specific frequency by adjusting the tip masses on in each blade. Cylindrical

blades were also used by Maynard and Trethewey [90-93, 96] in many research studies

(Figure 3.5) to simulate blade faults and for easy diagnosis of blade health conditions.

Figure 3.5: Blade fault diagnosis using cylindrical blades: (a) on test rig, (b) bladed disc [90]

Blade tip mass

(a) (b)


63

3.4 Final optimised model

According to the experimental results obtained from the test rig, which was

manufactured according to an acceptable design of the FEM, cylindrical blades with or

without tip masses were not sufficiently excited to detect blade faults during machine

running. On the other hand, the results seem to suggest no changes in the blade(s)

response for both healthy and faulty conditions of the blades. Moreover, five strong

magnets, type E1020, were added opposite one side of the blades, as shown in

Figure 3.6, to increase stimulation of excitation force on the blades during machine

operation (run-up or run-down). Also here, when using the magnets, there were no

changes in blade response for both healthy and faulty cases.

Figure 3.6: Five magnets with an attached ring opposite the cylindrical blades

8-Cylinderical

blades

5-Strong magnets type E1020


64

Therefore, according to the results, it was necessary to change the design from

cylindrical blades to rectangular blades that were flat and more similar to real turbine

blades, but with the same dimensions which were obtained using the FEM. The blades

were manufactured as flat plates with two sizes of blades (long and short) for different

types of experiments. Blade properties and dimensions are listed in Table 3.3.

Table 3-3: Shaft–disc–blade(s) data for long and short blades


The FE model was carried out to determine the blade(s) natural frequencies, which were

found to be within an acceptable range for the design. The model of a shaft-disc-blades

system for long and short blades was created using 8-noded rectangular solid elements

of type C3D8R. According to FE results obtained from the model, the natural

frequencies for the 8 long blade(s) bending were between 112.07 and 122.06 Hz due to

the mistuned effect, and those for the 8 short blades were between 184.50 and 201.64

Hz, as shown for the first mode of long and short blades in Figures 3.7 and 3.8. The

shaft frequency mode value determined was 141.00 Hz. These values of natural

Part Property Value

Shaft Material Steel ( E=210 GPa, =7800 kg/m3)

Length 600 mm

Diameter 20 mm

Disc Material Steel ( E=210 GPa, =7800 kg/m3)

Width 20 mm



Long Blade(s) (8 numbers) Material Steel ( E=210 GPa, =7800 kg/m3)

Length 110 mm

Width 20 mm

Thickness 2 mm

Short Blade(s) (8 numbers) Material Steel ( E=210 GPa, =7800 kg/m3)

Length 73 mm

Width 25 mm

Thickness 2 mm


65

frequency for long and short blades and shaft bending are within an acceptable range,

and they confirmed that the dimensions of the model formed an optimum design for rig

manufacturing.

Figure 3.7: FE model of long blades’ first natural frequency with matched mode shape

Figure 3.8: FEM of short blades’ first natural frequency with matched mode shape


66

3.5 Manufacturing of the experimental rig

For this research study, a rig was manufactured using dimensions in accordance with

the FEM, carried out using ABAQUS software. The rig was designed to simulate

rotating machine blades in steam turbines in order to detect blade faults due to vibration

problems arising from mistuned blades, blade root looseness and cracks in blade(s). The

rig was designed to allow measurements of the shaft torsion vibration, OBV and OCV

in order to investigate blade dynamic behaviour during machine operation of run-up or

run-down for blade health monitoring (BHM). The experimental work of this research

was conducted on the rig of the rotating part of shaft-disc-blade, which is located in the

Dynamics Lab at the school of MACE at the University of Manchester. A photograph of

the test rig including the measurement systems is shown in Figure 3.9.

Figure 3.9: Photograph of the experimental rig with rectangular blades

3.5.1 The experimental rig

In order to investigate the feasibility of torsional vibration, OBV and OCV

measurement techniques for incipient blade deterioration in rotating machinery, a small

experimental test rig was built in the Dynamics Lab at the school of MACE at the

University of Manchester for the purpose of this study. The rig was mainly designed to

study blade behaviour due to different fault conditions, such as: healthy with blade

mistuned effects, blade root looseness and cracks in blade(s), using the three

measurement techniques of shaft torsional vibration, OBV and OCV.

The test rig mainly consisted of the following parts, as shown in Figure 3.9:

Accelerometer

8- Rectangular Blades Tacho Sensor

Flexible Coupling Driver Motor

Bearing Encoder

Disc Shaft

Casing


67

(a) A driver 3-Phase motor of 1 HP power.

(b) 2 SKF ball bearings, type YS 20 TF.

(c) A steel shaft of 600 mm length and 20 mm diameter, holding one or more bladed

discs.

(d) A variable speed controller connected to the motor and PC for controls: motor

steady state, run-up or run-down speed.

(e) A flexible coupling between the motor shaft and rig rotor.

3.5.2 Parts of the experimental rig

The rig contained the following main parts, which are discussed in this section.

3.5.2.1 Motor

The motor used on the rig was manufactured by Beatson Fans & Motors Ltd. A

photograph of the motor, which drives the main rotor of the test rig, is shown in

Figure 3.10, and the specifications are listed in Table 3.4. The motor was connected to a

speed control unit for control of motor shaft rotating speed. The motor base was

integrated into a horizontal plate by means of four attachments, which consisted of a

hollow cylindrical support linked by four bolts passing through it and fixing it to the

rigid horizontal plate. The horizontal plate was attached to the foundation table by

means of four bolts.

Table 3-4: Specification of the motor

1 Maker Beatson Fans & Motors

2 Type Imperial B56 Frame

3 Power 720W/1 HP

4 Maximum Speed 2800 rpm

5 Poles 4, 1500 revs.

6 Quality High

7 Body Drip-Proof

8 Power supply 240V/415V AC Three Phase


68

Figure 3.10: Electrical motor

Every effort was made to align the motor shaft centre with that of the rotor centre by

using a dial gauge in order to prevent misalignment. In this case, a rim-face method was

used to align the motor shaft with the main shaft of the rig. Two dial indicators were

employed to find the relative position of the movable shaft of the rig with respect to the

stationary shaft of the motor. The following the steps were carried out: (1) removal of

all dirt and dust from the bottom of bearings and motor bases, (2) setting the bases in

their places not fully tightened, (3) using the dial gauges on the rim to set the two shafts

at the same level horizontally, (4) rotating the dial gauge around the rim to make sure

the two shafts were in line, and (5) using the dial gauge on the face of the shafts to make

sure the two faces were vertically aligned. When misalignment existed, shims were used

under the bearing bases until the gauge reading indicated alignment. Finally, the bolts

on the bearings were tightens and the gauges were removed.

3.5.2.2 Shaft

The main rig rotor was a solid steel shaft with a circular cross section of 20 mm

diameter and a length of 600 mm. The shaft was manufactured by SKF Company. The

steel shaft hardness was 60 HRC and mass was 1.47 kg.

3.5.2.3 Bladed disc

The blades and disk were of steel and were designed to simulate real blades in rotating

machines. The disc could be adjusted anywhere between the two bearings as required.

The disk had a central hole. The outer diameter, inner diameter, thickness and mass are


69

given as 50 mm, 20 mm, 20 mm and 1.176 kg, respectively. The disc was designed to

hold eight blades placed on the outer surrounding at an equal angle of 45 degrees

between each blade. The disc was designed with eight threaded holes at the mid-point of

the thickness of the outer surrounding of the disc, to install the blades. The disk was

fixed by 2 screws to the rotor shaft through two threaded radial holes of a diameter of 5

mm, and there were also 8 threaded holes, 4 holes on each side, for small screws to

tighten the blades’ roots and prevent any movement of the blades during rotation, as

shown in Figure 3.11 (a) and (b). The blades were manufactured in steel as rectangular

plates with dimensions as listed in Table 3.3. They were designed with threaded ends;

one to attach the blades to the disc and the other end being welded to the middle of the

flat plate. Two types of blades (long and short) were designed and manufactured in

order to conduct the experimental tests. A photograph of the blades is shown in

Figure 3.12.

Figure 3.11: Bladed discs: (a) Long blades, (b) Short blades


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Figure 3.12: Photograph of a long blade and a short blade

3.5.2.4 Ball bearing

There were two identical pedestal ball bearings used in the rig, which were SKF type

YS 20 TF as shown in Figure 3.13. Along with the bearing, cast housings and grub

screw locking were used.

Figure 3.13: Pedestal ball bearing unit

The bearing cast housing was fixed into a vertical rigid steel block by two bolts for each

bearing. The bearing was attached to the vertical plate by means of two threaded bolts

and the vertical plate itself was bolted to the base plate which was attached to the

horizontal plate along the rig. The bearings foundation was aligned along the rig plate

towards the motor foundation in such a way that the centre of the bearings’ holes was in

line with the motor shaft centre.


71

3.5.2.5 Flexible coupling

The flexible coupling with integral clamp attachment had a set screw at each end to

clamp it to the motor shaft and the rotor. It was manufactured by ABSSAC Company,

and was of type WAC50-20mm-16. The outside diameter was 50 mm and the length

54 mm, and it had standard bore diameters of 20 mm and 16 mm, similar to the rotor

and motor shaft diameters respectively, as shown in Figure 3.14. The specifications of

the coupling were as follows: shaft misalignment angular 5 degrees, parallel offset 0.25

mm and axial motion at ± 0.25 mm. It was made of 7075-T6 aluminium alloy and had a

minimum weight of about 232 grams and an inertia temperature ranging between -40

and +100C. The torque ranged between 0.59-20 Nm, the torsional stiffness rate was

0.31 degree/Nm, and the speed was designed to go up to 10000 rpm [125]. The flexible

couplings were designed to transmit torque while permitting some radial, axial, and

angular misalignment. Flexible couplings were capable of accommodating angular

misalignment of up to 5 degrees, as well as some parallel misalignment between the

motor shaft and the rotor [125].

Figure 3.14: Flexible coupling: (a) integral clamp attachment methods, (b) Unequal diameter

shafts [125]

The advantage of using a flexible coupling between the motor shaft and the rotor was

that it accepted both parallel and angular misalignment. The coupling was connected

between the motor shaft and the front end of the rotor as shown in Figure 3.15.


72

Figure 3.15: Flexible coupling installation with the motor shaft and the end of the rotor

3.5.2.6 Foundation table

The foundation table of the rig at the Dynamics Lab was made from bricks and had a

steel plate on its top surface with the dimensions of 1736 x 1242 x 30 mm for its length,

width and thickness, respectively. A 12 mm thickness vibration isolating material was

squeezed in between the steel plate and the steel frame of thickness of 50 mm, as shown

in Figure 3.16. The surface of the rectangular plate placed on top of the table was

machined to a smooth flat surface so that the experimental setup could be securely

attached.


73

Figure 3.16: Rig foundation table

The rectangular base plate for the experimental rig was 1500 x 150 x 20 mm in length,

width and thickness, respectively, and was secured tightly to the upper plate of table by

means of four bolts. The foundation of the motor and bearings pedestals was placed on

the smooth machined surface of this plate.

The rectangular plate had holes drilled at pre-defined locations, allowing the motor and

bearings foundation to be attached as required, as shown in Figure 3.16, allowing the

length of the rig to be increased or decreased.

3.5.2.7 Rig casing

A metal steel casing with two rectangular transparent windows was designed to cover

the test rig as a safety precaution. The transparent windows were designed with one at

the top and one at the front to allow monitoring of the rotating parts during tests, as

shown in Figure 3.17. The cover had four hinges on the back, to allow ease of handling

and access. An electrical safety switch was incorporated, which was attached to the

hinges allowing the motor to be switched off if the cover was opened by more than 7

Vibration isolating material

Brick base

Steel plate

Rectangular plate

Steel frame


74

degrees in relation to the surface of the rigid table, in which case the circuit was cut off

for safety reasons.

Figure 3.17: Rig safety cover with (a) Side monitoring windows, (b) Top monitoring windows,

(c) Electrical safety switch

3.5.3 Instrumentation

The instrumentation, including measurement and rig control devices used in the rig-

based experiments, are discussed in this section.

3.5.3.1 Incremental rotary encoder

A rotary shaft encoder was used to extract signals from the main rotor during rotation.

The encoder used was manufactured by Kübler (https://www.kuebler.com/) and is a 9

bit magnetic signal turn encoder with an AC/DC power supplier converter. The

technical specifications of the encoder are listed in Table 3.5. The encoder shaft of

4 mm diameter was attached to the free end of the rotor via an aluminium connector and

it rotated with the main rotor, as shown in Figure 3.18. The data was collected from the

encoder via a data acquisition card which was connected to the PC, on which special

LABVIEW software recorded and saved the data, which was then stored on the PC. A

typical rotary encoder used for the experiments, which generates 360 square pulses for

every complete rotation of the shaft, is shown in Figure 3.19.

https://www.kuebler.com/


75

Table 3-5: Specification of the encoder

1 Maker Kübler

2 Type 2400

3 Output signal Push-Pull

4 Pulses per revolution 360

4 Power supply 5-24 V, DC

5 Maximum measured speed 12000 rpm

6 Pulse shape Rectangular

7 Maximum switching frequency 160 kHz

8 Weight 60 g

Figure 3.18: Location of encoder at the end of the rotor

Figure 3.19: Rotary shaft encoder


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3.5.3.2 Optical tacho sensor

An optical tacho sensor used in the experiments was an S51-PA-2-A00-NK as shown in

Figure 3.20, and the sensor was manufactured by Farnell (http://uk.farnell.com/). Tacho

specifications are listed in Table 3.6.

Table 3-6: Specifications of the Tacho sensor

1 Maker Farnell

2 Type S51-PA-2-A00-NK

3 Maximum Switching frequency 500 Hz

4 Sensing Distance range 0.1 – 3 m

5 Response time 1 ms

6 Weight 25 g

7 Supply Voltage DC Range 10-30 V

Figure 3.20: Optical tacho sensor

It was placed on the fore section of the motor, pointing towards the motor. There was

reflective marker tape on part of the motor shaft from which the tacho sensor picked up

reflected optical signals to measure the rotating shaft speed. This device provided a

quick and convenient way of monitoring motor rotating shaft speed.

3.5.3.3 Tachometer screen

A tachometer screen DFM 125 was manufactured by Control Ability

(www.controlability.com). This was used in the experiments to obtain pulse signals

http://uk.farnell.com/

http://www.businessmagnet.co.uk/php/website-redirect.php?companyID=115712


77

from the rotating machine via a tacho proximity sensor to calculate and display the

approximate motor rotating shaft speed being monitored. It had an LED digital display,

giving clear indication of the RPM shaft rotating speed values. The tachometer also had

a front panel keypad where the user could readily change the programme to meet

operational requirements, as shown in Figure 3.21. By using the front panel features, the

following could be carried out as required; (i) auto calibration, (ii) fixed or automatic

range changes, (iii) simple scaling functions, (iv) display of update and timeout

facilities, and (v) provision of fixed or floating decimal points.

Figure 3.21: Tachometer screen

3.5.3.4 Speed controller

The speed controller used in this setup was a Newton Tesla (http://www.newton-

tesla.co.uk/) CL750, as shown in Figure 3.22. This provided direct control of the motor

speed by using control buttons for: starting and stopping motor operation, and also

forward or reverse rotation direction settings. However, increasing motor speed (to

reach 3000 rpm) could be controlled through a computer using special software. In

addition, the software could also be used to operate the motor for run-up or run-down

operations using fixed speed rate. The speed controller specifications are listed in Table

3.7.

Table 3-7: Specifications of the speed controller CL750

1 Maker Newton Tesla

2 Model CL750

3 Rated power 720W/1 HP

4 Speed range 0 - 1800 rpm

5 Speed direction Forward / Reverse Selector switch

6 Input Power 230V AC, Three Phase

http://www.newton-tesla.co.uk/

http://www.newton-tesla.co.uk/


78

7 Motor Output Power 0-230V AC, Three Phase

Figure 3.22: Speed controller

3.5.3.5 Data acquisition

The data were recorded on the PC using a National Instruments (http://uk.ni.com/) NI

USB-6221 eight-channel board, as shown in Figure 3.23. The NI USB-6221 board 16

bit M series could take up to 250,000 samples per second, and had a maximum clock

rate of 1 MHz and maximum source frequency of 80 MHz.

Figure 3.23: National Instruments NI USB-6221 board

http://uk.ni.com/


79

3.5.3.6 Accelerometer

Accelerometers are used to measure the acceleration signals and are commonly used to

measure vibration. The accelerometers used in this study were PCB Piezoelectric

(http://www.pcb.com/) accelerometers, as shown in Figure 3.24, a sensing transducer

that generated an electrical output signal proportional to the acceleration aspect of

object motion (vibration). This type of accelerometer is capable of measuring very high

acceleration transients, and is widely used in rotating machinery vibration measurement.

Figure 3.24: Accelerometer

3.5.3.7 Signal conditioning unit

A 4-channel signal conditioner was used in the research experiments, which was

manufactured by PCB Piezotronics (http://www.pcb.com/), Model 482C, 15 series, as

shown in Figure 3.25. The device was used to magnify the acceleration vibration signals

coming from accelerometers attached to the bearings pedestals and/or on the casing and

to transfer the data to a data acquisition board. The conditioning frequency response

range was between 0.05 Hz to 50000 Hz.

Figure 3.25: Front and back panel of 4-Channel signal conditioner PCB Piezotronics, 482C

http://www.pcb.com/

http://www.pcb.com/


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3.5.3.8 Measurement scheme

The schematic diagram of the measurements system used on the test rig, when the

experiments were conducted for the purpose of identifying and detecting blade vibration

due to various blade health conditions in order to use them in BHM, is given below. The

schema consists of the measurement devices of pickups, transducer system additions to

rig controls and signal treatment devices. Figure 3.26 illustrates a schematic

representation of the rig measurements and data acquisition system, which includes the

following devices:

1- One rotary shaft increment encoder with a power supply unit to measure the

shaft torsional vibration signals.

2- Four accelerometers attached on the bearings pedestals, 2 on the vertical and 2

on the horizontal direction for both the front and back bearings, to pick up on-

bearing vibrations.

3- One accelerometer attached on the casing cover, aligned towards the rotating

blades to pick up on-casing vibrations.

4- One tacho sensor and its tachometer screen, which was a sensor set towards the

rotating motor shaft to monitor motor rotating speed, which was displayed on

the tachometer display screen.

5- One data acquisition board of 8 channels, to show and record the signals

obtained from the encoder, tacho sensor and the accelerometers, and to sort all

data on the PC for further signal processing.

6- One or two 4-channel signal conditioner(s), depending on requirement, were

used to magnify the acceleration vibration signals picked up by the

accelerometers. In case of using more than 4 accelerometers (i.e. 4

accelerometers on the bearing pedestals, 2 in vertical direction and 2 in

horizontal direction, in addition to 1 accelerometer on the casing to measure case

vibration), another 4-channel signal conditioner was used at the same time.

7- One speed controller used to control the motor operation, motor speed levels and

rotation direction and speed run-up or run-down directly or through a computer

via special software.

8- One personal computer system for computerised data processing and control of

the motor speed. The PC was also used for data analysis software and storage of

data.


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Figure 3.26: Schematic diagram of the rig data acquisition system

3.6 Modal testing

Modal analysis refers to the process of estimating the modal properties, such as

resonance frequencies, stiffness, damping and mode shapes of a structure.

Generally, the dynamic behaviour of a structure can be predicted from knowledge of its

modal properties. In fact, the response of a linear system to excitation can be expressed

as a sum of the contributions from all the modes of the structure.

The dynamic parameters of the structure, such as dynamic stiffness and damping

constant, are vital technical information needed in engineering analysis and for rotating

machinery design. Those parameters are required for the finite element modelling as

well as for numerical simulation to predict the structural response to dynamic loading.

The modal testing is based on vibration responses of the structures which are used to

identify the dynamic performance and responses of structures. By using frequency

response functions (FRF) [126] to extract essential modal parameters, estimating modal

parameters in the initial design stages of the machinery is known to avoid any resonance

or near resonance effects during the running time of the machine. This is important to


82

minimise fatigue cycles which cause destruction in the structure, and to increase the life

duration of the machine [126]. The inherent information in FRF data is also used to

identify the location and severity of damage in structures by knowing the natural

frequency range for every component of structure as a fault detection method.

3.6.1 Long and short blades FRF

The modal testing for the blades and shaft was conducted on the test rig for the eight

blades for both long and short bladed discs in order to determine the‎ blades’‎ natural‎

frequencies by using the FRF test [126]. A schematic diagram and a photograph of

experimental procedures conducted for the blades modal test are presented in Figures

3.25 and 3.26 respectively. Each blade was excited using an instrumented impact

hammer (Type PCB-0860C03) and the vibration responses were measured using a tiny

accelerometer (Model 352C22, M/s PCB) weighing just 0.5 g. The responses were

calculated using a signal analyser unit and the data were recorded using a computer. The

blades natural frequencies were identified using the FRF calculated from the measured

force and acceleration data. The experimentally identified first natural frequencies for

each blade of the long and short blades after full assembly in the rig are listed in Table

3.8. A small deviation in blade(s) natural frequencies of 3.12 and 5.42 Hz for long and

short blades, respectively, showed the presence of blade mistuned effect, possibly due to

small deviation in blade manufacturing and/or fitting.

Table 3-8: Experimentally identified long and short blades first natural frequency

Long Blades Short Blades

Blade No. Natural frequency (Hz) Blade No. Natural frequency (Hz)

1 123.75 1 233.30

2 126.25 2 231.80

3 125.00 3 232.20

4 127.50 4 241.00

5 128.75 5 236.90

6 123.75 6 238.00

7 125.00 7 236.60

8 125.00 8 234.90

± % deviation 125.62 (± 3.12) Hz 235.58 (± 5.42) Hz


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Figure 3.27: Schematic diagram of blades modal testing

Figure 3.28: Photograph of modal testing setup

Typical FRF plots of magnitude, phase and imaginary part show blade frequency peaks

at 127.50 Hz and 234.90 Hz for blade 4 of the long blades and blade 8 of the short

blades respectively, as shown in Figures 3.29 (a-c) and 3.30 (a-c) respectively.


84

Figure 3.29: Typical FRF plots for a long blade (blade 4) first natural frequency at 127.50 Hz:

(a) Amplitude, (b) Phase, (c) Imaginary part

Figure 3.30: Typical FRF plots for a short blade (blade 8) first natural frequency at 234.90 Hz:

(a) Amplitude, (b) Phase, (c) Imaginary part

0 50 100 150 200 2500

5000

10000

15000

X: 127.5

Y: 1.103e+04

Frequency (Hz)

Acc

el./

Forc

e (g

/N)

0 50 100 150 200 250-180

-90

0

90

180

X: 127.5

Y: -79.31

Frequency (Hz)

An

gle

(d

egre

e)

0 50 100 150 200 250-15000

-10000

-5000

0

5000

X: 127.5

Y: -1.084e+04

Frequency (Hz)

Acc

el./

Forc

e (g

/N)

0 50 100 150 200 250 300 350 4000

5000

10000

X: 234.9

Y: 9652

Frequency (Hz)

Acc

el./

Forc

e (g

/N)

0 50 100 150 200 250 300 350 400-180

-90

0

90

180

X: 234.9

Y: -110.6

Frequency (Hz)

An

gle

(d

egre

e)

0 50 100 150 200 250 300 350 400-10000

-5000

0

5000

X: 234.9

Y: -8598

Frequency (Hz)

Acc

el./

Forc

e (g

/N)

(b)

(a)

(c)


85

3.7 Summary

An FEM was described for primary and final design of shaft-disc-blades assembly

(main core of the rotating components of the rig) to extract the optimum dimensions of

the experimental rig. The experimental rig manufacture based on the dimensions

obtained by the FEM was also described including the details of the parts and

instrumentation which were used to build the rig. Details of modal testing using FRF for

the long and short blades in order to determine blades and shaft natural frequencies were

also presented in this chapter.


86

CHAPTER 4

BLADE DIAGNOSIS USING ON-BEARING VIBRATION (OBV)

4.1 Introduction

In this chapter, details are presented of the results of tests of OBV signals extracted

from the measured acceleration data during machine run-up to understand the blade

vibration behaviour and then to explore the possibility of reliable assessment of blade

health condition. A signal is measured from on-bearing pedestals using accelerometers;

the measured vibration data are analysed by computing the responses at different engine

orders (EOs) related to the blade resonance frequencies and their higher harmonics to

understand the blade(s) dynamic behaviour. A series of experiments were carried out on

a test rig on two types of 8-bladed discs, with long and short blades, as shown in Figure

3.9, in three different cases of blade fault conditions; (1) healthy with mistuned effects,

(2) blade root looseness and (3) blade(s) with crack(s). These conditions are often

observed in practice in rotating machines, like steam turbines and aero-engines, and

hence early and reliable detection of blade fault conditions is very important to reduce

machine down time and maintenance costs and to maintain overall safety. The extracted

acceleration signal data from the front and/or the back bearing pedestals during machine

run-up were then order tracked at different engine order (EO) accelerations so that the

presence of blade resonance, their higher harmonics and dynamics behaviour could be

analysed and compared to be used for blade health monitoring (BHM).

4.2 Blade faults simulation

Three different blade faults were simulated for the experiments. These conditions are:

(a) Case 1: healthy blades with mistuned effects, (b) Case 2: blade root looseness and

(c) Case 3: crack(s) on blade(s). These are summarised in Table 4.1 and also discussed

in the following sections. Figure 4.1 illustrates the faulty blade(s) position with respect

to the tacho sensor location. The illustrated blade fault cases were tested for long blades

and only some blade fault cases were tested for short blades (Table 4.1). The reason for

testing only some cases for short blades is related to the results obtained from the

experiments conducted on long blades, which gave very similar results in blade fault


87

cases. Therefore, short blades experiments, which were performed later, were only

limited to two types of blade faults in order to compare them to healthy case 1; these

cases were: a crack on one blade (Case 3(i)) and cracks on two blades (Case 3(ii)). The

results of this study represent a proof of principle and time constraints played a large

role in the experimental design.

Table ‎4-1: Cases of blade faults conditions

Case Description Long Blade No. Short Blade No.

1 Healthy but mistuned All blades healthy with

mistuned effects

All blades healthy with

mistuned effects

2 Blade root looseness

(i) Blade No. 1 Not tested

(ii) Blade No. 5 Not tested

3 Crack(s) on blade(s)

(i) Blade No. 4, cracked at

22 mm from blade root

(i) Blade No. 5, cracked at

26 mm from blade root

(ii) Blade Nos. 2 & 4 (Two

cracked blades together)

(ii) Blade Nos. 5 & 7 (Two

cracked blades together)

(iii) Blade No. 2, crack at

37 mm from blade root Not tested

(iv) Blade No. 4, crack at

22 mm from blade root,

after 100 minutes of

machine operation

Not tested


88

Figure 4.1: Schematic diagram of the blade positions with respect to the tacho sensor

4.2.1 Healthy with mistuned effect

The healthy blades with mistuned effect (Case 1 as per Table 4.1) were tested initially.

The variation in the blades first natural frequencies is listed in Table 3.8. This case

represents the most likely fault condition for healthy blades in any real rotating machine

such as steam turbines and gas turbines.

4.2.2 Root looseness

If the blades are not properly mounted and assembled on the shaft disc then the blades

roots may be loose and that could result in rubbing during machine operation which

may lead to eventual failure in operation. Hence, this root looseness fault is simulated

by putting 2 free loose washers on the roots of randomly selected blades 1 and 5

separately as per Case 2 (i) and (ii) for the long blades as listed in Table 4.1. Figure 4.2

shows a photograph of the blade root looseness fault simulation.


89

Figure 4.2: Simulation of long blade root looseness fault

4.2.3 Crack simulation

A small cut of 0.6 mm width was made using a thin saw on 4 blades, 2 for each type of

blades, long and short, but at different locations. Photographs of crack simulation details

for long and short blades are shown in Figures 4.3 (a) to (d) and 4.4 (a) to (d),

respectively. A very thin metal sheet was placed in the cut of the cracked blade(s) using

adhesive glue on only one side of the cut so that breathing (opening and closing) of the

crack on the blade could be realized during vibration. The cracks made on the 2 long

blades at different locations are shown in Figure 4.5 (a). In addition, the cracks made on

the 2 short blades at different locations are shown in Figure 4.5 (b). The cracked blades

were randomly selected for Case 3 tests on cracked blades; for long blades, blade 2 and

blade 4 were selected and for short blades, blade 5 and blade 7 were selected, as per

Table 4.1. The blades are numbered with respect to their position from the tachometer,

as shown in Figure 4.1. For the long blades, a total of 4 tests were conducted for the

cracked blade cases 3 (i) to 3 (iv) in Table 4.1, to understand the dynamic behaviour of

cracked blade(s) in different combinations; (i) and (iii): crack on a single blade but at

different locations, (ii): cracks on two blades simultaneously and the impact on the

dynamic behaviour when there is a cracked blade, and (iv): one cracked blade is tested


90

after 100 minutes of machine operation. Moreover, two tests were conducted on the

case of cracked short blades as per Table 4.1, as in case 3; (i): one cracked blade on the

bladed disc, and (ii): cracks on 2 blades together on the bladed disc. These six tests were

done for one cracked blade and two cracked blades on the bladed disc for both long and

short blades to understand the changes in the dynamic behaviour of the different

cracked blades, as in case 3 in Table 4.1.

Figure 4.3: Long blade crack simulation: (a) front side of a crack, (b) back side of a crack, (c) a

very thin metal sheet in the crack, and (d) cracked blade location on the bladed disc on the rig

Figure 4.4: Short blade crack simulation: (a) crack dimensions, (b) cracked blade with shim

location on the bladed disc on the rig, (c) shim on crack adhesive side and (d) shim on crack

non-adhesive side


91

Figure 4.5: Cracks on the blades at different locations: (a) long blades (b) short blades

A photograph of cracked blade(s) on the bladed disc is also included in Figure 4.6 and

Figure 4.7 for both long and short blades, respectively.


92

Figure 4.6: Crack on one long blade on the bladed disc

Figure 4.7: Crack on two short blades on the bladed disc


93

4.3 Computation of engine order tracking (EOT)

Engine order tracking method is a commonly used in rotating machinery vibration

analysis, which is based on the orders representing rotational speed harmonics. It is

considered a useful technique for monitoring the condition of rotating machines, which

can be easily carried out using shaft rotational speed related vibration signals.

Conditions that can be monitored include shaft defects, blade cracks, gearbox teeth

faults and bearing wear. Order tracking analysis in its simple form is performed by

using a constant sample rate of vibration signal and then the constant sampling intervals

are synchronised with shaft rotational speed signals extracted using a tachometer. After

that, a fast Fourier‎transform (FFT) is computed by generating waterfall or contour plots

for frequency data with amplitude and phase data to determine the engine orders at

different run-up speeds. Finally, the order tracking is carried out at different speeds

related to engine orders. Rotating speed is measured using tachometer pulses when the

machine is in non-stationary operation during machine run-up or coast-down.

In this study, engine order tracking was used as a vibration analysis method for BHM in

order to determine blade behaviour under different conditions of blade health during

machine run-up using vibration signals. The EOT was computed based on the following

steps:

(i) Selecting real-time run-up operation by matching signals from the tachometer

(rotating shaft speed) with run-up speed signals as shown in Figure 4.8 (a) and (b),

which are determined at time (t1), i.e. when run-up is starting and time (t2) when run-up

is ending, as shown in Figure 4.8 (b), for a total run-up time of 30 seconds.


94

Figure 4.8: Tachometer signals: (a) rotating shaft speed, (b) blades EO1 of run-up speed (1X),

and (c) zoom view of (a)

(ii) Sampling vibration signal at fixed time intervals, by dividing the signal into

small windows segments of time; in every window, the starting signal time is (tn-1) and

the ending time is (tn) for time intervals (t1, t2, t3,‎…….,‎tn). The mean time (tmean) is then

0 5 10 15 20 25 30 35 40-5

0

5

10

Am

pli

tud

e, V

olt

ag

e (

V)

Time (s)

0 5 10 15 20 25 30 35 400

10

20

30X: 35.95

Y: 29.5

Time (s)

Sp

eed

(R

PS

)

X: 5.935

Y: 9.841

4.0 4.4 4.8 5.2 5.6 6.0 6.4 6.8 7.2 7.6 8.0-4

-2

0

2

4

6

8

Time (s)

Am

pli

tud

e, V

olt

ag

e (

V)

(a)

(c)

(b)

t1=5.935 sec t2=35.95 sec


95

calculated between every starting and ending time point for all the windows, where tmean

is calculated using the equation:

𝑡𝑚𝑒𝑎𝑛 =𝑡𝑛−1+ 𝑡𝑛

2 ……………..‎(4.1)

where‎n‎=‎1,‎2,‎3,‎……..,‎N.

The run-up speed values (in rpm) are then determined for every tmean for all the windows

using the tachometer run-up signal corresponding to tmean. Figure 4.9 illustrates a typical

measured vibration signal.

Figure 4.9: Measured vibration signal: (a) acceleration raw signal and (b) zoomed view of (a)

0 10 20 30 40 50-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Time (s)

Am

pli

tud

e, A

ccele

ra

tio

n (

m/s

2)

10 10.005 10.01 10.015 10.02-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Time (s)

Am

pli

tud

e, A

ccele

ra

tio

n (

m/s

2)

(a)

(b)


96

(iii) Synchronising the sampled rate of the vibration signal with constant shaft

rotational speed intervals using the tachometer signals.

(iv) Calculating the frequency domain using FFT for every time averaging segment

signal by generating waterfall or contour plots for frequency with rotating speed

(rpm) and amplitude using signal processing analysis performed using MATLAB

software to determine speed orders, as shown in Figure 4.10.

Figure 4.10: Typical contour plot of speed orders for on-bearing vibration response in

horizontal direction

(v) Extracting the speed order components using order tracking for the EOs related to

shaft rotating speed (which is calculating order amplitude and phase for the

vibration signal). Once blade resonance (BR) is obtained from contour plots, as

shown in Figure 4.10, order tracking can then be carried out for different speed

orders. The EO components related to blades’ natural frequency can then be

determined. This is obtained in this case for long blades at EO5 (5X) related to a

blade natural frequency of 122 Hz (5 x 24.40 Hz) as shown in Figure 4.11.


97

Figure 4.11: Typical measured on-bearing vibration data for engine order spectra of EO5 of

healthy blades

The OTA signal processing technique transforms the revolution domain to an order

spectrum, rather than a frequency spectrum (FFT), providing the signal amplitude and

phase as a function of the harmonic order related to the rotation frequency. The problem

in using FFT with variable machine speed is the resultant smearing of frequency

components (due to overlap), and therefore it is a more favourable method with constant

rotation speed. Order tracking is able to show clear signal peaks in the order domain,

providing good tracking of speed harmonics in rotating machines during machine run-

up or coast-down and simplified use for diagnosis related to rotational speed orders in

rotating machines. OTA was used in this study as a signal processing tool for

diagnosing blade health conditions, where all signal amplifications can be seen clearly

related to different blade resonance frequencies. The blades in these tests have multiple

peaks in the BR region related to the number of blades rather than a single peak in other

applications. Hence, EO is an effective and powerful tool when used with applications

which result in multiple peaks of signal amplifications in the frequency region, such as

60 80 100 120 140 1500

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

-4

Frequency (Hz)

EO

5, A

ccele

ra

tio

n (

m/s

2)

BR region

Sh

aft

mo

de

regio

n

Sh

aft

to

rsio

nal

mod

e re

gio

n


98

blades and gearboxes, and for the detection of faults in these applications, particularly

when machine rotational speed changes during run-up and coast-down operation.

4.4 Long blades experiments and data analysis

In this research study, the dynamics for both blade condition cases, healthy and faulty

blades, are studies conducted on a small experimental rig using OBV measured data

using accelerometers on the bearing pedestals on the front and rear bearing. The

instrumentation needed for OBV measurement is simple, cheap, non-intrusive and

indirect. The experiments are conducted on a test rig having 8 long bladed discs for the

blade condition cases of: healthy blades with mistuned effects, blade root looseness and

cracked blade(s), and the data are recorded using a computer during machine run-up for

further signal analysis. The measured vibration data are analysed by computing the

responses at different Eos related to the blade resonance frequencies and their higher

harmonics to understand the dynamic behaviour of blades in healthy and faulty cases.

The purpose of the study is to determine whether the method is effective for the purpose

of BHM, and also to compare results with the experiments of short blades used for the

same purpose.

4.4.1 Data analysis

The OBV signals during machine run-up are obtained. In addition, tachometer signals

relating to machine run-up speed are also collected as shown in Figure 4.8 (b).

Vibration signals are collected from both the front and back bearing pedestals in vertical

and horizontal directions, from four locations on the rig using 4 accelerometers; the data

are analysed for all four signals. The results of four vibration signals are similar, and

therefore in this chapter, the data from the front bearing in vertical direction are

presented. Short time Fourier‎transformation (STFT) is carried out in order to discover

the BR frequency region for the on-bearing acceleration signals; this is illustrated in

Figure 4.10. Once the BR and its higher harmonics are obtained, order tracking at

different EOs can be carried out. Contour plots show the BR peaks (1xBR) and the

related‎ higher‎ harmonics‎ (2xBR,‎ 3xBR….).‎Hence,‎ order tracking at different EOs is

then carried out using the tachometer signal of the OBV. The order tracking of

acceleration signals at EO5 and EO10 clearly shows the BR region and its higher


99

harmonics, respectively. Typical EO5 for healthy blades is shown in Figure 4.11. Such

order tracking can typically be shown as in Figures 4.14 to 4.16 for EO5 and Figures

4.17 to 4.19 for EO10. Figures 4.14 to 4.19 can be used to compare the order tracked

responses at EO5 and EO10 in the BR region for OBV signals for the cases: healthy

blades, blade looseness and cracked blade conditions. The‎ location‎ of‎ the‎

accelerometers‎ for‎ data‎ pickup‎ from‎ the‎ on-bearing‎ is‎ in‎ vertical‎ and‎ horizontal‎

directions‎as‎shown‎in‎Figure‎4.12.‎Also,‎ the‎frequency‎domain‎of‎vibration‎signals‎ is‎

performed‎using‎FFT; this provides the blade natural frequency (1xBR) and its higher

harmonics (2xBR) as shown in Figure 4.13.

Figure 4.12: Accelerometer location in relation to the on bearing pedestals in the vertical and

horizontal directions

Figure 4.13: Typical‎amplitude‎spectrum‎for‎long‎blades

0 100 200 300 400 500 600 700 800 900 10000

2

4

6

8

10

12

14

16

18

X: 386.4

Y: 7.112

Frequency (Hz)

Am

pli

tud

e

X: 258.2

Y: 10.09

X: 128.2

Y: 16.84

X: 644.5

Y: 3.252

X: 772.7

Y: 3.71X: 900.9

Y: 2.123


100

4.4.2 Observations and results

From the results observed in Figure 4.14 representing Case 1: healthy blades with

mistuned effects, amplification at around frequency 115 Hz (23 Hz x 5) to 135 Hz (27

Hz x 5) confirms the excitation of BR during machine run-up, based on the OBV data

collected using an accelerometer on the bearing pedestals to measure the vibrations. The

amplification of the BR region seems to be in a banded form due to the mistuned effect.

The higher harmonics of the banded BR region (2xBR) was also observed in EO10 data

shown in Figure 4.17 for healthy blades with mistuned effect. The mistuned effect in the

blades could possibly be the reason for the appearance of this amplification in the higher

harmonics even for the healthy case (Case 1) as per Table 4.1.

Case 2: blade root looseness for blade 1. The addition of 2 loosely held washers at the

root has not affected the natural frequency of blade 1 significantly but its EO5 and

EO10 responses, shown in Figures 4.15 and 4.18 respectively, show significantly

different behaviour compared to healthy blades in Case 1. The 1xBR region shows

distinct multiple peaks instead of a single banded peak around the 1xBR region for Case

1 for healthy blades as seen in Figures 4.14. Also, the higher harmonics 2xBR in

Figures 4.18 also show multiple peaks.

Case 3: cracks on blades 2 and 4. From on-bearing acceleration data shown in Figures

4.16 and 4.19, a single banded peak can be seen in blade(s) harmonics regions (1xBR

and 2xBR) related to the EO5 and EO10 acceleration responses, respectively. However,

this is very different from Case 1 of healthy blade condition. This can show that OBV

are useful as an indication of BHM. Figures 4.14, 4.15 and 4.16 are combined in

Figure A1 (in Appendix A) showing on-bearing vibration data analysis for EO5 in blade

health condition cases: healthy blades, blade root looseness and cracks on two blades. In

addition, Figures 4.17, 4.18 and 4.19 are combined in Figure A2 (Appendix A) for

EO10.


101

Figure 4.14: Measured‎on-bearing‎acceleration‎data‎for‎engine‎order spectra of EO5 for healthy

blades with mistuned effects (Case 1)

Figure 4.15: Measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎spectra of EO5 for blade

looseness (Case2 (ii): Blade no. 5)

115 120 125 130 1350

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

-4

Frequency (Hz)

EO

5, A

ccele

ra

tio

n (

m/s

2)

115 120 125 130 1350

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

-4

Frequency (Hz)

EO

5, A

ccele

ra

tio

n (

m/s

2)


102

Figure 4.16: Measured‎on-bearing‎acceleration‎data‎for‎engine‎order spectra of EO5 for two

cracked blades (Case3 (ii): Blades no. 2 and 4)

Figure 4.17: Measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎spectra of EO10 for

healthy blades (Case1)

115 120 125 130 1350

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

-4

EO5 Frequency (Hz)

Accele

rati

on

(m

/s2)

(e)

220 230 240 250 260 2700

0.5

1

1.5

2

2.5

3x 10

-4

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)


103

Figure 4.18: Measured‎on-bearing‎acceleration‎data‎for‎engine‎order spectra of EO10 for blade

looseness (Case 2 (ii): Blade no. 5)

Figure 4.19: Measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎spectra of EO10 for two

cracked blades (Case 3 (ii): Blade no. 2 and 4)

220 230 240 250 260 2700

1

2

x 10-4

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)

220 230 240 250 260 2700

0.5

1

1.5

2

2.5

3x 10

-4

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)


104

4.5 Short blades experiments and data analysis

The same procedures are discussed in Section 4.2 with short blades using the

dimensions and properties listed in Table 3.3. The BR region related to the blades’

natural frequency is observed between 220 and 260 Hz, which is banded due to the

blades’ mistuned effects.

4.5.1 Experimental setup

The experiments are conducted during the machine run-up from a speed of 600 rpm (10

Hz) to 1800 rpm (30 Hz). The run-up rate was kept constant at 40 rpm/s. The data were

then collected at 30000 samples/s and the data were stored on a personal computer (PC)

for further signal processing analysis using MATLAB.

Three different conditions of short blades faults were simulated in the experimental

tests. These conditions of blade health conditions are: healthy with mistuned effects, a

crack on one blade and cracks on two blades as listed in Table 4.1.

4.5.2 Data analysis

The‎ extracted‎ OBV‎ signals‎ are‎ processed‎ with‎ different‎ EOs‎ of‎ acceleration‎ to‎

understand‎ the‎ appearance‎ of‎ blade‎ resonance‎ and‎ blade‎ dynamics‎ behavior.‎ The‎

vibration‎response‎of‎the‎acceleration‎signal‎related‎to‎OBV‎is‎shown‎in‎Figure‎4.20.

Figure 4.20: Typical measured on-bearing acceleration signals at machine run-up from 600 to

1800 rpm

0 5 10 15 20 25 30 35 40 45-1

-0.5

0

0.5

1

1.5

2

Time (sec)

Accele

ra

tio

n (

m/s

2)


105


From‎the‎response‎results‎obtained‎for‎short‎blades,‎neither‎EO10‎nor‎EO20‎contain‎the‎

blade‎responses‎of‎healthy‎blades‎with‎mistuned‎effect‎or‎one‎cracked‎blade,‎as‎shown‎

in‎Figures‎ 4.21‎ and‎4.22‎ for‎EO10‎ and‎Figures‎ 4.24‎ and‎4.25‎ for‎EO20.‎However,‎ a‎

clear‎blade‎ response‎ can‎be‎ seen‎ in‎Case‎3,‎ two‎cracked‎blades,‎ in‎both‎EO‎plots,‎ as‎

shown‎in‎Figures‎4.23‎and‎4.26.‎BR‎can‎be‎observed‎clearly‎in‎Case‎3.‎The‎zoom‎view‎

of‎ Figures‎ 4.21‎ to‎ 4.23‎ in‎ the‎ frequency‎ range‎ 220‎ Hz‎ to‎ 260‎ Hz‎ can‎ be‎ made‎ to‎

illustrate‎the‎blade‎resonance‎(1xBR)‎region‎and‎its‎higher‎harmonics‎(2xBR),‎as‎shown‎

in‎ Figures‎ 4.24‎ to‎ 4.26‎ for‎ all‎ cases‎ for‎ the‎ purpose‎ of‎ clear‎ observation‎ and‎

comparison.‎

Case‎1:‎healthy‎with‎mistuned‎effects;‎ it‎ is‎observed‎from‎Figure‎4.21‎ that‎ in‎Case‎1,‎

healthy‎blades‎with‎mistuned‎effects,‎on-bearing‎vibration‎shows‎no‎amplification‎in‎the‎

BR‎region.‎Also,‎the‎same‎observation‎of‎a‎lack‎of‎banded‎BR‎region‎(2xBR)‎is‎seen‎in‎

its‎ higher‎ harmonics‎ in‎ the‎ EO20,‎ as‎ shown‎ in‎ Figure‎ 4.24‎ for‎ healthy‎ blades‎ with‎

mistuned‎effects.‎

Case‎2:‎one‎crack‎on‎blade‎5;‎likewise,‎there‎is‎no‎clear‎blade‎resonance‎in‎either‎EO10‎

or‎EO20‎responses‎as‎shown‎in‎Figures‎4.22‎and‎Figure‎4.25‎respectively.‎

Case‎3:‎cracks‎on‎two‎blades‎5‎and‎7;‎in‎this‎case,‎there‎are‎multiple‎distinct‎peaks‎in‎

the‎blade‎resonance‎(1xBR‎and‎2xBR)‎regions‎related‎to‎EO10‎and‎EO20‎responses,‎as‎

observed‎ in‎ Figures‎ 4.23‎ and‎ 4.26‎ respectively.‎ Figures 4.21, 4.22 and 4.23 are

combined in Figure A3 (in Appendix A) showing on-bearing vibration data analysis for

EO10 in blade health condition cases: healthy blades, crack on one blade and cracks on

two blades. In addition, Figures 4.24, 4.25 and 4.26 are combined in Figure A4

(Appendix A) for EO20.

This‎ shows‎ that‎ OBV‎ measurement‎ for‎ short‎ blades‎ provided‎ some‎ good‎ indication‎

blade‎conditions‎in‎the‎case‎of‎more‎than‎one‎cracked‎blade‎on‎the‎bladed‎disc.‎Hence,‎

the‎presence‎of‎the‎distinct‎multiple‎peaks‎in‎the‎BR‎region‎and‎its‎higher‎harmonics‎in‎

the‎case‎of‎2‎or‎more‎cracked‎blades‎can‎be‎considered‎as‎a‎useful‎feature‎of‎BHM.


106

Figure 4.21: Measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎spectra‎of‎EO10‎for‎

healthy‎blades‎with‎mistuned‎effects‎(Case 1)

Figure 4.22:‎Case3 (i): measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎spectra‎of‎EO10‎

for‎one‎cracked‎blade‎(Case 3 (i): Blade no. 4)

220 225 230 235 240 245 250 255 2600.016

0.018

0.02

0.022

0.024

0.026

0.028

0.03

0.032

0.034

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)

220 225 230 235 240 245 250 255 2600.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)


107

Figure 4.23:‎Measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎spectra‎of‎EO10‎for‎two‎

cracked‎blades‎(Case 3 (ii): Blades no. 2 and 4)

Figure 4.24:‎Measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎spectra‎of‎EO20‎for‎

healthy‎blades‎with‎mistuned‎effects‎(Case 1)

220 225 230 235 240 245 250 255 2600.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)

440 450 460 470 480 490 500 510 5200.01

0.012

0.014

0.016

0.018

0.02

0.022

Frequency (Hz)

EO

20

, A

ccele

ra

tio

n (

m/s

2)


108

Figure 4.25:‎Case3 (i): measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎spectra‎of‎EO20‎

for‎one‎cracked‎blade‎(Case 3 (i): Blade no. 4)

Figure 4.26: Measured‎on-bearing‎acceleration‎data‎for‎engine‎order‎spectra‎of‎EO20‎for‎two‎

cracked‎blades‎(Case 3 (ii): Blades no. 2 and 4)

440 450 460 470 480 490 500 510 5200.004

0.006

0.008

0.01

0.012

0.014

0.016

Frequency (Hz)

EO

20

, A

ccele

ra

tio

n (

m/s

2)

440 460 480 500 5200

0.002

0.004

0.006

0.008

0.01

0.012

0.014

Frequency (Hz)

EO

20

, A

ccele

ra

tio

n (

m/s

2)


109

4.6 Summary

The‎experiments‎described‎in‎this‎chapter‎were‎carried‎out‎using‎OBV‎measurement‎on‎

the‎experimental‎ test‎ rig‎ for‎ long‎and‎short‎blades‎ for‎ three‎cases‎of‎blade‎conditions;‎

healthy‎with‎mistuned‎effects,‎blade‎root‎looseness‎and‎cracked‎blade(s).‎The‎dynamic‎

behaviours‎for‎both‎blade‎sizes‎were‎studied‎when‎blades‎were‎excited‎during‎machine‎

run-up.‎The‎results‎indicated‎that‎the‎measured‎acceleration‎spectra‎at‎different‎Eos‎and‎

their‎higher‎harmonics‎show‎the‎appearance‎of‎BR‎when‎blades‎are‎self-excited‎during‎

the‎machine’s‎ transient‎ operation‎ in‎ all‎ simulated‎ cases‎ for‎ long‎blades‎ (healthy‎with‎

mistuned‎effects,‎blade‎root‎looseness‎and‎cracked‎blades),‎and‎this‎was‎only‎observed‎

in‎the‎third‎case‎for‎short‎blades‎(two‎cracked‎blades). In addition, it was also observed

that OBV obtained from long blades gave better indication for the detection of blade

health conditions. Hence, the presence of the distinct multiple peaks in the BR region

and its higher harmonics can be considered as a useful feature of BHM. It‎ was‎ also‎

observed‎from‎this‎test‎that‎the‎results‎related‎to‎short‎blades‎gave‎some‎good‎indication‎

only‎ in‎ the‎case‎of‎more‎ than‎one‎ cracked‎blade‎on‎ the‎bladed‎disc,‎ and‎ this‎may‎be‎

considered‎as‎a‎feature‎of‎BHM.


110

CHAPTER 5

BLADE DIAGNOSIS USING ON-CASING VIBRATION (OCV)

5.1 Introduction

This chapter summarises the results and observations of the tests for OCV signals

extracted using an accelerometer on the external side of the casing (safety metal cover)

towards the rotating blades to collect vibration signals which are affected by air

movement on the internal side of the casing while the blades are rotating in machine

run-up operation. This is carried out in order to understand the dynamic behaviour of

blade(s) and also to investigate the possibility of using this technique as a reliable

assessment for blade health conditions. The measured vibration data are then analysed

with further signal processing using MATLAB by computing blades’ responses at

different engine orders (EOs) related to the blade resonance frequencies and their higher

harmonics to understand and compare the results of blade(s) behaviour. A series of

experiments were conducted on a small rig with a 8-bladed discs, as illustrated in Figure

3.7, for three different cases of blade fault conditions; (a) Healthy blades with mistuned

effects, (b) Crack on one blade and (c) Cracks on two blades. These fault conditions

commonly occur in practice with real rotating machines such as steam turbines, gas

turbines, etc. Hence, early and reliable detection of blade health is very important to

reduce machine breakdown time and maintenance costs and to maintain overall safety.

5.2 Experiments on short blades

The specifications of the short blades used in these experiments are listed in Table 3.3.

The tests were carried out during machine run-up for three different cases of blade

health conditions as per Table 4.1. The modal testing also included the blades natural

frequencies as listed in Table 3.8.

5.2.1 Data analysis

The‎ on-casing‎ measured‎ vibration‎ signals‎ were‎ processed‎ with‎ different‎ EOs‎ to‎

understand‎ the‎ appearance‎ of‎ blade‎ resonance‎ (BR)‎ and‎ to‎ investigate‎ the‎ blade(s)‎

dynamic‎ behaviour.‎ The‎ location‎ of‎ the‎ accelerometers‎ that‎ pick‎ up‎ data‎ from‎ the‎

external‎surface‎of‎ the‎casing‎(safety‎cover)‎ is‎ towards‎the‎rotating‎blades‎from‎inside‎


111

the‎rig.‎A‎schematic‎diagram‎of‎the‎location‎of‎on-casing‎measurements‎on‎the‎test‎rig‎is‎

shown‎ in‎ Figure‎ 5.1‎ and‎ photographs‎ of‎ on-casing‎ measurements‎ are‎ shown‎ in‎

Figure 5.2‎(a)‎and‎(b).‎The‎measured‎acceleration‎response‎signal‎of‎the‎OCV‎response‎

is‎also‎shown‎in‎Figure‎5.3.

Figure 5.1:‎A‎schematic‎of‎on-casing‎measurement‎setup:‎(a)‎side‎view‎and‎(b)‎top‎view‎of‎the‎

rig

On casing accelerometer

towards rotating blades

View window Casing of

2 mm

thickness

8-Blades

On casing accelerometer

towards rotating blades

Bearing pedestal On-bearing accelerometer

(a)

(b)


112

Figure 5.2: On-casing‎measurement‎setup:‎(a)‎top‎view‎of‎rig‎showing‎the‎blades‎and‎the‎on-

casing‎accelerometer‎(b)‎rig‎backside‎casing


113

Figure 5.3: Typical on-casing measured acceleration data during machine run-up speed (600 to

1800 rpm)


Measured‎ data‎ are‎ analyzed‎ using‎ engine‎ order‎ tracking‎ for‎ vibration‎ signals.‎ The‎

results‎indicated‎that‎the‎EO10‎plot‎shows‎one‎distinct‎peak‎around‎the‎frequency‎238‎

Hz,‎which‎confirms‎excitation‎of‎BR‎during‎machine‎run-up.‎This‎also‎appears‎ in‎ the‎

higher‎harmonics‎(EO20)‎in‎all‎cases‎of‎blade‎conditions:‎healthy‎with‎mistuned‎effects,‎

a‎crack‎on‎one‎blade‎and‎cracks‎on‎two‎blades.‎The‎zoom‎views‎in‎Figures‎5.4‎to‎5.6‎in‎

the‎frequency‎range‎220‎Hz‎to‎260‎Hz‎were‎made‎to‎illustrate‎blade‎resonance‎(1xBR)‎

region‎and‎ the‎higher‎harmonics‎ (2xBR)‎are‎ shown‎ in‎Figures‎5.7‎ to‎5.9‎ for‎ all‎ three‎

cases‎of‎blade‎faults;‎these‎figures‎are‎shown‎in‎order‎to‎clearly‎illustrate‎and‎compare‎

the‎results.‎There‎was‎no‎amplification‎of‎the‎BR‎region,‎as‎observed‎in‎Figures‎5.4‎to‎

5.6‎for‎EO10,‎and‎only‎one‎distinct‎peak‎in‎the‎three‎blade‎health‎cases.‎The‎same‎result‎

was‎also‎observed‎in‎the‎higher‎harmonics‎of‎the‎banded‎BR‎region‎(2xBR)‎in‎the‎EO20‎

plots‎ shown‎ in‎ Figures‎ 5.7‎ to‎ 5.9‎ for‎ the‎ three‎ cases‎ of‎ blade‎ health‎ conditions.‎

Additionally,‎ it can be seen from the results that there was not much change in blade

resonance behavior in EO10 and EO20 plots for the faulty cases (Case 3(i) and Case

0 5 10 15 20 25 30 35 40 45-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time (sec)

Accele

ra

tio

n (

m/s

2)


114

3(ii)) compared with the healthy condition (Case 1). In other words, there are no

amplifications in BR in Cases 3(i) and (ii); as per Table 4.1. Figures 5.4, 5.5 and 5.6 are

combined in Figure B1 (in Appendix B) showing on-casing vibration data analysis for

EO10 in blade health condition cases: healthy blades, crack on one blade and cracks on

two blades. In addition, Figures 5.7, 5.8 and 5.9 are combined in Figure B2

(Appendix B) for EO20.

Figure 5.4: On-casing measured acceleration data for engine order EO10 spectra for healthy


220 230 240 250 2600

0.005

0.01

0.015

0.02

0.025

0.03

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)


115

Figure 5.5: On-casing measured acceleration data for engine order EO10 spectra for a crack on

one blade (Case 3(i))

Figure 5.6: On-casing measured acceleration data for engine order EO10 spectra for cracks on

two blades (Case 3(ii))

220 225 230 235 240 245 250 255 2600

0.005

0.01

0.015

0.02

0.025

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)

220 225 230 235 240 245 250 255 2600

0.005

0.01

0.015

0.02

0.025

0.03

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)


116

Figure 5.7: On-casing measured acceleration data for engine order EO20 spectra for healthy


Figure 5.8: On-casing measured acceleration data for engine order EO20 spectra for a crack on

one blade (Case 3(i))

440 450 460 470 480 490 500 510 5200.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Frequency (Hz)

EO

20

, A

ccele

ra

tio

n (

m/s

2)

440 450 460 470 480 490 500 510 5200

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

Frequency (Hz)

EO

20

, A

ccele

ra

tio

n (

m/s

2)


117

Figure 5.9: On-casing measured acceleration data for engine order EO20 spectra for cracks on

two blades (Case 3(ii))

5.3 Summary

The‎dynamic‎behaviour‎of‎short‎blades‎in‎rotation‎in‎different‎blade‎health‎conditions;‎

healthy‎ with‎ mistuned‎ effects,‎ a‎ crack‎ on‎ one‎ blade‎ and‎ cracks‎ on‎ two‎ blades,‎ was‎

studied‎by‎using‎OCV‎measurement‎when‎blades‎are‎excited‎during‎machine‎run-up.‎It‎

was‎ observed‎ that‎ the‎measured‎ acceleration‎ spectra‎ at‎ different‎Eos‎ and‎ their‎ higher‎

harmonics‎show‎the‎appearance‎of‎BR‎when‎blades‎are‎self-excited‎during‎the‎machine‎

run-up‎operation‎in‎all‎cases‎of‎blade‎conditions.‎However,‎from‎the‎results,‎it‎was‎also‎

observed‎that‎there‎was‎no change in the BR region of damaged blade(s) compared with

healthy ones, showing only a single distinct peak for all cases of blade health

conditions. This means that there was not much change in the dynamic behaviour of

blades during machine run-up for all three cases of blade health conditions for both

engine orders EO10 and EO20 with regard to BR regions, 1xBR and 2xBR,

respectively. Hence, based on these experimental tests, using the on-casing

measurement technique would not indicate any differences between healthy and cracked

blades and therefore would not be useful for blade health monitoring (BHM).

440 450 460 470 480 490 500 510 5200

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Frequency (Hz)

EO

20

, A

ccele

ra

tio

n (

m/s

2)


118

CHAPTER 6

BLADE DIAGNOSIS USING SHAFT TORSIONAL VIBRATION (IAS)

6.1 Introduction

This chapter gives details of the results of the tests of shaft instantaneous angular speed

(IAS) signals extracted from the measured encoder data during machine run-up to

understand the blade vibration and to explore the possibility of reliable assessment of

blade health conditions. Transverse blade vibration is often transmitted to the shaft as

torsional vibration. A series of experiments were conducted on a test rig with two types

of 8-bladed discs (long and short blades) as shown in Figure 3.9 for three different cases

of blade fault conditions (1) healthy blades with mistuned effects, (2) blade root

looseness and (3) blade(s) with crack(s). These conditions are often observed in practice

with rotating machines like steam turbines, gas turbines, and heavy industrial machines.

Hence, early and reliable detection of blade fault conditions is very useful to reduce

machine down time and maintenance costs and to maintain overall safety. The extracted

IAS signals from the encoder raw data during machine run-up were order tracked at

different engine order (EO) speeds related to blade frequency so that the presence of

blade resonance, its higher harmonics and dynamic behaviour could be analysed.

Finally, a comparison was carried out to determine the differences in EO response for

long and short blades for the purpose of blade health monitoring (BHM).

6.2 Instantaneous angular speed (IAS) measurement method

An encoder that measures 360 pulses for every complete shaft rotation was used in this

experiment. To aid understanding of the IAS signal extraction from the measured

encoder pulse train, a simplified measurement scheme of the encoder and the pulse train

is shown in Figure 6.1. The sensor simply measures the gap between each tooth on the

gear during its rotation, which results in generating a pulse train of the measured gap

voltage against time, as shown in Figure 6.2. A magnification of the encoder raw signals

is presented in Figure 6.6. The extraction of IAS signal using the pulse train in Figure

6.1 is discussed in the following steps:


119

Figure 6.1: Schematic of the encoder pulse train

Figure 6.2: Measured encoder pulse train of the rotating shaft

Rotary encoder

generates 360

pulses per

revolution

Δ=1

Magn

itu

de,

(V

)

t4 t5 t3 t2 t1 Time, (t)

t4 t3 t1 t2

0 5 10 15 20 25 30 35

-3

-2

-1

0

1

2

3

Time (sec)

Vo

lta

ge (

v)


120

(1) Each square pulse represents a tooth in the gear of the encoder; hence, the time

differences, 12 tt , 23 tt ,‎…., nn tt 1 ,‎……‎etc.‎represent‎the‎time‎intervals‎required‎

to cross the 1st, 2

nd,‎….,‎n

th tooth, respectively, which is written as

∆𝑡𝑛 = 𝑡𝑛+1 − 𝑡𝑛 …………….‎(6.1)

It is also assumed that the time interval for the nth

tooth is measured at time nT as

𝑇𝑛 =𝑡𝑛 + 𝑡𝑛+1

2 ……………….‎(6.2)

where n‎=‎1,‎2,‎3,‎4,‎5,…,‎N,‎the‎number‎of‎teeth‎in‎the‎gear‎of‎the‎encoder.

(2) The angular displacement,‎ Δθ,‎ for‎ the‎ each‎ equally‎ spaced‎ tooth‎ in‎ the‎ gear‎

wheel of the encoder can be written as

= 360/N = N

2 ………….….‎(6.3)

(3) Hence, IAS at time nT in terms of revolutions per second (rps) can be calculated

as

IAS (𝑓𝑠𝑛) at Tn =

(∆tn .2π)

1

∆tn.360……………….‎(6.4)

The extracted IAS signal from the measured pulse train from an encoder may appear as

shown in Figure 6.3 if the shaft is rotating at a constant speed. The ideal case is

expected to be when there is no fluctuation in speed during shaft rotation and/or no shaft

torsional vibration; i.e. Ntttt .....321 . However, in reality these time

intervals, nt , may not always be constant due to speed fluctuation and/or due to

presence of shaft torsional vibration and may be presented as shown in Figure 6.4. The

time vectors nT , and corresponding IAS, snf , may not be at equal time intervals, hence

the data are re-sampled with a uniform time interval before further signal processing.


121

Figure 6.3: Ideal shaft IAS showing a constant shaft speed without torsion

Figure 6.4: Typical shaft IAS showing the possibility of shaft torsion

6.3 Experiments conducted

Vibration experiments were carried out for all the cases listed in Table 4.1 (i.e., healthy

blades, root looseness and cracked blade(s)). Initially, the experiments were conducted

at different constant shaft speeds but the excitation from the shaft torsional vibration

was not observed to be significant; hence, further experiments were conducted during

the machine run-up from 600 rpm (10 Hz) to 1800 rpm (30 Hz). The run-up rate was

kept equal to 40 rpm/s. The analogue signals measured by the encoder and tachometer

sensor were then collected at 50000 samples/s and stored on the PC for further signal

processing. In this study, to ascertain the accuracy of results obtained using the rotary

encoder raw signals of shaft torsional vibration, the experimental tests were repeated

using different sampling frequencies of 30,000, 40,000 and 50,000 samples per second;

these gave the same results and did not give errors in signal. High sampling frequency

of more than twice the encoder tooth meshing frequency was used in the tests. The

(𝑓𝑠𝑛 ) is constant

Inst

an

tan

eou

s S

pee

d (𝒇𝒔𝒏

)

Time (Tn)

(𝑓𝑠𝑛 ) fluctuation

Inst

an

tan

eou

s S

pee

d (𝒇𝒔𝒏

)

Time (Tn)


122

encoder tooth meshing frequency is calculated by multiplying the number of encoder

teeth (360) by the maximum running speed (30 Hz), which is equal 10,800 Hz.

Therefore, the use of high sampling frequency, i.e. more than twice the encoder tooth

meshing frequency of 10,800 Hz (> 21,600 Hz), was applied to overcome signal errors.

6.4 Data analysis

The measured tacho sensor and encoder data were analysed for all cases to extract the

shaft speed with time and the IAS signal with time. A typical shaft speed profile from

the tacho sensor and the raw signals from the encoder for the healthy blade condition

(Case 1) are shown in Figures 6.5 and 6.6, respectively.

Figure 6.5: A typical rotor speed profile for the machine during run-up

Figure 6.6: Typical magnified measured encoder raw signals

5 10 15 20 25 30 35 405

10

15

20

25

30

Time (Sec)

Sp

eed

(R

PS

)

20 20.0005 20.001 20.0015 20.002 20.0025 20.003 20.0035 20.004 20.0045 20.005-3

-2

-1

0

1

2

3

Time (sec)

Vo

lta

ge

(V

)


123

Figure 6.7 shows a typical EO5 response for Case 1 (healthy condition) for long blades.

This figure shows peaks at around 94 Hz (purple coloured region) and at 108 Hz (dark

green coloured region) related to shaft torsional resonance (with flexible coupling to the

motor) and the critical speed of the rig (the rig’s natural frequency). The figure also

shows the frequency of blade(s) with mistuned effects reflected by the peak between

118 and 135 Hz (light green coloured region).

Figure 6.7: A typical IAS response at e.g. EO5 for Case 1: healthy blades illustrating frequency

modes

Additionally, for the short blades, Figure 6.8 shows a typical EO10 response for Case 1:

healthy blade condition, which illustrates the peak of casing frequency mode at 180 Hz

(light blue coloured region) and the cluster of blade(s) frequency with mistuned between

210 and 260 Hz (light green coloured region). Also, the figure shows a shaft second

frequency mode peak at 262 Hz.

60 80 100 120 1400

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Frequency (Hz)

EO

5, S

peed

Flu

ctu

ati

on

(R

PS

)

(a)

To

rsio

na

l fr

equ

ency

mod

e

Tra

nsv

erse

fre

qu

ency

mo

de

Bla

des

fre

qu

ency

mod

e


124

Figure 6.8: A typical IAS response at EO10 for short blades; Case 1: Healthy blades

6.5 Results of the experiments on long blades

For the long blades, the extracted IAS signals were processed with different engine

order (EO) speeds to understand the appearance of blade resonance, their higher

harmonics and dynamic behaviour. It was observed that the EO5 and its higher

harmonics‎(EO10,‎EO15‎…)‎all‎contained blade responses in the IAS signals. A hump

around 120 Hz to 130 Hz related to blade resonance (BR) indicates that the blades were

excited during the machine run-up and related in a banded resonance due to blade

mistuning. The figures are magnified around the BR region which shows the long

blade(s) frequency range from 115 Hz to 135 Hz so that the blade response in the

resonance region can be clearly seen. The EO5 responses in BR in the frequency band

between 115 Hz and 135 Hz for Cases 2 and 3 are shown in Figures 6.9 to 6.15 to

facilitate comparison with Case 1: healthy conditions. Similarly, Figures 6.16 to 6.22

are shown to compare the IAS response in the frequency band between 240 Hz and 270

Hz for faulty cases (Cases 2 and 3) with the healthy case (Case 1) at EO10. In addition,

Figures 6.23 to 6.29 are shown to compare the IAS response in the frequency band

between 345 Hz and 405 Hz for faulty cases (Cases 2 and 3) with the healthy case

(Case 1) at EO15. Figures 6.9 to 6.15 are combined in Figure C1 (Appendix C) showing

IAS data analysis for EO5 in blade health condition cases: healthy blades, blade root

looseness (Blade 1 or Blade 5), crack on one blade (Blade 2 or Blade 4) and cracks on

100 125 150 175 200 225 250 275 3000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ate

d (

RP

S)

Short Blades

frequency mode

210-260 Hz Casing frequency

mode

Shaft 2nd

mode


125

two blades (Blades 2 and 4). In addition, Figures 6.16 to 6.22 are combined in

Figure C2 for EO10 and Figures 6.23 to Figure 6.29 are combined in Figure C3 for

EO15.

Figure 6.9: Measured encoder (IAS) data for engine order EO5 spectra for healthy blades

(Case 1)

Figure 6.10: Measured encoder (IAS) data for engine order EO5 spectra for blade root

looseness (Case 2(i): Blade no. 1)

115 120 125 130 1350

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Frequency (Hz)

EO

5, S

peed

Flu

ctu

ati

on

(R

PS

)

115 120 125 130 1350

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Frequency (Hz)

EO

5, S

peed

Flu

ctu

ati

on

(R

PS

)


126


looseness (Case 2(ii): Blade no. 5)

Figure 6.12: Measured encoder (IAS) data for engine order EO5 spectra for a crack on one

blade (Case 3(i): Blades no. 4)

115 120 125 130 1350

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Frequency (Hz)

EO

5, S

peed

Flu

ctu

ati

on

(R

PS

)

115 120 125 130 1350

0.05

0.1

0.15

0.2

0.25

0.3

Frequency (Hz)

EO

5, S

peed

Flu

ctu

ati

on

(R

PS

)


127

Figure 6.13: Measured encoder (IAS) data for engine order EO5 spectra for cracks on two

blades (Case 3(ii): Blades no. 2 and 4)


blade (Case 3(iii): Blade 2)

115 120 125 130 1350

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Frequency (Hz)

EO

5, S

pee

d F

luct

ua

ted

(R

PS

)

115 120 125 130 1350

0.05

0.1

0.15

0.2

0.25

Frequency (Hz)

EO

5, S

peed

Flu

ctu

ate

d (

RP

S)


128


blade after 100 minutes of machine operation (Case 3(iv): Blade 4)


(Case 1)

115 120 125 130 1350

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Frequency (Hz)

EO

5, S

peed

Flu

ctu

ati

on

(R

PS

)

230 235 240 245 250 255 260 265 2700.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ati

on

(R

PS

)


129





230 235 240 245 250 255 260 265 2700.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ati

on

(R

PS

)

230 235 240 245 250 255 260 265 2700.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ati

on

(R

PS

)


130

Figure 6.19: Measured encoder (IAS) data for engine order EO10 spectra for a crack on

one blade (Case 3(i): Blade no. 4)



230 235 240 245 250 255 260 265 2700

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ati

on

(R

PS

)

230 235 240 245 250 255 260 265 2700

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ate

d (

RP

S)


131


blade (Case 3(iii): Blade no. 2)


blade after 100 minutes of machine operation (Case 3(iv): Blade no. 4)

230 235 240 245 250 255 260 265 2700

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ate

d (

RP

S)

230 235 240 245 250 255 260 265 2700.02

0.04

0.06

0.08

0.1

0.12

0.14

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ati

on

(R

PS

)


132


(Case 1)



350 360 370 380 390 4000.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Frequency (Hz)

EO

15

, S

peed

Flu

ctu

ate

d (

RP

S)

350 360 370 380 390 4000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Frequency (Hz)

EO

15

, S

peed

Flu

ctu

ati

on

(R

PS

)


133



Figure 6.26: Measured encoder (IAS) data for engine order EO15 spectra for a crack on

one blade (Case 3(i): Blade no. 4)

350 360 370 380 390 4000.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Frequency (Hz)

EO

15

, S

peed

Flu

ctu

ati

on

(R

PS

)

350 360 370 380 390 4000.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Frequency (Hz)

EO

15

, S

peed

Flu

ctu

ati

on

(R

PS

)


134




blade (Case 3(iii): Blade no. 2)

350 360 370 380 390 4000.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

Frequency (Hz)

EO

15

, S

peed

Flu

ctu

ate

d (

RP

S)

(c)

350 360 370 380 390 4000.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

Frequency (Hz)

EO

15

, S

peed

Flu

ctu

ate

d (

RP

S)


135


blade after 100 minutes of machine operation (Case 3(iv): Blade no. 4)

6.6 Results of the experiments on short blades

The vibration experiments were carried out for all the cases listed in Table 4.1 (i.e.

healthy blades, a crack on one blade and cracks on two blades). The same conditions

applied to long blades as described in Section 6.4 were also applied to short blades

during the experiments carried out for machine run-up. Also, here the extracted IAS

signals were processed with different EO speeds to understand the appearance of blade

resonance, their higher harmonics and dynamic behaviour. It was observed that EO10

spectra contained blade response in IAS signals. A hump around 210 Hz to 260 Hz

related to the BR region indicates that the blades were excited during the machine run-

up and related in a banded resonance due to blade mistuning. The magnified regions

covering BR related to blade frequencies are taken from IAS response signals and are

shown in Figures 6.30 to 6.32. The EO10 responses in BR in the frequency band

between 210 Hz and 260 Hz for Cases 3 are also shown in Figures 6.30 to 6.32 to

facilitate comparison with Case 1 of healthy conditions. Figures 6.30 to 6.32 are

combined in Figure C4 (Appendix C) showing IAS data analysis for EO10 in blade

health condition cases: healthy blades, crack on one blade and cracks on two blades.

350 360 370 380 390 4000

0.05

0.1

0.15

0.2

0.25

Frequency (Hz)

EO

15

, S

peed

Flu

ctu

ati

on

(R

PS

)


136


(Case 1)


blade (Case 3(i): Blade no. 5)

210 220 230 240 250 2600

0.05

0.1

0.15

0.2

0.25

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ate

d (

RP

S)

210 220 230 240 250 2600

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ate

d (

RP

S)


137



6.7 Observations and results

It is observed from the IAS response in the BR region in Figures 6.9 and 6.30 for long

and short blades, respectively, that the amplification of the BR region seems to be in a

banded form in Case 1: healthy blade conditions. The mistuned effect in both blades’

natural frequencies possibly resulted in the banded response. A typical EO5 and EO10

response in 1xBR region for the healthy blade case is shown in Figures 6.9 and 6.30 for

long and short blades, respectively. The presence of higher harmonics of BR for healthy

blades or higher harmonics of shaft speed for healthy machines is often observed in

experimental rigs and rotating machines. This is often due to a degree of misalignment

in the rotor at the coupling during machine assembly. However, it is important to

observe the dynamic behaviour and changes in the cases of faulty blade conditions.

Cases 2(i) and (ii) represent long blade root looseness at Blade no. 1 and Blade no. 5

separately as per Table 4.1. The addition of two loosely held washers at the root of

Blades no. 1 or 5 did not affect the natural frequency of the blades significantly; but the

210 220 230 240 250 2600

0.05

0.1

0.15

0.2

0.25

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ate

d (

RP

S)


138

EO5, EO10 and EO15 responses of Blade no. 1 and Blade no. 5, shown in Figures 6.10

and 6.11 for EO5 and Figures 6.17 and 6.18 for EO10 and Figures 6.24 and 6.25 for

EO15, respectively, show significantly different behaviour compared to healthy

conditions (Case 1). It was observed that the 1xBR, 2xBR and 3xBR responses show

two or more distinct peaks instead of the single banded peak seen for Case 1: healthy

conditions.

Cases 3 represent tests related to cracked blades which consist of six tests, four tests

conducted on long blades and two tests on short blades as shown in Table 4.1. The tests

were related to either a single crack on one blade or two cracked blades together on the

same disc for either long or short blades. Distinct multiple peaks were observed in the

1xBR, 2xBR and 3xBR regions related to EO5, EO10 and EO15 for long blades,

respectively, and 1xBR region related to EO10 for short blades. These have been

observed for all crack related cases in Cases 3 for all six on long and short blades. This

distinct multiple peaking is evident from EO5 spectra in Figures 6.12 to 6.15, EO10

spectra in Figures 6.19 to 6.22 and EO15 spectra in Figures 6.26 to 6.29 for the four

crack related tests based on Cases 3 for long blades, and also in EO10 spectra in Figures

6.31 and 6.32 for the two tests on cracked short blades. It was observed that the 1xBR

plots show more distinct peaks instead of the single banded peak seen for Case 1 of

healthy blade condition for both blade types.

Crack breathing (opening and closing of cracks) that occurs with cracked blades and

interaction due to blade root looseness seem to be responsible for the multiple peaks in

the BR region and its higher harmonics. From the results of the three cases, it can be

observed that shaft torsional vibration based on IAS signals and the appearance of

multiple peaks during machine run-up may be useful for blade health monitoring

(BHM).

6.8 Summary

The measured shaft torsional vibration based-on IAS signal based on encoder data for

long and short blades during machine run-up operation was used to understand the

dynamics of the rotating blades with and without faults and to compare the behaviour of

long and short blades under different health conditions. Experiments were conducted for


139

three different blade health conditions; healthy blades with mistuned effects, blade root

looseness and cracked blades, in the case of long blades, and for two conditions; healthy

with mistuned effects and cracked blades, in the case of short blades. The IAS signals

for blades when order tracked with EO5 and its higher harmonics (EO10 and EO15) for

long blades and EO10 for short blades show the existence of blade resonance (BR) for

all three cases. It was observed that the single banded peak for healthy blades (Case 1)

in the 1xBR, 2xBR and 3xBR changes to multiple peaks in 1xBR, 2xBR and 3xBR for

damaged conditions in the cases of both long and short blades. The results show a

distinct difference between healthy and faulty blade conditions and hence these

observations may be useful for BHM.


140

CHAPTER 7

COMPARATIVE STUDY BETWEEN OBV, OCV AND IAS METHODS

7.1 Introduction

This chapter presents a comparison between the three measurements: on-bearing

vibration (OBV), on-casing vibration (OCV) and shaft torsional vibration based-on

instantaneous angular speed (IAS), discussed in Chapters 4, 5 and 6, respectively. The

measurements are used in the experimental work of this research study in order to

investigate‎ blades’‎ dynamic‎ behaviour‎ during‎ machine‎ run-up under three different

blade health conditions; (a) healthy blades with mistuned effects, (b) blade root

looseness, and (c) cracked blades, for two blade sizes (long and short). The purpose of

this study is to investigate which of these measurements represents a more useful and

reliable method to use for diagnosis and detection of blade health conditions. The full

details of the three measurements, including blade/rig design and blade faults simulation

are discussed in Chapters 3, 4, 5 and 6. Figure 7.1 shows a schematic diagram of the

procedures followed for the selection of the most suitable method with the best

measurement that can be used as a tool for blade health monitoring (BHM) of rotating

machines. Table 7.1 and Table 7.2 show a comparison of the results of the

measurements for short and long blades, respectively.

Figure 7.1: A schematic flowchart for the processes that are followed to select the best

measurement for BHM of rotating machines

ROTATING MACHINES BLADES

VIBRATION MEASUREMENT

TECHNIQUES FOR BHM

OBV OCV

IAS

Investigate Measurements

Best Method could be selected as a

diagnoses tool


141

Table 7-1 : Comparison between the results of OBV, OCV and IAS for short blades

Blade

condition

Short blades

OBV OCV IAS

Case 1:

Healthy

with

mistuned

effects

There are no responses in the blade resonance

(BR) regions (1xBR).

There is one distinct peak around the

frequency 238 Hz confirming excitation of

blade resonance (1xBR).

Existence of BR in the 1xBR region

indicates blades are excited during the

machine run-up and related in a banded

resonance due to the blade mistuning; one

banded peak was observed.

220 225 230 235 240 245 250 255 2600.016

0.018

0.02

0.022

0.024

0.026

0.028

0.03

0.032

0.034

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)

220 230 240 250 2600

0.005

0.01

0.015

0.02

0.025

0.03

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)

210 220 230 240 250 2600

0.05

0.1

0.15

0.2

0.25

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ate

d (

RP

S)


142

Case 3(i):

Crack on

one blade

No BR and no changes in the harmonics region

of (1xBR).

There are no changes in the blade behaviour

related to EO10 in (1xBR) region compared to

Case 1: healthy conditions; only a single

distinct peak was observed.

The existence of BR in 1xBR region was

observed and 1xBR shows more distinct

peaks instead of a single banded peak for

Case 1, healthy conditions.

Case 3(ii):

Cracks on

two blades

There are distinct multiple peaks in the 1xBR

regions related to the EO10 response.

As in Case 3(i); no changes were observed in

the blade harmonics region of (1xBR)

compared to Case 1, healthy conditions.

The existence of BR in 1xBR region.

Again, more distinct peaks in 1xBR

region were observed instead of a single

banded peak for Case 1, healthy

conditions.

220 225 230 235 240 245 250 255 2600.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)

220 225 230 235 240 245 250 255 2600

0.005

0.01

0.015

0.02

0.025

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)

210 220 230 240 250 2600

0.05

0.1

0.15

0.2

0.25

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ate

d (

RP

S)

220 225 230 235 240 245 250 255 2600.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)

220 225 230 235 240 245 250 255 2600

0.005

0.01

0.015

0.02

0.025

0.03

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)

210 220 230 240 250 2600

0.05

0.1

0.15

0.2

0.25

Frequency (Hz)

EO

10

, S

peed

Flu

ctu

ate

d (

RP

S)


Table 7-2: Comparison between the results of OBV and IAS for long blades

Blade

condition

Long Blades

OBV IAS

Case 1:

Healthy

with

mistuned

effect

There is one peak around 122 Hz,

which represents BR response in

(1xBR) region.

Existence of BR in (1xBR) region

indicates the blades are excited during

the machine run-up and related in a

banded resonance due to the blade

mistuning; one banded peak was

observed.

Case 2:

Blade root

looseness

There are distinct multiple peaks in

the 1xBR regions related to the EO5

response.

The existence of BR in 1xBR region;

more distinct peaks were observed in

the 1xBR region instead of the single

banded peak seen for Case 1, healthy

condition.

Case 3(i):

Crack on

one blade

There are distinct multiple peaks in The existence of BR in 1xBR region. It

115 120 125 130 135

0

0.5

1

1.5

2

x 10

-7

EO5 Frequency (Hz)

Ac

ce

le

ra

tio

n (m

/s

2

)

(a)

115 120 125 130 1350

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Frequency (Hz)

EO

5, S

peed

Flu

ctu

ati

on

(R

PS

)

(a)

115 120 125 130 1351

1.5

2

2.5

3

3.5

4

4.5

5

5.5x 10

-4

EO5 Frequency (Hz)

Accele

ra

tio

n (

m/s

2)

(c)

115 120 125 130 135

0

0.05

0.1

0.15

0.2

E05 Frequency (Hz)

Sp

ee

d F

lu

ctu

atio

n (R

PS

)

(d)

115 120 125 130 1350.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2x 10

-4

Frequency (Hz)

EO

5, A

ccele

ra

tio

n (

m/s

2)

115 120 125 130 1350

0.05

0.1

0.15

0.2

0.25

Frequency (Hz)

EO

5, S

peed

Flu

ctu

ate

d (

RP

S)

(b)


144

the 1xBR regions related to the EO5

response.

was observed that the 1xBR shows

more distinct peaks instead of the

single banded peak seen for Case 1,

healthy condition.

Case 3(ii):

Cracks on

two blades

There are distinct multiple peaks in

the (1xBR) regions related to the

EO5 response.

The existence of BR in 1xBR region.

More distinct peaks were observed in

the 1xBR region instead of the single

banded peak for Case 1, healthy

condition.

7.2 Results and observations

7.2.1 Comparison of the three measurements for monitoring short blades

The‎results‎of‎the‎three‎measurements‎OBV,‎OCV‎and‎IAS‎are‎compared‎in‎Table‎7.1.‎

The‎ three‎measurements‎were‎ used‎ to‎ detect‎ and‎ diagnose‎ blade‎ health‎ conditions‎ in‎

different‎cases‎of‎blade‎ faults‎ in‎order‎ to‎ select‎which‎of‎ these‎ three‎measurements‎ is‎

more‎effective‎and‎reliable‎to‎be‎used‎for‎BHM.‎The‎observations‎show‎that:

1- The‎results‎obtained‎from‎OBV‎signals‎provided‎some‎good‎indication‎for‎blade‎

fault‎detection‎only‎ in‎ the‎cases‎of‎more‎ than‎one‎cracked‎blade‎on‎ the‎bladed‎

disc,‎as‎shown‎in‎Case‎3(ii)‎in‎Table‎7.1.‎This‎was‎detected‎by‎the‎existence‎of‎

distinct multiple peaks in the BR region of 1xBR related to the EO10 response.

2- The‎results‎obtained‎from‎OCV‎signals‎showed‎that‎there‎were‎no changes in the

BR region for damaged blades in Cases 3(i) and 3(ii) compared with Case 1 of

healthy conditions, as shown in Table 7.1. Only one distinct peak was observed

for all three cases.

3- The‎ results‎ obtained‎ based‎ on‎ IAS‎ signals‎ provided‎ a‎ good‎ indication‎ for‎ the‎

detection‎of‎blade‎ fault‎ conditions;‎one‎banded‎peak‎was‎observed‎ for‎healthy‎

115 120 125 130 1350

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

-4

Frequency ( Hz)

EO

5, A

ccele

ra

tio

n (

m/s

2)

115 120 125 130 1350

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Frequency (Hz)

EO

5, S

peed

Flu

ctu

ate

d (

RP

S)

(c)


145

blades‎ in‎Case‎1‎ in‎Table‎7.1‎ in‎ the‎blade‎resonance‎region,‎which‎changed‎ to‎

more‎peaks‎in‎the‎BR‎region‎for‎damaged‎conditions‎in‎Cases‎3(i)‎and‎3(ii).‎

7.2.2 Comparison of the two measurements for monitoring long blades

The‎ comparison‎ results‎ are‎ provided‎ in‎ Table‎ 7.2,‎ which‎ includes‎ a‎ full‎ comparison‎

between‎ the‎ two‎measurements,‎OBV‎ and‎ IAS,‎ applied‎ in‎ four‎ cases‎ of‎ blade‎ health‎

conditions.‎The‎observations‎show‎that:

1- The‎ results‎ extracted‎ from‎ OBV‎ signals‎ provided‎ a good indication for the

detection of blade fault conditions: the presence of distinct multiple peaks in the

BR region for damaged blades in Cases 2 and 3 instead of one peak in the BR as

in Case 1, healthy conditions as shown in Table 7.2.

The‎ results‎ of‎ IAS‎ signals‎ gave‎ a‎ good‎ indication‎ for‎ the‎ detection‎ of‎ blade‎ fault‎

conditions;‎ a‎ single‎ banded‎ peak‎ for‎ Case‎ 1,‎ healthy‎ blade‎ conditions,‎ in‎ BR‎ region‎

changes‎to‎more‎peaks‎in‎the‎BR‎region‎for‎damaged‎blade‎conditions‎as‎seen‎in‎Cases‎

2‎and‎3,‎as‎shown‎in‎Table‎7.2.

7.2.3 Final conclusion

The‎results‎shown‎in‎Tables‎7.1‎and‎7.2,‎including‎the‎figures‎of‎engine‎orders‎(EOs)‎of‎

the‎1xBR‎region‎ for‎ short‎and‎ long‎blades‎during‎machine‎ run-up‎describe‎ the‎use‎of‎

OBV,‎OCV‎and‎IAS‎measurements‎in‎order‎to‎investigate which measurement‎are more

useful for BHM. The results indicate that:

- OCV‎is‎not‎useful‎as‎a‎feature‎in‎BHM‎based‎on‎the‎results‎of‎this‎study.‎Further‎

experiments‎in‎future‎studies‎are‎recommended.‎

- OBV‎provided‎a good indication to detect faults in long blades. However, the

results related to short blades also provided some‎ good‎ indication‎ only‎ in‎ the‎

cases‎when‎there‎was‎more‎than‎one‎cracked‎blade‎on‎the‎bladed‎disc.‎Hence the

presence of distinct multiple peaks in the BR region can be considered as a

feature of BHM.

- IAS‎provided‎a‎good‎indication‎to‎monitor‎blade‎health‎conditions‎for‎both‎short‎

and‎ long‎blades.‎The‎presence‎of‎distinct‎multiple‎peaks‎ in‎ the‎BR‎ region‎can‎

therefore‎be‎considered‎as‎a‎highly‎useful‎feature‎of‎BHM.‎Indeed,‎the‎shaft‎IAS‎


146

signal‎seems‎to‎give‎a‎much‎better‎indication‎for‎BHM‎compared‎to‎OBV‎and‎

OCV‎measurements.‎

In‎ addition‎ to‎ the‎ above,‎ Table‎ 7.3‎ illustrates‎ a‎ summarised‎ comparison‎ between‎ the‎

three‎measurement‎ techniques‎ in‎published‎work.‎These‎represent‎ the‎ results‎obtained‎

from‎ these‎measurements‎ which‎ have‎ been‎ published‎ in‎ international‎ journals‎ or‎ the‎

proceedings‎of‎conferences.

Table 7-3: Articles published related to this study in the research area of blade vibration fault

detection using different measurements

Blade‎

condition

Short‎blades Long‎blades

OBV OCV IAS OBV IAS

Article‎Published

Healthy

VETOMAC-X‎‎‎

2014‎[127]

VETOMAC-X‎‎‎

2014‎[127]

ASME‎

2014‎[128]

SOP‎ 2014‎

[129]

ICOVP‎ 2013‎

[130]

MSSP‎ 2014‎

[131]

ASME‎ 2014‎

[128]

SOP‎ 2014‎

[129]

ICOVP‎ 2013‎

[130]

1‎Crack

2‎Cracks

Root‎

looseness

--------

--------

--------

7.3 Summary

A comparison between the results of the three measurements of OBV, OCV and IAS

was discussed in this chapter. These measurements were‎ used‎ to‎ investigate‎ blades’‎

dynamic behaviour under different types of blade fault conditions in order to choose

which measurement is the most suitable to be used as a tool for BHM. From the results

listed in Tables 7.1 and 7.2 for both short and long blades, the shaft‎IAS‎measurement

seems‎to‎provide‎the‎best‎indication‎for‎the‎detection‎of‎blade‎faults‎compared‎to‎OBV

and OCV measurements.‎Hence,‎shaft‎IAS‎vibration‎could‎be‎considered‎as‎a‎feature‎of‎

BHM.


CHAPTER 8

DEVELOPMENT OF POLAR PLOT PRESENTATION (P3)

METHOD

8.1 Introduction

In this chapter, a novel approach was used for presenting the vibration data by using

polar plot coordinates relating to blade order angles and the vibration amplitude of on-

bearing vibration (OBV), on-casing vibration (OCV) and shaft torsional vibration based

on instantaneous angular speed (IAS) signals. The polar plot presentation (P3) is a two

dimensional coordinate system in which each point in the graph is determined by an

angle and a distance. The polar presentation is used to detect blade faults in rotating

machines and to determine the feasibility of using the polar plot method for blade health

monitoring (BHM). In this research, a P3 presentation method is applied by

representing‎ the‎ summation‎ of‎ time‎ synchronizing‎ averaging‎ (TSA)‎ data‎ of‎ vibration‎

measurements‎related‎to‎different‎engine‎orders‎of‎blade(s)‎resonance‎(BR)‎frequency.‎

The P3 method was used for analysis of experimental vibration data of a rotating 8-

bladed discs during machine run-up in order to detect blade faults using three cases of

blade health conditions: (a) healthy with mistuned effects, (b) blade root looseness and

(c) crack(s) on blade(s).

8.2 Signal processing concept developed

Signal processing developed for the P3 method is discussed in the following sections.

8.2.1 Filter for each blade resonance related to the engine orders

In order to determine the BR related to the engine order (EO) of first resonance

frequency of blades (1xBR), a band-pass filter was used for the data analysis using

MATLAB to complete this task. 1xBR was firstly determined from the blade natural

frequency, which was obtained through modal testing using a frequency response

function (FRF) method, as described in Section 3.6. The EOs were then computed in

relation to the BR frequency. The band-pass filter was then used to determine blades

higher harmonics region (2xBR,‎3xBR…).‎The‎P3‎process‎was‎subsequently‎applied‎in‎

relation to the BR region for accurate data analysis.


148

8.2.2 Combining engine orders

In addition to the use of a single EO, the combination of different engine orders related

to BR frequency when using the P3 method also provided good results. The

combinations of EOs was done by summation of a random selection of two, three or

four of different EOs related to different BR frequency harmonics (1xBR, 2xBR, 3xBR

and 4xBR), i.e, for long blades a combination of EO5+EO10+EO15 was selected,

which is related to BR frequencies 1xBR, 2xBR and 3xBR respectively. This can be

used to determine which combination of EOs gives a clear result when comparing data

for faulty blades with healthy blades for the purpose of diagnosing blade conditions.

The use of combinations of different EOs provides a wide range of results from

analysed data leading to a more reliable P3 method leading to more effective BHM.

8.2.3 Time synchronous averaging for each engine order related to blade

resonance

TSA is a signal processing method which is used to extract waveform signals from

other noisy data. TSA was used in this study for the P3 method to enhance the time

domain data after application of the band-pass filter to remove the noise from the

vibration signals. It is a very powerful tool, used to eliminate signal noise components

that are not synchronous with the shaft torsional rotation, such as noise generated by the

electrical motor, the bearing, and any vibration not related to the rotating shaft. This is

effective‎ when‎ used‎ to‎ separate‎ blades’‎ response‎ via‎ shaft‎ torsional‎ vibration‎ that‎ is‎

coupled with its vibration from other noisy signals. To achieve this, tachometer signals

are needed as a reference (for shaft rotation), together with the angular position of the

rotating shaft with blades. On the other hand, the TSA is also essential, which will

repeat the vibration signals related to the blades on the rotating shaft periodically, by

dividing the vibration signal into adjacent segment windows with the same length, then

sampling the segments until the shaft rotation is enhanced and other parts of the signals

can be removed. The TSA waveform is calculated based on the shaft torsional vibration

(IAS), OBV and OCV, together with the tachometer signals. The TSA corresponding to

shaft rotation of one full revolution can be obtained from the tachometer signal. The fast

Fourier transformation (FFT) is then calculated on the angular domain instead of the

time domain signal for every segment after resampling the time domain data. Finally,


149

the polar plot presentation is applied to the FFT data to discover the blade vibration

behaviour for healthy and faulty cases, which are then compared.

8.3 Polar plot

The P3 method is a novel approach‎used‎for‎presenting‎the‎blades’‎vibration‎behaviour

using the polar coordinates (angle and amplitude) of engine orders related to blade order

angles and the vibration amplitude of three measurements: shaft torsional vibration, on-

bearing vibration and on-casing vibration. The polar plot is a two dimensional

coordinate system in which each point in the graph is determined by an angle and a

distance. The radius of the system corresponds to the blade vibration signal amplitude

and the 360 angular coordinate is used to represent the 360 degrees of the full rotation

of the shaft. The novelty of this method is in its application to the detection of faulty

blades. This is done by representing‎ the‎ summation‎ of‎ TSA‎ data‎ of‎ blade‎ vibration‎

related‎to‎blades‎EOs‎using‎the‎following‎steps:‎applying‎a‎band-pass‎filter‎around‎the‎

frequency‎ region‎ of‎ the‎ first‎ blade‎ resonance‎ (1xBR),‎ followed‎ by‎ all‎ its‎ higher‎

harmonics‎(2xBR,‎3xBR‎and‎4xBR)‎using‎IAS,‎OBV‎and‎OCV‎data‎extracted‎from‎the‎

encoder,‎the‎bearing‎pedestals‎and‎the‎casing‎respectively.‎This‎procedure‎is‎applied‎to‎

remove‎ other‎ effect‎ signals‎ not‎ related‎ to‎ BR.‎ Next,‎ BR-related‎ signals‎ are‎ added‎

together‎with‎ reference‎ to‎ tachometer‎ signals‎using‎ the‎TSA‎method.‎Finally,‎ the‎data‎

are‎plotted‎in‎2D‎polar‎coordinates.‎

8.3.1 Polar plot diagnosis approach

P3 is a novel method used in this study to diagnose and detect blade health conditions in

rotating machines. The radius in the plot represents the amplitude of the signal, and the

angle‎represents‎ the‎rotor’s‎full‎rotation cycle of 360 degrees, as shown in Figure 8.1.

P3 is related to a rotating 8-blade disc spaced by 45 angles, and the amplitude of the

vibration signals of single EO and/or combination of EOs (IAS, OBV and OCV) is

related to blade resonance frequency (1xPR, 2xPR, 3xPR and 4xPR). By comparing the

P3‎plots‎of‎healthy‎with‎faulty‎blades’‎conditions,‎blade‎looseness,‎a‎crack‎on‎one‎blade‎

and cracks on two blades can be detected, and this can be utilized as an effective tool for

BHM.


150

Figure 8.1: Typical sample of the polar plot presentation model

The P3 approach works by computing the number of leaves (L) and the number of

coupled‎leaves‎(C)‎and‎comparing‎the‎changes‎in‎the‎leaves’‎profile‎shape‎for‎the‎two‎

cases of blade health conditions (healthy versus faulty) to help diagnose blade

conditions. The typical P3 model shown in Figure 8.1 can be divided leaves shape into

three types: (L) represents a single leaf, (C2) represents two leaves coupled together

which are joint at point (a1), and (C3) denotes three leaves coupled together, joint at two

points (b1) and (b2). In the same way, different numbers of coupled leaves can be

written‎together‎as‎C4,‎C5,‎and‎C6…etc.‎In‎the‎case‎where‎more‎than‎one‎of‎each‎type‎

is seen, this can be written as a set, such as 5L, 3C2 or 2C3 etc. In the case presented in

Figure 8.1, the set of eleven single and coupled leaves can be counted as: two single

leaves (2L), three of two coupled leaves (3C2) and one of three coupled leaves (1C3),

and therefore the whole set can be written as 11L = 2L+3C2+1C3.

The P3 method analysis processes are followed in order to discover and detect blade

faults and are carried out by comparing the differences in polar plot shapes between

a1

b2

b1

3 coupled

leaves (C3)

Single leaf (1L)

2 coupled

leaves (C2)


151

cases of healthy and faulty blade conditions. The plots can be compared and monitored

based on the following parameters:

(a) The total number of leaves in the plot.

(b) The number and nature of the coupled leaves.

(c) The deviation of the leaves from the centre of the plot.

(d) The symmetry and/or regularity of the leaves in the plot.

(e) The full profile and the size of the single leaves and/or combined leaves.

(f) The amplitude of the blade frequency in each case.

8.4 Polar plot presentation (P3) for long blades

For long blades, the region of blades natural frequency is determined at different EOs

using a band-pass filter based on MATLAB software. This is determined for long

blades at EO5 in the range between 115 Hz and 135 Hz and then the process proceeds to

its higher harmonics‎(EO10,‎EO15,‎EO20‎…).‎The‎polar‎plot‎is‎then‎applied‎using‎polar‎

coordinates of angle and signal amplitude at one mean or 2 means of speed engine order

(EO5)‎related‎to‎the‎long‎blades’‎first‎resonance‎frequency‎(1xBR)‎to‎avoid‎any‎noise‎at‎

the root of the signal, which may affect the quality of analysis, as illustrated in Figure

8.2.‎ By‎ applying‎ polar‎ plots,‎ blades’‎ behaviour‎ can‎ be‎ compared‎ at‎ different‎ blade‎

health cases of: (a) healthy blades with mistuned effects, (b) blade root looseness, (c) a

crack on one blade, and (d) cracks on two blades. The data can be extracted from the

rotating blades during machine run-up by using an encoder for torsional vibration based

on IAS signal and accelerometers for acceleration vibration signals from the bearing

pedestals and from the casing.


152

Figure 8.2: Mean speed of EO5 for IAS data from healthy long blades

8.4.1 Encoder data analysis

The polar plot presentation method was conducted for the encoder torsional vibration

based on IAS signals in order to compare blades dynamic behaviour in four cases of

blade health conditions; (a) healthy with mistuned effects, (b) blade root looseness, (c) a

crack on one blade, and (d) cracks on two blades, at different EOs with and without

combination of EOs as shown in Figures 8.3 to 8.7 and Tables 8.1 to 8.5.

90 100 110 120 130 140 1500

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

X: 117.1

Y: 0.0479

Frequency (Hz)

EO

5, S

peed

(m

/s)

X: 135.9

Y: 0.04793

Blades resonance frequencey (BR)

Mean of EO5 (Y=0.0479)

Polar plot apply at this red line

(RP

S)


153

Figure 8.3: Polar plot of IAS measured data of EO5 for cases: (a) healthy blades, (b) blade root

looseness, (c) a crack on one blade and (d) cracks on two blades

Table 8-1: The numbers of single leaves and coupled leaves in the polar plot of EO5 for the

four cases of blade health conditions based on IAS data

Case Healthy blades

(a)

Blade looseness

(b)

Crack on one blade

(c)

Cracks on two

blades (d)

EO5 5L

(5L)

5L

(1L+1C4)

5L

(1L+1C4)

5L

(1C5)

0.005

0.01

0.015

0.02

0.025

30

210

60

240

90

270

120

300

150

330

180 0

0.05

0.1

0.15

30

210

60

240

90

270

120

300

150

330

180 0

0.01

0.02

0.03

0.04

30

210

60

240

90

270

120

300

150

330

180 0

0.01

0.02

0.03

30

210

60

240

90

270

120

300

150

330

180 0

(d) (c)

(a) (b)


154

Figure 8.4: Polar plot of IAS measured data of EO10 for cases: (a) healthy blades, (b) blade

root looseness, (c) crack on one blade and (d) cracks on two blades


four cases of blades health conditions based on IAS data

Case Healthy blades

(a)

Blade looseness

(b)

Crack on one blade

(c)

Cracks on two blades

(d)

EO10 10L

(4L+1C6)

9L

(4L+1C5)

9L

(3L+1C6)

9L

(3L+1C6)

0.05

0.1

0.15

0.2

30

210

60

240

90

270

120

300

150

330

180 0

0.05

0.1

0.15

0.2

30

210

60

240

90

270

120

300

150

330

180 0

0.1

0.2

0.3

0.4

30

210

60

240

90

270

120

300

150

330

180 0

0.02

0.04

0.06

0.08

0.1

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(d) (c)

(b)


155

Figure 8.5: Polar plot of IAS measured data of EO15 for cases: (a) healthy blades, (b) blade

root looseness, (c) crack on one blade and (d) cracks on two blades


four cases of blades health conditions based on IAS data

Case Healthy blades

(a)

Blade looseness

(b)

Crack on one blade

(c)


(d)

EO15 14L

(14L)

15L

(2L+1C13)

15L

(1L+1C14)

14L

(3L+1C11)

0.05

0.1

0.15

0.2

0.25

30

210

60

240

90

270

120

300

150

330

180 0

0.05

0.1

0.15

30

210

60

240

90

270

120

300

150

330

180 0

0.05

0.1

0.15

0.2

30

210

60

240

90

270

120

300

150

330

180 0

0.02

0.04

0.06

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(d) (c)

(b)


156

Figure 8.6: Polar plot of IAS measured data of EO5+EO10 for cases: (a) healthy blades, (b)

blade root looseness, (c) crack on one blade and (d) cracks on two blades

Table 8-4: The numbers of single leaves and coupled leaves in the polar plot of combination of

EO5+EO10 for the four cases of blades health conditions based on IAS data

Case Healthy blades

(a)

Blade looseness

(b)

Crack on one

blade (c)

Cracks on two

blades (d)

EO5+EO10 10L

(4L+1C6)

9L

(1C2+1C7)

10L

(3C2+1C4)

9L

(3L+1C6)

0.05

0.1

0.15

0.2

30

210

60

240

90

270

120

300

150

330

180 0

0.2

0.4

0.6

30

210

60

240

90

270

120

300

150

330

180 0

0.05

0.1

0.15

0.2

30

210

60

240

90

270

120

300

150

330

180 0

0.02

0.04

0.06

0.08

0.1

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (d)

(b)


157

Figure 8.7: Polar plot of IAS measured data of EO5+EO10+EO15 for cases: (a) healthy blades,

(b) blade root looseness, (c) crack on one blade and (d) cracks on two blades


EO5+EO10+EO15 for the four cases of blades health conditions using IAS data

Case Healthy blades

(a)

Blade looseness

(b)

Crack on

one blade (c)


(d)

EO5+EO10+EO15 14L

(2C3+2C4)

11L

(1L+2C2+2C3)

13L

(1C3+1C10)

11L

(1L+1C10)

0.1

0.2

0.3

0.4

30

210

60

240

90

270

120

300

150

330

180 0

0.2

0.4

0.6

0.8

30

210

60

240

90

270

120

300

150

330

180 0

0.1

0.2

0.3

30

210

60

240

90

270

120

300

150

330

180 0

0.05

0.1

0.15

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (d)

(b)


158

8.4.2 Encoder data observations and discussion

It is observed from the polar plot presentation for encoder IAS response of blades’‎

behaviour in Figures 8.3 to 8.7 for the four cases of blade health conditions that the

number of leaves are the same for the four cases of blade condition of EO5, however the

number of combined leaves and the profile are different in faulty blade cases (b), (c) and

(d) compared to the healthy blades case (a), as shown in Figure 8.3 and Table 8.1. For

EO10, it can be clearly seen that the number of leaves changed from 10 in the healthy

case (a) to 9 leaves in the three faulty cases (b), (c) and (d), as shown in Figure 8.4 and

Table 8.2. In Figure 8.5 for the data of EO15, there are 14 full regular separate leaves in

case (a) of healthy blades, which changed to 15 irregular leaves, some of which were

combined, in faulty blade cases (b) and (c), and 14 leaves in case (d), also with irregular

shapes and featuring some combined leaves. Also, the same result was observed in the

combination between different engine orders, (EO5+EO10) and (EO5+EO10+EO15), as

shown in Figures 8.6 and 8.7, respectively. These show that the number of leaves

changed from 10 for the healthy case (a) to 9 leaves for the three faulty cases (b), (c)

and (d), with different sets of combined leaves as shown in Figure 8.6 and Table 8.4.

Likewise, Figure 8.7 and Table 8.5 show a change in the number of leaves from 14 for

the healthy blades case (a) to 11 and 13 for faulty blade cases, with different sets of

combined leaves for the combination of three EO’s (EO5+EO10+EO15). Hence, from

the results of the four cases of blade health conditions, it can be observed that the polar

plot presentation method can be useful to analyse shaft torsional vibration data based on

IAS signals in order to diagnose blade health conditions under different blade faults, as

the changes in the shape and number of separate and combined leaves and the number

of leaves in each coupling during machine run-up can be indicative of blade health

conditions.

8.4.3 On-bearing data analysis

The polar plot presentation method was also used to analyse data of blade(s) vibration

response obtained from the OBV, using an accelerometer in order to compare the long

blades’‎dynamic‎behaviour‎ in‎ four‎cases‎of‎blade‎health‎conditions, as listed in Table

4.1: (a) healthy with mistuned effect, (b) blade root looseness, (c) a crack on one blade,

and (d) cracks on two blades using different Eos and a using combination of several

engine orders, as shown in Figures 8.8 to 8.11.


159

Figure 8.8: Polar plot of acceleration (OBV) measured data of EO15 for cases: (a) healthy

blades, (b) blade root looseness, (c) crack on one blade and (d) cracks on two blades


four cases of blade health conditions using OBV data

Case Healthy

blades (a)

Blade looseness

(b)

Crack on one

blade (c)

Cracks on two

blades (d)

EO15 13L

(3L+1C13)

15L

(9L+1C6)

16L

(3L+1C13)

16L

(4L+1C12)

0.0002

0.0004

0.0006

30

210

60

240

90

270

120

300

150

330

180 0

0.0002

0.0004

0.0006

30

210

60

240

90

270

120

300

150

330

180 0

0.0001

0.0002

0.0003

0.0004

0.0005

30

210

60

240

90

270

120

300

150

330

180 0

0.0005

0.001

0.0015

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (d)

(b)


160

Figure 8.9: Polar plot of acceleration (OBV) measured data of EO5+EO10 for cases: (a)

healthy blades, (b) blade root looseness, (c) crack on one blade and (d) cracks on two blades

Table 8-7: The numbers of single leaves and coupled leaves in the polar plot of a combination

of EO5+EO10 for the four cases of blade health conditions using OBV data

Case Healthy

blades (a)

Blade looseness

(b)

Crack on one

blade (c)

Cracks on two

blades (d)

EO5+EO10 9L

(1C2+1C7)

10L

(5C2)

15L

(1C3+1C12)

10L

(5C2)


0.0002

0.0004

0.0006

0.0008

0.001

30

210

60

240

90

270

120

300

150

330

180 0

0.0005

0.001

0.0015

0.002

30

210

60

240

90

270

120

300

150

330

180 0

0.0005

0.001

0.0015

30

210

60

240

90

270

120

300

150

330

180 0

0.0005

0.001

0.0015

0.002

0.0025

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (d)

(b)


161

Figure 8.10: Polar plot of acceleration (OBV) measured data of EO5+EO10+EO15 for cases:

(a) healthy blades, (b) blade root looseness, (c) crack on one blade and (d) cracks on two blades


EO5+EO10+EO15 for the four cases of blade health conditions using OBV data

Case Healthy

blades (a)

Blade looseness

(b)

Crack on one blade

(c)

Cracks on two

blades (d)

EO5+EO10 12L

(1C12)

14L

(1C2+4C3)

14L

(1L+1C2+2C3+1C5)

13L

(2C2+3C3)

0.0005

0.001

0.0015

30

210

60

240

90

270

120

300

150

330

180 0

0.0005

0.001

0.0015

30

210

60

240

90

270

120

300

150

330

180 0

0.0002

0.0004

0.0006

0.0008

0.001

30

210

60

240

90

270

120

300

150

330

180 0

0.001

0.002

0.003

30

210

60

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150

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180 0

(a)

(c) (d)

(b)


162


healthy blades, (b) blade root looseness, (c) crack on one blade and (d) cracks on two blades


EO10+EO20 for the four cases of blade health conditions using OBV data

Case Healthy

blades (a)

Blade looseness

(b)

Crack on one

blade (c)

Cracks on two

blades (d)

EO10+EO20 15L

(3C2+1C9)

20L

(6C2+1C8)

20L

(6C2+1C3+1C5)

20L

(3C3+1C14)

0.0005

0.001

0.0015

30

210

60

240

90

270

120

300

150

330

180 0

0.0005

0.001

0.0015

30

210

60

240

90

270

120

300

150

330

180 0

0.0005

0.001

0.0015

30

210

60

240

90

270

120

300

150

330

180 0

0.0005

0.001

0.0015

0.002

0.0025

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (d)

(b)


163

8.4.4 On-bearing data observations and discussion

The polar plot presentation method for long‎ blades’‎ acceleration‎ response behaviour

during machine run-up is shown in Figures 8.8 to 8.11 for the four cases of blade health

conditions. The blade response using the P3 method for EO15 shows the number of

leaves changed from 13 leaves for the healthy case (a) to 15 leaves for the case of blade

root looseness (b), and to 16 leaves in the cases of cracked blades (c) and (d), with

different numbers of coupled leaves for all four cases, as shown in Figure 8.8 and Table

8.6. Upon combination between different EOs (EO5+EO10), (EO5+EO10+EO15) and

(EO10+EO20), as shown in Figures 8.9-8.11 and the related Tables 8.7-8.9 respectively,

it can be observed that the number of leaves increased in all three cases of faulty blade

conditions (cases (b), (c) and (d)) compared to healthy conditions (case (a)), and the

shapes of separate leaves and coupled leaves, along with the number of coupled leaves

in the profiles, are different compared to the case of healthy blade conditions. Hence,

from the results of the four cases of blade health conditions, it can be observed that the

P3 method gave a good indication for the diagnosis of blade health conditions and

provided a useful visual means when used to analyse on-bearing vibration data response

to discover different blade faults. The visual features include changes in the shape and

number of separate leaves, changes in the shape and number of coupled leaves, and the

number of leaves in each coupling during machine run-up.

8.5 Polar plot presentation (P3) for short blades

The region of blades natural frequency for short blades was determined at different EOs

using a band-pass filter using MATLAB software. This region was found for short

blades at EO10 to be within the range between 220 Hz and 260 Hz, and in the same

way, its higher harmonics (EO20, EO30, EO40‎…) were also determined. Polar plot

was applied using polar coordinates, angle and signal amplitude, at 2 means from the

top peak of the engine order signal related to first blade resonance frequency (1xBR), in

order to avoid any noise at the root of the signal and to improve the accuracy of the

results. Subsequently, FFT was computed at different engine orders and TSA was

performed for each signal sample in the time domain when the tachometer signal was

triggered, to avoid all non-synchronous parts of the signal in the spectrum. Finally, the

polar plot was applied to the data using single EO and combinations of different EOs to


164

compare the blades’ behaviour in different blade health cases of: (a) healthy blades, (b)

a crack on one blade, and (c) cracks on two blades. The data were extracted from the

rotating blades during machine run-up by using the data of the encoder for torsional

vibration based on IAS signals and accelerometers for OBV and OCV.

8.5.1 Encoder data

The polar plot presentation method was conducted on encoder torsional vibration based

on IAS signals in order to compare the blades’ dynamic behaviour in three cases of

blade health conditions: (a) healthy, (b) a crack on one blade, and (c) cracks on two

blades, using different EOs and combinations of EOs, as shown in Figures 8.12-8.15.


165

Figure 8.12: Polar plot of IAS measured data of EO10 for cases: (a) healthy blades, (b) crack

on one blade and (c) cracks on two blades


three cases of blade health conditions using IAS data

Case Healthy

blades (a)

Crack on one

blade (b)

Cracks on two

blades (c)

EO10 10L

(10L)

10L

(2L+1C8)

10L

(1L+1C9)

0.05

0.1

0.15

30

210

60

240

90

270

120

300

150

330

180 0

0.05

0.1

0.15

30

210

60

240

90

270

120

300

150

330

180 0

0.02

0.04

0.06

0.08

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


166

Figure 8.13: Polar plot of IAS measured data of EO20 for cases: (a) healthy blades, (b) crack

on one blade and (c) cracks on two blades


three cases of blade health conditions using IAS data

Case Healthy

blades (a)

Crack on one

blade (b)

Cracks on two

blades (c)

EO20 21L

(7L+1C14)

20L

(7L+1C5+1C8)

19L

(2L+1C17)

0.05

0.1

0.15

30

210

60

240

90

270

120

300

150

330

180 0

0.05

0.1

0.15

0.2

30

210

60

240

90

270

120

300

150

330

180 0

0.05

0.1

0.15

0.2

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


167

Figure 8.14: Polar plot of IAS measured data of EO10 + EO20 for cases: (a) healthy blades, (b)

crack on one blade and (c) cracks on two blades

Table 8-12: The numbers of single leaves and coupled leaves in the polar plot of combination

of EO10+E20 for the three cases of blade health conditions using IAS data

Case Healthy

blades (a)

Crack on one

blade (b)

Cracks on two

blades (c)

EO10+EO20 19L

(4C2+1C11)

20L

(1C20)

20L

(1C2+1C18)

0.05

0.1

0.15

0.2

0.25

30

210

60

240

90

270

120

300

150

330

180 0

0.1

0.2

0.3

30

210

60

240

90

270

120

300

150

330

180 0

0.05

0.1

0.15

0.2

0.25

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


168

Figure 8.15: Polar plot of IAS measured data of EO10+EO30 for cases: (a) healthy blades, (b)

crack on one blade and (c) cracks on two blades


of EO10+E30 for the three cases of blade health conditions using IAS data

Case Healthy

blades (a)

Crack on one

blade (b)

Cracks on two

blades (c)

EO10+EO30 27L

(3C3+1C18)

29L

(1C3+1C26)

30L

(1L+1C9+1C20)

0.05

0.1

0.15

0.2

0.25

30

210

60

240

90

270

120

300

150

330

180 0

0.1

0.2

0.3

0.4

30

210

60

240

90

270

120

300

150

330

180 0

0.05

0.1

0.15

0.2

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


169

8.5.2 Encoder data observations and discussion

It is observed from the P3 presentation for the encoder data of shaft torsional vibration

based on IAS response signals for short blades, as shown in Figures 8.12-8.15 for three

cases of blade health conditions, that the number of leaves is the same for the three

cases of blade conditions at EO10, however the shape and number of combined leaves

are different in faulty blade cases (b) and (c) compared to the healthy blade case (a),

which featured very regular shapes as shown in Figure 8.12 and Table 8.10. Also, the

second‎blades’‎ resonance‎ frequency‎ at‎EO20 clearly shows that the number of leaves

changed from 21 with uniform shapes of leaves for the healthy case (a) to 20 and 19

leaves with irregular shapes for the faulty cases (b) and (c) respectively, as shown in

Figure 8.13 and Table 8.11. Upon combination between different EOs of (EO10+EO20)

and (EO10+EO30), as shown in Figures 8.14 and 8.15 respectively, it was observed that

the number of leaves in faulty blade conditions, cases (b) and (c), was higher compared

to the healthy case (a) for both combinations. In addition, the shape of the separate

leaves and coupled leaves and the number of coupled leaves changed compared to the

healthy blade case (a). Hence, from the results of the three cases of blade health

conditions, it can be observed that the P3 method is effective in detecting and

discovering blade health conditions under different blade faults when used to analyse

shaft torsional vibration based on IAS signals, and the changes in the numbers and

shapes of separate and coupled leaves, in addition to the number of leaves in each

coupling, can provide a good indication of blade health, and therefore this tool could be

useful in BHM.

8.5.3 On-bearing data analysis

The polar plot presentation method was used for analysis of short blades’ vibration

responses during machine run-up, which was obtained from the bearing pedestal using

an accelerometer in order to describe and compare the blades’ dynamic behaviour in

three cases of blade health conditions; (a) healthy, (b) a crack on one blade, and (c)

cracks on two blades, at different combinations of EOs, as shown in Figures 8.16-8.19.


170


healthy blades, (b) crack on one blade and (c) cracks on two blades


of EO10+E20 for the three cases of blade health conditions using OBV data

Case Healthy

blades (a)

Crack on one

blade (b)

Cracks on two

blades (c)

EO10+EO20 20L

(10C2)

20L

(1C20)

20L

(1C20)

0.02

0.04

0.06

0.08

30

210

60

240

90

270

120

300

150

330

180 0

0.02

0.04

0.06

30

210

60

240

90

270

120

300

150

330

180 0

0.01

0.02

0.03

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


171





Case Healthy blades

(a)

Crack on one blade

(b)


(c)

EO10+EO40 35L

(3C4+1C23)

40L

(1L+1C39)

40L

(3L+1C3+1C34)

0.02

0.04

0.06

0.08

0.1

30

210

60

240

90

270

120

300

150

330

180 0

0.02

0.04

0.06

0.08

30

210

60

240

90

270

120

300

150

330

180 0

0.01

0.02

0.03

0.04

0.05

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


172





Case Healthy blades

(a)

Crack on one blade

(b)


(c)

EO20+EO40 35L

(5L+15C2)

38L

(5C2+1C28)

40L

(6L+1C34)

0.02

0.04

0.06

0.08

30

210

60

240

90

270

120

300

150

330

180 0

0.02

0.04

0.06

30

210

60

240

90

270

120

300

150

330

180 0

0.01

0.02

0.03

0.04

0.05

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


173

Figure 8.19: Polar plot of acceleration (OBV) measured data of EO10+EO20+EO30 for cases:

(a) healthy blades, (b) crack on one blade and (c) cracks on two blades


of EO10+EO20+E30 for the three cases of blade health conditions using OBV data

Case Healthy blades

(a)

Crack on one blade

(b)


(c)

EO10+EO20+EO30 33L

(5L+10C3)

30L

(7C3+1C9)

30L

(1C30)

0.02

0.04

0.06

0.08

30

210

60

240

90

270

120

300

150

330

180 0

0.02

0.04

0.06

0.08

30

210

60

240

90

270

120

300

150

330

180 0

0.02

0.04

0.06

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


174

8.5.4 On-bearing data observations and discussion

Results observed from the polar plot presentation of data for short blades’ vibration

response during machine run-up in three cases of blade health conditions at

combinations of different EOs of (EO10+EO20), (EO10+EO40), (EO20+EO40) and

(EO10+EO20+EO30) are shown in Figures 8.16, 8.17, 8.18 and 8.19 respectively.

Results based on the combination EO10+EO20 show that in case (a) of healthy

conditions, the plot features a regular symmetrical distribution of 10 coupled leaves of 2

(C2); however in the faulty cases of one crack on one blade, case (b), and cracks on two

blades, case (c), the leaves are merged in one coupling of 20 leaves (C20) with different

shapes of leaves, but with the same total number of leaves (20) for the three cases, as

shown in Figure 8.16 and Table 8.14. Upon combination of (EO10+EO40), the number

of leaves changed from 35 in the healthy case (a) to 40 leaves for the cracked blade

cases (b) and (c), with different profile shapes and different numbers of coupled leaves

compared to case (a) of healthy conditions, as shown in Figure 8.17 and Table 8.15.

Likewise, for the combination of (EO20+EO40), the number of leaves changed from 35

in the healthy case (a) to 38 and 40 leaves in the case of one crack on one blade (b) and

the case of cracks on two blades (c), respectively, with different profile shapes and

different numbers of coupled leaves compared to case (a) of healthy blade conditions,

which featured leaves distributed regularly as couples of 2 (C2), as opposed to the plots

for the faulty blade cases that showed irregular distributions of large leaf couplings of

(C28) and (C34), as shown in Figure 8.18 and Table 8.16. Again, for the combination of

(EO10+EO20+EO30), the number of leaves changed from 33 for the healthy blade case

(a) to 30 leaves for the faulty blade cases (b) and (c), also with very different profile

shapes and numbers of coupled leaves compared to case (a) of healthy condition.

Leaves were distributed in regular couplings of 3 leaves (C3) in case (a), whereas for

faulty blade cases, leaves were distributed irregularly as one coupling of nine leaves

(C9) and 7 couples of 3 leaves (C3) in the case of one crack on one blade, and one

coupling of 30 leaves (C30) in the case of two cracked blades, as shown in Figure 8.19

and Table 8.17.


175

Hence, from the results of the three cases of blade health conditions, it can be suggested

that the P3 method is able to detect blade conditions when used for analysis of OBV

data under different blade faults. Changes in the shape and number of individual leaves

and coupled leaves and also in the number of leaves in each coupling can give a good

induction of the blade health conditions and therefore can be a useful feature for BHM.

8.5.5 On-casing data analysis

The polar plot presentation (P3) method was used in this section to analyse short‎blades’‎

vibration response obtained from the casing towards the rotating blades during machine

run-up by using an accelerometer in order to describe and compare blades’ dynamic

behaviour under three cases of blade health conditions; (a) healthy blades, (b) a crack on

one blade, and (c) cracks on two blades at different individual and combined EOs, as

shown in Figures 8.20-8.25.


176

Figure 8.20: Polar plot of acceleration (OCV) measured data of EO30 for cases: (a) healthy

blades, (b) crack on one blade and (c) cracks on two blades


three cases of blade health conditions using OCV data

Case Healthy blades

(a)

Crack on one blade

(b)


(c)

EO30 30L

(30L)

30L

(11L+1C19)

30L

(15L+1C15)

0.005

0.01

0.015

30

210

60

240

90

270

120

300

150

330

180 0

0.01

0.02

0.03

30

210

60

240

90

270

120

300

150

330

180 0

0.005

0.01

0.015

0.02

0.025

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


177

Figure 8.21: Polar plot of acceleration (OCV) measured data of EO10+EO30 for cases: (a)



of EO10+E30 for the three cases of blade health conditions using OCV data

Case Healthy blades

(a)

Crack on one blade

(b)


(c)

EO10+EO30 30L

(10L+10C2)

30L

(3C3+1C21)

30L

(6C3+1C12)

0.01

0.02

0.03

30

210

60

240

90

270

120

300

150

330

180 0

0.01

0.02

0.03

0.04

0.05

30

210

60

240

90

270

120

300

150

330

180 0

0.01

0.02

0.03

0.04

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


178





Case Healthy blades

(a)

Crack on one blade

(b)


(c)

EO10+EO40 21L

(1C21)

32L

(5C4+1C12)

40L

(3C4+1C28)

0.01

0.02

0.03

30

210

60

240

90

270

120

300

150

330

180 0

0.01

0.02

0.03

0.04

30

210

60

240

90

270

120

300

150

330

180 0

0.005

0.01

0.015

0.02

0.025

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


179





Case Healthy blades

(a)

Crack on one blade

(b)


(c)

EO20+EO40 20L

(20L)

37L

(7C2+1C23)

37L

(6C2+1C25)

0.01

0.02

0.03

0.04

30

210

60

240

90

270

120

300

150

330

180 0

0.005

0.01

0.015

0.02

30

210

60

240

90

270

120

300

150

330

180 0

0.005

0.01

0.015

0.02

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


180

Figure 8.24: Polar plot of acceleration (OCV) measured data of EO20+EO30+EO40 for cases:



of EO20+EO30+E40 for the three cases of blade health conditions using OCV data

Case Healthy blades

(a)

Crack on one blade

(b)


(c)

EO20+EO30+EO40 22L

(11C2)

34L

(6C3+4C4)

30L

(1C30)

0.01

0.02

0.03

0.04

0.05

30

210

60

240

90

270

120

300

150

330

180 0

0.01

0.02

0.03

0.04

30

210

60

240

90

270

120

300

150

330

180 0

0.01

0.02

0.03

0.04

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


181

Figure 8.25: Polar plot of acceleration (OCV) measured data of EO10+EO20+EO40 for cases:



of EO10+EO20+E40 for the three cases of blade health conditions using OCV data

Case Healthy blades

(a)

Crack on one blade

(b)


(c)

EO10+EO20+EO40 20L

(1C20)

32L

(2C2+4C3+4C4)

32L

(1C32)

0.02

0.04

0.06

30

210

60

240

90

270

120

300

150

330

180 0

0.01

0.02

0.03

0.04

30

210

60

240

90

270

120

300

150

330

180 0

0.01

0.02

0.03

30

210

60

240

90

270

120

300

150

330

180 0

(a)

(c) (b)


182

8.5.6 On-casing data observations and discussion

The results were obtained using a P3 method by analysing‎short‎blades’‎vibration data

response during machine run-up, for the three different cases of blade health conditions

using individual and/or combinations of different EOs of (EO30), (EO10+EO30),

(EO10+EO40), (EO20+EO40), (EO20+EO30+EO40) and (EO10+EO20+EO40), as

shown in Figures 8.20, 8.21, 8.22, 8.23, 8.24 and 8.25, respectively. Results obtained at

engine order EO30 show that the number of leaves was the same for the three cases of

blade conditions: (a) healthy blades, (b) one crack on one blade, and (c) cracks on two

blades; however the shape of the leaves and the couplings between them were different

between the three cases. In the faulty blade cases, there were merged leaves in couplings

of 19 leaves (C19) and 15 leaves (C15) for cases (b) and (c), respectively, along with a

number of separate leaves. In the healthy blades case (a), the plot featured a regular set

of 30 single leaves without any couples, as shown in Figure 8.20 and Table 8.18. In the

combination EO10+EO30, all leaves in the healthy conditions case (a) were distributed

in coupled sets of 2 leaves (C2) in a regular distribution of a total of 10 couples spaced

by 10 further small single leaves. However, in the faulty cases featuring one crack on

one blade (case (b)) and cracks on two blades (case (c)), a number of leaves were

merged in coupled sets of 21 leaves (C21) and 12 leaves (C12) for cases (b) and (c)

respectively, with different shapes of leaves. The same total number of leaves for the

three cases was observed (30 leaves), as shown in Figure 8.21 and Table 8.19. In the

combination of (EO10+EO40), the number of leaves changed from 21 leaves for the

healthy case (a) to 32 leaves for the cracked blade case (b) and 40 leaves for the cracked

blade case (c), with different shapes and numbers of coupled leaves compared to case

(a) of healthy conditions, as shown in Figure 8.22 and Table 8.20. Likewise, in the

combination of (EO20+EO40), the number of leaves changed from 20 leaves for the

healthy case (a) to 37 leaves for the two faulty blade cases (b) and (c), with different and

irregular profile shapes and different numbers of coupled leaves compared to case (a) of

healthy conditions, which featured individual leaves distributed in a very regular

arrangement, as shown in Figure 8.23 and Table 8.21. Finally, in the two remaining

combinations of (EO20+EO30+EO40) and (EO10+EO20+EO40), the number of leaves

also changed from 22 and 20 leaves respectively in the healthy blade case (a), to 30 or

more leaves for the faulty blade cases (b) and (c) in the two combinations, showing a


183

regular shape of leaves in the healthy case (a) and different irregular profile shapes of

leaves and different numbers of coupled leaves for the faulty blade cases (b) and (c), as

shown in Figures 8.24 and 8.25 and Tables 8.22 and 8.23 respectively for the two

combinations.

Hence, from the results of three cases of blade health conditions, it can be suggested

that the P3 method is able to detect blade conditions when used to analyse on-casing

vibration data under different blade fault conditions, based on changes in the shape and

number of individual and coupled leaves and the number of leaves in each coupling,

which provides a good indication of the blade health conditions and therefore, this tool

can be useful as a feature of BHM.

8.6 Summary

In this chapter, a novel signal processing application based on a P3 method has been

described and applied to the analysis of measured vibration data for long and short

blades using three different measurements: shaft torsional vibration based on IAS

signals, OBV and OCV during machine run-up operation. This method was applied in

order‎ to‎ diagnose‎ rotating‎ blades’‎ health‎ conditions‎ with‎ and‎ without‎ faults.‎ The‎

experiments were conducted for three different blade health conditions: healthy blades

with mistuned effects, blade root looseness and cracks on blades. The data were

analysed using the novel signal processing technique P3 at different engine orders

related‎to‎the‎blades’‎resonance‎frequency‎and‎also‎at‎different‎combinations‎of‎engine‎

orders in order to describe and detect blade health conditions under different blade

faults. From the results, it was observed that the P3 is useful for the diagnosis of blade

condition. The differences in the shape and number of separate and coupled leaves and

the differences in the number of leaves in each coupling between healthy and faulty

blade cases are features that provide a good indication for detecting blade faults. This

was observed based on all the data from the three measurements mentioned above.

Therefore, it is suggested that this novel application can be useful as a means of

diagnosis in the process of BHM.


184

CHAPTER 9

MATHEMATICAL MODEL

9.1 Introduction

A simple mathematical model was created for a shaft-disc-blades system in order to

derive the equations of motion for the system for a single degree of freedom (SDOF)

representing the 8 blades rotor disc. A rotor of 8 blades was created to understand the

dynamic behaviour of healthy and cracked blades in transient motion using a simplified

method. This chapter provides further understanding of blades dynamics observed in the

experiments presented in Chapters 4, 5, 6 and 8.

9.2 Simple mathematical model

The model of the 8-blades rotor is shown in Figure 9.1. It represents the parameters

including the mass of the rotor, mr, supported by the shaft that has stiffness, kr, and the

damping, c, is considered with 8 blades to understand the experimental behaviour of the

system. The rotor is initially modelled as a SDOF system connected with 8 SDOF

systems representing the 8 blades of masses (mb1, mb2, …..‎mb8), stiffness values (kb1,

kb2,….‎kb8) and damping values (cb1, cb2,….‎cb8). The values of the rotor parameters and

the blade masses [Mb], corresponding stiffness [Kb] and damping [Cb] are chosen such

that the model gives natural frequencies of long blades close to the experimental values.

Table 9.1 provides the values of the parameters used in the model. The natural

frequencies of the rotor are computed to be 97.22 Hz and 118.15 Hz to 131.66 Hz for

the blades with mistuned effects, which are very close to the experimental values. The

damping in the mathematical model is assumed to be 0.1% and 0.5% for the rotor and

blades, respectively. The rotor is rotating with angular velocity‎ (ω).‎ The‎ unbalanced‎

responses for the rotor are then calculated during the run-up speed from 600 rpm (10Hz)

to 1800 rpm (30Hz) for 30 seconds for the following two cases:

1- Healthy but mistuned blade conditions in frequency band of 118.15 Hz to131.66 Hz.

2- 10% crack on Blade 2 on the bladed disc.


185

Table 9-1: Rotor/ blade parameters used in the mathematical model

Rotor

Rotor

Mass (mr) Stiffness (Kr) Damping ratio (Cr)

50.00 2.1544 x107 1.0000 x10

-3

Blades

Blade no. Blade mass, (mb) Blade Stiffness (kb)

1 1.00 6.2147 x105

2 1.00 6.5630 x105

3 1.00 5.4632 x105

4 1.00 6.3019 x105

5 1.00 6.1559 x105

6 1.00 5.7188 x105

7 1.00 5.9537 x105

8 1.00 6.1623 x105

Figure 9.1: Simplified rotor model with 8 blades

9.3 Crack simulation

The crack on Blade 2 is simulated a breathing of the 10% of blade width, while the

response is estimated by assuming the change in Blade 2 stiffness when the

displacement in the blade is positive (open crack) using the equation:


186

kkk 2b …………………………‎(9.1)

and when the displacement in the blade is zero (normal position) or the displacement in

the blade is negative (closed crack), the following equation is used:

kk 2b …………………………‎(9.2)

where k is the initial value of blade stiffness and the change in the stiffness, k10.0k

for 10% crack on Blade 2.

9.4 Equation of motion

By‎applying‎Newton’s‎ second‎ law‎of‎motion‎ (m‎ .‎a‎=‎F),‎ the‎equations‎of‎ translation

motion for the system are obtained from the summation of forces using the free force

diagram as illustrated in Figure 9.2, which can easily determine the summation of forces

for the system (m = mass, a = acceleration and F = Force).

9.4.1 Shaft forces components

The bounce of forces for the shaft is determined from the free body diagram as shown in

Figure 9.2, and is given by:

mr xr = ∑ Fi8i=1 …………………….‎(9.3)

mr xr = ∑ [kbi(xbi − xr) + cbi(xbi − xr)]8i=1 −

kr

2 xr −

kr

2 xr − c xr ……….‎(9.4)


187

Figure 9.2: Free body diagram for rotor forces

The parameters above are defined as:

mb1 - mb8: mass of blades 1-8

kb1 - kb8: stiffness of blades 1-8

cb1 - cb8: damping of blades 1-8

xb1 - xb8: acceleration of blades 1-8

xb1 -xb8: velocity of blades 1-8

xb1 -xb8: displacement of blades 1-8

mr: rotor mass

kr: rotor stiffness

cr: rotor damping

xr : rotor acceleration

xr : rotor velocity

xr : rotor displacement


188

9.4.2 Blades forces components

The equations of motion of the rotor with 8 blades are determined from the free body

diagram as shown in Figure 9.2 and are given by force equations:

mb xbi = ∑ Fi8𝑖=1 …………………….‎(9.5)

where, (i‎=‎1,‎2,‎……….,‎8)

9.4.3 The unbalancing disc force components

The unbalancing forces in rotating machines are the main factors causing vibration. The

rotor response due to mass imbalance excitation and the unbalanced forces equations

can be written as follows, as shown in Figure 9.3.

𝐹 = 𝑚 r 𝜔2 …………………….‎(9.6)

𝐹𝑢𝑛𝑏 = mu r𝜔2 ∗ sin(𝜔t + 30) …………………….‎(9.7)

mr xr + 𝐹𝑢𝑛𝑏 = mu r𝜔2 ∗ sin(𝜔t + 30) …………………….‎(9.8)

In this model, r = 0.02 m and unbalanced mass (mu =0.01 kg) are chosen.

where:

mr : rotor mass (kg)

mu : unbalancing mass (kg)

r : radius (m)

𝜔 : angular velocity (RPS)

Funb : unbalanced force (N)

and‎the‎system’s‎natural‎frequency‎in‎rps‎can‎be‎determined‎using‎the‎equation:

𝜔 = √𝐾

𝑚 …………………….‎(9.9)


189

Figure 9.3: Free body diagram of unbalanced mass disc forces in x-y plane

9.5 Dynamic equations of the mathematical model

The dynamic equations of the model including unbalanced disc forces can be solved

using matrices. The number of equations of transient motion for the system is 9,

including rotor motion in Equation 9.4, blades motion in Equation 9.5 and unbalancing

force in Equation 9.7.

The general equation of motion for the system using the matrix system can be derived

by:

[𝑀 ]. {��} + [𝐶 ]. {��} + [𝐾 ]. {𝑋} = {𝐹𝑢𝑛𝑏} …………………….‎(9.10)

Where:

{��} : The acceleration vector

{��} : The velocity vector

{𝑋} : The displacement vector

{𝐹𝑢𝑛𝑏} : The unbalanced force vector

[M] : The mass matrix

[C] : The damping matrix

[K] : The stiffness matrix

Funb= mu r 2

Rotating disc

mu


190

The modal analysis of the rotor with 8-bladed disc are calculated using MATLAB

software by solving the equation of modal analysis using the matrix equation 9.11 to

identified the mode shapes and natural frequencies.

[[𝐾] − 𝜔𝑛2 [𝑀] ]. {𝜃} = 0 …………………….‎(9.11)

where:

[M]: mass matrix

[K]: Stiffness matrix

{𝜃}: is the mode shapes matrix, 𝜔𝑛 is the nth angular natural frequency, 2𝜋𝑓𝑛, where 𝑓𝑛

is the nth natural frequency

The natural frequencies of blades and shaft are obtained using the mathematical model

analysis and are listed in Table 9.2.

Table 9-2: First mode shape frequencies for blades and shaft obtained using the mathematical

model

Blade No. Natural frequency (Hz) Blade No. Natural frequency (Hz)

1 118.15 5 125.88

2 119.83 6 128.05

3 122.33 7 130.29

4 124.17 8 131.66

Shaft Natural Frequency (Hz) 97.25

The modal analysis results were observed to be close to the experimental results

obtained using frequency response function (FRF), experimental test as listed in Table

3.8.

9.5.1 Derivation of the matrices system

The equations of motion of the rotor with eight blades model of SDOF with 9 equations

of motion can be established when the contribution from rotation degrees of freedom is

included in the mass, stiffness and damping matrices using Equations 9.4, 9.5 and 9.7,

which can be used to derive the matrices system of the model and then solved by

MATLAB.


191

The mass matrix for the system is derived as:

[𝑀]=

[ 𝑚𝑏1

00000000

0𝑚𝑏2

0000000

00𝑚𝑏3

000000

000𝑚𝑏4

00000

0000𝑚𝑏5

0000

00000𝑚𝑏6

000

000000𝑚𝑏7

00

0000000𝑚𝑏8

0

00000000𝑚𝑟]

…………………….‎(9.12)


192

And the stiffness matrix is derived as:

[𝐾] =

[ 𝑘𝑏10000000

−𝑘𝑏1

0𝑘𝑏2000000

−𝑘𝑏2

00𝑘𝑏300000

−𝑘𝑏3

000𝑘𝑏40000

−𝑘𝑏4

0000𝑘𝑏5000

−𝑘𝑏5

00000𝑘𝑏600

−𝑘𝑏6

000000𝑘𝑏70

−𝑘𝑏7

0000000𝑘𝑏8 −𝑘𝑏8

−𝑘𝑏1−𝑘𝑏2−𝑘𝑏3−𝑘𝑏4−𝑘𝑏5−𝑘𝑏6−𝑘𝑏7−𝑘𝑏8

(𝑘𝑏1 + 𝑘𝑏2 + 𝑘𝑏3 + 𝑘𝑏4 + 𝑘𝑏5 + 𝑘𝑏6 + 𝑘𝑏7 + 𝑘𝑏8 − 𝑘𝑟)]

…………….....….‎(9.13)

The derivation of damping matrix is as follows:

[𝐶] =

[ 𝑐𝑏10000000

−𝑐𝑏1

0𝑐𝑏2000000

−𝑐𝑏2

00𝑐𝑏300000

−𝑐𝑏3

000𝑐𝑏40000

−𝑐𝑏4

0000𝑐𝑏5000

−𝑐𝑏5

00000𝑐𝑏600

−𝑐𝑏6

000000𝑐𝑏70

−𝑐𝑏7

0000000𝑐𝑏8 −𝑐𝑏8

−𝑐𝑏1−𝑐𝑏2−𝑐𝑏3−𝑐𝑏4−𝑐𝑏5−𝑐𝑏6−𝑐𝑏7−𝑐𝑏8

(𝑐𝑏1 + 𝑐𝑏2 + 𝑐𝑏3 + 𝑐𝑏4 + 𝑐𝑏5 + 𝑐𝑏6 + 𝑐𝑏7 + 𝑐𝑏8 − 𝑐𝑟)]

…………………...……. (9.14)

The vectors of acceleration, velocity, displacement and force are derived as:


193

Acceleration Vector {��} =

{

��𝑏1��𝑏2��𝑏3��𝑏4��𝑏5��𝑏6��𝑏7��𝑏8��𝑟 }

…………………….‎(9.15)

Velocity Vector {��} =

{

��𝑏1��𝑏2��𝑏3��𝑏4��𝑏5��𝑏6��𝑏7��𝑏8��𝑟 }

…………………….‎(9.16)

Displacement Vector {𝑋} =

{

𝑥𝑏1𝑥𝑏2𝑥𝑏3𝑥𝑏4𝑥𝑏5𝑥𝑏6𝑥𝑏7𝑥𝑏8𝑥𝑟 }

…………………….‎(9.17)

And the unbalanced disc force vector is

{𝐹𝑢𝑛𝑏} =

{

00000000

mu 𝜔2 r ∗ sin(𝜔t + 30)}

………….‎(9.18)


194

The equation of motion for the unbalancing disc of transient motion of the rotor can be

derived using Equation 9.10; by substituting Equations 9.4, 9.5 and 9.7 into Equation

9.10, the general equation of motion for the model can be obtained as shown in

Equation 9.19


195

[ 𝑚𝑏1

00000000

0𝑚𝑏2

0000000

00𝑚𝑏3

000000

000𝑚𝑏4

00000

0000𝑚𝑏5

0000

00000𝑚𝑏6

000

000000𝑚𝑏7

00

0000000𝑚𝑏8

0

00000000𝑚𝑟]

.

{

��𝑏1��𝑏2��𝑏3��𝑏4��𝑏5��𝑏6��𝑏7��𝑏8��𝑟 }

+

[ 𝑐𝑏10000000

−𝑐𝑏1

0𝑐𝑏2000000

−𝑐𝑏2

00𝑐𝑏300000

−𝑐𝑏3

000𝑐𝑏40000

−𝑐𝑏4

0000𝑐𝑏5000

−𝑐𝑏5

00000𝑐𝑏600

−𝑐𝑏6

000000𝑐𝑏70

−𝑐𝑏7

0000000𝑐𝑏8 −𝑐𝑏8

−𝑐𝑏1−𝑐𝑏2−𝑐𝑏3−𝑐𝑏4−𝑐𝑏5−𝑐𝑏6−𝑐𝑏7−𝑐𝑏8

(𝑐𝑏1 + 𝑐𝑏2 + 𝑐𝑏3 + 𝑐𝑏4 + 𝑐𝑏5 + 𝑐𝑏6 + 𝑐𝑏7 + 𝑐𝑏8 − 𝑐𝑟)]

.

{

��𝑏1��𝑏2��𝑏3��𝑏4��𝑏5��𝑏6��𝑏7��𝑏8��𝑟 }

+


196

[ 𝑘𝑏10000000

−𝑘𝑏1

0𝑘𝑏2000000

−𝑘𝑏2

00𝑘𝑏300000

−𝑘𝑏3

000𝑘𝑏40000

−𝑘𝑏4

0000𝑘𝑏5000

−𝑘𝑏5

00000𝑘𝑏600

−𝑘𝑏6

000000𝑘𝑏70

−𝑘𝑏7

0000000𝑘𝑏8 −𝑘𝑏8

−𝑘𝑏1−𝑘𝑏2−𝑘𝑏3−𝑘𝑏4−𝑘𝑏5−𝑘𝑏6−𝑘𝑏7−𝑘𝑏8

(𝑘𝑏1 + 𝑘𝑏2 + 𝑘𝑏3 + 𝑘𝑏4 + 𝑘𝑏5 + 𝑘𝑏6 + 𝑘𝑏7 + 𝑘𝑏8 − 𝑘𝑟)]

.

{

𝑥𝑏1𝑥𝑏2𝑥𝑏3𝑥𝑏4𝑥𝑏5𝑥𝑏6𝑥𝑏7𝑥𝑏8𝑥𝑟 }

=

{

00000000

mu 𝜔2 r ∗ sin(𝜔t + 30)}

…………………….‎(9.19)


197

9.6 Results and observations

The run-up acceleration responses of the long blades using MATLAB software have

been calculated using Equation 9.19. The typical acceleration signal of healthy and

cracked blade responses is shown in Figure 9.4 (a) and (b). A contour plot is then

generated in order to discover blade resonance (BR) in the frequency regions for both

cases of healthy and cracked blade. The results that showed a big significant difference

in BR regions between the cases of healthy blades compared to cracked blades for both

blade resonances of 1xBR and 2xBR, as shown in Figures 9.5 and 9.6 respectively.

Responses were then order tracked at EO5, which is used to obtain the vibration

response of the rotor, as shown in Figure 9.7 (a) and (b). The results showed the

presence of a peak around 97 Hz in Figure 9.7, indicating the critical speed of the rotor.

It is also evident from Figure 9.7 (a) that the healthy blade case gives a banded peak in

the BR region; however, two distinct peaks can be seen for the cracked blade case, as

shown in Figure 9.7 (b). Hence, this simple analysis of the mathematical model supports

and verifies the experimental observations related to blade damage detection. Therefore,

the presence of distinct multiple peaks in the BR region for cracked blades instead of

one distinct peak for healthy blades can be considered a useful feature to identify blade

fault (s).


198

Figure 9.4: Typical acceleration run-up responses signal, (a) Healthy blades, (b) Crack on

Blade

0 5 10 15 20 25 30-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Time (sec)

Accele

ra

tio

n (

m/s

2)

0 5 10 15 20 25 30-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Time (sec)

Am

pli

tud

e, A

ccele

ra

tio

n (

m/s

2)

(a)

(b)


199

Figure 9.5: Typical contour plot of BR frequency (1xBR), (a) Healthy blades, (b) Crack on

Blade

Frequency (Hz)

Tim

e (

sec)

100 120 140 160 180

2

4

6

8

10

12

14

16

18

10

20

30

40

50

60

70

80

Frequency (Hz)

Tim

e (

sec)

100 120 140 160 180

2

4

6

8

10

12

14

16

18

10

20

30

40

50

60

70

80

(b)

(a)


200

Figure 9.6: Typical contour plot of BR frequency (2xBR), (a) Healthy blades, (b) Crack on

Blade

Frequency (Hz)

Tim

e (s

ec)

200 220 240 260 280

2

4

6

8

10

12

14

16

18

5

10

15

20

25

30

35

40

Frequency (Hz)

Tim

e (

sec)

200 220 240 260 280

2

4

6

8

10

12

14

16

18

5

10

15

20

25

30

35

40(b)

(a)


201

Figure 9.7: Typical estimated acceleration responses at EO5, (a) Healthy blades, (b) Crack on

Blade 2

9.7 Summary

A simple mathematical model of a rotor with 8-blade configuration is presented in this

chapter.‎ The‎ equations‎ of‎ transient‎motion‎ of‎ the‎ rotor‎were‎ derived‎ using‎Newton’s‎


202

second law of motion for the rotor and blades, including the unbalanced force of the

rotating disc. The modal analysis for the rotor was computed, and the natural

frequencies for the 8 blades and shaft identified. Nine equations of motion of SDOF

were solved using MATLAB, whereby the dynamic acceleration responses of the model

for healthy and cracked blades were extracted. The results of simple analysis of the

mathematical model verified and supported the experimental observations.


203

CHAPTER 10

CONCLUSIONS AND FUTURE WORK

10.1 Overview

Rotating blades are considered to be one of the most common cause of failures in

rotating machinery. The blade failure modes normally occur as a result of cracking, high

cycle fatigue (HCF), blade rubbing, blade root looseness, and degradation from erosion

and corrosion. Early fault detection is therefore necessary to reduce blade related

failures and hence there is a need for a reliable, indirect and simple measurement

method to be used for blade health monitoring (BHM). There are some measurements

that have recently been used for BHM, such as blade tip timing (BTT) and measurement

of strain on the blades during machine operation. However, both BTT and strain

measurement methods are intrusive and expensive. Consequently, there is an imperative

need for a reliable and simple but robust method to meet the requirements of BHM.

For these reasons, this study attempted to demonstrate that vibration measurements such

as shaft torsional vibrations based on instantaneous angular speed (IAS), on-bearing

vibrations (OBV) and on-casing vibrations (OCV) could detect changes in blade(s)

dynamic behaviour due to blade(s) fault conditions and could be useful for BHM. In this

study, extensive experiments were performed on a small test rig having a rotor with a

single stage bladed disc holding 8-blades during machine run-up, in addition to a

mathematical model which was also developed in order to describe blade(s) behaviour.

The results show that the mathematical model supports the experimental work in

detecting and diagnosing blade health conditions and determining blade faults due to

mistuned effects, blade root looseness and blade cracks. All measurement methods can

be considered useful for BHM. Engine order tracking (EOT) method was shown to be

useful for blade fault detection during the machine run-up. In addition, a polar plot

presentation related to blade order angle and amplitude of vibration signal showed the

changes in vibration response of blade(s) behaviour, and was a practically useful

technique to detect blade faults.


204

10.2 Review of project objectives, achievements and contributions

The main achievements and of this research work and its contributions to knowledge are

described and presented below with matched objectives of this project study as

presented in Section 1.3.

Objective 1

To design and manufacture a test rig suitable for simulating rotating machine blades and

detecting blade faults due to vibration problems arising from mistuned blades, blade

root looseness and blade cracks using vibration condition monitoring.

Achievement and contribution 1

The required small test rig was designed and manufactured with dimensions in

accordance with a finite element model (FEM) analysis results. The rig was designed to

simulate rotating machine blades in steam or gas turbines in order to be used for detect

blade(s) faults of mistuned blades, blade root looseness and cracks in blade(s). The rig

was designed to allow measurements and to be equipped with a speed controller for

operation at different speeds. Furthermore, a simulation of blade faults, such as blade

looseness and blade cracks, was done for different experiments.

Objective 2

To apply the following measurements during machine running-up and/or running-down

operation in order to examine blade vibration fault detection:

- Torsion vibration on shaft using incremental shaft encoder.

- Measurements of on bearing pedestal vibrations using accelerometers.

- Measurements of on casing vibrations using accelerometers.


The three measurements of the shaft torsional vibration based on IAS, OBV and OCV

were applied on the test rig in order to discover blade(s) dynamic behaviour during

machine run-up operation to be used for BHM.


205

Objective 3

To investigate blade vibration behaviour with these faults: blade mistuning effects,

blade root looseness and cracked blades, using the three measurements stated in

Objective 2.


(1) The‎ results‎ obtained‎ from‎ OBV‎ signals‎ provided‎ a‎ good‎ indication‎ for‎ long‎

blades‎in‎cases‎of‎blade‎root‎looseness‎and‎cracked‎blade(s),‎and‎also‎provided‎

some‎good‎indication‎for‎short‎blades‎only‎in‎the‎case‎of‎more‎than‎one‎cracked‎

blade‎in‎ the‎bladed‎disc. This was apparent in the presence of distinct multiple

peaks in the blade resonance (BR) region in the case of damaged blades instead

of a single peak in the BR region in the case of healthy blade(s).

(2) The‎results‎obtained‎from‎OCV‎signals‎ for‎short‎blades‎showed‎no changes in

the BR region in the case of cracked blades compared with blades in healthy

conditions. The results showed only one distinct peak of BR for all cases,

healthy and faulty.

(3) The‎ results‎ of‎ IAS‎ signals‎ provided‎ a‎ good‎ indication‎ to‎ detect‎ blade‎ health‎

conditions‎for‎both‎long‎and‎short‎blades.‎This‎was‎observed‎as‎a‎single‎banded‎

peak‎in‎the‎BR‎region‎in‎the‎case‎of‎healthy‎blades‎compared‎to‎more‎peaks‎in‎

the‎BR‎region‎in‎the‎cases‎of‎blade‎damage‎conditions.

Objective 4

To compare and analyse the results obtained using the proposed three measurements

and to investigate which measurement is most useful to detect and diagnose blade

health conditions.


(1) OCV‎could‎not‎be‎found‎to‎be‎a‎good‎measurement for‎BHM‎for‎the‎rig‎but‎it‎

may‎be‎useful‎for‎rotating‎machines‎in‎plants.‎This‎was‎because‎the‎OCV‎gave‎

greatly‎ amplified‎ BR‎ for‎ the‎ laboratory‎ rig‎ and‎ the‎ casing‎ in‎ the‎ rig‎ was‎ not‎

designed‎properly.‎

(2) OBV‎ provided‎ a‎ good‎ indication‎ to‎ detect‎ long‎ blades’‎ faults.‎ However,‎ the‎

results‎for‎short‎blades‎only‎provided‎some‎good‎indication‎for‎fault‎detection‎in‎


206

the‎cases‎when‎more‎than‎one‎blade‎was‎cracked‎in‎the‎bladed‎disc.‎Hence,‎the‎

presence‎ of‎ distinct‎ multiple‎ peaks‎ in‎ the‎ BR‎ region‎ can‎ be‎ considered‎ as‎ a‎

feature‎for‎BHM‎in‎these‎cases‎based‎on‎this‎measurement.‎

(3) IAS‎provided‎a‎good‎indication‎to‎detect‎blade‎health‎conditions‎for‎both‎short‎

and‎ long‎ blades.‎Hence,‎ the‎ presence‎ of‎ the‎ distinct‎multiple‎ peaks‎ in‎ the‎BR‎

region‎can‎be‎considered‎as‎a‎highly‎useful‎feature‎to‎be‎used‎for‎BHM.

Objective 5

To select the best measurement for monitoring purposes with a unique signal processing

method to identify blade mistuning effects, blade root looseness and cracked blades.


From‎ the‎comparative‎study‎described‎ in‎Chapter‎7,‎ the‎ results‎observed‎ indicate‎ that‎

the‎ shaft‎ IAS‎ signal‎ seems‎ to‎ provide‎much‎ better‎ indication‎ for‎ BHM‎ compared‎ to‎

OBV‎ and‎ OCV‎ measurements.‎ In‎ addition,‎ a‎ novel‎ and‎ unique‎ signal‎ processing‎

method‎to‎represents‎the‎summation‎of‎time‎synchronizing‎averaging‎(TSA)‎data‎related‎

to‎different‎engine‎orders‎in‎the‎polar‎plots‎was‎used‎for‎diagnosis,‎based‎on‎vibration‎

signals‎obtained‎from‎OBV,‎OCV‎and‎IAS‎to‎determine‎blade(s)‎health‎conditions‎due‎

to‎blade‎mistuning‎effects,‎blade‎root‎ looseness‎and‎cracked‎blade(s).‎The‎novel‎polar‎

plot‎method‎provided‎a‎good‎indication‎of‎potential‎to‎be‎utilised‎as‎a‎tool‎for‎BHM.

Objective 6

To execute a theoretical simulation analysis to compare the experimental observations

with simulations in order to understand blade(s) vibration dynamic behaviour.


A simple mathematical model of 8 blades single stage configuration was developed.

The acceleration responses were calculated for the transient motion of run-up for cases

of healthy and cracked blade(s), and then short time Fourier transform (STFT) contour

plots and order tracking were carried out on the acceleration response to obtain the

vibration response of the rotor. The results of analysis of the mathematical model

verified and supported the experimental observations and the model can be considered a

useful feature to identify blade fault(s).


207

10.3 Overall conclusion

The‎ shaft‎ torsional‎ vibration‎ based‎ on‎ IAS‎ signals‎ provided‎ the‎ highest‎ quality‎

indication‎of‎fault‎detection‎compared‎to‎OBV‎and‎OCV‎measurements‎for‎the‎purpose‎

of‎ diagnosing‎ blade‎ health‎ conditions‎ in‎ the‎ cases‎ of:‎ healthy‎ blades‎ with‎ mistuned‎

effect,‎ blade‎ root‎ looseness‎ and‎ cracked‎ blade(s).‎ The‎ results‎ were‎ based‎ on‎ the‎

observation‎of‎the‎presence‎of‎distinct‎multiple‎peaks‎in‎the‎BR‎region‎for‎faulty‎blades‎

compared‎to‎a‎single‎banded‎peak‎in‎the‎cases‎of‎healthy‎blades,‎using‎the‎analysis‎of‎

EOT‎method.‎The‎distinct‎ feature‎ for‎ the‎ faulty‎blades‎ is‎ also‎clearly‎observed‎ in‎ the‎

proposed‎novel‎polar‎plots‎using‎TSA‎data‎of‎the‎blade‎resonance‎related‎EOs.‎Hence,‎

IAS‎signals‎are‎highly‎recommended‎as‎a‎measurement‎to‎be‎used‎as‎a‎feature‎of‎BHM‎

based‎on‎current‎research‎study.

10.4 Novel features

The research study presented in this thesis incorporated a number of important aspects

that are novel and have not been previously implemented by other researchers or

practitioners. These aspects of novelty are summarised below.

Novelty 1

The author believes that the way in which IAS vibration signals were used for blade

fault diagnosis and examined using experimental tests with further signal processing

analysis techniques supported by a simplified mathematical model to successfully

predict faults is novel.

Novelty 2

The author believes that the polar plot presentation method, presented in Chapter 8,

which was based on a 2D polar coordinates system and was used for the detection and

diagnosis of blade health conditions due to different blade faults, is entirely novel. In

this approach, a polar plot of 360° angular coordinates related to the‎blades’‎order‎angle‎

and‎the‎blades’‎vibration‎signal‎amplitude‎is‎used.‎The‎radius‎of‎the‎system‎corresponds‎

to the vibration signal amplitude and the 360° angular coordinates are used to represent

the 360° angular duration of the shaft’s full rotation. The approach of polar presentation

is used for the 8-blade system, which means that the angle between every two blades is

45°. This presentation method is unique and no work has been carried out previously


208

using a polar plot presentation as a tool for the detection and diagnosis of blade health

conditions for the purpose of BHM.

10.5 Future work

There is a number of possible future research study that can enhance the confidence in

the proposed detection and diagnosis of faults and enhance BHM. These are listed

below.

1- To investigate the use of multi-stages of bladed discs with and without blade

faults in different stages in order to diagnose and detect blade faults at different

stages.

2- To investigate the use of wireless measurement systems on the bladed disc itself

to determine the ability of the method to diagnose blade health conditions due to

blade(s) faults.

3- To investigate twisted blades like real turbine blades with and without faults in

order to diagnose and detect blade health condition with accurate diagnosis of

blade faults.

4- To examine the vibration measurements which were used in this study for

investigating blade faults in rotating machines in plant.

5- To investigate the applicability of shaft torsional vibration measurement to

locate cracked or faulty blade(s) in a bladed disc whilst the machine is in

operation.

6- To conduct further experiments using on-casing measurement to investigate the

applicability of this method for BHM. This is easy for instrumentation and

measurement.

APPENDICES

209

APPENDICES

Appendix A

Combined figures of on-bearing vibration data analysis results for blades health

condition cases:

(a) Long blades



blades 2 & 4

110 115 120 125 130 1350

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

-4

Frequency (Hz)

EO

5, A

ccele

ra

tio

n (

m/s

2)

Case 1

Case 2 (ii)

Case 3 (ii)

APPENDICES

210



blades 2 & 4

220 230 240 250 260 2700

0.5

1

1.5

2

2.5

3x 10

-4

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)

Case 1

Case 2 (ii)

Case 3 (ii)

APPENDICES

211

(b) Short blades

Figure A 3: Combined curves of bearing measured acceleration data for short blades for engine


blades 2 & 4

220 225 230 235 240 245 250 255 2600

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (

m/s

2)

Case 1

Case 3 (i)

Case 3 (ii)

APPENDICES

212

Figure A 4: Combined curves of bearing measured acceleration data of short blades for engine

order EO20 spectra for: Case (1) healthy blades, (3-i) crack on blade 4, (3-ii) cracks on

blades 2 & 4

440 450 460 470 480 490 500 510 5200

0.005

0.01

0.015

0.02

0.025

Frequency (Hz)

EO

20

, A

ccele

ra

tio

n (

m/s

2)

Case 1

Case 3 (i)

Case 3 (ii)

APPENDICES

213

Appendix B

Combined figures of on-casing vibration data analysis results for blades health

conditions cases for short blades:



blades 2 & 4

220 225 230 235 240 245 250 255 2600

0.005

0.01

0.015

0.02

0.025

0.03

Frequency (Hz)

EO

10

, A

ccele

ra

tio

n (m

/s2)

Case 1

Case 3 (i)

Case 3 (ii)

APPENDICES

214



blades 2 & 4

440 450 460 470 480 490 500 510 520 530 5400

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Frequency (Hz)

EO

20

, A

ccele

ra

tio

n (

m/s

2)

Case 1

Case 3 (i)

Case 3 (ii)

APPENDICES

215

Appendix C

Combined figures of shaft torsional vibrations based on instantaneous angular speed

signal data analysis results for blades health conditions cases:

(a) Long blades


Case (1) healthy blades, Case (2-i) blade 1 root looseness, Case (2-ii) blade 5 root looseness, (3-

i) crack on blade 4, (3-ii) cracks on blades 2 & 4, (3-iii) crack on blade 2, (3-iv) crack on blade 4

after 100 minute of running

115 120 125 130 1350

0.05

0.1

0.15

0.2

0.25

0.3

Frequency (Hz)

EO

5, S

peed

(R

PS

)

Case 1

Case 2 (i)

Case 2 (ii)

Case 3 (i)

Case 3 (ii)

Case 3 (iii)

Case 3 (iv)

APPENDICES

216





230 235 240 245 250 255 260 265 2700

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Frequency (Hz)

EO

10

, S

peed

(R

PS

)

Case 1

Case 2 (i)

Case 2 (ii)

Case 3 (i)

Case 3 (ii)

Case 3 (iii)

Case 3 (iv)

APPENDICES

217





350 360 370 380 390 4000

0.05

0.1

0.15

0.2

0.25

0.3

Frequency (Hz)

EO

15

, S

peed

(R

PS

)

Case 1

Case 2 (i)

Case 2 (ii)

Case 3 (i)

Case 3 (ii)

Case 3 (iii)

Case 3 (iv)

APPENDICES

218

(b) Short blades

Figure C 4: Combined curves of measured encoder (IAS) data of short blades for engine order

EO10 spectra: Case (1) healthy blades, (3-i) crack on blade 4, (3-ii) cracks on blades 2 & 4

220 225 230 235 240 245 250 255 2600

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Frequency (Hz)

EO

10

, S

peed

(R

PS

)

Case 1

Case 3 (i)

Case 3 (ii)

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VIBRATION DIAGNOSIS OF BLADES OF ROTATING MACHINES