2016 zhengyi jiang - research explorer

DESIGN, DEVELOPMENT AND TESTING OF AN

AUTOMATED SYSTEM FOR MEASURING WALL

THICKNESSES IN TURBINE BLADES WITH COOLING

CHANNELS

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

PhD

in the Faculty of Faculty of Engineering and Physical Sciences

2016

ZHENGYI JIANG

SCHOOL OF MECHANICAL, AEROSPACE AND CIVIL ENGINEERING

VOLUME I OF II

2

Contents

VOLUME I

CONTENTS 2

LIST OF TABLES 10

LIST OF FIGURES 13

LIST OF EQUATIONS 22

ABSTRACT 25

DECLARATION 26

COPYRIGHT STATEMENT 27

ACKNOWLEDGEMENT 28

30

34

Ultrasonics 35

3

Definition of ultrasound 35

Capabilities and limitations 35

Characteristics of ultrasonic testing 36

Data Processing 39

Application 41

Conclusion 43

Reverse engineering 44

Digitization 45

Registration 50

Triangulation 54

Surface fitting 58

Parameterisation 65

Conclusion 68

69

Robot, ultrasonic probe and laser sensor 72

Robot 72

Ultrasonic probe and ultrasonic card 73

Laser sensor and analogue data acquisition 74

Design of the water tank 76

Overview of the design 76

Detailed parts and dimensions 78

Finite element analysis of the water tank 84

Float switches, pump and solenoid valve 86

Design of the shaft-bearing system 88

Overview 89

Designed parts and detailed dimensions 91

Water sealing mechanism 94

Bearing arrangement 95

FEA of the shaft 95

Transmission system for the shaft 99

Design of the rotary axis pedestal 102

Overview 102

Detailed dimensions 106

4

Design of a tool change system 109

Design of the tool holder for the Keyence laser sensor 111

Design of the tool holder for the Olympus ultrasonic probe 115

Design of the tool magazine 119

Design of the base structure 125

The conceptual designs 125

The final design 128

Fixture 134

Design overview 135

FEA of the fixture design 136

The final assembly 138

Procedure for assembling the inspection machine 138

The assembled inspection machine 140

144

Robot control 145

Robot motion and variables 146

Vibrations 147

Communication and dynamic-link library 148

Control software block diagrams 152

Laser digitizing algorithm 153

Ultrasonic measurement algorithm 159

163

Ultrasonics 164

Determination of thickness 164

Noise 167

Bubbles 168

Angle of incidence 170

Reverse engineering 172

Digitizing turbine blades 172

Fitting methods tested in the early stages. 174

Triangulation 176

5

Parameterisation 187

B-spline surface fitting 195

Localisation 199

Closest point problem 199

Least square transformation 200

ICP with initial alignment error correction 202

Performance test 204

Probe path 210

Definition of a probe path 210

Calculation of a probe path 211

Regions of inspection 214

Dividing and grouping of a probe path 217

220

Effect of varying water paths 222

Background, aim and methodology 222

Experiment setup and procedures 222

Results and discussions 224

Conclusion 228

Calibration 229


Experiment setup and procedures 230


Effect of varying angle of incidence 232


Experimental setup and procedures 233


Conclusion 240

Measuring a curved component from curved surface 241




Conclusion 243

Measuring the disc blade on a 4-axis milling machine 244

6




Conclusion 247

Measuring the disc blade on the inspection machine 248




Conclusion 252

Reverse engineering of the PSM104 turbine blade 253




Summary 262

Measuring three PSM104 turbine blades with a common probe path 263




Summary 277

278

280

REFERENCES 281

292

310

313

316

318

7

VOLUME II

CONTENTS 321

CHAPTER 1 C# CODES 324

1.1 Robot control 325

1.1.1 Connect to the robot 325

1.1.2 Number register 328

1.1.3 Position register 330

1.1.4 Robot program 333

1.1.5 Robot program execution 335

1.1.6 File header fix 337

1.1.7 Variables and configurations 338

1.1.8 Advanced robot position enquiry 339

1.1.9 Advanced robot motion control 346

1.2 Ultrasonic control 352

1.3 DAQ device 363

1.3.1 Connect to the DAQ device 363

1.3.2 Data transmission 364

1.3.3 Error message handling 368

1.3.4 Special function 369


1.3.6 Advanced Digital IO control 370

1.3.7 Advanced analog IO control 370

1.4 Stepper motor control 372

1.4.1 Connect to the stepper motor 372

1.4.2 Stepper motor instructions 373


1.4.4 Advanced stepper motor control 376

1.5 Matlab interaction 381

1.6 Miscellaneous classes 383

1.6.1 Extended type conversions 383

8

1.7 Demo software 385

1.7.1 Initilisation 385

1.7.2 Connect to equipment 386

1.7.3 Private Methods 388

1.7.4 Laser digitization 391

1.7.5 Probe path localisation 395

1.7.6 Ultrasonic data acquisition 397

1.7.7 Wall thickness evaluation 405

CHAPTER 2 MATLAB CODES 407

2.1 Reverse engineering 408

2.1.1 The main Matlab function 408

2.1.2 B-spline curve 410

2.1.3 Shape-preserving parameterisation 412

2.1.4 B-spline surface 415

2.2 Probe path calculation 421

2.2.1 Data preparation 421

2.2.2 The main path calculation function 422

2.2.3 Tangent vectors in u direction 428

2.2.4 Tangent vectors in w direction 430

2.3 Localisation 434

2.3.1 Initialisation 434

2.3.2 Multi-approach algorithm 435

2.3.3 Quaternion method 438

2.3.4 Closest point 438

2.4 Path grouping 440

2.4.1 The main function 440

2.4.2 Path grouping sub-function 445

2.4.3 Probe path transformation sub-function 447

2.4.4 Path ordering sub-function 448

2.4.5 Robot rotation parameter calculation 449

2.5 Thickness evaluation 451


2.5.2 Interface echo detection 452

2.5.3 Backwall echo detection and thickness calculation 456

9

Final word count: 98443

10

List of Tables

Table 3.1-1 Specifications of a Keyence IL-S065 ............................................................................... 75

Table 3.3-1 Mechanical properties of the materials used in FEA ..................................................... 97

Table 3.4-1 Specifications of timing pulleys and belt (all units in mm) .......................................... 100

Table 3.7-1 Conceptual design marking in scale of 1-5 .................................................................. 128

Table 5.2-1 Example input and output of t=Delaunay(u,w) [121] in Matlab .................................. 187

Table 5.3-1 ICP configurations and results ..................................................................................... 205

Table 6.1-1 Standard deviations of the evaluated time of flight at each step ............................... 224

Table 6.1-2 Theoretical optimal water path for each steps ............................................................ 224

Table 6.1-3 Optimum receiver gain found for different thickness range ....................................... 228

Table 6.2-1 Planned calibration set ................................................................................................ 230

Table 6.2-2 Calibration results for seven different thickness sets .................................................. 231

Table 6.3-1 Maximum ΔT and standard deviations of ΔT ............................................................... 236

Table 6.3-2 Wall thicknesses and signal-to-noise ratio of the backwall echoes measured at

different angles of incidence at five holes (units in mm otherwise specified) ............................... 237

Table 6.3-3 Comparison of time differences between peaks in interface echoes at various angles

of incidence ..................................................................................................................................... 239

Table 6.4-1 Comparison between CMM results and Ultrasonic results ......................................... 242

Table 6.5-1 Wall thicknesses measured with ultrasonic probe compared with CMM results ....... 245

Table 6.6-1 Comparison between errors of evaluated thicknesses from two experiments .......... 251

Table 6.7-1 Linear errors of surface fitting of B1 (units in mm) ..................................................... 256

Table 6.7-2 Mean errors and standard deviations of wall thicknesses measured on the inspection

machine and using the touch probe ............................................................................................... 261

Table 6.8-1 Linear errors of surface fittings of B2 and B3 (units in mm) ........................................ 267

Table 6.8-2 Comparison of the three turbine blades ...................................................................... 270

Table 6.8-3 Differences in measured wall thickness ....................................................................... 276

Table I-1 Variations of amplitudes of the first backwall echo ........................................................ 292

Table I-2 Variations of amplitudes of the second backwall echo ................................................... 292

Table I-3 Variations of amplitudes of the interface echo ............................................................... 293

11

Table I-4 Variations of interpreted time of flight ............................................................................ 293


Table I-6 Variations of amplitudes of the second backwall echo ................................................... 294

Table I-7 Variations of amplitudes of the interface echo ............................................................... 295

Table I-8 Variations of interpreted time of flight ............................................................................ 295


Table I-10 Variations of amplitudes of the second backwall echo ................................................. 297

Table I-11 Variations of amplitudes of the interface echo ............................................................. 297

Table I-12 Variations of interpreted time of flight .......................................................................... 298

Table I-13 Variations of amplitudes of the first backwall echo ...................................................... 298




















Table III-1 Wall thicknesses measured on the curved component with angles of incidence from 0°

to 1.98° ............................................................................................................................................ 313

Table III-2 Wall thicknesses measured on the curved component with angles of incidence from

2.475° to 4.455° .............................................................................................................................. 313

12

Table III-3 Wall thicknesses measured on the curved component with angles of incidence from

4.95° to 5.94° .................................................................................................................................. 314

Table V-1 Thicknesses measured on B1 using P1, P2, P3 and a touch probe at ELE ...................... 318

Table V-2 Thickness measured on B2 using P1, P2, P3 and a touch probe at ELE .......................... 318

Table V-3 Thickness measured on B3 using P1, P2, P3 and a touch probe at ELE .......................... 318

13

List of Figures

Fig. 2.1-1 (a) A CAD model of a turbine blade. (b) A cross-section of the blade and the wall

thickness. .......................................................................................................................................... 30

Fig. 2.1-2 (a) An illustration of ultrasonic delay-line transducer. (b) The ultrasonic probe is kept

normal to the surface of the blade at various inspection locations ................................................. 31

Fig. 2.1-1 Different bands of sound frequencies............................................................................... 35

Fig. 2.1-2 Near field and far field [11] ............................................................................................... 36

Fig. 2.1-3 -6dB focal zone .................................................................................................................. 37

Fig. 2.1-4 Normalized beginning and ending points of the -6dB focal zone [11]. ............................. 38

Fig. 2.1-5 Variation of relative increase in signal amplitude with normailized focal length SF [11]. 38

Fig. 2.1-6 Focal point shifts when an ultrasonic wave enters the workpiece. Reproduced from

Olympus NDT (2011) [11]. ................................................................................................................ 39

Fig. 2.1-7 Different modes for time of flight measurement. ............................................................ 40

Fig. 2.1-8 Errors in time of flight (ToF) measurement (reproduced from Hammond [16]) .............. 41

Fig. 2.1-9 Blood flow in the carotid artery bifurcation [21] .............................................................. 42

Fig. 2.2-1 Surface of a turbine blade generated by lofting from a set of cross section profiles [29]45

Fig. 2.2-2 Examples of different probe actuators ............................................................................. 46

Fig. 2.2-3 A Nikon hand-held laser scanning system [42] ................................................................. 47

Fig. 2.2-4 Principle of laser triangulation [50] ................................................................................... 48

Fig. 2.2-5 (a) 2D laser scanning; (b) acquired data points structure in 2D laser scanning.

Reproduced from Woo et al. (2002) [54] .......................................................................................... 49

Fig. 2.2-6 Measuring vertical surfaces with a touch probe and a laser probe. Reproduced from

McDonald, J.A. (2001) [56]. .............................................................................................................. 50

Fig. 2.2-7 Registration of two separated surfaces of a cylinder ....................................................... 50

Fig. 2.2-8 Two partially-overlapping surfaces ................................................................................... 51

Fig. 2.2-9 (a) A free-form surface, (b) extracted regions (1’, 2’, 3’, 4’ and 5’) from the measured

surface and (c) extracted regions (1, 2, 3, 4 and 5) from the target surface. Figure is reproduced

from Li and Gu [72] ........................................................................................................................... 53

Fig. 2.2-10 A parametric representation of a torus is shown at the top left corner. Three points are

selected from the torus and the corresponding signature image of each point is plotted. [73] ..... 54

Fig. 2.2-11 Delaunay triangulation .................................................................................................... 55

Fig. 2.2-12 A Voronoi diagram .......................................................................................................... 55

Fig. 2.2-13 Bisectors and the Voronoi diagram ................................................................................. 55

14

Fig. 2.2-14 Generate Delaunay triangulation based on Voronoi diagram ........................................ 56

Fig. 2.2-15 The non-uniqueness problem ......................................................................................... 56

Fig. 2.2-16 Two Delaunay triangulations computed with implementation of preferred direction

rule at two different selected directions [84] ................................................................................... 56

Fig. 2.2-17 (a) A fine Delaunay tetrahedron and (b) a distorted Delaunay tetrahedron. Figure is

reproduced from Cavendish et al (1985) [78]................................................................................... 57

Fig. 2.2-18 Tetrahedrons in through the thickness of the blade ...................................................... 57

Fig. 2.2-19 Effect of control points on a seven degree Bezier curves ............................................... 59

Fig. 2.2-20 A cubic B-spline curve ..................................................................................................... 60

Fig. 2.2-21 (a) a Hermite bicubic patch and a F-surface patch ......................................................... 60

Fig. 2.2-22 A Bezier patch and its characteristic polyhedrons .......................................................... 61

Fig. 2.2-23 (a) clamped B-spline surface and (b) unclamped B-spline surface [91] .......................... 62

Fig. 2.2-24 Mesh refinement: original mesh (bold meshes) and refined mesh (thin lines) [92] ...... 62

Fig. 2.2-25 The quad-net corresponding to the vertex of the refined mesh [92] ............................. 63

Fig. 2.2-26 Examples of smooth surfaces reconstructed based on coarse meshes [92] .................. 63

Fig. 2.2-28 A set of input points (left) and the approximating mesh (right) ..................................... 64

Fig. 2.2-28 Triangular base complex (left) and quadrilateral base complex (right) .......................... 64

Fig. 2.2-29 Control polyhedron (left), B-spline surface (middle) and refined surface (right) .......... 64

Fig. 2.2-30 Representation of a section curve, reproduced from [96] ............................................. 65

Fig. 2.2-31 Triangulated model ......................................................................................................... 66

Fig. 2.2-32 Shape preserving parameterisation (left) and surface approximation (right) ................ 67

Fig. 2.2-33 The three mapping methods ........................................................................................... 68

Fig. 3.1-1 The purchased Fanuc LRMate 200iD robot and R-30iB controller .................................... 72

Fig. 3.1-2 (a) An Olympus V316-SU ultrasonic probe and (b) a USUltratek PCIUT3100 ultrasonic

card ................................................................................................................................................... 73

Fig. 3.1-3 (a) A Keyence IL-S065 CMOS laser sensor and (b) a Keyence IL-1000 amplifier ............... 74

Fig. 3.1-4 A USB-1208FS DAQ by Measurement Computing ............................................................ 75

Fig. 3.2-1 Different views of the water tank (units in mm) ............................................................... 77

Fig. 3.2-2 An exploded view of the water tank ................................................................................. 78

Fig. 3.2-3 Detailed dimensions of the water tank body (units in mm) ............................................. 80

Fig. 3.2-4 Detailed dimensions of the Perspex window (units in mm) ............................................. 81

Fig. 3.2-5 Detailed dimensions of the pipe connectors (units in mm) .............................................. 82

Fig. 3.2-6 Detailed dimensions of the inlet manifold (units in mm) ................................................. 83

15

Fig. 3.2-7 Finite element stress analysis of the water tank .............................................................. 85

Fig. 3.2-8 Deflection of the water tank ............................................................................................. 85

Fig. 3.2-9 The purchased Cynergy3 SSF212 float switch, Asco Joucomatic S210 valve and Flotec VIP

130/6 Auto pump .............................................................................................................................. 87

Fig. 3.3-1 Different views of the shaft-bearing system (units in mm) .............................................. 89

Fig. 3.3-2 An exploded view of the shaft-bearing system ................................................................. 90

Fig. 3.3-3 Detailed dimensions of the shaft-bearing housing (units in mm) ..................................... 92

Fig. 3.3-4 Detailed dimensions of the in-tank flange (units in mm).................................................. 93

Fig. 3.3-5 Detailed dimensions of the shaft (units in mm) ................................................................ 93

Fig. 3.3-6 Seals and possible water paths ......................................................................................... 94

Fig. 3.3-7 A sectional view of the shaft-bearing system ................................................................... 95

Fig. 3.3-8 Model of the blade, fixture and the shaft for analysis (units in mm) ............................... 96

Fig. 3.3-9 Finite element stress analysis of the blade, fixture and the shaft .................................... 97

Fig. 3.3-10 Deflection of the blade, fixture and the shaft ................................................................. 97

Fig. 3.4-1 Transmission system assembled on the shaft (units in mm) ............................................ 99

Fig. 3.4-2 Detailed dimensions of the motor and the gearbox (units in mm) ................................ 100

Fig. 3.5-1 Different views of the rotary axis pedestal (units in mm) .............................................. 102

Fig. 3.5-2 Different views of the rotary axis pedestal with shaft-bearing system and transmission

system assembled ........................................................................................................................... 103

Fig. 3.5-3 Assembling the shaft-bearing system onto the rotary axis pedestal .............................. 103

Fig. 3.5-4 An exploded view of the rotary axis pedestal ................................................................. 104

Fig. 3.5-5 Assembling the motor and gearbox onto the rotary axis pedestal ................................ 104

Fig. 3.5-6 Assembling the rotary axis pedestal onto the cast iron table......................................... 105

Fig. 3.5-7 Detailed dimensions of the top plate (units in mm) ....................................................... 106

Fig. 3.5-8 Detailed dimensions of the base (units in mm) .............................................................. 107

Fig. 3.5-9 Detailed dimensions of the mounting plate (units in mm) ............................................. 108

Fig. 3.6-1 Robot face plate .............................................................................................................. 109

Fig. 3.6-2 An exploded view of a Schunk SWS005 pneumatic tool change system ........................ 109

Fig. 3.6-3 Detailed dimensions of a Schunk SWK005 and SWA005 (units in mm) .......................... 110

Fig. 3.6-4 A Schunk quick-change adaptor SWA005 stored in a SWM-TSS storage plate .............. 111

Fig. 3.6-5 Detailed dimensions of a Keyence ILS065 laser sensor (units in mm) ............................ 111

Fig. 3.6-6 Different views of the laser sensor holder (units in mm) ............................................... 112

Fig. 3.6-7 An exploded view of the laser sensor holder .................................................................. 113

Fig. 3.6-8 Detailed dimensions of the L plate (units in mm) ........................................................... 114

16

Fig. 3.6-9 Detailed dimensions of the adaptor (units in mm) ......................................................... 115

Fig. 3.6-10 Dimensions of an Olympus V316-SU ultrasonic probe (units in mm) ........................... 116

Fig. 3.6-11 The ultrasonic probe holder (units in mm) ................................................................... 116

Fig. 3.6-12 An exploded view of the ultrasonic probe holder......................................................... 117

Fig. 3.6-13 Sectional view of the ultrasonic probe holder with the probe and O-rings assembled

........................................................................................................................................................ 117

Fig. 3.6-14 Detailed dimensions of the probe holder lower part (units in mm) ............................. 118

Fig. 3.6-15 Detailed dimensions of the probe holder upper part (units in mm) ............................ 119

Fig. 3.6-16 An SWA005 quick-change adaptor and support bolts by Schunk (units in mm) .......... 120

Fig. 3.6-17 Detailed dimensions of a Schunk SWM-TSS storage plate ........................................... 120

Fig. 3.6-18 Detailed dimensions of a Schunk proximity sensor and a sensor bracket (units in mm)

........................................................................................................................................................ 121

Fig. 3.6-19 Model of the tool magazine .......................................................................................... 121

Fig. 3.6-20 An exploded view of the tool magazine ........................................................................ 122

Fig. 3.6-21 Detailed dimensions of the stand profile ...................................................................... 123

Fig. 3.6-22 Detailed dimensions of the mounting plate for tool magazine (units in mm) .............. 123

Fig. 3.6-23 Detail dimensions of the storage plate adapter (units in mm) ..................................... 124

Fig. 3.7-1 The first design of base structure.................................................................................... 125

Fig. 3.7-2 The second design of base structure .............................................................................. 126

Fig. 3.7-3 The third design of base structure .................................................................................. 127

Fig. 3.7-4 The 101.6mm*76.2mm cast iron surface table .............................................................. 128

Fig. 3.7-5 Assembling components onto the cast iron surface ....................................................... 129

Fig. 3.7-6 Components installed on the cast iron table .................................................................. 130

Fig. 3.7-7 Detailed dimensions of the locating block (units in mm) ............................................... 130

Fig. 3.7-8 Arrangement of the locating blocks on the cast iron table ............................................ 131

Fig. 3.7-9 Dimensions of (a) the base [112] and (b) the operating space of [113] of FANUC LR Mate

200iD Robot .................................................................................................................................... 131

Fig. 3.7-10 Detailed dimensions of the robot pedestal (units in mm) ............................................ 132

Fig. 3.7-11 Assembling the robot onto the robot pedestal ............................................................ 133

Fig. 3.7-12 Assembling the robot pedestal onto the cast iron table .............................................. 133

Fig. 3.8-1 The fir-tree root of the test blade ................................................................................... 134

Fig. 3.8-2 A jaw with four inserts on each side clamped on the fir-tree root ................................. 134

Fig. 3.8-3 Different views of the fixture .......................................................................................... 135

Fig. 3.8-4 An exploded view of the fixture ...................................................................................... 135

17

Fig. 3.8-5 Definition of the load and contacts for the analysis ....................................................... 136

Fig. 3.8-6 (a) Von Mises Stress distribution and (b) Displacement distribution ............................. 137

Fig. 3.9-1 Guards ............................................................................................................................. 140

Fig. 3.9-2 The water tank, rotary axis and robot............................................................................. 140

Fig. 3.9-3 Rotary axis consisting of the stepper motor, timing pulleys and belt, and spindle housing

........................................................................................................................................................ 141

Fig. 3.9-4 The in-tank flange............................................................................................................ 141

Fig. 3.9-5 The water tank ................................................................................................................ 141

Fig. 3.9-6 Pipe connectors ............................................................................................................... 142

Fig. 3.9-7 The tool magazine ........................................................................................................... 142

Fig. 3.9-8 Rear view of the table showing the cabinet and the robot control ................................ 142

Fig. 3.9-9 The Keyence laser sensor mounted in the laser sensor holder ...................................... 143

Fig. 3.9-10 The Olympus ultrasonic probe mounted in the ultrasonic probe holder ..................... 143

Fig. 4.1-2 Six axes of the Fanuc robot [112] .................................................................................... 145

Fig. 4.1-1 Fanuc teach pendant ....................................................................................................... 145

Fig. 4.1-3 Effects of using CNT0 and CNT100 at P2 and P3 .............................................................. 146

Fig. 4.1-4 Vibration of the robot during a linear motion ................................................................ 147

Fig. 4.1-5 Vibration at the end of the motion ................................................................................. 147

Fig. 4.1-6 Accessing the robot controller using a web browser ...................................................... 148

Fig. 4.2-1 Block diagrams legend .................................................................................................... 152

Fig. 4.2-2 A general laser digitizing procedure – initialisation ........................................................ 153

Fig. 4.2-3 A general laser digitizing procedure – motion loop 1 ..................................................... 154

Fig. 4.2-4 A general laser digitizing procedure – motion loop 2 ..................................................... 156

Fig. 4.2-5 A general procedure of ultrasonic data acquisition – initialisation and robot motion ... 159

Fig. 4.2-6 A general procedure of ultrasonic data acquisition - Ultrasonic data acquisition .......... 161

Fig. 5.1-1 A schematic drawing of the path of ultrasound for immersion ultrasonic testing ......... 164

Fig. 5.1-2 Ultrasonic signals in time domain ................................................................................... 165

Fig. 5.1-3 Two types of bubbles that affect ultrasonic testing ....................................................... 168

Fig. 5.1-4 Effect of having bubbles on surface of inspection and probe lens ................................. 169

Fig. 5.1-5 Nose caused by surface bubbles at receiver gain = 70 ................................................... 170

Fig. 5.1-6 Refraction and reflection of ultrasonic signal ................................................................. 171

Fig. 5.2-1 The five regions defined on the surface of the blade ..................................................... 173

18

Fig. 5.2-2 Acquired surface points and calculated points on the B-spline surface ......................... 173

Fig. 5.2-3 Generated CMM path based on the calculated 1404 points .......................................... 174

Fig. 5.2-4 Failed surface triangulation extraction result ................................................................. 175

Fig. 5.2-5 Triangulation of a sphere surface ................................................................................... 177

Fig. 5.2-6 Starting points of each cross section in 2D and 3D ......................................................... 178

Fig. 5.2-7 Spherical surface after B-spline curve fitting and the line connecting the end points of

the cross sections ............................................................................................................................ 179

Fig. 5.2-8 Triangulation result based on points generated by B-spline curves ............................... 180

Fig. 5.2-9 Triangulated surface of a turbine blade .......................................................................... 181

Fig. 5.2-10 Calculation procedures in the triangulation algorithm ................................................. 182

Fig. 5.2-11 (a) number of control points = 50, degree of curve = 10; (b) number of control points =

65, degree of curve = 45 ................................................................................................................. 184

Fig. 5.2-12 Measured points and control points ............................................................................. 185

Fig. 5.2-13 Cross-sections of the sphere fitted B-spline curves ...................................................... 186

Fig. 5.2-14 Triangulation results with above input and output ...................................................... 187

Fig. 5.2-15 Local parameterisation of a sub-triangulation. Reproduced from Floater (1997) [100]

........................................................................................................................................................ 189

Fig. 5.2-16 The straight line 𝑙 passing through 𝑝𝑙 and 𝑝𝑖 and intersects the polygon at a second

point. ............................................................................................................................................... 190

Fig. 5.2-17 Mapping a Polyhedron onto a 2D plane ....................................................................... 192

Fig. 5.2-18 Parameterised spherical surface based on a coarse triangular mesh .......................... 193

Fig. 5.2-19 Parameterised spherical surface based on a refined triangular mesh ......................... 194

Fig. 5.2-20 Parameterised turbine blade surface (see Fig. 5.2-9 for the triangular mesh) ............. 194

Fig. 5.2-21 Control points calculated for (a) the spherical surface and (b) the surface of the blade

........................................................................................................................................................ 197

Fig. 5.2-22 Surfaces calculated with B-spline surface for (a) the sphere and (b) the turbine blade

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

Fig. 5.3-1 Two conditions of convergence ...................................................................................... 203

Fig. 5.3-2 Flowchart of the ICP algorithm ....................................................................................... 204

Fig. 5.3-3 The surface created with a peak function used for testing the ICP algorithm ............... 205

Fig. 5.3-4 B-spline surfaces for localisation ..................................................................................... 206

Fig. 5.3-5 B-spline surfaces matched using the ICP algorithm ........................................................ 207

Fig. 5.3-6 Convergence plot for matching the B-spline surfaces .................................................... 207

Fig. 5.3-7 Turbine blade surfaces for localisation ........................................................................... 208

19

Fig. 5.3-8 Blade surfaces matched using the ICP algorithm ............................................................ 208

Fig. 5.3-9 Convergence plot for matching the turbine blade surfaces ........................................... 209

Fig. 5.4-1 Coordinate systems and axes in the inspection machine ............................................... 210

Fig. 5.4-2 B-spline surface representation of a blade and evaluated surface normals .................. 212

Fig. 5.4-3 Acquiring points from a CAD model ................................................................................ 214

Fig. 5.4-4 Positions of holes ............................................................................................................ 215

Fig. 5.4-5 Regions of inspection ...................................................................................................... 216

Fig. 5.4-6 A complete probe path for the convex side of a cross section ....................................... 217

Fig. 5.4-7 Maximum angle of swing ................................................................................................ 217

Fig. 5.4-8 Robot arm is restricted by the water tank ...................................................................... 218

Fig. 5.4-9 probe path grouping ....................................................................................................... 219

Fig. 6.1-1 (a) The Inconel stepped specimen and (b) the clamping of the stepped component .... 222

Fig. 6.1-2 Amplitudes of the first backwall echoes ......................................................................... 225

Fig. 6.1-3 Low limit and high limit of noise ..................................................................................... 226

Fig. 6.1-4 Effect of varying gain regarding noise ............................................................................. 226

Fig. 6.1-5 Signals captured with different receiver gains ................................................................ 227

Fig. 6.2-1 Peak-to-peak calibration was used in the experiment ................................................... 229

Fig. 6.2-2 A linear curve fitted to the ultrasonic data acquired at Step 1 and Step2...................... 230

Fig. 6.3-1 (a) The curved component and (b) dimensions of the component (units in mm).......... 232

Fig. 6.3-2 Clamp of the curved component .................................................................................... 233

Fig. 6.3-3 Ultrasonic inspection image interpreted from experiment results obtained at 𝜃1 = 0°

........................................................................................................................................................ 234

Fig. 6.3-4 Errors of measured wall thickness at 𝜃1 = 0 ................................................................. 234

Fig. 6.3-5 ΔT against angle of incidence for each wall thickness .................................................... 235

Fig. 6.3-6 Variation of signal-to-noise ratio of the backwall echoes with angle of incidence ........ 237

Fig. 6.3-7 Distorted interface echoes .............................................................................................. 238

Fig. 6.3-8 Ultrasonic inspection image interpreted from experiment results obtained at 𝜃1 =

5.94°................................................................................................................................................ 239

Fig. 6.3-9 Time differences between peaks in interface echoes increase with angles of incidence

........................................................................................................................................................ 240

Fig. 6.4-1 The curved component ................................................................................................... 241

Fig. 6.4-2 Experimental setup for measuring the curved component on the OKK milling machine

........................................................................................................................................................ 241

20

Fig. 6.4-3 Processed ultrasonic thickness data ............................................................................... 243

Fig. 6.5-1 The long blade and wall thicknesses from both convex and concave surfaces (units in

mm) ................................................................................................................................................. 244

Fig. 6.5-2 Distorted interface echoes captured above Hole 1 from (a) the convex surface and (b)

the concave surface, gain = 60 compared with (c) a healthy interface echo ................................. 246

Fig. 6.6-1 Clamp of the disc blade on the inspection machine ....................................................... 248

Fig. 6.6-2 Fitted B-spline surfaces (units in mm) ............................................................................. 249

Fig. 6.6-3 Surface normals at the top cross section (units in mm) ................................................. 250

Fig. 6.6-4 Comparison between thicknesses obtained from difference sources (units in mm) ..... 252

Fig. 6.7-1 (a) A PSM104 turbine blade with the fixture; (b) the turbine blade being measured on

the CMM ......................................................................................................................................... 253

Fig. 6.7-2 Five regions defined on the surface of the blade............................................................ 254

Fig. 6.7-3 Procedures of measuring blades in the prototype cell ................................................... 254

Fig. 6.7-4 Turbine blade fixed on the shaft of the inspection machine .......................................... 255

Fig. 6.7-5 (a) CMM data points collected on Blade 1, (b) generated Model 1 and (c) Model 2 (units

in mm) ............................................................................................................................................. 256

Fig. 6.7-6 Surface fitting error of (a) the convex surface and (b) the concave surface of Model 1,

and (a) the convex surface and (b) the concave surface of Model 2 (units in mm) ....................... 257

Fig. 6.7-7 (a) CMM points measured at section A and B; (b) Mismatch between two sets of data

points when the same surface was measured but with different CMM orientations of the probe

on the CMM; (c) Unmatched points on the convex surface have been removed; (d) B-spline curve

smoothed out the displacement found in CMM data after unmatched points were removed. (units

in mm) ............................................................................................................................................. 258

Fig. 6.7-8 Probe path for measuring from the convex surface ((a) and (b)); probe path for

measuring from the concave surface ((c) and (d)) (units in mm) ................................................... 259

Fig. 6.7-9 Wall thicknesses obtained from a CT image of the blade cross section (units in mm) .. 260

Fig. 6.7-10 Wall thicknesses measured using the inspection machine and touch probe compared

with the reference values ............................................................................................................... 261

Fig. 6.8-1 The four regions A, B, C and D defined on the surface of the blade ............................... 263

Fig. 6.8-2 Procedures of measuring blades in the prototype cell ................................................... 264

Fig. 6.8-3 (a) CMM data points measured on B2; (b) Fitted B-spline surfaces of B2; (c) CMM data

points measured on B3; (d) Fitted B-spline surfaces of B3 (units in mm) ...................................... 266

Fig. 6.8-4 Linear deviation between the CMM points and the fitted (a) convex and (b) concave

surface of B2, and the fitted (c) convex and (d) concave surface of B3 (units in mm) ................... 267

21

Fig. 6.8-5 Rate of change in slopes of the (a) convex and (b) concave B-spline surfaces of B2, (c)

convex and (d) concave B-spline surfaces of B3 and (e) convex and (f) concave B-spline surfaces of

B1 (units in mm) .............................................................................................................................. 268

Fig. 6.8-6 Blade surface section profiles and CMM points on the concave surface, at Z ≈ -101 mm

(all point data were localised to B1 CMM points and units in mm) ............................................... 269

Fig. 6.8-7 Linear deviations compared between each two of the three blades (units in mm) ....... 271

Fig. 6.8-8 Slope deviations compared between each two of the three blades (units in mm) ........ 273

Fig. 6.8-9 Cross sections of the localised B-spline surfaces and surface normals (units in mm) .... 274

Fig. 6.8-10 Comparison between different probe paths (units in mm) .......................................... 275

Fig. II-1 Ultrasonic image for angle of incidence from 0° to 1.485° ................................................ 310

Fig. II-2 Ultrasonic image for angle of incidence from 1.98° to 3.96° ............................................. 311

Fig. II-3 Ultrasonic image for angle of incidence from 4.4455° to 5.94° ......................................... 312

Fig. IV-1 Variations of amplitude of backwall echoes at the first 12 holes (excluding hole 2) ....... 316

Fig. IV-2 Variations of amplitude of backwall echoes at the last 11 holes ..................................... 317

22

List of Equations

Eq. 2.1-1 ............................................................................................................................................ 37

Eq. 2.1-2 ............................................................................................................................................ 37

Eq. 2.1-3 ............................................................................................................................................ 37

Eq. 2.1-4 ............................................................................................................................................ 39

Eq. 2.1-5 ............................................................................................................................................ 40

Eq. 2.1-6 ............................................................................................................................................ 40

Eq. 2.1-7 ............................................................................................................................................ 41

Eq. 2.1-8 ............................................................................................................................................ 42

Eq. 2.2-1 ............................................................................................................................................ 51

Eq. 2.2-2 ............................................................................................................................................ 52

Eq. 2.2-3 ............................................................................................................................................ 65

Eq. 2.2-4 ............................................................................................................................................ 66

Eq. 2.2-5 ............................................................................................................................................ 67

Eq. 2.2-6 ............................................................................................................................................ 67

Eq. 2.2-7 ............................................................................................................................................ 67

Eq. 5.1-1 .......................................................................................................................................... 164

Eq. 5.1-2 .......................................................................................................................................... 166

Eq. 5.1-3 .......................................................................................................................................... 171

Eq. 5.1-4 .......................................................................................................................................... 171

Eq. 5.1-5 .......................................................................................................................................... 171

Eq. 5.2-1 .......................................................................................................................................... 182

Eq. 5.2-2 .......................................................................................................................................... 182

Eq. 5.2-3 .......................................................................................................................................... 182

Eq. 5.2-4 .......................................................................................................................................... 184

Eq. 5.2-5 .......................................................................................................................................... 184

Eq. 5.2-6 .......................................................................................................................................... 185

Eq. 5.2-7 .......................................................................................................................................... 186

Eq. 5.2-8 .......................................................................................................................................... 188

Eq. 5.2-9 .......................................................................................................................................... 188

Eq. 5.2-10 ........................................................................................................................................ 189

23

Eq. 5.2-11 ........................................................................................................................................ 189

Eq. 5.2-12 ........................................................................................................................................ 190

Eq. 5.2-13 ........................................................................................................................................ 190

Eq. 5.2-14 ........................................................................................................................................ 191

Eq. 5.2-15 ........................................................................................................................................ 191

Eq. 5.2-16 ........................................................................................................................................ 191

Eq. 5.2-17 ........................................................................................................................................ 191

Eq. 5.2-18 ........................................................................................................................................ 191

Eq. 5.2-19 ........................................................................................................................................ 192

Eq. 5.2-20 ........................................................................................................................................ 195

Eq. 5.2-21 ........................................................................................................................................ 195

Eq. 5.2-22 ........................................................................................................................................ 195

Eq. 5.2-23 ........................................................................................................................................ 196

Eq. 5.2-24 ........................................................................................................................................ 196

Eq. 5.3-1 .......................................................................................................................................... 200

Eq. 5.3-2 .......................................................................................................................................... 200

Eq. 5.3-3 .......................................................................................................................................... 201

Eq. 5.3-4 .......................................................................................................................................... 201

Eq. 5.3-5 .......................................................................................................................................... 201

Eq. 5.3-6 .......................................................................................................................................... 201

Eq. 5.3-7 .......................................................................................................................................... 201

Eq. 5.3-8 .......................................................................................................................................... 201

Eq. 5.3-9 .......................................................................................................................................... 202

Eq. 5.3-10 ........................................................................................................................................ 202

Eq. 5.4-1 .......................................................................................................................................... 212

Eq. 5.4-2 .......................................................................................................................................... 212

Eq. 5.4-3 .......................................................................................................................................... 212

Eq. 5.4-4 .......................................................................................................................................... 213

Eq. 5.4-5 .......................................................................................................................................... 213

Eq. 5.4-6 .......................................................................................................................................... 213

Eq. 5.4-7 .......................................................................................................................................... 213

Eq. 5.4-8 .......................................................................................................................................... 213

Eq. 5.4-9 .......................................................................................................................................... 213

Eq. 6.3-1 .......................................................................................................................................... 235

25

Abstract

Cooling channels are designed in blades to protect the blades from damage at high

temperature in a gas turbine. ELE Advanced Technology Ltd. is a UK company specialised

in machining cooling channels in turbine blades using electro-chemical techniques. The wall

thicknesses between these cooling channels and the surface of the turbine blade influences

the performance of cooling channels and are required to be accurately machined and then

inspected. At present, the company measures the wall thicknesses using a hand-held contact

ultrasonic probe, which is time-consuming and not very accurate.

In this project, an inspection machine has been designed and built for the purpose of

automating the procedure of measuring wall thicknesses in turbine blades. The inspection

machine measures wall thicknesses based on immersion ultrasonic testing technique and the

actuator is a six-axis industrial robot controlled by a computer. Control algorithms have been

developed to automate the entire measuring process. Acquired ultrasonic data is also

automatically processed using Matlab scripts for wall thickness evaluation. However, prior

to the ultrasonic measurement, the probe path has to be calculated.

Matlab script has been developed to automatically calculate a probe path using a point cloud

of the blade digitized on a CMM as an input. The calculation of the probe path, in general,

involves triangulation, parameterisation and B-spline surface approximation. Normal 3D

triangulation methods were tested; nevertheless, the results were unsatisfactory. Therefore, a

triangulation algorithm is developed based on B-spline curve and 2D Delaunay triangulation.

After the probe path is calculated, a localisation method, based on iterative closest point

algorithm, is implemented to transform the probe path from CMM to the inspection machine.

Several experiments were designed and conducted to study the capability of the ultrasonic

probe. Experimental results confirmed the feasibility of using an immersion ultrasonic probe

for measuring the wall thicknesses; however, the experiments revealed several limitations of

immersion ultrasonic testing, such as the angle of incidence of ultrasonic waves must be

maintained within an angular deviation of ±1° from the surface normal to achieve accurate

test results. Wall thicknesses of three turbine blades from one batch were measured on the

inspection machine. A CT scan image was used as reference to compare the measured wall

thicknesses with results obtained using contact probes. The comparison showed the wall

thicknesses measured on the inspection machine were much more accurate than using

contact probes.

The University of Manchester

Zhengyi Jiang

PhD

Design, development and testing of an automated system for measuring wall thicknesses in

turbine blades with cooling channels

13/07/2016

26

Declaration

I 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.

Zhengyi Jiang

2016

27

Copyright Statement

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

certain copyright or related rights in it (the “Copyright”) and s/he has given The 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”), which may 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 University IP

Policy (see http://documents.manchester.ac.uk/display.aspx?DocID=24420), in any

relevant Thesis restriction declarations deposited in the University Library, The University

Library’s regulations (see http://www.library.manchester.ac.uk/about/regulations/) and

in The University’s policy on Presentation of Theses

28

Acknowledgement

First and foremost, I want to express my deepest appreciation to my supervisor Professor Srichand

Hinduja. He is one of the most dedicated scientist and teacher I have ever met. It has been a great

honour to be one of his Ph.D. student. He has taught me patiently and enthusiastically. He would

miss a train home to guide me through a mathematical formula. For every piece of knowledge I

learnt during this journey, I owe my gratitude to him. He has a kind heart and thoughtful mind. I

want to thank him for all the afternoon teas he bought me. I thank him for offering me financial

assistance when my funding was discontinued and the following year he tried hard, and succeeded,

in obtaining funding which I greatly appreciate.

I would like to show my gratitude to Dr Robert Heinemann for his immense knowledge in design

and metrology that helped me throughout the study. I appreciate his contributions of time and

ideas to make the design of the inspection machine successful. I also want to thank him for those

excellent suggestions regarding testing of the machine.

I will forever be thankful to Dr John Atkinson. He taught me and supported me as an academic

tutor during my undergraduate study and recommended me as a candidate for this Ph.D. project.

Without him, I would not have become aware of this project.

I gratefully acknowledge the funding received towards my Ph.D. from ELE Advanced Technologies

Ltd and Knowledge Transfer Partnerships. I also want to thank Mr Peter Calderbank from ELE for

his contributions of ideas during the first two years.

My thanks also go out to all my collaborators: to Mohammed Saeed Ali Aljommah and C Indrajid

for their ideas and work in testing the ultrasonic probe; to Guolong Zhong, Kai Zhang and Ziyu

Meng for their explorations and findings in reverse engineering turbine blades; to Sigurdur Thor

Larusson for his ideas and work towards localisation algorithms. Without them, this Ph.D. would

not have been achievable.

I would like to offer a special thanks to all the team members in DigitME at the University of

Central Lancashire. They help in robot control and robot programming is greatly appreciated. Their

C# examples were the most precious resources during the early stage of software development.

I appreciate all the support Dr Hugh Frost provided me during selecting and assembling electronic

devices for the inspection machine. I would like to thank Robert Brown for the tips he provided

regarding control of the robot and testing of the machine. I also want to thank Phil Oaks and all

29

the technicians on A floor in the Pariser building for all the components they machined for me and

all the assistance during experiments.

Lastly, I would like to thank my families for all their love and encouragement. I thank my mum and

dad who raised me up, cared me and taught me. They believed in me and funded me throughout

the journey of this nearly eight-year overseas study. And for my beloved wife who came to the UK

from China and supported me in life during the final stage of this Ph.D., I thank you.

Zhengyi Jiang

30

Introduction

A turbine blade is an important component in a gas engine, which is responsible for extracting

energy from high temperature and high pressure gases that are produced by the combustor. In

order to increase the efficiency of an aero-engine, combustion occurs at temperatures in excess of

1100°C. Turbine blades are mostly made of nickel based super alloys, namely Inconel, by

investment casting. The melting points of different classes of Inconel are between 1390°C and

1425°C. These high temperatures make the turbine blades vulnerable to damages such as creep

and corrosion [1]. To protect the turbine blade from these damages, multiple cooling channels, as

shown in Fig. 2.1-1 (a), are machined in the blades through which cold air is forced through, thus

lowering the overall temperature of the turbine blade [2].

Fig. 2.1-1 (a) A CAD model of a turbine blade. (b) A cross-section of the blade and the wall thickness.

ELE Advanced Technologies Ltd (hereafterwards referred to as ELE) is a company located in the

North West of England and it specializes in the machining of cooling channels in blades using

electro-chemical techniques for industrial gas turbines. Cooling channels are designed and

machined so that they are at a certain distance from the high and low pressure surfaces of the

blade. The distance from the surface of the blade is referred to as the wall thickness, illustrated in

Fig. 2.1-1 (b). Wall thickness is an important parameter as it influences the effectiveness of the

(a) (b)

Wall thickness

31

cooling channels, and hence the performance of the blade. Thus clients of ELE (like Siemens, Rolls

Royce, etc.) insist on the company measuring the wall thicknesses of cooling channels at several

positions on the blade accurately.

At present, ELE measures the wall thickness manually using an ultrasonic delay-line transducer. At

first, one blade from the batch is selected and scanned by X-ray to identify the locations of cooling

channels. These locations for inspection are then marked onto a mask and then marked onto

blades for inspection. As shown in Fig. 2.1-2, the operator applies a thin layer of couplant covering

the entire area of the transducer’s wear cap and then presses the transducer onto the desired

location of the blade surface precisely and firmly. In the process of inspection, the ultrasonic probe

must be kept normal to the blade surface all the time to obtain the maximum signal from the

ultrasonic probe. However, even a skilled operator requires time and skill to ensure that the probe

is normal to the desired position on the blade surface in practice. In addition, there are positional

tolerances and shape tolerances during the manufacture of both the turbine blade (investment

casting) and cooling channel machining (EDM), which means the blade shape and the position of a

cooling channel might be different from the original CAD drawing. If the shape of the blade is

different, even if the probe is exactly perpendicular to the designed blade surface, the result may

still not be the correct wall thickness. Unacceptable errors may show up during the inspection

process. Moreover, for a blade of typical size (blades inspected by ELE vary from 100 to 500 mm in

length), there are about 64 positions that need to be inspected. When the number of positions is

combined with the time required to find the normal direction at each position, inspection of a blade

becomes a time- consuming task. At the moment, it takes an operator just over half an hour to

measure, and record, the wall thicknesses for an average-sized blade.

A system is therefore required which would automate the inspection of wall thicknesses in turbine

blades. The requirements of such a system are listed below.

Fig. 2.1-2 (a) An illustration of ultrasonic delay-line transducer. (b) The ultrasonic probe is kept normal to the surface of the blade at various inspection locations

Couplant

Ultrasonic probe

Test piece

Pressure

Wear cap

(b) (a)

32

i. Ultrasonics and CT scanning are two techniques that can be employed for measuring wall

thicknesses. However, a CT scanner is expensive (costs involved are in in excess of £750k)

and the time required for scanning and analysis can be a few hours. Both these factors

make it uneconomical for a small company like ELE. The company has been using

ultrasonics for a long time and has considerable expertise in this area; therefore, ELE

would like to continue using ultrasonics.

ii. The system should be more accurate and consistent than current practice. At the moment,

the accuracy that can be achieved with a hand-held ultrasonic probe is around 0.5 mm.

Therefore, the target accuracy for this project is 0.2 mm.

iii. The CAD blade geometry will be different from the actual manufactured blade and

therefore the former cannot be used to generate the probe path.

iv. The time for inspecting a blade should be less than that required for manual inspection.

v. Incorporate a high degree of automation.

vi. Be cost effective. A budget of around £45000 was set by ELE.

Research direction

i. In ultrasonic testing, both contact and non-contact probes are available. To automate the

testing procedures, contact probes can be used but a mechanism must be designed to

avoid damaging the probe caused by operator’s mistakes. This mechanism may however

result in errors and increase the complexity of the project. Non-contact probes, on the

other hand, are usually preferred [3]. Non-contact probes are immersion ultrasonic probes

which use water as the coupling medium. In this case, only a water tank is needed to

immerse the test workpiece (i.e. turbine blade in our case) as well as the probe.

ii. The accuracy requirement of the inspection system can be easily achieved with a

computer-controlled actuator. This actuator must have at least five degrees of freedom

because it is necessary to keep the ultrasonic probe normal to the surface of inspection

during measuring. In practice, a six-axes system would be required as it would not be able

for the actuator to measure all the wall thicknesses of a blade in one pose. The sixth axis

would rotate the blade through a certain angle.

iii. Similar to CNC machining, a path for the tool, in our case the probe, needs to be

determined. This would require knowledge of the geometry of the turbine blade. Since a

CAD model cannot be used, a mathematical model of the blade has to be constructed,

based on which the probe path can be calculated.

33

iv. As reverse engineering each blade is time consuming and this may violate the time

requirement for the inspection system, research should be conducted to investigate if the

same free-form representation and probe path can be used for all the blades in a batch.

v. Apart from the actuator, to achieve a high degree of automation, the PC should also

control the entire system, including the ultrasonic PCI card that would be required to

acquire the probe data.

Aim and objectives

The main aim of this project is to develop an inspection system to automatically measure wall

thicknesses of turbine blades.

The objectives are summarized as follows:

i. Test and study the capabilities of the ultrasonic probe, investigating the parameters that

affect its accuracy.

ii. Design and manufacture a prototype of the inspection machine.

iii. Develop algorithms for reverse engineering turbine blades and probe path generation.

iv. Investigate whether a common probe path can be used for all blades from the same batch.

v. Develop software to integrate and control the various parts of the inspection machine i.e.

robot control, blade rotation, loading/unloading of ultrasonic probe and laser probe.

vi. Develop software to anlyse and extract the wall thicknesses from the acquired ultrasonic

signals.

vii. Test and evaluate the inspection machine for a range of components including blades.

The thesis is mainly divided into four parts. The first part (Chapter 1 and Chapter 2) includes the

Introduction and Literature Review, which will help the reader to understand the main aim and

methods used in this thesis. The second part (Chapter 3 and Chapter 4) presents the design of the

inspection machine and control algorithms. In the third part (Chapter 5), theories and algorithms

for reverse engineering and probe path generations are discussed. The last part (Chapter 6)

discusses research results including the capabilities of the ultrasonic probe, geometry deviations of

turbine blades and ultrasonic measuring turbine blades on the inspection machine.

34

Literature Review

In industry, the current method of measuring wall thicknesses in turbine blades is to use an

ultrasonic contact probe. However, this method is time-consuming and sometimes there are

problems in obtaining accurate results. Automation of the measuring process would require an

ultrasonic immersion probe, which could be attached to an actuator and moved above the surface

of the turbine blade for taking measurement. In this case, the probe paths for the actuator have to

be calculated.

Literature reviews in the field of ultrasonics reveal that during ultrasonic testing, the probe has to

be held normal to the surface. This means that the surfaces of turbine blades need to be reverse

engineered and from the reverse engineered models surface normals can be calculated in order to

compute the probe paths.

In this chapter, literature reviews are presented for both ultrasonic testing and reverse

engineering.

35

Ultrasonics

Definition of ultrasound

Fig. 2.1-1 Different bands of sound frequencies

The term “ultrasound” refers to a cyclic acoustic pressure wave (expansion and compression) at

frequencies beyond the audible range, i.e. above 20 kHz [4]. The different bands of sound

frequencies are shown in Fig. 2.1-1.

Sound with a frequency below 20Hz is called infrasound, which has special applications in geology,

seismology and medicine; from 20Hz to 20kHz is the audible range; above 20kHz is ultrasound.

The ultrasonic range can be further classified into three regions depending on the magnitude of

the operating frequency [4]:

20kHz – 100kHz, power ultrasonics, used for sensitive chemical systems where physical

and chemical alterations are desired.

100kHz – 1MHz, high frequency ultrasonics.

1MHz – 500MHz, diagnostic ultrasonics, within which from 2MHz to 200MHz is the non-

destructive testing (NDT) frequency range.

Capabilities and limitations

Ultrasonics has the capability of detecting both surface and subsurface discontinuities and

determining reflector location with high accuracy and high resolution. This capability of ultrasonics

defines its importance in flaw detection and thickness gauging. Other advantages of ultrasonic

testing include no requirement for samples to be prepared or a severely controlled environment [5]

[6].

On the other hand, the main disadvantage of ultrasonic testing, noted by Cawley [7], is that when

ultrasonics is employed for scanning a large area, the process can be time consuming. This is due

to the fact that the inspection area of one pulse is essentially limited to a small zone.

The accuracy of ultrasonic thickness measurement is affected by surface roughness of the

inspected object. Due to surface roughness, ultrasonic waves may travel in several different sound

20Hz 20KHz 2MHz 200MHz

Infrasound Acoustic Ultrasound NDE1 range

1 Non-destructive evaluation

36

paths in the material which causes wave interference. Therefore, the shapes of the returning

echoes may be distorted and the accuracy of thickness measurement lowered [8]. Blitz and

Simpson [9] suggest that the effect of surface roughness on measurement accuracy should be

considered on both the front and back walls.

Another limitation of ultrasonic testing, according to Thompson [10], is that materials with a

microstructure larger than the wavelength of the ultrasonic transducer can cause excessive

attenuation and backscattering.

In addition, both Cawley [7] and Thompson [10] argue that the correct alignment of ultrasonic

beam is sometimes challenging. During ultrasonic inspection, it is essential to maintain the

ultrasonic beam perpendicular to the surface of inspection to avoid refraction at interfaces. This

becomes especially challenging when inspecting a non-planar surface. Thompson [10] notes that

this problem becomes even more severe when inspecting metal which is submerged in a coupling

medium (such as water) rather than the direct contact technique because the difference between

acoustic velocities in water and metal is usually greater than threefold.

Characteristics of ultrasonic testing

While use of the immersion technique in inspecting curved surfaces brings more challenge, a

specific type of immersion transducer, a point-target focused (PTF) transducer, is employed to

overcome this problem. A point-focused transducer gradually narrows the spread of ultrasonic

energy giving a boost in signal strength within the focal zone. Besides, the area of attack of an

ultrasonic wave at interfaces is reduced and consequently refraction of ultrasonic wave is

minimized. Other benefits of using a focused immersion transducer include improved resolution,

sensitivity and precision within the focal zone [6].

Fig. 2.1-2 Near field and far field [11]

37

For both focused and unfocused ultrasonic waves, near field and far field (see Fig. 2.1-2) are

important characteristics. The near field is defined by a region directly in front of the transducer

face where the intensity of the ultrasound is affected by interference both constructively and

destructively. Owing to the two modes of wave interference, within the near field distance 𝑁, the

intensity of ultrasound varies significantly [12].

The end of the near field is referred as the natural focus of ultrasound. Beyond the natural focus

begins the far field where ultrasound waves are relatively uniform whereas the intensity reduces

gradually. Near field distance can be calculated by:

𝑁 =𝐷2𝑓

4𝑉 Eq. 2.1-1

where 𝐷 is the element diameter of the transducer, 𝑓 the frequency of ultrasound and 𝑉 the

acoustic velocity.

Due to fluctuation of the intensity of ultrasound in the near field, it is suggested that in ultrasonic

flaw detection or distance gauging, the reflector should be placed beyond the near field [12] [13].

Focused ultrasound enjoys a shortened focal distance, which means a uniform ultrasonic beam is

formed faster. Olympus [11], an ultrasonic transducer manufacturer, has documented their

research on focused transducers. The -6dB focal zone1, 𝐹𝑍, of a transducer can be calculated using

Eq. 2.1-2.

𝐹𝑍 =2𝑁𝑆𝐹

2

1 + 0.5𝑆𝐹

Eq. 2.1-2

where 𝑆𝐹 is the normalized focal length given by Eq. 2.1-3.

𝑆𝐹 = 𝐹 𝑁⁄ Eq. 2.1-3

where 𝐹 is the focal length.

Fig. 2.1-3 -6dB focal zone

1 The focal zone wherein the amplitudes of on-axis ultrasonic signals are within -6db of the amplitude at the focal point, also see Fig. 2.1-3

38

For a specific focal length, the normalized beginning point of the focal zone, SB, and the

normalized ending point, SE, can be obtained using Fig. 2.1-4.

Fig. 2.1-4 Normalized beginning and ending points of the -6dB focal zone [11].

These equations can be used to determine an optimized water path for positioning the transducer

such that the ultrasonic wave attacks interfaces around the beginning point of its focal zone and

hits the reflector before it reaches the ending point. Therefore, this requires a transducer with a

correct focal length that is sufficient to provide a focal zone to cover the entire material path,

which is the distance between the interface and reflector. Nevertheless, such requirement is

difficult to achieve if the reflector is deep inside the test piece. This is because the focal length for

transducers of a given element diameter and frequency is limited in practice. As shown in Fig.

2.1-5, Olympus [11] notes that the increase in signal strength is inversely proportional to the focal

length. To avoid a weakly focused transducer, the focal length should not exceed 0.8 times the

near field.

Fig. 2.1-5 Variation of relative increase in signal amplitude with normailized focal length SF [11].

Besides, Olympus [11] suggests that the focal length is normally shortened due to the effect of

refraction at the interface, as shown in Fig. 2.1-6. According to Snell’s Law, the optimum water

path (path at which the response is a maximum) can be calculated using Eq. 2.1-4. Due to the fact

39

that the sound velocity is usually faster in the test piece than in water, for inspecting deep

subsurface features, the focal length must be sufficient to work out a positive amount of water

path.

𝐹𝐸𝑛𝑒𝑤 = (𝐹𝐸 − 𝑊𝑃) (𝑐𝑤

𝑐𝑡𝑝

) Eq. 2.1-4

where 𝐹𝐸𝑛𝑒𝑤 is the shifted end point of the focal zone, 𝐹𝐸 is the new end point of focal zone, 𝑊𝑃 is

the length of water path, 𝑐𝑤 is the acoustic velocity in water and 𝑐𝑤 is the acoustic velocity in the

test piece.

Fig. 2.1-6 Focal point shifts when an ultrasonic wave enters the workpiece. Reproduced from Olympus NDT

(2011) [11].

Data Processing

2.1.4.1. Time of flight

Blitz and Simpson [9] summarise that ultrasonic testing includes the measurement of “time of flight

(or delay) of the waves, path length, frequency, phase angle, amplitude, impedance and angle of

wave deflection (reflection and refraction)”. Some measurements such as time of flight, path

length, frequency etc. can be simply deduced from ultrasonic signal plots.

In amplitude-vs-time plots, known as the time domain, valleys and peaks of reflected sound waves

can be identified as they are usually strong spikes. The measurement of the time difference

between these valleys and peaks, i.e. the measurement of the time of flight, can be used for

evaluating the thicknesses or locations of flaws [14]. For time of flight measurement, depending on

the selection of pulses or echoes, Fowler et al. [8] classify the method into three basic modes:

WP

F

Transducers

Water

Workpiece

Focal point in workpiece

Focal point in water

i. Mode 1: the measurement is taken between the

excitation pulse and the first backwall echo.

40

Fig. 2.1-7 Different modes for time of flight measurement.

Mode 2 is typically used for curved shapes. Mode 3 usually gives the highest accuracy and best

resolution, but it is only practical when sound attenuation is low and the material has a high

acoustic impedance which is usually the case with fine-grained metals. [8]

2.1.4.2. Calibration

Calibration, as defined by Berke [15], is a linear representation, from the zero position on the

scale, of a certain distance range of the test sample. The zero position is usually the surface of the

test sample. The calibration must be associated with the material of the test sample because the

sound path is always half the product of the sound velocity in the material and the time of flight of

the sound wave, expressed by Eq. 2.1-5.

𝑆 =𝑐𝑡

2

Eq. 2.1-5

where 𝑆 is the sound path, 𝑐 the acoustic velocity in material and 𝑡 the time of flight.

However, Berke [15] states that this equation is not essential for calibration procedures. The

calibration is established by placing the transducer over a series of known thicknesses of a

calibration block, which is made with the same material as the test sample, and linearly relating

the associated scale position with the thicknesses, or sound path:

𝑇𝑖 =𝑆𝑖

𝑘

Eq. 2.1-6

where 𝑇𝑖 is the scale position of the ith echo, 𝑆𝑖 is the sound path of the ith echo and 𝑘 is the scale

factor.

Fowler et al. [8] observed that for ultrasonic thickness measurement, one calibration is only

accurate to a degree in the thickness range the calibration is performed. It is particularly the case

for materials with non-uniform grain structures, such as some cast metals. Therefore, sets of

calibration should be performed for different thickness ranges to achieve most accurate calibration

results.

ii. Mode 2: the measurement is taken between the first

interface echo and the first backwall echo.

iii. Mode 3: the measurement is taken between two backwall

echoes.

41

Fowler et al. [8] also argue that due to the variation in the types of transducer, cable length and

the meansuring mode, a zero offset is needed. A modified equation is shown in Eq. 2.1-7.

𝑇𝑖 =𝑆𝑖

𝑘+ 𝑐

Eq. 2.1-7

where 𝑐 is the zero offset.

2.1.4.3. Error

Hammond [16] identifies three types of

error in determining an accurate time

of flight.

As shown in Fig. 2.1-8, the

determination of time of flight is

affected by two errors, ΔRϕ and Δθ

[16]. ΔRϕ is the error caused by the

sampling rate. Δθ is called phase angle

error, which results from cropping of a

peak at the detection threshold of

signal strength level. This error,

however, can be avoided by using a lower receiver gain to reduce the amplitude of the peak below

the detection threshold [16].

Determination of time of flight is also affected by another error, Δø, related to the precision of the

internal clock. Nevertheless, with modern precision electronics, this error is usually negligible.

2.1.4.4. Noise

Along with ultrasonic wave signals, noise or unexpected signals are captured by the receiver.

According to Diederichs [17], noise usually originates from:

(a) probe noise;

(b) weak echo due to material grain, texture and composition;

(c) electronic noise due to amplifier, pulser reverberations and reflection in cable [8], and

(d) interferences due to electro-magnetic.

Application

In science, industry and medicine, ultrasonic testing has a broad range of applications [18].

True ToF Δθ

Detection

Time Tick Evaluated ToF ΔRϕ

Threshold

Fig. 2.1-8 Errors in time of flight (ToF) measurement (reproduced from Hammond [16])

42

In medicine and the field of biology, ultrasound, along with X-ray and nuclear, is one of the

important diagnostic tools. It is employed mainly for measuring and visualizing biological tissues

and organs as well as detecting tumours [19] [20]. Recent developments in ultrasonics have

significantly extended the application of ultrasound in biology, such as flow speed detection based

on Doppler effect (see Fig. 2.1-9 (a)) [21], delivering drugs to skin [22] and assisting microsurgery

for Cushing’s Disease [14].

Fig. 2.1-9 Blood flow in the carotid artery bifurcation [21]

In engineering, ultrasonic testing is widely used in inspecting subsurface features, e.g. air gap and

cracks, in different objects. Krautkraemer, one of the companies specializing in ultrasonic

inspection highlights many different ultrasonic applications in [23], including crack detection in a

disk brake, measurement of corrosion tension cracks in aluminium and wall thickness

measurement of bent copper tubes.

Amulele et al [24] carried out experiments in which a cylindrical component and a gas turbine

blade were measured using a focused ultrasonic immersion probe. Both components were made of

the same nickel-based superalloy, i.e. Inconel. They used a CMM to obtain the external surface

profile of the test pieces, from which probe paths were calculated. During their experiments, the

probe was kept normal to the surface of the test piece at a distance equal to the focal length of

the probe. Regarding thickness determination, they used a velocity-time equation:

𝑑 =𝑣(𝐿)𝑡

2

Eq. 2.1-8

where 𝑣(𝐿) is the velocity of longitudinal wave and 𝑡 is time of flight.

43

In order to find an accurate value of 𝑣(𝐿), three elastic constants of the Inconel were determined

using Laue X-ray diffraction. The thickness measurement results were compared between CMM

and ultrasonic results, which show a 2% differences for the cylindrical test piece and 10% for the

turbine blade.

Conclusion

Ultrasonic testing is widely used as a non-destructive testing technique. The accuracy of ultrasonic

testing depends upon, amongst other factors, the accuracy of calibration, sampling rate and the

amount of phase angle error. For measuring turbine blades, an immersion probe was used in the

research conducted by Amulele et al [24]. However, the difference between the CMM and the

ultrasonic measured values, in the case of turbine blades, is as much as 10%. Investigations are

therefore required whether these differences can be reduced by considering not only the above

mentioned factors but also the length of the water path and the normality between the probe and

the surface of the component.

44

Reverse engineering

In order to obtain accurate wall thicknesses from ultrasonic testing, it is essential that the probe

path is calculated accurately. This probe path requires not only precise X-, Y- and Z-coordinates

but also precise angular positions so that the probe is kept normal to the surface of the test piece.

To calculate the probe path, a mathematical model of the turbine blade must be established such

that the probe path at a particular surface point is represented by a vector that is normal to the

surface at that point. This vector can be obtained from the cross product of the tangent vectors at

this point. Since the aerofoil part of a turbine blade is a free-form surface, the mathematical model

can only be obtained by reverse engineering. The CAD model of the blade cannot be used because

of differences between it and the actual manufactured blade.

A typical reverse engineering procedure consists of the following steps [25] [26] [27] [28]:

1. 3D digitizing;

2. registration;

3. pre-processing and triangulation;

4. data editing and segmentation, and

5. surface fitting and CAD model generation.

In the digitization process, the physical object is scanned to acquire point data on the surface of

the object. These points are usually unordered and separated. Ordering and combining of the

points are done in the process of registration. After registration, pre-processing takes place to

remove noisy points [27]. The remaining points are triangulated and a point cloud mesh is

generated. Next, the point cloud mesh is revised, edited and refined for a most precise

representation of the original object. Examples of editing are edge sharpening, boundary repair

and surface smoothing [26]. At the end of the editing process, a refined polygon model is

generated. In segmentation, the polygon model is divided into surface patches and these patches

are, in the next step, fitted with surfaces [27]. Surfaces are finally stitched together and a CAD

model is generated.

In the following chapter, published literature for digitization, registration, triangulation and surface

fitting including parameterisation is reviewed.

45

Digitization

The surfaces of turbine blades are commonly constructed from a set of parallel cross sections by

lofting [29].

Fig. 2.2-1 Surface of a turbine blade generated by lofting from a set of cross section profiles [29]

Digitization can be accomplished with either contact or non-contact methods depending on the

equipment deployed [27] [30].

2.2.1.1. Contact methods

In contact methods, measurements are performed based on mechanical contact between a

contact-type probe and the physical object. Modern contact-type probes are available in two forms,

touch-trigger probes or analogue scanning probes [31]. A touch-trigger probe performs a point-to-

point measurement whilst an analogue scanning probe provides a continuous measure of

deflections of the probe that can be associated with machine positions and thereby translated into

surface point data [32]. An analogue scanning probe typically measures up to three-times faster

than a touch-trigger probe [33].

The actuator of the probe can be either a coordinate measurement machine (CMM), a computer

numerical control (CNC) machine, an articulated mechanical arm or a robot [30] [31]. The

accuracy of contact measurements is highly related to probe positioning, as a contact-type probe is

usually very accurate in itself. For example, the accuracy of a TP200 touch-trigger probe from

Renishaw is, in the worst case, ±1.4µm [34]. CMM and CNC machines are normally more accurate

than a robot or an articulated mechanical arm. A Nikon LK V bridge CMM has a volumetric accuracy

46

of ±2.1µm [35] and this is still not the most accurate CMM, as they can have an accuracy of less

than 1 µm [35]. The accuracy of a calibrated robot, Fanuc LR Mate 200iC, according to Joubair and

Bonev’s work [36], is 32µm at best. One of the most accurate articulated mechanical arm, Faro

Gage is 18µm [37]. On the other hand, robots and articulated arms offer more degrees of

freedoms than a CMM or a CNC machine tool. For example, both the Fanuc LR robot and the Faro

Gage can provide six degrees of freedoms [38] [37]. This is particularly useful when measuring

components with complex shapes.

Fig. 2.2-2 Examples of different probe actuators

Contact methods usually suffer from many disadvantages when applied for numerous measuring

points on 3-D free-form surfaces such as low efficiency, inadequate data points, complicated tip

radius compensation and accelerated wear of the probe tip [39].

2.2.1.2. Non-contact methods

Non-contact methods are commonly based on the principle of acoustic, optical, magnetic and x-ray

[27] [30]. Geometric data of the scanned part are evaluated using time of flight (acoustic),

triangulation (optical), wave interference information (magnetic) and image processing techniques

(x-ray) [25]. Devices employ sound, magnetic field and x-ray are exceptionally effective in

obtaining 2D cross-sectional images. Optical devices, such as laser sensors and vision systems

(consists of a projector and a camera) [40], are mainly used for scanning the outer skin of an

object.

Non-contact probes can be equipped on hand-held devices such as the Nikon K-Scan MMDx laser

scanner shown in Fig. 2.2-3 (a), which offers full freedom. Hand-held devices usually work with a

series of other non-contact probes, such as the Nikon K600 laser tracker shown in Fig. 2.2-3 (b),

which continuously measure the location and orientation of the hand-held device and thereby

(a) A Nikon LK V CMM [35] (b) A Fanuc LR Mate 200iC robot [38] (c) A Faro Gage [37]

47

interpret the geometric data of the object. The actuators of non-contact probes can also be CMMs

[41], CNC machines, robots and articulated arms.

Fig. 2.2-3 A Nikon hand-held laser scanning system [42]

The biggest advantage of using non-contact methods is the significant increase in sampling

rate/digitizing speed. For example, a 2D laser scanner is capable of taking 2500 data points per

second with a resolution of 10µm [43], while a CMM with a touch probe needs 2s to take one point

[44]. Another advantage that is mentioned by several researchers [45] [25] is non-contact

methods enable the capability of measuring soft objects.

Although many researchers prefer to use CMMs with a touch probe to acquire reference surfaces

for their research [40] [43] [46], it is difficult to justify the accuracy of a non-contact system over

a contact system when the probe actuator is different. A cheap Keyence 1D laser sensor, IL-S025,

offers an average accuracy of ±7.5 µm [47], compared with ±1.4µm accuracy offered by an

expensive touch-trigger probe [34]. However, with modern technologies, ultra-high accuracy laser

sensors are also available, such as a Keyence LK-H008W laser sensor, which offers an average

accuracy of ±0.5 µm and a repeatability of 0.005 µm and it is still a lot cheaper than the TP200

touch probe [47].

Vision system and laser sensor

In our case, the test objects are the aerofoil surfaces of turbine blades for industrial gas turbines

and therefore efficiency and accuracy are both our concerns.

Chen and Lin [48] explain an approach for reverse engineering a wax model of a turbine blade

incorporating a vision system and a CMM. In their approach, an initial triangulation representation

of the model was obtained rapidly with the vision system, based on which probe exploration paths

were calculated for a subsequent detailed digitization using the CMM.

(a) A Nikon K-Scan MMDx laser scanner (b) A Nikon K600 laser tracker

48

In 2001, Carbone et al [40] demonstrated a method to digitize a turbine blade using a vision

system. In their vision system, a projector was used for projecting a dense mesh of points onto the

surface of the blade and a video camera was used to capture images of the mesh, which were

then processed to obtain surface data. The surface of the blade was also re-digitized with a CMM

to set up a reference point cloud. The maximum digitizing errors using the vision system are

0.155mm and 0.658mm on the concave and the convex surface respectively.

In a more recent research, Gameros et al [46] reverse engineered a turbine blade with three

different methods using a CMM, which was used to obtain a reference surface, a 3Shape Q800

laser scanner and a Zeiss METROTOM 1500 CT scanner. The surface constructed from point data

obtained with the laser scanner shows a closer representation to the reference surface, with

majority of the deviation values within ±20µm. A CT scanner has a relatively poorer accuracy with

most of the deviation values within ±60µm.

In both researches, CMM results are used as references, and three types of non-contact digitizing

methods are tested. It is found that the laser scanner is the most accurate device, even though a

3Shape Q800 is only an industrial laser scanner for general purposes [49].

Triangulation is the theory of distance measurement for most laser sensors [25]. As shown in Fig.

2.2-4, the principle employs a laser diode or a source for laser beam to project a high-energy light

spot on the surface of an object and the reflection of the light spot is focused through a lens at a

known angle to the laser beam and captured by a sensor, usually a charge-coupled device (CCD)

[50] [51]. The coordinate of the reflected light on the sensor is recorded and the distance of the

object can then be calculated.

Fig. 2.2-4 Principle of laser triangulation [50]

The major contributors to errors in laser measurement are the high surface smoothness, surface

curvature and slope, volume scattering and inhomogeneous surface texture [52]. In the case of a

turbine blade, the aerofoil section has various surface curvatures, which could distort the laser spot

49

thereby reducing accuracy of laser measurement. Hüser-Teuchert et al. [50] simulated distance

measurement of an inclined surface and a 2mm sphere using a laser sensor. They note that a

surface inclined by 60° can cause an error of 1.7µm and a curvature of a 2mm sphere can cause

an error of 6µm. In a more recent research by Vukašinović [53], the problem was studied

experimentally. They found the accuracy decreases dramatically when measuring a surface beyond

an angle of inclination of 55°. They also suggest the use of the minimum possible measuring

distance as the accuracy also decreases with an increase in measuring distance.

The most developed laser sensors are of the 1D and 2D type. A 1D laser sensor only measures one

point at a time, while a 2D laser sensor measures a stripe on the surface containing thousands of

points as shown in Fig. 2.2-5 [54] [45]. Thus, a 2D laser sensor is considerably faster than a 1D

laser sensor in acquiring a substantial size of point cloud. However, 1D laser sensors typically

offers higher accuracy and repeatability than 2D laser sensors. The previously mentioned Keyence

LK-H008W laser sensor is the most accurate 1D laser sensor in current Keyence production line

while the most accurate Keyence 2D laser sensor, LJ-G015K, offers an average accuracy of ±1 µm

[47].

Fig. 2.2-5 (a) 2D laser scanning; (b) acquired data points structure in 2D laser scanning. Reproduced from Woo et al. (2002) [54]

It is essential to properly select the size of sampling for digitization [55]. Although the non-contact

technique improves the efficiency of the digitization process, allowing more points to be acquired

in a short time, excessive number of points only burdens subsequent data processing. Besides, as

a 1D scanner normally cost less, it is very logical to consider reducing the density of data points

required so that the cheaper option becomes viable.

One major disadvantage of laser measurement, as McDonald et al [56] point out, is its inability to

measure surfaces parallel to the axis of the laser as shown in Fig. 2.2-6. Thus either the test

object or the laser sensor has to be re-positioned. This means that several sets of data points

should be combined together to have a common system of co-ordinates, a procedure known as

registration. Registration will result in a unified model for the entire object.

Laser sensor

Laser stripe

Test piece

Scanning direction

(a) (b)

… …

Sca

nnin

g d

irect

ion

… …

…

…

… …

Stripe 1 Stripe 2

50

Registration

A single view represents one part of an object, e.g. top view or front view. In order to obtain a

complete model, sets of points from multiple views need to be merged. This step is referred to as

registration. It involves transforming points in other views to one of the views used as the

coordinating system. The view used as coordinating system is referred to as the fixed view, while

the others are floating views, as shown in Fig. 2.2-7. [27]

Fig. 2.2-7 Registration of two separated surfaces of a cylinder

One method of obtaining the correct transformation for an object consisting of a general surface is

to measure three fixed points (which are not co-linear) in each view used. These points have to be

marked on the actual part so that they can be found again [27] [57]. In this case, transformation

matrices can be easily found between the three fixed points on the fixed surface and the three

other points on each of the floating surfaces.

2.2.1.1. Iterative closest point algorithm

However, if the floating surface overlaps the fixed surface as shown in Fig. 2.2-8, the

transformation is best solved by minimizing the distances between the points in the two point

meshes. The minimization problem is usually presented in form of least squares and is commonly

solved iteratively, known as the iterative closest point (ICP) algorithm.

Missed feature

Fig. 2.2-6 Measuring vertical surfaces with a touch probe and a laser probe. Reproduced from McDonald, J.A. (2001) [56].

(a) a touch probe (b) a laser probe

(a) Fixed view (b) Floating view (c) A complete surface

Fixed points

51

Fig. 2.2-8 Two partially-overlapping surfaces

In a typical ICP algorithm, one of the objects, 𝑄, is fixed being the target of the other, 𝑃, to get

the closest match iteratively. An ICP algorithm is usually constructed by looping the following steps

until convergence is achieved:

1. For each point in 𝑃, find its closest match in 𝑄.

2. Estimate a combination of rotation and translation that can align 𝑃 and 𝑄 as closely as

possible by minimizing the square errors between the matched points.

3. Transform 𝑃 with the transformation obtained in Step 2. Replace 𝑃 with the transformed

point set.

Depending on the required accuracy of the final result and the size of the point sets, ICP can be

especially time-consuming. This is because the conventional method for minimizing the function

developed in Step 2 involves iteratively solving nonlinear equations and this is repeated in every

loop, such as solving Eq. 2.2-1 by differentiating 𝐹 proposed by Menq and Sahoo [58].

𝐹𝑘 = ∑ ∑‖𝑇𝑘−1𝒑𝑖,𝑗 − 𝒒𝑖,𝑗‖

2

𝑁𝑃

𝑗=1

𝑁𝑄

𝑖=1

Eq. 2.2-1

where 𝑘 = 1,2,3… representing the number of iteration, 𝒑 ∈ 𝑃 = {𝒑𝑖}, 𝒒 ∈ 𝑄 = {𝒒𝑗}, 𝑁𝑄 is the total

number of points in 𝑄, 𝑁𝑃 is the total number of points in 𝑃, and 𝑇 is the transformation matrix

estimated in Step 2.

𝑇 is a 4 × 4 matrix consisting of zeros and one and six variables 𝑡𝑥, 𝑡𝑦 , 𝑡𝑧, 𝛼, 𝛽, 𝛾, which quantifies

the amount of translation along the x-axis, y-axis and z-axis and rotations about these axes

respectively. Solving these six unknowns involves differentiating a non-linear equation for each of

them, so the solutions are achieved iteratively. In the next step, 𝑇 is substituted into Eq. 2.2-1 and

for each 𝒑 the corresponding 𝒒 must be found to obtain a minimum 𝐹 in this iteration and again

this process is iterative.

(a) Before registration (b) After registration

52

2.2.1.2. Modified ICP and variants

Many researchers have developed different techniques to improve efficiency in solving Eq. 2.2-1.

Menq et al [59] introduced Eq. 2.2-2 to determine the transformation matrix 𝑇 by pseudoinverse.

𝑇𝑘 = (𝑃𝑘𝑃𝑘𝑇)(𝑄𝑘𝑃𝑘

𝑇)−1 Eq. 2.2-2

The algorithm starts with computing a transformation matrix with the original sets of points, i.e. 𝑃

and 𝑄 . After the first transformation matrix is found, 𝑃 is transformed with the transformation

matrix and a new set of points 𝑃𝑘+1 is obtained, which is used as the measured point set for the

next iteration. The target point set for the next iteration, 𝑄𝑘+1, is also replaced by a new set of

points which is created by projecting 𝑃𝑘+1 onto 𝑄, the target surface for this iteration. The new

standard deviation is, therefore, calculated between the two new surfaces.

The efficiency of the pseudoinverse technique was confirmed by Huang et al [60]. However, they

suggested parameterising the target surface and using control points instead of projected

measurement points to improve the accuracy.

So far in this literature survey, all researchers use axial-angle-based transformation matrix to

represent rotation, whereas Faugeras and Hebert [61], Horn [62], and Besl and McKay [63]

demonstrated quaternion representations of the transformation matrix, which can be solved non-

iteratively.

Arun et al. [64] also illustrated a non-iterative solution for solving the transformation matrix using

singular value decomposition (SVD). Haralick et al. [65] extended the previous work on SVD and

proposed a robust algorithm to solve 3D pose estimation problems. Their algorithm identifies

outliers which quaternion methods are not capable of, which is especially useful when localising a

small surface patch. However, the SVD method sometimes fails to determine a correct rotation

matrix [66].

Li et al. compares both Menq’s [59] and Besl’s [63] algorithms in [67], along with two other

algorithms, referred to as the variational algorithm [68], which is based on SVD, and Hong-Tan’s

algorithm [69]. In another research [70], a localisation method based on cyclic optimisation is

compared with Hong-Tan’s algorithm [69] and tangent algorithm [67]. Both researchers agree that

Hong-tan algorithm is the most accurate and fastest.

2.2.1.3. Two-step localisation

According to Campbell and Flynn [71], one of the most significant drawbacks of the above

discussed ICP method is that it is only effective when the two surfaces are initially closely aligned.

In order to overcome this problem, it is useful to set up a two-step localisation procedure where a

general localisation is first performed to reduce the initial alignment error between the two

53

surfaces and then the ICP algorithm is applied. Li and Gu [72], Yamany and Farag [73] and

Galantucci et al [74] demonstrated different methods for general localisation.

Fig. 2.2-9 (a) A free-form surface, (b) extracted regions (1’, 2’, 3’, 4’ and 5’) from the measured surface and

(c) extracted regions (1, 2, 3, 4 and 5) from the target surface. Figure is reproduced from Li and Gu [72]

In the general localisation procedure, Li and Gu [72] divide both the measured and target surfaces

into several regions which are characterised by either convex, concave, saddle or flat. To define

these regions, curvatures at each point are first calculated. Depending on the characteristics of the

curvature, each point is assigned with a shape code. Adjacent points with the same shape code are

grouped and this group of points is now a region. An illustration of a free-form surface defined by

regions is shown in Fig. 2.2-9, where both surfaces shown in (b) and (c) are divided into five

regions, which are labelled by 1’, 2’, 3’, 4’, 5’ and 1, 2, 3, 4, 5 respectively [72]. The shape codes

of the regions on one surface are then compared with those on the other. A general localisation

between two surfaces is found when the deviation in the shape codes of all regions is a minimum

and the transformation to roughly align the two surfaces can be calculated.

Yamany and Farag [73] introduce another algorithm for general localisation wherein simplex points

are generated and encoded with signatures for surface comparison. Simplexes can be obtained

from triangulation of the model. For each landmark point, 𝑃𝑙 , the signature contains two

components. The first component is the distance between 𝑃𝑙 and all other points in the model, 𝑃𝑙𝑖.

The second component is the angles between the normal vector at 𝑃𝑙 and the direction vectors

𝑃𝑙− 𝑃𝑙𝑖

‖𝑃𝑙−𝑃𝑙𝑖‖. With these signatures, a reduced representation of the surface at landmark points can be

obtained. A signature image can be plotted to visualise the representation as shown in Fig. 2.2-10

[73]. Once signatures are established in both models, the models can be brought together and the

transformation can be obtained.

Comparing the above two methods, it is obvious that Li’s method is more efficient in terms of

computational power as it does not require further complex calculation after the curvature at each

point is obtained. However, the effectiveness of Li’s method is limited when the model contains

very few geometric features that can be categorised into different patches, such as an aerofoil

surfaces of a blade where there are often two distinct features only, the high-pressure and low–

pressure sides which are convex and concave. Yamany’s method is slower; however, it is not

effective in surfaces of revolution, e.g. a cylinder and a cone but should be suitable for an aerofoil

surface.

(b) (c) (a)

54

Fig. 2.2-10 A parametric representation of a torus is shown at the top left corner. Three points are selected

from the torus and the corresponding signature image of each point is plotted. [73]

Triangulation

The purpose of triangulation is to establish the topological relationships amongst the data points

acquired during the digitization process, thereby creating a faceted surface in the form of a

triangular mesh generated by joining the acquired points [31].

One of the most well-known triangulation algorithms is the Delaunay triangulation, published by

Boris N. Delaunay in 1934 [75]. One important and distinctive property of a 2D Delaunay

triangulation is the empty circle constraint. This is defined as:

For a set of points S in the plane, a triangulation T is a Delaunay triangulation if no point in S is

inside the circumcircle of any triangle in T [76] [77].

Fig. 2.2-11 displays an illustration of a Delaunay triangulation. Consider the finite point set of

seven points {P0, P1, …, P6} as shown in Fig. 2.2-11 (a). There are different ways of constructing

triangles to form a triangular mesh. In Fig. 2.2-11 (b), P0, P1 and P2 are connected and this

defines a Delaunay triangle as there is no point inside the circumcircle of this triangle. Continuing

to connect P0, P2 and P3, P0, P3 and P4, etc., a Delaunay triangulation (Fig. 2.2-11 (c)) can be

Dis

tance

D

ista

nce

Dis

tance

Angle Angle

Angle

①

③

②

55

created. However, if P1, P2 and P3 are connected, as shown in Fig. 2.2-11 (d), a non-Delaunay

triangle is formed, because P0 is inside the circumcircle of this triangle and continuing connecting

other points does not create a Delaunay triangulation ( Fig. 2.2-11 (e)). It is clear from the figure

that the Delaunay triangulation is a better mesh compared to the non-Delaunay triangulation, in

which two of the triangles, P1-P2-P3 and P1-P0-P3, contain small acute angles. The empty circle

constraint ensures that the quality of the mesh is optimised i.e. acute angles in the triangular mesh

are maximised and obtuse angles minimised [78].

Fig. 2.2-11 Delaunay triangulation

A 2D Delaunay triangulation is easily generated from the Voronoi

diagram, also known as Dirichlet Tessellation, of the data points [78].

Fig. 2.2-12 demonstrates a Voronoi diagram of the finite point set

shown in the above figure. The Voronoi Diagram consists of cells, one

for each data point [31]. In a Voronoi cell, any point p inserted inside

the cell is nearer to Pi than any other data point; and if this point p is on

the edge of the cell, the distance between Pi and p is equal to the

distance between p and another point that is in the cell which shares the edge. The cell, in other

words, is a collection of the bisectors between two points, as shown in Fig. 2.2-13.

Fig. 2.2-13 Bisectors and the Voronoi diagram

The simple rule for generating the mesh is to draw the perpendicular bisector between each two

points and connect [79]. Thus, each vertex in the Voronoi diagram becomes the circumcentre for

(d) A non-Delaunay triangle

(c) A Delaunay triangulation (b) A Delaunay triangle

(e) A non-Delaunay triangulation

(a) A finite point set

P6

P1

P2 P3

P4

P5

P0

(a) Perpendicular bisectors (b) A Voronoi diagram

Fig. 2.2-12 A Voronoi diagram

p

P6

P1

P2 P3

P4

P5

Pi

56

its nearest three points as shown in Fig. 2.2-14 (a). Connecting points on the same circumcircle

produces a triangulation satisfying Delaunay’s empty circle constraint as shown in Fig. 2.2-14 (b).

Fig. 2.2-14 Generate Delaunay triangulation based on Voronoi diagram

Many works have been devoted into calculating Delaunay triangulation for the convex hull of the

point set based on the divide and conquer algorithm [80] [81] [76] [82]. In this algorithm, a

complete point set is divided into several subsets and triangulation is computed within each subset.

These subsets are then merged to construct a complete triangulation for the point set. Lee and

Schachter [76] also introduced a method to construct Delaunay triangulation by iteratively adding

points to existing triangulation.

Nonetheless, Delaunay triangulation is not

always unique. Non-uniqueness happens

when there are more than three points

which lie on the circumcircle [83], as

shown in Fig. 2.2-15. Four points ABCD all

lie on the same circle and there are two

solutions to Delaunay triangulation. It is obvious, however, that Fig. 2.2-15 (a) presents a better

triangulation than Fig. 2.2-15 (b). In order to compute a unique Delaunay triangulation, Dyken and

Floater [84] implemented a preferred direction rule in Lawson’s [80] local optimisation algorithm

for Delaunay triangulation. The preferred direction rule selects the diagonal in a convex

quadrilateral that is at a smaller angle to the selected direction.

Fig. 2.2-16 Two Delaunay triangulations computed with implementation of preferred direction rule at two different selected directions [84]

(a) Circumcentres and Circumcircles (b) Delaunay triangulation

(a) (b)

A

B

C

D

A

B

C

D

Fig. 2.2-15 The non-uniqueness problem

57

In a 3D Delaunay triangulation, tetrahedrons are generated instead of triangles and circumspheres

are used as a boundary criterion instead of a circumcircle as shown in Fig. 2.2-17 (a). An efficient

procedure to generate Delaunay tetrahedrons is proposed by Watson [85]. However, Cavendish et

al [78] found a serious flaw in Watson’s method as well as in 3D Delaunay triangulation. For a

Delaunay tetrahedron ABCD, fixing points A, B and C and moving D to any other position on the

circumsphere makes the tetrahedron ABCD still valid. Taking an extreme case as shown in Fig.

2.2-17 (b), if point D is moved to position D’ just above the circumcircle defined by ABC, ABCD’ still

defines a Delaunay tetrahedron but it is ill-constructed. This problem seems to be more common in

3D free-form surfaces with small but cluttered surface variations or a very scattered point set.

Golias and Dutton [83] found a solution to avoid distorted Delaunay tetrahedrons by inserting new

nodes at the middle of edges to subdivide the tetrahedrons.

Fig. 2.2-17 (a) A fine Delaunay tetrahedron and (b) a distorted Delaunay tetrahedron. Figure is reproduced from Cavendish et al (1985) [78].

In our case, the aerofoil surfaces are relatively smooth so distorted Delaunay tetrahedrons are

unlikely to occur. The use of tetrahedrons means that these solid elements are even created

between the high and low pressure surfaces of the blade i.e. through the thickness of the blade.

In our case, this is not required and all such elements must be deleted. Angelo et al [86] describe

a method to extract the triangulated surface from a full 3D Delaunay triangulation.

Fig. 2.2-18 Tetrahedrons in through the thickness of the blade

A

B C

D

C

A

B

D’

(a) (b)

58

Surface fitting

3D surfaces, similar to 2D curves, can be represented in both non-parametric and parametric

forms. In non-parametric form, x, y and z coordinates are related by functions whilst in parametric

forms, x, y and z coordinates are related by parameters, such as u and w, defined by functions.

Non-parametric representations are not commonly used in either 2D or 3D fitting problems

because in non-parametric representations, curve or surface evaluation is difficult [87]. Therefore,

non-parametric representations are not discussed herein.

Parametric representation usually involves control points and blending functions. Control points are

points defined in Cartesian coordinate systems that control the shape of the curves or surfaces.

Blending functions are functions of parameters used to weight the effect of the control points.

It is reasonable to understand 2D problems first because many 3D fitting approaches are

developed based on 2D fitting approaches.

2.2.3.1. Curve fitting approaches

Historically, curve fitting problems were solved using interpolation techniques, such as Hermite

curves [88] [87]. Hermite curves are most commonly seen as cubic curves, because every increase

in the degree of curve beyond three introduces small oscillations in the shape of curves and a

considerable increase in computation power [89]. The shape of any Hermite cubic curve is

determined by one position vector and one tangent vector at each end of the curve. Modification in

the shape of the curve is allowed by intuitively changing the vectors. However, it is difficult to

calculate the correct magnitude of the tangent vectors [87].

In the 1960s, Bezier developed a different curve fitting method, which is based on approximation

techniques, known as Bezier curves [90]. A significant departure from interpolation techniques is,

in approximation techniques, fitted curves pass around given data points rather than pass through

as in the case of interpolation techniques. This adds additional flexibility in controlling the curve

shape [89]. The shape and degree of Bezier curves is determined by vertices called control points;

an nth degree curve is defined by n+1 control points [90]. Higher order Bezier curves can be

obtained by increasing the number of control points with a reasonable amount of extra computing,

which in turn produce smoother curves. Shown in Fig. 2.2-19 are three seven-degree Bezier

curves, where dots and dashed lines represent control points and characteristic polygons defined

by control points. As the third control point is moved, the shape of the curve changes accordingly.

It can be observed that the first and the last control points in a Bezier curve constrain the two

ends of the curve and the remaining points define “the order, derivatives and shape of the curve”

[89]. The tangents at the two ends are defined by the first and last segments of the characteristic

polygon. This enables implementation of continuity between two Bezier curves.

59

Fig. 2.2-19 Effect of control points on a seven degree Bezier curves

While Bezier curves offer many advantages, its disadvantages are very obvious when Bezier curves

are employed for representing a complex shape. In this situation, there are two options. The first

option is to define this shape with many control points and consequently, a very high degree curve

must be calculated. Nevertheless, a high degree curve may introduce undesirable oscillations and

increase computational cost. The second option is to segment the shape and use many lower

degree curves. The problem with this option, however, is the difficulty in defining continuities

between each two of the Bezier curves while maintaining the shape of the curve [87]. Another

problem of Bezier curves is its global modification property, which means it is impossible to

selectively modify the shape of one part of the curve without affecting the rest parts of the curve.

This effect can be reduced by introducing additional control points. Nevertheless, the degree of the

curve is increased as well as computational cost. As shown in Fig. 2.2-19, moving P2 affects the

shape of the entire curve [87].

An approach known as B-spline curves overcomes these disadvantages found in Bezier curves. In a

B-spline curve, the shape of the curve is controlled by control points as well as some vectors that

divide the curve into several segments. These vectors are called knot vectors. The degree of the B-

spline curve, n, is defined by the degree of these segments and between each segment Cn-1

continuities are achieved automatically by merit of the equation of the blending function. Thus, the

degree of the B-spline curve is independent of the number of control points, which allows a low

degree curve that is defined by a large number of control points [89]. The number of segments is

determined from the number of control points, assuming that the degree of each segment has

𝑃0

𝑃1

𝑃2’ 𝑃4

𝑃2

𝑃2’’

𝑃5

𝑃6

𝑃7

𝑃3

60

already been decided upon. The shape of the curve can also be edited locally because the knot

vectors limit the effective range of control points. As shown in Fig. 2.2-20, moving P2 to P2’ or P2’’

only affects the part of the curve up to P4.

Fig. 2.2-20 A cubic B-spline curve

2.2.3.2. Surface fitting approaches

Similar to Hermite curves, a legacy approach to solve surface fitting based on interpolation is

known as Hermite surface. Two forms of Hermite surfaces are found in literature, bilinear and

bicubic surfaces. Bilinear surfaces are determined with four corner points with linear blending

functions and the resultant surfaces are generally flat [87].

(a) (b)

Fig. 2.2-21 (a) a Hermite bicubic patch and a F-surface patch

𝑃0

𝑃1

𝑃2’ 𝑃4

𝑃2

𝑃2’’

𝑃5

𝑃6

𝑃7

𝑃3

61

The bicubic surface is an extension of Hermite bicubic curves. As shown in Fig. 2.2-21 (a), the

shape of a bicubic surface patch is determined by the u and w coordinates, tangent vectors in u

and w direction (Pw and Pu) and a twist vector (Pt) at each corner. Bicubic surfaces are more

often used in form of surface patches that can be combined into a complete surface with C1

continuity at boundaries [89]. A simplified bicubic patch know as Ferguson surface patch (F-surface

patch) is useful in design and machining applications. As shown in Fig. 2.2-21 (b), a F-surface

patch is generated by assigning zeros to all twist vectors [89]. However, F-surfaces are generally

inaccurate and thus, rarely used in surface fitting problems.

The problems found in Hermite bicubic curves can also be found in bicubic patches, such as

difficulties in calculating tangent vectors, dramatic increase in computation for higher degrees, etc.

These problems are addressed in Bezier surface or Bezier patch, which is considered as an

extension of Bezier curve. The shape of a Bezier patch is defined by the control points and

characteristic polyhedrons as shown in Fig. 2.2-22. The four corners of a Bezier patch are given by

the four corner control points and the tangents at the corners in u and w directions are given by

the slopes of the segment and the remaining control points determines the boundary and internal

shape of the patch. Similar to Bezier curves, the degree of a Bezier patch in a certain direction is

given by the number of control points in that direction minus one [89] [87]. Continuities can be

specified at boundaries of Bezier patches to stitch several of them into one complete surface.

Fig. 2.2-22 A Bezier patch and its characteristic polyhedrons

However, when representing a complex surface, Bezier surfaces inherits similar disadvantages

from Bezier curves. Oscillations and additional computational cost are introduced if a Bezier surface

of high degrees is used; if multiple Bezier patches of lower degrees are used, it is difficult to

maintain continuity without excessively altering the shape of the patch which is constrained by

limited number of control points [87]. The extension of the B-spline curve, i.e. B-spline surface,

overcomes these problems.

Similar to B-spline curves, the degree of the surface is not related to the number of control points

and continuity between patches, which are divided by knot vectors, is automatically maintained by

62

the blending function. The B-spline surface also provides local control of the shape. Thus, the B-

spline surface is often suggested as a better surface fitting method over others [89].

2.2.3.3. B-spline surface fitting

The B-spline surface can be categorised into different types, such as uniform and non-uniform

B-splines, clamped and unclamped B-splines and non-uniform rational B-splines (NURBS). This

is also the case for the B-spline curve.

In uniform B-splines, knot vectors are uniformly spaced whereas in non-uniform B-splines knot

vectors are not. The use of non-uniform knot vectors offers additional flexibility in changing the

shape of the surface. Interpolation of corner points of the control polyhedron (indicated in red

colour), as can be seen in Fig. 2.2-23 (a) [91], is possible by repeating the corresponding knot

vectors several times; these B-splines are commonly referred as clamped B-splines. Fig. 2.2-23

(b) shows an unclamped B-spline surface, which does not interpolate corner points.

Fig. 2.2-23 (a) clamped B-spline surface and (b) unclamped B-spline surface [91]

The NURBS is the rationalised form of the B-spline. In the NURBS, each control point is assigned

with a weight which adjusts the level of effect of the control point on the local shape. This feature

is especially important in design since more shape variations can be achieved by manipulating both

the control points and the weights when fixed

knots were given.

Loop [92] demonstrated an algorithm for

generating smooth spline surfaces using

irregular meshes as input. The mesh is first

refined by generating more vertices, edges and

faces that corresponds to the vertices and faces

of the original mesh as shown in Fig. 2.2-24.

Next, based on the vertices of the refined

mesh, a “quad-net” (see Fig. 2.2-25) is

constructed. Quartic triangular patches can

(a) (b)

Fig. 2.2-24 Mesh refinement: original mesh (bold meshes) and refined mesh (thin lines) [92]

63

thereby be constructed by connecting the vertices in the “quad-net”. These patches are united in

the final step to form a complete B-spline. The outcome of this algorithm is quite good. Several

smooth surfaces generated using this algorithm are shown in Fig. 2.2-26.

Fig. 2.2-25 The quad-net corresponding to the vertex of the refined mesh [92]

Fig. 2.2-26 Examples of smooth surfaces reconstructed based on coarse meshes [92]

64

Similar to Loop’s work, Eck and Hoppe [93] introduced an algorithm for creating a tensor product

B-spline surface. Their algorithm is generalised for any topological type and can use an

unorganised set of points as input.

The B-spline surface is created in

five steps.

In the first step (see Fig. 2.2-28

(a)), a dense approximating mesh is

constructed from an unorganised

point set using a surface

reconstruction method introduced in

[94] and [95]. Based on this

approximating mesh, the points can

be parameterised.

The second step (see Fig. 2.2-28

(b), left) is to construct a simple

triangular base complex over which

the input points are re-

parameterised using a harmonic

map built upon the approximating

mesh.

The third step (see Fig. 2.2-28 (b),

right) starts with merging triangular faces of the triangular base complex to form a quadrilateral

base complex. Then the input points are taken for a final parameterisation.

In the fourth step, B-spline surface is used to reconstruct a surface. Finally, the re-constructed

surface is refined by subdividing the quadrilateral base complex (see Fig. 2.2-29).

Fig. 2.2-29 Control polyhedron (left), B-spline surface (middle) and refined surface (right)

Fig. 2.2-28 (a) A set of input points (left) and the approximating mesh (right)

Fig. 2.2-28 (b) Triangular base complex (left) and quadrilateral base complex (right)

65

2.2.3.4. Fitting of turbine blade surfaces

In the case of representing the surface of a turbine blade, Lin et al [96] use lofting methods to

create a surface model of a turbine blade from several cross sections. For approximating the cross

sections, they use two separate B-spline curves to model the low pressure and high pressure side

and two circular arcs to approximate the leading and trailing edge, as shown in Fig. 2.2-30, where

the blue curves are B-spline curves and the orange curves are circular arcs.

Fig. 2.2-30 Representation of a section curve, reproduced from [96]

The lofting method is also deployed by Lin et al. in [97]. The lofting algorithm is literally a curve

fitting method. The cross sections of a turbine are first fitted with B-spline curves with fixed

number of control points. Then B-spline curves are fitted in the vertical direction using the control

points corresponding to the same index number on each cross section. The accuracy of this

method is slightly poor than generic B-spline surface, but is more efficient in terms of computation.

Parameterisation

The B-spline surface fitting algorithm requires the Cartesian co-ordinates of each point to be

transformed into curvilinear iso-parameteric u and w co-ordinates. This process of transforming

from 3D into 2D is known as parameterisation. Many different parameterisation methods have

been developed for a 2D B-spline curve, such as uniform, exponential, universal, hybrid, chord

length and an extended exponential method proposed by Haron et al [98]. These methods also

work for a 3D problem by applying the same method twice, i.e. once for u and the other for w

[99]. Haron et al [98] also summarised the merits and drawback of these methods. In general, the

accuracy of these methods is limited and highly dependent on the shape of the object.

Nevertheless, some of these methods, such as the chord length method, are widely used for their

simplicity and fine accuracy in many less complex problems.

Chord length is the Euclidean metric between two neighbour points Pi, Pi+1 on the curve:

|PiPi+1| = √(𝑥𝑖+1 − 𝑥𝑖)2 + (𝑦𝑖+1 − 𝑦𝑖)

2 + (𝑧𝑖+1 − 𝑧𝑖)2 Eq. 2.2-3

For example, chord length between P1, P2 can be calculated by:

|P1P2| = √(𝑥1 − 𝑥2)2 + (𝑦1 − 𝑦2)

2 + (𝑧1 − 𝑧2)2

66

The u co-ordinate of one point on the curve is equal to the sum of all chord lengths before it

divided by the total chord length.

In terms of one B-spline segment, the u-coordinates are defined in the criterion [0,1], i.e.

𝑢1 = 0, and 𝑢𝑛 = 1.

𝑢1 = 0

𝑢2 =|𝑃1𝑃2|

|𝑃1𝑃2|+|𝑃2𝑃3| + |𝑃3𝑃4| + ⋯+ |𝑃𝑛−1𝑃𝑛|

𝑢3 =|𝑃1𝑃2|+|𝑃2𝑃3|

|𝑃1𝑃2|+|𝑃2𝑃3| + |𝑃3𝑃4|+⋯+ |𝑃𝑛−1𝑃𝑛|

⋮

𝑢n =|𝑃1𝑃2|+|𝑃2𝑃3| + |𝑃3𝑃4|+⋯+ |𝑃𝑛−1𝑃𝑛|

|𝑃1𝑃2|+|𝑃2𝑃3| + |𝑃3𝑃4|+⋯+ |𝑃𝑛−1𝑃𝑛|= 1

2.2.4.1. Barycentric mappings

Floater [100] demonstrated parameterisation of 3D points using a variation of Barycentric

mapping, known as shape preserving parameterisation. Barycentric mappings are widely used to

parameterise 2D images as well as in some 3D applications. It is based on the equation of affine

combination [101]:

∑𝜆𝑖𝑥𝑖

𝑛

𝑖=1

, ∑𝜆𝑖

𝑛

𝑖=1

= 1 Eq. 2.2-4

where 𝜆 are coefficients whose summation is equal to 1, 𝑥

can be vectors in which case, the equation represents a

linear combination.

In Barycentric mappings, 𝑥 either represents 3D points or the

parameterised representation of points, referred as the

barycentres. 𝜆 define the relationships between neighbouring

points in the triangular mesh, referred as barycentric

coordinates. The differences between different barycentric

mappings are basically the differences in weight functions

P2(𝑥2, 𝑦2, 𝑧2)

P3(𝑥3, 𝑦3, 𝑧3)

P𝑛(𝑥𝑛, 𝑦𝑛, 𝑧𝑛) P1(𝑥1, 𝑦1, 𝑧1)

Fig. 2.2-31 Triangulated model

67

which calculate barycentric coordinates.

In Floater’s [100] shape preserving parameterisation, the barycentric coordinates are weighted by

calculating the areas of triangles defined uniquely at each vertex for each barycentre. This weight

method preserves the solid angles at each vertex. He compared the quality of the shape

preserving parameterisation with two other parameterisation method, uniform and weighted least

square parameterisation by surface approximating a trangulated model shown in Fig. 2.2-31. The

result shows only the surface based on shape preserving parameterisation is smooth and accurate.

Fig. 2.2-32 Shape preserving parameterisation (left) and surface approximation (right)

Other well-known mapping methods are Wachspress mapping, discrete harmonic mapping and

mean value mapping [101].

The earliest work that demonstrates a weight function is done by Wachspress in 1975. The

equation he published is the Wachspress mapping [102]:

𝜆𝑖 =cot 𝛾𝑖−1 + cot 𝛽𝑖

𝑟𝑖2 Eq. 2.2-5

Discrete harmonic mapping is published by Eck et al [103] in 1995:

𝜆𝑖 = cot 𝛽𝑖−1 + cot 𝛾𝑖 Eq. 2.2-6

Mean value mapping is the most recent method developed by Floater [104]:

𝜆𝑖 =tan (

𝛼𝑖−1

2) + tan(

𝛼𝑖

2)

𝑟𝑖 Eq. 2.2-7

The unknowns used in these equations are shown in Fig. 2.2-33.

68

Fig. 2.2-33 The three mapping methods

Conclusion

For blade data acquisition, a fast and accurate method would be to use a laser sensor on a CMM. A

robot could also be used for acquiring data, but the positioning accuracy of the robot is likely to be

lower, likely to be around 32µm for a calibrated robot [36].

Free-form surfaces are commonly represented by B-spline surfaces. Non-uniform B-splines and

NURBS are typically useful in design-oriented tasks where the shape of the surface is required to

be modified. Uniform B-spine offers less flexibility in changing shapes but is the simplest form of B-

splines.

The Bezier surface and the B-spline surface are two good surface fitting techniques. Compared

with the Bezier surface, the B-spline surface is easier to control and eliminates the difficulties of

maintaining continuities. However, the Bezier surface is relatively easier to be programmed and is

probably sufficiently accurate for turbine blade surfaces.

Both fitting techniques require the surface to be parameterised which can be achieved using

Barycentric mapping methods such as Floater’s shape preserving parameterisation [100]. However,

Barycentric mapping requires surface triangulation. Delaunay’s triangulation calculates the

optimum triangulation for a given surface. Additional algorithm such as mesh growing algorithm

[86] should be used to extract the surface triangular mesh.

𝑣𝑖

𝛽𝑖 𝛾𝑖−1

𝑣𝑖−1

𝑣𝑖+1 𝑟𝑖

𝑣

𝑟𝑖

𝑣𝑖+1

𝑣𝑖 𝑣𝑖−1

𝑣

𝛼𝑖−1

𝛼𝑖

𝑣𝑖

𝛾𝑖

𝛽𝑖−1

𝑣𝑖+1

𝑣𝑖−1

(a) Wachspress mapping (b) Discrete harmonic mapping (c) Mean value mapping

69

Design of the Prototype Machine

The specifications as discussed earlier are as follows:

1. the accuracy must be lower than 0.3mm;

2. the system must have a high degree of automation;

3. it must make use of ultrasonics;

4. the cost of the system must be less than £45,000.

Since the cost of the system must be less than £45,000, the use of a five-axis machine is ruled out,

although the positioning accuracy obtainable with such a machine could be around five microns or

less. Therefore, the only other alternative is to use a six-axis robot.

Since an ultrasonic immersion probe must be used, an underwater environment must be provided

for inspection. Therefore, a water tank is required. Since the turbine blade is immersed in the

water tank and restricted by the limited space inside the tank, only part of the blade surface can

be measured at a time. In order to measure the entire blade, the blade must be rotated to allow

different parts of the surface to be inspected. Therefore, the system should be able to rotate the

blade through a specified angle, i.e. the system must have a rotary axis.

The use of an ultrasonic probe requires probe paths that are capable of maintaining normality

between the probe and blade surfaces during inspection. This requires knowledge of the blade

geometry. Since the cast blade is likely to be different from its CAD model, the blade has to be

reverse engineered. Therefore, the blade surfaces need to be measured and due to the low cost

requirement, a single point laser sensor should be used.

In order to achieve a higher level of automation, filling and draining of the water in the tank must

be controllable from a PC using software; therefore, float switches, a pump, a solenoid valve and a

compatible digital/analogue input/output device are required. The change of end effectors, i.e. the

tool attached to the face plate of the robot, should be completed with minimum human

intervention.

Finally, a rigid table is needed to accommodate the above-mentioned equipment.

70

The design of the system aims to create an inspection facility that uses an ultrasonic immersion

probe, a laser sensor, robot and computer to automate the inspection process. The proposed

design of the prototype machine, as shown in Fig. 3-1, consists of the following major

components:

1. a cast iron table that supports all the other components;

2. a FANUC robot;

3. an Olympus ultrasonic probe and an ultrasonic tool holder;

4. a Keyence laser sensor and a laser tool holder;

5. a water tank including a solenoid valve, a pump and two float switches;

6. a shaft-bearing system that holds blades;

7. a transmission system that drives the shaft;

8. a rotary axis pedestal for 6 and 7;

9. a tool change system that enables automatic tool change during the inspection process;

10. a wire mesh guard with two safety switches and relays;

11. other electronic equipment including a digital/analog I/O box and a PC, and

12. a fixture to hold the blade to be inspected.

71

Fig. 3-1 Rendered 3D model of the prototype inspection machine (mesh guard removed for clarity purposes)

72

Robot, ultrasonic probe and laser sensor

Robot

Because of this budget limitation, purchase of a five/six-axes machine tool, which would cost more

than £100k, was ruled out. Instead, it was decided that the actuator would be an industrial robot.

In this case, the inspection machine would have one additional rotary axis about which the spindle,

holding the blade, would be rotated.

The robot purchased was a Fanuc LRMate 200iD robot, as shown in Fig. 3.1-1 (a). It is a six-axis

robot and has a maximum reach of 717mm. The repeatability of the robot is ±0.02mm. Although

its motion accuracy is not specified by the manufacture, the accuracy of the predecessor of this

type of robot, LRMate 200iC, has been studied by Vincent et al [105].They found an uncalibrated

robot has a mean error of 0.195mm and a standard deviation of 0.15mm. After calibration, the

error was almost reduced by half. In more recent researches, Joubair et al [36] [106] calibrated

another 200iC robot, and they were able to reduce the mean error to 0.0132mm with a standard

deviation of 0.0102mm.

Purchased with the robot was a Fanuc R-30iB controller, as shown in Fig. 3.1-1 (b).

Communication between the controller and the PC can be established using different methods,

such as RS232 and TCP/IP protocol. More details of the robot and the controller are discussed in

Chapter 4.1

Fig. 3.1-1 The purchased Fanuc LRMate 200iD robot and R-30iB controller

(a) (b)

73

Ultrasonic probe and ultrasonic card

The ultrasonic immersion probe is a V316-SU transducer manufactured by Olympus, as shown in

Fig. 3.1-2(a). It is a point target focus (PTF) probe with a focal length of 20.32 mm. It is a single

element transducer of diameter 3.175 mm, producing 20MHz longitudinal waves with quarter

wavelength layer acoustically matched to water.

The ultrasonic card is a PCIUT3100 PCI card manufactured by USUltratek, as shown in Fig. 3.1-2(b).

The card can transmit ultrasonic pulse and receive returned ultrasonic data via a single port, which is

suitable for communicating with a single element transducer. The card is capable of sending

ultrasonic pulses with a maximum frequency of 17MHz triggered with software at a rate set by the

user. The returned ultrasonic data can be captured at a minimum rate of 100MHz, i.e. every 10ns.

Due to this high data acquisition rate, the captured data are temporarily stored in the card’s internal

memory and when the amount of data stored reaches the buffer size, which can be defined by the

user, all the data in memory are transferred to the PC via PCI port. With currently installed amount of

memory, the card can store up to 16382 data points (i.e. the maximum buffer size).

Other adjustable parameters include pulse voltage, damping, receiver gain, DC offset, low-pass

filter, high-pass filter, rectifications and adjustable trigger delay.

Fig. 3.1-2 (a) An Olympus V316-SU ultrasonic probe and (b) a USUltratek PCIUT3100 ultrasonic card

3.1.2.1. Focal zone of the Olympus V316-SU ultrasonic probe

Given the frequency and diameter of the probe, the near field length, 𝑁, of an immersion probe

can be calculated with Eq. 2.1-3 (see Chapter 2.1.3). For a probe of the same frequency and

diameter as the V136-SU, the near field length in water at 20°C (𝑉 = 1482𝑚/𝑠) is calculated as:

𝑁 =𝐷2𝑓

4𝑉=

3.1752 × 20 × 106

4 × 1482 × 103= 34.01𝑚𝑚

(a) (b)

74

Normalised focal length of V136-SU can then be calculated using Eq. 2.1-3:

𝑆𝐹 = 𝐹 𝑁⁄ =20.32

34.01= 0.60

Therefore, the normalised beginning and ending point of the focal zone are 𝑆𝐵 = 0.45 and 𝑆𝐸 = 0.9

respectively, as can be found in Fig. 2.1-4. This means the focal zone starts at 15.3mm and ends

at 30.609mm from the transducer face.

Laser sensor and analogue data acquisition

In the current marketplace, the most widely used laser sensors for distance gauging are single-

point laser sensor (also known as 1D laser sensors), and beam laser sensors (also known as 2D

laser sensors). A 2D laser sensor offers considerable superiority in measuring efficiency over a 1D

laser sensor. However, due to oscillation and heating problems, and for the same price, a 2D laser

sensor is often inferior to a 1D laser sensor in terms of accuracy and repeatability.

The accuracy of a laser sensor also varies with its measurement range. Usually the narrower the

measurement range is, the higher the accuracy. According to ELE, when the blade is held

horizontally, the difference in height between the lowest and the highest points on any cross

section is approximately 30mm.

As the budget was limited, a 1D laser sensor, Keyence IL-S065 shown in Fig. 3.1-3 (a), was

purchased. Specification of the laser sensor is shown in Table 3.1-1. The laser sensor is powered

via a compatible amplifier IL-1000 which also translates data acquired from the laser head into

distance reading presented on the imbedded screen. The amplifier also includes output cables that

transmits laser data in analogue form.

Fig. 3.1-3 (a) A Keyence IL-S065 CMOS laser sensor and (b) a Keyence IL-1000 amplifier

(a) (b)

75

Table 3.1-1 Specifications of a Keyence IL-S065

Measurement range 55mm to 75mm

Spot diameter (at 65mm) 55 x 1700µm

Repeatability 2µm

Accuracy 55mm to 65mm ±5µm

55mm to 75mm ±7.5µm

The analogue data from the amplifier output can be transmitted to a PC via a USB DAQ device, for

example a Measurement Computing USB-1208FS as shown in Fig. 3.1-4. This device receives

analogue data input and transmits the data to the PC via a USB cable at a maximum rate of

50kB/s.

Fig. 3.1-4 A USB-1208FS DAQ by Measurement Computing

76

Design of the water tank

The water tank is one of the essential components of the inspection rig. The tank must be

sufficiently large to accept the biggest blade in the production range, which, according to ELE

Advanced Technologies Ltd, can be 500 mm long and 200 mm wide. Since a large amount of water

is held in the tank, the side walls and the floor of the tank are subject to pressure. Thus, the tank

must be strong enough to avoid excessive deflection that may affect the accuracy of other

components, e.g. the rotary axis. Therefore, a finite element analysis is required to check the

deformation of the tank and ensure that the maximum stress is within the safe working limit for

the material.

To reduce the cycle time, automatically filling and draining of the tank should be completed within

a very short time, say one minute. Therefore, to automate the process, electronic equipment such

as a pump, solenoid valves and float switches are required. For completing the task of filling or

draining within a limited time, a high flow rate is expected, so calculations of flow rate are required

to select an appropriate pump, with hoses and pipes that match the output of the pump. A high

flow rate may give rise to water splashing problems, which must be avoided to prevent damage to

non-waterproof electric devices and non-stainless steels. The selection of these electronic

equipment is discussed in Chapter 3.4.

Besides, a transparent window is needed for monitoring the inspection process. The potential risks

of leaking must be handled.

The key considerations involved in the design are summarised as follows:

- Large enough to accommodate a turbine blade up to 500mm in length and 200mm in

width

- Be stiff enough to avoid excessive deflection when fully loaded with water.

- Fast filling and draining of the tank.

- A transparent window in one of the side walls of the tank.

- Complete water seal and ensure that there is no water splashing

To meet these requirements, a tank was designed.

Overview of the design

Overall, as shown in Fig. 3.2-1 (a), (b) and (c), the water tank is 1096mm in length, 600mm in

width and 403mm in height. The design of the water tank, in general, consists of four parts (as

labelled in Fig. 3.2-2): (1) a tank body, (2) a Perspex window, (3)-(5) pipe connectors and (6) an

77

inlet manifold. Parts (3-5) are the pipe connectors, (3) being the overflow2, (4) the inlet, and (5)

the outlet. The inlet manifold was designed to reduce water splashing during the filling process.

Apart from the Perspex window, all parts are made of stainless steel.

The internal dimensions of the tank, neglecting the folded structures, tubes and inlet manifold, are

1000*494*400 mm, thereby yielding a capacity of approximately 20 litres. The overflow was

designed 350mm above the bottom of the tank; therefore, the maximum operational capacity is

approximately 17.5 litre. Pipe connectors and the inlet manifold were welded onto the tank body.

The perspex window was fixed by twenty M5 bolts and nuts and the gap between the Perspex

window and the tank body was sealed with silicon glue.

2 On the parts list, the OD50 stands for 50mm outer diameter

Fig. 3.2-1 Different views of the water tank (units in mm)

(a) Front view (c) Left view

(b) Top view

(d) Isometric view

78

Fig. 3.2-2 An exploded view of the water tank

Detailed parts and dimensions

3.2.2.1. The tank body

The main tank body is made of five 3 mm thick stainless steel sheets, welded together. The sheets

that form the front and back walls are 1000*475 mm; the sheets for the two side walls are

646*400 mm; and the sheet for the bottom is 1006*500 mm.

The sheets for the front, back and two side walls are oversized to account for the ribs that run

along the length of the tanks at the top. The top two ribs were formed by folding the sheets as

shown in Fig. 3.2-3 (b), (c) and (d) whereas two 50*50*3 mm tubes were welded onto both the

front and back walls at the bottom of the tank, as can be seen in (d).

On the front wall of the tank, a 200mm*750mm cut-out was made for fitting the Perspex window.

Twenty M5 clearance holes were drilled around the cut-out for fixing the Perspex window. Four

trapezium plates were welded at the bottom in the four corners, as shown in (b) and (c). A

Ø6.6mm hole was drilled on the surface for fixing the tank onto the table.

On the right wall, there are three holes of different sizes. The bottom left one is 40mm in diameter

for the water outlet, with its centre 20mm from the bottom inner surface of the tank, such that the

hole is tangent to the base of the tank. The second outlet hole is 50mm in diameter, with its centre

Inlet manifold

79

28 mm from the outer bottom surface. The connector was designed to be inserted into the hole to

let the surface of the ring on the plane of the inside wall. The third hole in the right wall is for the

overflow. This hole is at a height of 350mm from the inner bottom surface of the tank and this

fixes the maximum water level i.e. 350mm.

(a) Front view

(b) Top view

(c) Details A

(d) Section B-B

80

Fig. 3.2-3 Detailed dimensions of the water tank body (units in mm)

On the left wall, a Ø162mm hole was machined at a height of 215mm from the outside bottom

surface. This hole was designed to fit Ø160mm protrusion the spindle-bearing housing, as shown

in Fig. 3.3-3(b) The height of the hole was determined so that even for the biggest blade, the

water level is 32mm above the top of the blade and there is 112 mm clearance from the bottom of

the tank. The 112mm clearance allows for additional items such as the inlet manifold.

3.2.2.2. The Perspex window

The Perspex window was made from an 810mm*260mm*6mm Perspex panel.

A pattern of twenty holes was drilled in the front wall of the tank. These holes are all Ø5.5mm

drilled through the material so that they can accept M5 bolts which fix the Perspex window to the

front wall of the tank. On its back surface, there is a cuboid protrusion which is 1mm high, 199mm

wide and 749mm long, as shown in Fig. 3.2-4 (b), (c) and (d).

The Perspex window was installed from the inside of the tank with one surface being in contact

with the back surface of the front wall and the other in contact with the water. The 1 mm

protrusion on the back surface, as shown in (d), was fitted into the rectangular cut-out on the

front wall of the tank; silicon glue was applied in between the stainless steel and Perspex sheets to

make the joint water-tight.

(e) Right view

(f) Left view

81

3.2.2.3. The pipe connectors

Fig. 3.2-5 shows the three pipe connectors i.e. the overflow, inlet and outlet. All the connectors

were welded onto the right wall of the tank. On each connector, two trapezium plates at an angle

of 90° were designed to be welded onto the tank to provide extra strength for welded connections

between the pipe and the tank. The internal diameters of all the connectors are 39.5mm with BSP

G 1.25 ins threads. The outer diameters of the overflow and the outlet connectors are 50mm. The

outer diameter of the inlet connector is 49mm and a 3mm protrusion was designed at the end

which can be fitted into the hole on the tank. A flat surface was cut on the bottom of the outlet to

create a 3 mm wall thickness; thus the bottom surface of the outlet is in the same plane as the

base surface of the tank.

Fig. 3.2-4 Detailed dimensions of the Perspex window (units in mm)

(a) Front view

(b) Top view

(d) Details A

(c) Side view

82

Fig. 3.2-5 Detailed dimensions of the pipe connectors (units in mm)

(a) Overflow

(b) Inlet

(c) Outlet

83

3.2.2.4. The inlet manifold

Fig. 3.2-6 Detailed dimensions of the inlet manifold (units in mm)

The inlet manifold was designed to reduce the turbulence caused by the high speed flow at the

inlet.

It is assumed that the pump must be able to raise the water level to the required height in less

than one minute. The amount of water that has to be pumped into the tank can be calculated as

follows:

𝑉 = ℎ𝑒𝑖𝑔ℎ𝑡 ∗ 𝑎𝑟𝑒𝑎 = (350 − 100) ∗ 500 ∗ 1000 ∗ 10−6 = 125 𝑙𝑖𝑡𝑟𝑒, 𝑜𝑟 0.125𝑚3

Based on the assumption that the hydraulic diameter, at the inlet, is equal to the diameter of the

pipe, the calculation of Reynolds number is shown below:

𝑄𝑖𝑛 =0.125

60= 0.00208𝑚3/𝑠

𝑣𝑖𝑛 =𝑄𝑖𝑛

𝐴𝑖𝑛

=0.00208

(0.0395

2)

2

𝜋

= 1.7000𝑚/𝑠

𝑅𝑒𝑖𝑛 =𝜌𝑣𝑖𝑛𝐷𝐻,𝑖𝑛

𝜇=

1000 ∗ 1.7 ∗ 0.0395

0.001= 67150

The calculation shows the flow forward speed is 1.7m/s at the inlet and the Reynolds number is

67150. This shows that the flow is fully turbulent. This suggests that the speed of the flow has to

be reduced.

The exit on the designed inlet manifold is a rectangle of 194mm wide and 16mm high. The

hydraulic diameter at the exit of the inlet manifold is four times the area of the rectangle divided

by the length of the perimeter and the volumetric flow rate is constant. Therefore, the Reynolds

number at the exit is given by:

84

𝐷𝐻,𝑜𝑢𝑡 =4 ∗ 𝐴

𝐶=

4 ∗ 0.194 ∗ 0.016

0.194 ∗ 2 + 0.016 ∗ 2= 0.02956𝑚

𝑣𝑜𝑢𝑡 =𝑄𝑜𝑢𝑡

𝐴𝑜𝑢𝑡

=0.00208

194 ∗ 16 ∗ 10−6= 0.67010𝑚/𝑠

𝑅𝑒𝑜𝑢𝑡 =𝜌𝑣𝑜𝑢𝑡𝐷𝐻,𝑜𝑢𝑡

𝜇=

1000 ∗ 0.67010 ∗ 0.02956

0.001= 19808.156

The calculation shows the Reynolds number at the exit of the inlet manifold is reduced by 29.5%.

Due to the limited amount of time, a CFD analysis was not performed. If the performance of the

inlet manifold is not acceptable, the flow rate can be adjusted to reduce turbulence in the

prototype machine. However, if another machine is built, and if a better solution is required, then a

CFD analysis will become necessary.

Finite element analysis of the water tank

Although the tank is not a critical component of the system, a finite element analysis of it was

performed in order to determine its deflection especially that of the left side wall, excessive

deflection of which may affect the performance of the seal between the rotary axis housing and

the water tank (see Chapter 3.3).

To assess the stiffness of the design, a finite element analysis (FEA) was carried out. It is noted

that as a first approximation, the pipe connectors were ignored.

The boundary conditions were specified as follows:

The bottom of the tank is completely constrained.

Pressure loads are added to all the vertical walls of the tank. The pressure loads are

defined by the following equation:

𝑃 = 𝜌𝑔 ∗ 𝑧𝑚𝑎𝑥 − 𝜌𝑔𝑧 = 1000 ∗ 9.81 ∗ 0.4 − 1000 ∗ 9.81 ∗ 𝑧 = 3924 − 9810𝑧

where z is the height displacement from the bottom of the tank. The model simulates the pressure

load generated by water that is filled beyond the overflow and up to the top of the tank.

As can be seen from Fig. 3.2-7, the FEA suggests that the maximum von Mises stress, 3.62MPa,

occurs at the edge of the cut-out on the front wall. Since the elastic limit for stainless steel is

approximately 200 MPa, it gives a factor of safety of well over 50. According to Fig. 3.2-8, the

maximum displacement, 0.0406mm, occurs in the middle of the Perspex window. The wall which is

in contact with the shaft housing has a maximum displacement of 0.0032mm. These displacements

are very small and will not affect the performance of the inspection machine.

85

Fig. 3.2-7 Finite element stress analysis of the water tank

Fig. 3.2-8 Deflection of the water tank

Max

86

Float switches, pump and solenoid valve

As mentioned earlier, the tank must be filled and drained automatically i.e. the water level must be

adjusted automatically during inspection. During laser scanning, the water level must be lowered

until the blade is fully exposed to air so that refraction of laser beam can be avoided. Completely

emptying the tank is unnecessary. Thus, a float switch is needed to determine the minimum water

level. On the other hand, during ultrasonic scanning, the blade must be submerged in water with

the water level at least 30 mm above the blade surface. Therefore, a second float switch is needed

to stop filling the tank when the appropriate water level is reached. Automation of the filling and

drainage further requires a pump and a solenoid valve controlled by two relays. The relays are

connected to the digital ports of the digital I/O box which are controlled by a program coded in

C#.

Two SSF212 float switches, as shown in Fig. 3.2-9 (a), were purchased from Cynergy3 and they

are installed on a rack/stand placed inside the water tank, but at different heights. Float switch A is

installed slightly below the overflow, approximately 340mm from the bottom of the tank; and float

switch B is installed at approximately 100mm from the bottom. Float switch A determines the

maximum level of water that can be pumped into the tank, while float switch B determines the

minimum water level when the solenoid valve is closed during the draining stage. It is noted that

the mentioned heights of the float switches only represent two extreme conditions and are used

for determining the specification of the pump; both values can always be adjusted to heights which

are appropriate for a particular blade size.

In order to determine the pump size, it is assumed that the pump must be able to raise the water

level to the required height in less than one minute. As calculated in Chapter 3.2.2.4, a pump with

a minimum flow rate of 125litre/min is required.

A Flotec VIP 130/6 Auto pump (see Fig. 3.2-9 (c)) has a maximum flow rate of 130 litre/min and

therefore this pump is adequate to raise the water level from 100mm to 350mm within 1 minute.

The new Reynolds number at the exit of the inlet manifold (see Chapter 3.2.2.4) can be calculated:

𝑣 =𝑄

𝐴=

0.1360

194 ∗ 16 ∗ 10−6=

0.69802𝑚

𝑠

𝑅𝑒 =𝜌𝑣𝐷𝐻

𝜇=

1000 ∗ 0.69802 ∗ 0.0395

0.001= 27571.952

The solenoid valve should match the pipe size, i.e. 1 ¼ inch, as well as the required flow rate, i.e.

130litre/min. A Series 210 solenoid valve was purchased from Asco Joucomatic (see Fig. 3.2-9 (b)).

It has a pipe diameter of 1.25” and a maximum allowable flow rate of 213 litre/min.

87

Fig. 3.2-9 The purchased Cynergy3 SSF212 float switch, Asco Joucomatic S210 valve and Flotec VIP 130/6 Auto pump

(a) Float switch

(c) Pump (b) Solenoid valve

88

Design of the shaft-bearing system

The shaft-bearing system is a part of the rotary axis, the blade being rotated about this axis.

During the inspection process, this system carries the blade and cooperates with the robot to

accurately rotate the blade by pre-determined angles. The mechanical components that need to be

designed are the shaft, housing and bearings.

Because the accuracy of positioning the blade plays a critical role in the inspection process, this

part of the machine must be designed and manufactured with appropriate tolerances. In order to

keep the deflection caused by the weight of the turbine blade to a very small value, the rigidity of

the system, especially the rigidity of the shaft, is one of the greatest concerns. Since part of the

system is submerged under water, water sealing is another important issue to be taken into

consideration.


- High stiffness.

- High positioning accuracy.

- Complete water seal.

- Cost effectiveness and ease of manufacturing.

89

Overview

The shaft-bearing system, as shown in Fig. 3.3-1 consists of three machined bodies: a shaft-

bearing housing, an in-tank flange and a shaft.

The housing is a cylindrical component, which can be machined on a turning machine. It was

designed to accommodate three bearings: two front bearings and one rear bearing. The additional

bearing in the front reduces the load on the other front bearing as well as the effective distance of

bending force exerted on the shaft thereby reducing the bending moment. The arrangement of

these bearings are discussed later in this section. The shaft is also a cylindrical component

designed with several steps for fixing bearings as well as a keyway at the both end to allow the

use of keys for torque transmission. The In-tank flange is used to fix the shaft-bearing system on

the tank wall as well as seal water path ways. All components of the system can be clearly seen in

Fig. 3.3-2.

Determination of the dimensions and tolerances of the shaft and the housing were referred to

standards provided by SKF [107], a company specialised in bearing and seals manufacturing. The

recommended tolerances for shaft and housing for SKF 60142RS1 bearings under “light and

variable loads” are H7 and k6 respectively. Basic static load rating is 31kN and fatigue load limit is

1.3kN.

This design cooperates with the pedestal shown in Chapter 3.5.

Fig. 3.3-1 Different views of the shaft-bearing system (units in mm)

90

As all components may be in contact with water, the system must be made of non-rusting

material, such as aluminium alloy and stainless steel. To avoid excessive displacement caused by

bending when the blade is attached, the system must also be sufficiently stiff. Therefore, stainless

steel was chosen over aluminium alloy.

Fig. 3.3-2 An exploded view of the shaft-bearing system

91

Designed parts and detailed dimensions

The system was fixed on a supplementary pedestal (see Chapter 3.5) with four M8 tapped holes

(B1, B2, B3 and B4) designed on the shaft-bearing housing as shown in Fig. 3.3-3 (e). As the

system is one of the key components that determine the relative position of the test blade with the

robot base coordinate system, the positioning of the system must be repeatable. Therefore, in

addition to the tapped holes, two 6mm H6 dowel holes (A1 and A2 in Fig. 3.3-3 (e)) were designed

to lock the relative position between the system and the pedestal.

The system is also in contact with the water tank. A Ø160mm protrusion was designed on the front

surface of the housing, as can be seen in Fig. 3.3-3 (a) and (b). This protrusion can be loosely

fitted into the Ø162mm hole on the water tank wall as shown in Fig. 3.2-3(f). The front face of the

protrusion was designed with six M5 tapped holes evenly arranged along a pitch circle with a

radius of 70mm. These holes are coupled with six Ø5.2mm clearance holes on the flange shown in

Fig. 3.3-4, for bolting the housing and in-tank flange together. It is noted that the protrusion was

designed 0.1mm longer than the thickness of the water tank. This clearance reduces the effect of

water tank deformation on the system.

As seen in Fig. 3.3-3 (d), the interior of the housing was designed with three bores of two different

sizes. The two H6 tolerated Ø110mm bores were designed to accommodate the SKF bearings. It is

noted that although H7 is recommended by SKF [107], H6 was selected for better fitting accuracy.

The 55mm deep Ø110mm bore was also used to position the in-tank flange on the h5 Ø110

cylindrical surface, as shown in Fig. 3.3-4(b). The H6 and h5 tolerance set suggests a sliding fit.

92

The shaft is the most complicated component in this system. It has several different diameters to

fit and hold various components. As shown in Fig. 3.3-5(b) and (d), from the front face, the first

section, which is Ø65mm and h11 toleranced, was designed to position and hold the fixture, which

in turn will hold the blade. The fixture can be locked in position with the M10 tapped hole on the

front face of the shaft (see Fig. 3.3-5(a)) and the ISO standard keyway machined on the cylinder.

This diameter was also designed to fit two rotary seals; thus, the surface must be plunge ground

to 0.3µm Ra to reduce wear on the seals [108]. The two symmetric rectangular grooves, each

10mm wide, enable the use of a spanner for holding the shaft during installation of the fixture and

Fig. 3.3-3 Detailed dimensions of the shaft-bearing housing (units in mm)

(a) Front view (rotated by 90° counter-clockwise)

(b) Top view (c) Back view (rotated by 90° counter-clockwise)

(d) Section A-A

(e) Bottom view

93

test blade. The next section, which is Ø70mm and k6 tolerated [107], fits the inner rings of the

two front bearings. The M70x2 threads were designed for the lock nut.

Fig. 3.3-4 Detailed dimensions of the in-tank flange (units in mm)

(a) Front view

(b) Top view

(c) Section C-C

(d) Detailed view D

Fig. 3.3-5 Detailed dimensions of the shaft (units in mm)

(a) Front view (b) Side view (c) Back view

(d) Top view

94

From the back, the 24mm, g6 tolerated diameter with a ISO standard 8mm keyway was designed

for fitting a timing pulley, which is a part of the transmission system as shown in Chapter 3.4. The

M8 tapped hole on the back face of the shaft (see Fig. 3.3-5(c)) can be used to assist in the

installation of the pulley. The next diameter, Ø70mm and k6 tolerated, fits the rear bearing. The

2.65mm wide groove was designed for an ANSI B 27.7M circlip (see the parts list in Fig. 3.3-2).

Water sealing mechanism

The in-tank flange was designed to seal the gap between the shaft and the water tank. This is

done by blocking the water paths between (i) the shaft and the flange and (ii) the water tank and

the flange. As can be seen in Fig. 3.3-6, there are three possible paths for the water to leak

through the flange:

1. path A is the gap between the shaft and the flange;

2. path B is the gap between M5 bolts and the flange;

3. path C is the gap between the water tank and the flange.

In order to block path A, two rotary seals were fitted into the gap. The outer diameters of the

rotary seals fitted in the H8 r44.97mm bore on the flange shown in Fig. 3.3-4 (c) and the inner

diameters fitted on the h11 Ø 65mm cylindrical surface on the shaft shown in Fig. 3.3-5 (b) and

(d). Path B is blocked with washer seals and path C is blocked with an O-ring of a cross-sectional

diameter of 5.3mm. The groove for the O-ring, as shown in Fig. 3.3-4 (d), follows the standard

described in Parker O-Ring Handbook [109] and provides a 16.6% compression ratio.

Fig. 3.3-6 Seals and possible water paths

Path A

Path B

Path C

Bearings

Water tank

In-tank

Lock nut

Seals

95

Bearing arrangement

The bearings must be arranged properly to avoid axial movement at the front of the shaft and

allow changes in shaft length caused by thermal expansion. This requires that the front bearings to

be fixed on both the shaft and housing, i.e. namely fixed bearings, while the bearings at the other

end must enable axial displacement, i.e. namely floating bearings.

In this design, the front two bearings were fixed by using the shoulders on the shaft and housing,

the lock nut and the inserted part of the in-tank flange, which can be clearly seen in Fig. 3.3-7.

The rear bearing was arranged as the floating bearing with an open end on the outer ring and a

slot with 0.1mm clearance for its inner ring.

It is noted that in the housing, the depth of the bore for fitting the two front seals is 55.00mm−0.05+0.00

(see Fig. 3.3-3 (d)). The width of one bearing is 20.00mm+0.05+0.025. Therefore, deducting the width for

two bearings, the depth of the bore left for the insertion of the in-tank flange has a worst-case

maximum of 15mm and a worst-case minimum of 14.85mm. The length of the inserted part of the

in-tank flange is 15.12mm+0.00+0.01, which suggests an extra length in worst-case minimum 0.12mm

and worst-case maximum 0.28mm. This ensures sufficient pressure is applied on the outer ring of

the front bearing.

FEA of the shaft

Due to the weight of the blade (maximum of 25kg according to ELE), the shaft will bend but the

amount by which it does depends on the design of the shaft, the overhang distance and the weight

of the blade. However, even if the shaft is bent slightly, due to its length of the blade, the

displacement at the tip of a blade can be significant. To determine the extent by which the shaft

deflects, a FEA was performed. Fig. 3.3-8, shows the components of the system that have

modelled.

They include a section of the shaft with two front bearings, a simplified fixture for the blade and a

turbine blade with its fir-tree root. The two bearings were modelled as a solid cylinder with a

Bearings

Water tank

Seals

In-tank flange

Fig. 3.3-7 A sectional view of the shaft-bearing system

Lock nut

Floating bearing Fixed bearings

96

central hole fit to the shaft. The turbine blade was constructed as a solid body with no subsurface

features, such as cooling channels. The total weight of the blade and the fixture was 51.65kg.

Fig. 3.3-8 Model of the blade, fixture and the shaft for analysis (units in mm)

Several assumptions were made in this finite element analysis. They are listed below.

1. The joint between the bearings and the shaft was assumed to be rigid. Thus, any relative

displacement between the bearing and the shaft was ignored.

2. The fixture was rigidly connected to the shaft and so was the blade to the fixture.

3. The effect which the cooling channels have on the position of the centre of gravity of the

blade was neglected.

4. The effect of water pressure was ignored.

The setup for this FEA is described as follows:

The bearings were fully constrained on the back surface and the side surface.

97

The only load applied was the body force.

The material of the turbine blade was Inconel 718 and the material of the fixture, the shaft

and bearings were stainless steel. Mechanical properties of the materials are shown in

Table 3.3-1.

Table 3.3-1 Mechanical properties of the materials used in FEA

Material Density

(kg/m3)

Young’s

modulus

(x103MPa)

Shear

modulus

(x103MPa)

Poisson’s

ratio

Yield

strength

(MPa)

Tensile

strength

(MPa)

Inconel 718 [110]

[111] 7445.894 199.948 77.221 0.29 1034.214 1241.056

Stainless steel 7999.492 192.984 85.978 0.30 250.000 540.000

Fig. 3.3-9 Finite element stress analysis of the blade, fixture and the shaft

Fig. 3.3-10 Deflection of the blade, fixture and the shaft

98

As shown in Fig. 3.3-9, the maximum von Mises stress of 10.9MPa occurs in the vicinity of the

shoulder on the shaft and the locknut and the resulting stress causes a displacement of 0.002 mm.

From Fig. 3.3-10, the maximum displacement, 0.035mm, occurs at the tip of the blade, which is

acceptable.

99

Transmission system for the shaft

The transmission system was designed to accurately rotate the shaft through a specific angle as

required by the inspection process. Since the blade is to be rotated at a very low speed, the

maximum available torque of the motor can be utilised.


- Capable of providing enough torque to drive the shaft and the heaviest blade

- The resolution of the angle of rotation to be less than 0.1°.

As can be seen in Fig. 3.4-1, the unit consists of four components: a stepper motor with a gearbox

(○1 ), a 60-teeth timing pulley (○2 ), a 12-teeth timing pulley (○3 ) and a 270-teeth timing belt (○4 ).

The stepper motor was purchased from Zapp Automation, model number SYS57STH56-3008B. This

motor is capable of producing a maximum torque of 1 Nm at 300 PPS. Each step rotates the shaft

by 1.8° and this angle can be reduced by one sixteenth with micro stepping offered by its

controller. The gearbox is from Siboni, model number RE55 NEMA23. It delivers an input-to-output

ratio of 1:6. Therefore, the combination of the gearbox and the motor produces 6 Nm at 50 PPS

and each step results in a 0.3° rotation of the gearbox output shaft. It is noted that this gearbox

Fig. 3.4-1 Transmission system assembled on the shaft (units in mm)

100

has a 5 arcmin, i.e. approximately 0.083°, of backlash which should be compensated when the

direction of the shaft is reversed.

The 60-teeth and 12-teeth pulleys were attached to the motor shaft and gearbox output shaft,

respectively. This pulley set introduces a 1:5 output-input ratio, which further increases the torque

available to 30 Nm at 10 PPS. The step resolution is also reduced to 0.06°. Furthermore, with

micro stepping, the minimum achievable angle per step is 0.00375°. However, it was found

experimentally that the micro stepping introduces inaccuracy and should be avoided when

possible.

The specifications of the pulleys and the belt are listed in Table 3.4-1 and the dimensions of the

motor and gearbox are shown in Fig. 3.4-2.

Table 3.4-1 Specifications of timing pulleys and belt (all units in mm)

Part number No. of teeth Width across teeth Outer diameter Length

12L075 timing pulley 12 25.4 36.38 N/A

60L075 timing pulley 60 25.4 181.91 N/A

270L075 timing belt 270 19.05 N/A 685.8

(a) An SYS57STH56-3008B motor by Zapp Automation

(b) A RE55 gearbox by Siboni

Fig. 3.4-2 Detailed dimensions of the motor and the gearbox (units in mm)

101

The labelled dimensions in the figure are shown below (units in mm):

L1 L2 L3 L4 D1 D2 D3 D4

52 25 3 60 6.35 38.1 66.67 5.5

102

Design of the rotary axis pedestal

The rotary axis pedestal which carries the shaft-bearing and transmission systems plays two

important roles. The first is to raise the height of the shaft thereby allowing the shaft to pass

through the hole in one of the walls of the water tank. The second is to provide a platform so that

the shaft-housing system can be repeatedly positioned accurately.


- High rigidity.

- High positioning accuracy and repeatability.

- Cost effectiveness and ease of manufacturing.

Overview

The pedestal is made of mild steel and has an overall length of 340mm, a width of 198mm and a

height of 140mm, as can be seen in Fig. 3.5-1. The pedestal consists of two distinct parts: a 30mm

thick plate on the top used for mounting the rotary axis, i.e. the shaft-bearing system, as well as

the transmission unit, and a base block underneath for raising the rotary axis to the required

height and fixing the pedestal onto the table.

As can be seen in Fig. 3.5-3, the shaft-bearing housing was bolted onto the pedestal top plate

from the bottom of the plate with four M8 bolts through holes C1, C2, C3 and C4 (see Fig. 3.5-7).

These holes were countersunk so that the bolt heads are below the surface of the pedestal top

plate which can then be placed over the base block. Two locating pins were used to ensure that

the housing and top plate are always assembled in the same position.

Fig. 3.5-1 Different views of the rotary axis pedestal (units in mm)

103

The top plate of the pedestal was bolted onto the base only after the shaft-bearing housing was

fixed. Five M8 bolts were arranged closely around the area where the housing was fixed, as can be

seen in Fig. 3.5-4. It is noted that one of the bolts was placed in line with the rotary axis to reduce

displacement caused by bending. Repeatable positioning between the top plate and the base block

is ensured by two 6mm dowel pins inserted in holes A1 and A2 on the top plate (see Fig. 3.5-7)

and holes C1 and C2 on the base block (see Fig. 3.5-8 ).

Fig. 3.5-2 Different views of the rotary axis pedestal with shaft-bearing system and transmission system assembled

Fig. 3.5-3 Assembling the shaft-bearing system onto the rotary axis pedestal

104

Apart from the shaft-bearing system, the transmission system was also attached to the top plate.

This was done with the help of a mounting plate, as shown in Fig. 3.5-5 (a). The motor and gear

box was first fixed on to the mounting plate without the 12-teeth timing pulley installed, as shown

in Fig. 3.5-5 (b) and (c); then the mounting plate was bolted to the top plate through the slot at

the bottom. The tension of the belt can be varied by adjusting the position of the plate sideways in

the slot. Details of this mounting plate are discussed later in this section.

Fixing the pedestal onto the table was done with four M10 bolts and two locating dowel pins, as

can be seen in Fig. 3.5-6.

Fig. 3.5-4 An exploded view of the rotary axis pedestal

Fig. 3.5-5 Assembling the motor and gearbox onto the rotary axis pedestal

(a) (b) (c)

105

Fig. 3.5-6 Assembling the rotary axis pedestal onto the cast iron table

106

Detailed dimensions

Fig. 3.5-7 Detailed dimensions of the top plate (units in mm)

(a) Back view

(c) Side view (b) Bottom view

107

Fig. 3.5-8 Detailed dimensions of the base (units in mm)

(a) Front view (b) Side view

(c) Top view (d) Isometric view

108

As shown in Fig. 3.5-7, the top plate is 290mm*180mm*30mm. The distance between the two

mounting holes drilled for fixing the mounting plate, as seen in Fig. 3.5-7 (a), is 20mm, which

leaves a distance of 24.5mm for tensioning the belt in the 44.5 mm slot (see Fig. 3.5-9 (d)). The

head length for a M8 pocket head bolt (ISO 4762) is 8mm−0.36+0.00; therefore, the countersunk depths

of holes C1, C2, C3 and C4 in the top plate were determined to be 8.50mm.

The base block, as shown in Fig. 3.5-8, is a rectangular block with steps around it on three sides.

On the one of the steps, there are two 52mm wide cut-outs. These two cut-outs were designed for

locating blocks (see Fig. 3.7-7) which can be fitted in the slots and used as a backup positioning

method in case any of the two locating pins shifts.

The mounting plate is 10mm thick with four chamfered corners. A Ø22mm hole with a Ø32mm

+0.05/+0.02, 2.6mm countersink was designed to fit the 32mm boss on the gearbox, as shown in

Fig. 3.4-2 (b).

(a) Front view

(b) Side view

(c) Top view

(e) Isometric view

(d) Back view

Fig. 3.5-9 Detailed dimensions of the mounting plate (units in mm)

109

Design of a tool change system

Since there are two tools (ultrasonic probe and laser sensor) and since only one of them is

attached to the face plate at any one time, an automatic tool change system is required.

Fig. 3.6-1 Robot face plate

The robot face plate is a standard robotic mounting plate, as shown in Fig. 3.6-1, which has a

4mm dowel hole and four M5 mounting holes. There are a variety of pneumatic tool grippers that

adapt to the face plate available in the marketplace. Fig. 3.6-2 shows one of the pneumatic tool

change systems, SWS005, from a German tool gripper manufacturer, Schunk. It has a maximum

payload of 8kg and a repeat accuracy of 0.01mm.

Fig. 3.6-2 An exploded view of a Schunk SWS005 pneumatic tool change system

The system mainly consists of two parts, a “male” part fixed on the robot and a “female” part fixed

on the tool. The “male” part is complete with a robot face plate adaptor and a SWK005 quick-

change head; the “female” part is complete with a SWA005 quick-change adaptor and three

110

supporting bolts. The automation of tool change process is done by pneumatically

attaching/detaching the “female” part to/from the “male” part. Multiple sets of “female” parts can

be purchased to match the number of tools involved in the automatic tool change process, two in

our case.

Tool holders are not included in the SWS005 package and thus must be designed and

manufactured by the end user accordingly for different tools. It is noted that any weight added on

the robot face plate potentially affects the accuracy of the robot, and therefore the tool holders

should be as light as possible. To reduce the effort in post-calibration of the tool axis3, these tool

holders must also be designed such that the axis of the laser beam and ultrasonic beam is known

to the robot axis, ideally co-linear with the axis of the faceplate.

The dimensions for the quick-change tool adaptor, SWA005, are shown in Fig. 3.6-3.

Fig. 3.6-3 Detailed dimensions of a Schunk SWK005 and SWA005 (units in mm)

3 Tool axis is the axis of the ultrasonic beam or laser beam represented in the robot base coordinate system

111

Fig. 3.6-4 A Schunk quick-change adaptor SWA005 stored in a SWM-TSS storage plate

For each quick-change adaptor, SWA005, there are three supporting bolts fixed on the side

surface. These supporting bolts rest on the V-shaped indentations on the Schunk SWM-TSS

storage plate, as shown in Fig. 3.6-4.

Design of the tool holder for the Keyence laser sensor

As discussed above, in order to couple with the Schunk SWA005 adaptor, a tool holder needs to be

designed for each tool, including the laser sensor and the ultrasonic probe.

Fig. 3.6-5 Detailed dimensions of a Keyence ILS065 laser sensor (units in mm)

112

The laser sensor weighs only 75 grams and is approximately 52.5mm*24.1mm*42.8mm in size, as

shown in Fig. 3.6-5. Therefore, the design of the holder is not focused on the structural rigidity or

weight. The axis of the laser beam is approximately 10.50 mm and 10.20 mm from the sides of the

laser sensor. Unfortunately, because there are no tolerances placed on the dimensions and there is

no dowel hole on the laser sensor body, there is no reference point on the laser body which can

act as the datum. The two Ø3.5mm mounting holes on the side surfaces only loosely fit two M3

bolts. This suggests that the positioning of the laser sensor is unrepeatable and the axis of the

laser beam cannot be accurately aligned with the robot face plate axis, and therefore, the laser

tool axis must be calibrated.

3.6.1.1. Overview

The design of the laser sensor holder consists of two parts, a main body and an adaptor, as shown

in Fig. 3.6-6 and Fig. 3.6-7. The main body is an L plate and the adaptor is cylindrical in shape.

The two parts were bolted together with one M6 bolt and located by two dowel pins. The overall

weight of the holder is approximately 210g, when made of aluminium alloy.

Fig. 3.6-6 Different views of the laser sensor holder (units in mm)

(a) Top view

(c) Front view (b) Left view (d) Right view

(e) Bottom view (f) Isometric view

113

3.6.1.2. Detailed dimensions

Two M3 threaded holes were drilled on the side of the L plate as shown in Fig. 3.6-8 (a), which are

used for mounting the laser sensor. A head room of 10.8mm is left between the top of the laser

sensor and the L plate surface, which is sufficient for the laser cable to be bent and pass through

the Ø10mm hole designed on the top of the L plate. As discussed, the adaptor was bolted on the L

plate with a M6 bolt. The bolt was passed through the Ø6.6mm hole with Ø11.2mm countersink

(see Fig. 3.6-8 (d)) from the bottom and a Ø14mm H7 recession was designed on the other end of

the hole (see Fig. 3.6-8 (c)) which couples with the Ø14mm h6 protrusion on the bottom of the

adaptor, as shown in Fig. 3.6-9 (e). The tolerances specified for the recession and protrusion

create a high-precision sliding fit, which is used to locate the adaptor. For the same purpose, two

Ø3mm dowel holes were additionally designed. To avoid over-determining the position, only two

dowels should be used at a time.

The adaptor was designed with four Ø5.5mm clearance holes and one Ø3mm H7 dowel hole that

couple with the adapting surface of the SWA005. The Ø25mm protrusion (see Fig. 3.6-9 (b)) fits

into the Ø25mm H8 recession on the SWA005.

Fig. 3.6-7 An exploded view of the laser sensor holder

114

Fig. 3.6-8 Detailed dimensions of the L plate (units in mm)

(c) Top view

(a) Front view

(b) Side view (e) A-A section

(d) Bottom view (e) Isometric view

(g) Detail B

115

Design of the tool holder for the Olympus ultrasonic probe

Just as for the laser sensor, a tool holder has been designed for the ultrasonic probe to hold the

Schunk SWA005 adaptor.

The Olympus V316-SU ultrasonic probe is cylindrical in shape. The overall length of the probe is

124mm and the biggest diameter is 19.18mm. The first 71mm, as shown in Fig. 3.6-10 (a), is

made of metal and the rest is rubber. There is no mounting hole designed in the body or any

feature for precise location; however, the different sections of the probe are utilised for this

purpose. The first 30mm, which is a ground surface of Ø15.79mm (see Fig. 3.1-2 (a)), can be used

for locating. The step right after this diameter and the step at the end of the first 71mm can be

used for locating and holding the probe in its holder. Because the probe must be immersed in

Fig. 3.6-9 Detailed dimensions of the adaptor (units in mm)

(c) Top view

(a) Front view

(b) Side view

(d) Bottom view

(e) Isometric view

116

water, although the two-part connection is already sealed with a supplied O-ring, it is still

necessary to seal the tool holder to eliminate any risk of short circuit.

3.6.2.1. Overview

The design consists of two parts, a lower and an upper part. Its overall length is 175.9mm and the

biggest diameter is 58mm and weighs approximately 360g. The two parts were bolted together

with three M5 bolts and located by the recess on the lower part and protrusion on the upper part.

Fig. 3.6-10 Dimensions of an Olympus V316-SU ultrasonic probe (units in mm)

(a) Side view (b) Front view (c) Back view

(d) Iso view

Fig. 3.6-11 The ultrasonic probe holder (units in mm)

117

The axis of the tool holder is collinear with the axis of the ultrasonic beam, making it unnecessary

to have one additional dowel to fix the rotational degree of freedom.

As shown in Fig. 3.6-14, the probe (shown in red) was pressed against the shoulder in the lower

part (shown in orange) by a M5 bolt screwed into the threaded hole in the upper part. An O-ring

was fitted into the interior of the lower part and another was applied at the interface of the two

parts.

Fig. 3.6-12 An exploded view of the ultrasonic probe holder

Fig. 3.6-13 Sectional view of the ultrasonic probe holder with the probe and O-rings assembled

The O-rings

118


The axis of the ultrasonic beam was located by the Ø15.79mm H7 bore (see Fig. 3.6-14(c)) in the

lower part, which couples with the Ø15.79mm cylindrical part on the probe. A 14.6x2.4 O-ring was

fitted into the O-ring groove designed on the surface of the bore to prevent water from entering

the tool holder from the bottom opening. With a groove depth of 1.8mm, the O-ring is compressed

by 25%. A Ø26mm H7 recession was cut from the top of the lower part to couple with the Ø26mm

h6 protrusion designed on the upper part (see Fig. 3.6-15 (e)). A 29.6x2.4 O-ring was fitted in the

O-ring groove designed on the top surface. This O-ring is compressed by approximately 20.8%

with the designed groove depth of 1.9mm.

The design of the adaptor for the SWA005 on the upper part is similar to the design deployed for

the laser sensor holder. A Ø5.8mm hole was designed on the body to pass the probe cable.

Fig. 3.6-14 Detailed dimensions of the probe holder lower part (units in mm)

(a) Front view (c) A-A section

(d) Detail B (b) Top view

119

Design of the tool magazine

As discussed earlier, the tools can be stored on the Schunk SWM-TSS storage plate. This first

requires, as shown in Fig. 3.6-19, installing three support bolts, which are cylinders with M5

Fig. 3.6-15 Detailed dimensions of the probe holder upper part (units in mm)

(b) Bottom view

(a) Front view (d) C-C section

(c) Top view (e) Isometric view

120

threads at one end purchased from Schunk, on the SWA005 quick-change adaptor. With these

supporting bolts, SWA005 can be rested on the V-shaped indentations on the storage plate.

The storage plate was designed with two Ø9mm countersunk holes and two Ø8mm cylindrical pins

standardised as Ø8mm dowels as shown in Fig. 3.6-17. With these features, the storage plate can

be fixed on, for example, a beam. A proximity sensor, shown in Fig. 3.6-18 (b), can be passed

through the Ø9mm hole drilled in the mid-indentation to detect the existence of stored tool. Each

proximity sensor is also supplied with a bracket as shown in Fig. 3.6-18 (a).

Fig. 3.6-17 Detailed dimensions of a Schunk SWM-TSS storage plate

Fig. 3.6-16 An SWA005 quick-change adaptor and support bolts by Schunk (units in mm)

Assembly

Mounting holes on SWA005

Support bolt

121

As there are in total two tools, two storage plates are required. The height at which these storage

plates should be fixed at, is dependent on the length of the tools and the reachability of the robot.

The longest tool is the ultrasonic probe and its tool holder is 175.9mm long.

3.6.3.1. Overview

Fig. 3.6-19 Model of the tool magazine

Fig. 3.6-18 Detailed dimensions of a Schunk proximity sensor and a sensor bracket (units in mm)

Sensor bracket

(b) Proximity sensor

122

The tool magazine consists of a stand profile, two proximity sensors, an L-shaped mounting plate,

a storage plate adaptor and two storage plates as shown in Fig. 3.6-20. The tool magazine was

designed for only two tools and the height of the tools is 443.54mm. The tool magazine should be

fixed on the table at a location that is easily accessible by the robot.

Fig. 3.6-20 An exploded view of the tool magazine


As shown in Fig. 3.6-21, Fig. 3.6-22 and Fig. 3.6-23, in addition to the Ø9mm clearance holes for

the M8 bolts, there are several Ø8mm or Ø7mm (undersized) holes in all the three components for

dowel pins. It is not absolutely necessary to dowel these components, however, because the robot

programs which are used to instruct the robot to pick and store tools can always be easily modified

to cater for different positions for coupling and uncoupling.

The storage plate adaptor, apart from the four mounting holes designed near the centre line, is a

symmetric component. As shown in Fig. 3.6-23 (d), on either end, two Ø8.1mm H6 holes were

designed for fitting the cylindrical pins on the storage plate. Instead of having two Ø9mm

clearance holes, two M8 threaded holes were designed to fix the storage plate with M8 bolts. A

rectangular cut-out of 30mm wide and 12mm deep was designed to fit the proximity sensor

bracket.

123

The L-shaped mounting plate is 12mm thick which is thick enough to accommodate the Ø8mm

dowels. The inner corner is rounded for ease of manufacturing.

Fig. 3.6-21 Detailed dimensions of the stand profile

Fig. 3.6-22 Detailed dimensions of the mounting plate for tool magazine (units in mm)

(a) Top view

(c) Front view

(b) Side view

(d) Iso view

124

Fig. 3.6-23 Detail dimensions of the storage plate adapter (units in mm)

(a) Top view

(b) Front view

(d) Bottom view

(c) Side view

125

Design of the base structure

The base structure provides a rigid platform for fixing all the other components. The structure

must be stiff enough to support a weight of approximately 317kg without any appreciable

deformation. The structure must also ensure repeatability of assembly for both the rotary axis and

robot. Relative displacement between the rotary axis and the robot must be avoided.


- High stiffness.

- Repeatable positioning of the rotary axis and the robot.

Three initial designs are considered before the final design is made.

The conceptual designs

3.7.1.1. Conceptual design 1

This structure, as can be seen from Fig. 3.7-1 (a), consists of a stainless steel sheet placed on top

of a tube-channel structure. It is 1500mm in length, 620mm in width and 305mm in height. This

structure was designed to support the shaft-bearing system, the drive system, and a mains water

tank as shown in Fig. 3.7-1 (b). A secondary tank is to be placed underneath the table. A separate

(a) The exploded view (b) The structure assembled with a water tank, shaft-bearing system and driving system assembled

Fig. 3.7-1 The first design of base structure

126

pedestal was planned for placing the robot. However, before the design of the robot pedestal was

started, a FEA showed that this design was not stiff enough.

The finite element analysis determined the deformation of the structure caused by a pressure4 of

4365.7 Pa acting on the bottom surface of the water tank. This load results in a maximum

deflection of 0.667mm at the centre of the table and 0.092mm at the rotary axis.


This design also uses metal sheets and a tube-channel structure. In general, this design is

1277mm in length, 880mm in width and 402mm in height. This design uses two separate tables,

one for water tank and the other for the robot and rotary axis. This eliminates the deformation on

the rotary axis or the robot caused by the weight of water and water tank. However, the robot and

rotary axis table is not stiff enough especially the parts connecting the robot and the rotary axis

pedestal, which is a single tube. Any displacement occurring directly below the robot or the rotary

axis could cause relative displacement between the two. The table also tends to tilt towards the

water tank if a heavy blade is loaded on the shaft while the robot arm is fully extended.

4 P = P_𝑤𝑎𝑡𝑒𝑟 + P_𝑡𝑎𝑛𝑘 = ρgh + mg/A = 1000 ∗ 9.81 ∗ 0.4 + 23 ∗ 9.8/0.506 = 4365.7Pa

(a) The overview of the CAD model

Fig. 3.7-2 The second design of base structure

(b) The exploded view of the robot and rotary axis table

127


The third design still employs a tube-channel structure, but it is greatly strengthened by using

heavy tubes and channels. The combined dimensions of the water tank table and the robot and

rotary axis table are 1290mm* 850mm*524mm and the dimensions of the base are

2100mm*1660mm*210mm. The robot and rotary axis table sit on three adjustable legs and the

table itself is a hollow tube structure with doors fixed at both ends. This enables the table to be

filled with sand to reduce vibration caused by mechanical movements. The legs can be fixed on the

designed base so that tilting can be avoided. The base is a 5mm thick cast iron sheet which is

heavily ribbed underneath. The gap between the ribs allows the use of a fork lift to lift the entire

rig. The base also provides extra room for placing other equipment such as a table and a PC.

Fig. 3.7-3 The third design of base structure

(b) The exploded view of the base

(c) The exploded view of the robot and rotary axis table

(a) The overview of the CAD model

128

However, the entire base is approximately 570kg and the area is 2100mm*1660mm, which is

difficult to be transported in a regular van.

3.7.1.4. Summary of the conceptual designs

Table 3.7-1 Conceptual design marking in scale of 1-5

Stability Rigidity

Accuracy of positioning

Cost of making

Ease of transportation

Overall

Design 1 3 2 1 5 4 15/25

Design 2 1 3 3 4 4 15/25

Design 3 5 5 5 1 1 17/25

All three conceptual designs are evaluated on a scale of 1 to 5 (1 being the lowest and 5 being the

highest) using five different design criteria: stability, rigidity, accuracy of positioning, cost of

making and ease of transportation. The values were arrived at by consultation with fellow

colleagues in the design office at ELE. It is found that Design three scores the highest although its

scores in cost of making and ease of transportation are the lowest.

The final design

While it is an option to reduce the weight

and area in Conceptual design 3 by

removing the extra room reserved for a

table and a PC, it is still costly, in terms of

both time and budget, to manufacture this

structure. The next approach takes a look at

some existing products, such as a cast iron

table, available in the market. The

merits of this are that by avoiding all the

design and manufacturing stages, time is

saved and a surface table is usually well

engineered and should be stable and stiff.

The table finally used is a second-hand cast iron table as shown in Fig. 3.7-4. This table has two

separate parts: the upper part and the lower part. The upper part is a 101.6mm*76.2mm*28mm

cast iron surface, heavily ribbed underneath. The surface is supported on three adjustable legs

sitting on the lower part, which is a rigid structure to raise the height of the top surface.

Fig. 3.7-4 The 101.6mm*76.2mm cast iron surface table

129

It was decided not to perform a finite element analysis of the structure because it was thought

that this steel table is much stronger than conceptual design 1 which resulted in a deflection of

0.667 mm.

In order to fix the water tank, robot pedestal, rotary axis pedestal and the tool storage stand, the

surface of the table was drilled with threaded holes as seen in Fig. 3.7-5. The robot pedestal was

bolted with four M10 bolts and located by two 8mm locating pins. The water tank, however, has

insufficient wall thickness (3mm) to be doweled. Instead, three locating blocks were designed and

fixed against two walls of the water tank.

Fig. 3.7-5 Assembling components onto the cast iron surface

130

Fig. 3.7-6 Components installed on the cast iron table

3.7.2.1. Locating blocks

The locating blocks are made from steel and are of size 50mm*20mm*20mm. They were bolted

onto the table with M8 bolts and doweled as shown in Fig. 3.7-7 and Fig. 3.7-8. The locating

blocks prevent any movement of the tank in the horizontal plane and they were screwed on to the

surface table after the water tank is firmly fixed on the table.

Fig. 3.7-7 Detailed dimensions of the locating block (units in mm)

131

3.7.2.2. The robot pedestal

As the water tank is approximately 400mm in height, it blocks the area directly in front of the

FANUC LR Mate 200iD robot, making it impossible for the robot to reach into the water tank.

Therefore, a robot pedestal had to be introduced to raise the robot to an appropriate height.

Fig. 3.7-9 Dimensions of (a) the base [112] and (b) the operating space of [113] of FANUC LR Mate 200iD

Robot

Fig. 3.7-8 Arrangement of the locating blocks on the cast iron table

(a) (b)

132

As shown in Fig. 3.7-9 (b), the 2nd axis of the robot, which leans the robot forwards and

backwards, is 330mm from the bottom. The area directly in front of this axis must be clear so that

the robot is free to lean forward. Therefore, the minimum height of the pedestal should be 70mm.

The robot height could be raised by 277mm so that it can reach the lower bound of its operating

space. However, this may not be necessary since the robot only needs to reach areas that are

relatively close to it.

(b) Left view (c) Right view (a) Front view

(d) Bottom view

(e) Top view (f) Iso view

Fig. 3.7-10 Detailed dimensions of the robot pedestal (units in mm)

133

Since the robot is only 27kg, aluminium alloy is used as the material for the robot pedestal. The

base of the robot was designed with four Ø11mm

mounting holes, suitable for M10 bolts, as shown in

Fig. 3.7-9 (a). However, the base does not have any

dowel holes, and lacks the ability to fix it at the

same position repeatedly.

The robot pedestal is 250mm in height, as can be

seen from Fig. 3.7-10. This height ensures that the

robot is free to lean forward and able to reach into

the water tank. It requires three other parts: a

20mm thick top plate, a 200 *200 *210 mm mid-

block and a 20mm base plate. Both top plate and

base plate were bolted onto the mid-block with four

M8 bolts each. The robot was, as shown in Fig.

3.7-11, bolted onto the pedestal with another four

M10 bolts through holes C1, C2, C3 and C4 (see Fig.

3.7-10 (e)). No locating features were designed for positioning the robot, which means the

inspection cell must be recalibrated once the robot is re-installed on the pedestal.

As shown in Fig. 3.7-12, the pedestal was bolted onto the cast iron surface with four M10 bolts

through holes A1, A2, A3 and A4 (see Fig. 3.7-10 (d)). Two 10mm dowel pins, which were fitted

into B1 and B2 (see Fig. 3.7-10 (d)), are used to position the pedestal.

Fig. 3.7-12 Assembling the robot pedestal onto the cast iron table

Fig. 3.7-11 Assembling the robot onto the robot pedestal

134

Fixture

Even if two turbine blades were manufactured as per the CAD drawing, it would not be possible to

use the same probe path for ultrasonic scanning if the fixturing introduces an error that results in a

probe being out-of-normal to the blade surface by more than 1° or 2° (see Chapter 6.3). Therefore,

it is necessary to design a fixture that minimises the introduction of errors introduced in the fixturing

process and can locate the turbine blade repeatedly and reliably. It is noted that, as the target area

of inspection, the aerofoil section of a turbine blade has to be accessible which means that the fir-

tree root is the only part of a turbine that can be utilised for fixturing.

Fir-tree roots are typically machined and ground for high-precision locating purposes and therefore are

perfect references for locating turbine blades. However, the blades that were supplied by ELE (Model

number PSM104, see Fig. 6.7-1) had the fir-tree roots already ground. This greatly simplified the fixture

design. Design a fixture without a ground fir-tree root is beyond the scope of this thesis.

Apart from locating and holding the turbine blade rigidly and with high accuracy and repeatability, the

fixture itself has to be located on the shaft and held in position rigidly; it will be subject to a bending

moment caused by the weight of the blade and therefore its connection to the shaft must be

sufficiently rigid. Also therefore must be no slip between the shaft and the fixture when the former is

rotated by the stepping motor. The rotation of the turbine blade will be measured by the rotation of the

shaft and therefore there is need for non-slip torque transfer to the fixture, which is possible by making

use of the keyway on the shaft.

Fig. 3.8-1 The fir-tree root of the test blade

The fir-tree roots of the test blades are ground to an

accuracy of ±10 µm. As seen in Fig. 3.8-1 (b), on each side

of the fir-tree root, there are four indentations that can be

used for locating. The counterpart of these indentations can

be adopted for the design of the jaw, if the inserts are of

larger radii (see Fig. 3.8-2); this makes, in total, sixteen line

contacts between the jaw and the fir-tree root. It can be

argued that this design over-determines the locating and due

to manufacturing tolerances, it is very possible that only three of the surfaces are utilised. On the

(a) (b)

Fig. 3.8-2 A jaw with four inserts on each side clamped on the fir-tree root

Fir-tree root of the test blade

Jaw with inserts of

larger radii

135

other hand, if fewer line contacts, say three, not enough rigidity may be obtained; also the

stainless steel (the fixture is made of this material) is a softer material than Inconel5 and therefore

by having more line contacts, it will reduce the long-term wear of the jaws.

The side faces of the fir-tree root have several grounded surfaces which are utilised for locating

the blade in the transverse direction.

Design overview

Fig. 3.8-3 Different views of the fixture

Fig. 3.8-4 An exploded view of the fixture

5 Rockwell B hardness of stainless steel (AISI 304) is 70 and Inconel 718 is 109.

136

The fixture design separates the shaft adaptor and the jaws, which enables different jaws to be

fitted to the fixture so that different blades can be held by the same fixture. The shaft adaptor was

designed with a Ø65mm H7 bore which loosely fits the Ø65mm h11 shaft. The interface was

designed for a loose fit because the adaptor will not be removed from the shaft until the jaws

designed for the upcoming test blades cannot be fitted in the adaptor. A standard key slot was

designed on the bore to enable use of a key to transfer the torque positively, thereby avoiding any

slip between the shaft and the fixture. A clearance hole was designed coaxially with the shaft for

M10 bolts which are used to fasten the adaptor.

Clamping of the blade is achieved by having one fixed jaw and one sliding jaw. The former is fixed

to the adaptor with two M6 bolts and the sliding jaw is pushed towards the fixed jaw by four M6

bolts. The M6 bolts are fed through threaded holes on the top plate. Two slider guides are fixed on

the adaptor to restrict the sliding jaw from any transverse movement.

FEA of the fixture design

A finite element analysis was performed to ascertain the stiffness of the design. The fixture does

not experience any other external forces other than the weight of the blade and the resistance

from water as the shaft is rotated. However, due to the fact that the rotation is only completed at

a very low speed, the resistance only poses a small load upon the fixture and was therefore

ignored in the analysis.

Fig. 3.8-5 Definition of the load and contacts for the analysis

Because a complete solid model of the blade is unavailable, only the fir-tree root is modelled for

this analysis. This section of the fir-tree root is approximately 20.7mm from the bottom. A remote

force of 250N, which is approximately the weight of the blade, is applied at a distance of 100mm

100mm

250N

Sliding

contacts

137

away from the top face of the fir-tree root, as shown in Fig. 3.8-5. The worst case scenario is when

only the bottom locators are in contact with the root. This situation was simulated by having

0.1mm deep and 2mm wide slots on the lines of contact for the other four locators. As shown in

the inset diagram in Fig. 3.8-5, only four sliding contacts are defined in the analysis.

The results from FEA are shown in Fig. 3.8-6. The stress is below 20MPa on the surfaces of the

fixture in contact with the blade. The maximum stress is 100.4MPa which is well below the elastic

limit for stainless steel. The load causes a maximum displacement of 0.002414 mm at the top of

the fir-tree root. Assuming that the blade itself is rigid, the displacement at the tip of the blade can

be determined using similar triangles:

0.002414 ∗252.2

20.7= 0.029411𝑚𝑚

This displacement is acceptable, which proves that the design is stiff enough.

Fig. 3.8-6 (a) Von Mises Stress distribution and (b) Displacement distribution

(a) (b)

138

The final assembly

Procedure for assembling the inspection machine

1) Place the cast iron table on a flat surface and level the table using the three adjusting

bolts.

2) Place the water tank on the table and move the water tank to the correct position.

3) Place the three locating blocks on the table; position these blocks using two dowels for

each; then bolt them onto the table.

4) Push the water tank against the locating blocks, and then bolt the water tank onto the

table. (for a first time installation, fix the water than first and then fix and dowel the

locating blocks.)

5) Place and fix the robot pedestal on the table.

6) Place and bolt the robot onto the pedestal.

7) Place the base of the rotary axis pedestal onto the table; position the base using two

dowels and then bolt the base onto the table.

8) Place the shaft housing on the top of the top plate of the rotary axis; position the housing

using two dowels from underneath; bolt the shaft housing from underneath.

9) Slide the first front bearings onto the shaft till the back of the bearing hits the wall on the

shaft; slide the front second bearing onto the shaft till the bearing sits against the first

bearing.

10) Fasten the lock nut on the shaft till the bearings are firmly locked and then fasten the grab

screw on the lock nut to fix the position of the lock nut.

11) Slide the shaft into the housing from the front face till the bearing hits the wall on the

housing.

12) Slide the rear bearing onto the shaft till it hits the wall on the housing.

13) Clip the circlip into the groove on the shaft; push it towards the bearing till it is against the

bearing. Then fasten the circlip.

14) Place the top plate of the rotary axis pedestal onto its base; slide the plate until the

protrusion on the housing passes through the hole on the water tank; position the top

plate using two dowels and then bolt it onto the base.

139

15) Install the O-ring (ID170) into the groove on the in-tank flange; then bolt the flange onto

the housing.

16) Slide the two lip seals on to the shaft respectively till they all fit inside the in-tank flange.

17) Install the gearbox onto the motor; then bolt the driving unit mounting plate onto the gear

box.

18) Loosely bolt the mounting plate onto the rotary axis pedestal.

19) Install the key and the 12-teeth timing pulley onto the gearbox shaft; install the key and

the 60-teeth timing pulley onto the end of the rotary axis shaft; install the timing belt.

20) Tension the timing belt and then fasten the two M5 bolts on the mounting plate.

21) Bolt the mounting plate for tool change system onto the robot pedestal.

22) Install the Schunk tool storage plates and proximity sensors onto the tool storage plate

adaptor; then bolt the adaptor onto the mounting plate.

23) Install the SWK005 onto the robot mounting plate.

24) Install one of the SWA005s onto the mounting plate of the laser sensor holder and Install

the mounting plate onto the L plate using two dowels and a M6 bolt.

25) Install the laser sensor in the L plate.

26) For the ultrasonic probe holder, firstly, slide the O-ring (ID14.6) into the groove inside the

bore; secondly, pass the cable of the probe through the hole on the upper part of the

probe holder; thirdly, slide the probe into the holder; fourthly, place the other O-ring

(ID29.6) in the groove on the mounting surface of the lower part; finally, bolt the lower

part and the upper part using three M5 bolts and fasten the bolt on the inclined surface.

27) Install the other SWA005 onto the mounting plate of the ultrasonic tool holder.

28) Install three Schunk support bolts on the side of each SWA005 and place the assembled

components on the storage plates.

29) Install the guards onto the table.

140

The assembled inspection machine

The different components in the inspection machine are shown in the following figures.

Fig. 3.9-1 Guards

Fig. 3.9-2 The water tank, rotary axis and robot

141

Fig. 3.9-3 Rotary axis consisting of the stepper motor, timing pulleys and belt, and spindle housing

Fig. 3.9-4 The in-tank flange

Fig. 3.9-5 The water tank

142

Fig. 3.9-6 Pipe connectors

Fig. 3.9-7 The tool magazine

Fig. 3.9-8 Rear view of the table showing the cabinet and the robot control

143

Fig. 3.9-9 The Keyence laser sensor mounted in the laser sensor holder

Fig. 3.9-10 The Olympus ultrasonic probe mounted in the ultrasonic probe holder

144

Robot Control

The Fanuc LRMate 200iD can be either controlled manually using a device called “Teach Pendant”

or a PC with a licensed dynamic-link library. The former method of controlling the robot is rather

simple and intuitive and works very well for tasks with little user input involving repetitive

movements. However, when the robot is required to visit hundreds of points in one task, which is

our case, manual control becomes impractical and automatic control of the robot using a PC is

useful here. In this chapter, a brief introduction to the robot is given at the beginning, regarding

the motion and communication with PCs. At the end of this chapter, the core algorithms for

controlling the robot to complete the task of measuring a turbine blade are presented in form of

block diagrams.

145

Robot control

As mentioned in Chapter 3.1, the robot used in this project is a Fanuc LRMate 200iD robot. This

robot has six axes, as labelled in Fig. 4.1-2. This means moving from one position to another, in

most cases, require the cooperation among many axes and there are many possible ways to

complete the motion. This would involve enormous amount of calculation without the Fanuc R-30iB

robot controller.

Fig. 4.1-2 Six axes of the Fanuc robot [112]

With the controller, users can control the robot easily using a device

called “Teach Pendant” from Fanuc, as shown in Fig. 4.1-1. A user can

use this device to monitor, configure, jog as well as program the robot.

However, as the name suggests, programming of the robot using this

device is literally jogging the robot to visit various places and “teach”

the robot to remember these places and the paths from one to the

next. This is ideal for repetitive tasks with a small number of path

points, but in our case the number of points are in the hundreds for a

single blade. And, worse still, these points will change if another blade

with a different geometry is used. Therefore, a computer is needed to

control the robot automatically with minimum human interaction. Fig. 4.1-1 Fanuc teach

pendant

146

Robot motion and variables

4.1.1.1. Motion type and Motion commands

There are four different motion types: linear, circular, joint and arc. In the linear mode, the robot

moves from one position to another in a straight line, whereas in the circular/arc mode, the robot

moves in a circular path. Joint motion is particularly useful when one or more robot arms are in

singularity when other motion types can no longer function.

Since the turbine blade surface is not circular or spherical, it is not possible to use circular or arc

motion. Joint motion requires accurate interpolation from xyz position to joint angles, which is a

very difficult task. In this context, only linear motion is used.

Due to the fact that the surface of the blade is non-linear, it is also not possible to smoothly trace

the surface of the blade in linear mode. In this project, performing a non-linear path is achieved

with a number of short linear moves. The length of each move is typically between 0.1mm and

0.2mm depending on the application.

The command for linear motion contains four

elements: motion code, position, speed and CNT.

Motion code defines the type of motion of this move;

for linear motion, it is L. Position is the coordinate of

the robot at the end of the motion. Speed determines

the velocity at which the robot travels. CNT defines

the amount of rounding off at a corner (see Fig.

4.1-3). CNT has very limited use in this project, as

most of the motions must be carried out accurately

and CNT has to be set to zero.

4.1.1.2. Robot variables

There are different types of variables regarding this robot. The most commonly used variables are

called registers.

There are two types of registers, position registers and number registers. Position registers are

used to define robot positions that are used in motion commands. Number registers are more like

float- or integer-type variables in traditional programming languages that can be used for various

purposes, such as specifying the values for speed and CNT in motion commands.

System variables are also useful for monitoring the status of the robot, such as CPU usage and

current task number. It also enables modification to some parameters to suit a user’s use.

CNT100 CNT0

P1

P3 P2

Fig. 4.1-3 Effects of using CNT0 and CNT100 at P2 and P3

P4

147

Robot IO are special variables. They only have two values, on or off. Robot IO are used specifically

for controlling pneumatic systems installed on the robot, such as Schunk’s tool change system.

Vibrations

During the experiments, it was noticed that the robot vibrated when carrying out a linear motion.

Fig. 4.1-4 shows the distance measured using the laser sensor when the robot was instructed to

move from one end of a slip gauge to the other with linear motion at a speed of 10 mm/s. The

surface of the slip gauge is at an angle to the robot movement, because the slip gauge was not

levelled, whereas the robot was travelling in a horizontal direction. In spite that in an ideal

situation the robot should move linearly along the dash line indicated in orange, the laser

measurement shows the mean deviation of the robot motion from the orange line is approximately

0.048mm with a standard deviation of 0.08mm. This deviation is more significant when the robot

moves at a higher speed. This suggests that it is not possible to take an accurate measurement

when the robot is moving.

Fig. 4.1-4 Vibration of the robot during a linear motion

Fig. 4.1-5 Vibration at the end of the motion

148

It was also noticed that at the end of each robot motion, the robot needs a small amount of time

to recover from the inertia forces which caused a small vibration. The amount of time as well as

the intensity of the vibration increases with increasing speed. At 10mm/s, it is approximately

140ms and causes a 0.005mm oscillation in distance. Although at this speed, the influence is

negligible, it is still reasonable to delay data acquisition for at least 150ms to avoid capturing this

oscillation.

Communication and dynamic-link library

Two-way data transmission can be established between the controller and a PC in various ways

such as RS232-C and TCP/IP protocol. In this project, the TCP/IP protocol is used for data

transmission because it is relatively more friendly for programming.

Communication via the TCP/IP protocol can be established by connecting the controller and the PC

using an Ethernet cable. The controller is assigned with an IP address which becomes accessible

using a web browser after the communication is established, as shown in Fig. 4.1-6.

Fig. 4.1-6 Accessing the robot controller using a web browser

However, this web address only allows the user to monitor the status of the robot or browse files

that are already there in the controller’s hard drive. Controlling the robot or uploading files

149

requires a software interface which was available as part of the dynamic-link library (DLL)

purchased from Fanuc.

This DLL can be used in multiple programming languages, such as C# and C++. This allows the

user to build applications and software on PCs to control the robot. There are a number of

methods included in this DLL library. In this chapter, variable types used in these methods are

explained first, core methods used in the current control software are then introduced and finally

the algorithms of communication and data transmission are explained.

4.1.3.1. Core methods

There are two major types of methods: connect methods and data table methods.

Connect methods are used for connecting to the robot or disconnecting from the robot. The

methods are rather simple:

bool Connect(string IPAddress)

bool Disconnect()

Both methods return a Boolean type true if the action succeeds, otherwise, false.

Data table methods are used for transmitting data, such as retrieving current robot position and

uploading position registers.

There are 12 methods in total of which 6 have been used.

FRRJIf.DataTable get_DataTable()

FRRJIf.DataCurPos AddCurPos(FRRJIf.FRIF_DATA_TYPE DataType, int Group)

FRRJIf.DataCurPos AddCurPosUF(FRRJIf.FRIF_DATA_TYPE DataType, int Group, int UF)

FRRJIf.DataNumReg AddNumReg(FRRJIf.FRIF_DATA_TYPE DataType, int StartIndex, int EndIndex)

FRRJIf.DataPosReg AddPosReg(FRRJIf.FRIF_DATA_TYPE DataType, int Group, int StartIndex, int EndIndex)

FRRJIf.DataSysVar AddSysVar(FRRJIf.FRIF_DATA_TYPE DataType, string SysVarName)

bool Refresh()

Before the data table can be used, a data table must be first created using get_Datatable()

method. After the data table is created, variables of different types can be inserted into the table.

The latest data can be transmitted between the PC and the robot controller using Refresh()

method.

150

The data types listed above are current position (for AddCurPos and AddCurPosUF), number

register (for AddNumReg), position register (for AddPosReg) and system variable of integer, string

or float type (for AddSysVar).

With data type current position, it is possible to acquire the current position of the robot in

different coordinate systems, such as world coordinate system and a user coordinate system.

Position register type and number register type are more frequently used in uploading coordinates

and speed values for robot motion. System variable type is useful for obtaining various information

of the robot and instructing the robot to run a specific robot program that is stored in the

controller hard drive.

With position registers and system variables, the motion of the robot can be controlled by a PC by

updating the coordinates of a position register that is contained in a robot program and then

instructing the robot to run that program.

4.1.3.2. Examples

An example to instruct the robot to move to a coordinate of [230, 330, 123] is shown below:

In the robot controller:

Program name: MoveToPR1.TD

Line 1: L PR(1) 100 CNT0

On a PC:

Line 1: string programName = “MoveToP1.TD”;

Line 2: int index = 1;

Line 3: Float[] position = {230,330,123,0,0,0};

Line 4: PosRegister_PR1.SetValueXyzwpr(index, position, ~);

Line 5: SysVar_selectProg.SetValue(programName);

Line 6: SysVar_runProg.SetValue(1);

In the robot controller, a robot program called “MoveToPR1.TD” is created and saved. The

program contains only one line, which specifies the motion type (linear motion), a position register

(PR(1)) where the number 1 in parenthesis is the index of the position register, motion speed

(100mm/s) and a CNT value of 0.

151

On the PC, three variables were first defined. The string “programName” specifies the name of the

program that needs to run in the robot controller, which in this example is “MoveToPR1”. The

integer “index” specifies the index of the position register that is referred to in the robot program,

i.e. 1. The float array “position” contains the specified coordinates. These three variables are next

uploaded into the robot controller via the data table and finally, the system variable

“SysVar_runProg” is given a value of 1 which in turn executes the program in the robot controller.

The speed of the motion can also be controlled from the PC. In this case, a number register is

used:

In the robot controller:

Program name: MoveToPR1.TD

Line 1: L PR(1) R(3) CNT0

On a PC:

Line 1: int index = 3;

Line 2: int speed = 100;

Line 3: NumRegister_R1.SetValue (index, value);

In this example, a value of 100 is assigned to number register R(3) in the robot controller. Since

R(3) is in the position of the speed value in the motion command, it reflects a speed of 100mm/s

when this line is executed.

152

Control software block diagrams

There are two core procedures in a complete measurement of a turbine blade, laser digitizing and

ultrasonic measurement. In this section, the algorithms for these two procedures are presented in

the form of block diagrams.

For laser digitizing, there are three block diagrams describing the whole procedure. In the first

diagram, laser digitizing is initialised. The second and third diagrams together describe the main

digitizing process.

For ultrasonic measurement, there are two block diagrams. The first diagram shows the algorithm

for controlling the robot. The second diagram shows the procedures of acquiring ultrasonic data.

The blocks used in the diagrams are explained in Fig. 4.2-1.

Fig. 4.2-1 Block diagrams legend

A decision to be made

A variable to be modified or assigned with a value

A process to be carried out

The beginning or ending of a program

An input operation or output operation

A program in a separate flowchart

153

Laser digitizing algorithm

4.2.1.1. Initialisation

Fig. 4.2-2 A general laser digitizing procedure – initialisation

Step 1: Read input parameters: Zsafe, imax, jmax and laser path; meanwhile initialise variables, such

as i =0 and j =0.

Step 2: Move to the home position.

Step 3: Check if the lower float switch is triggered:

- If true:

This means the water level is above the lower float switch and is not suitable for

laser scanning. Drain water and go to Step 3.

- Otherwise, go to Step 4.

Step 4: Check if the laser sensor is already attached to the robot:

- If true, go to Step 5

- Otherwise, attach the laser sensor and go to Step 5.

Drain water

Move to home

position

Attach laser

sensor

Laser sensor

attached?

Move to [X0,0, Y0,0, Z0,0+200]

Y

N

N

N

Z0,0 >= Zsafe?

Water level

low?

Y

Y

P0 = [X0,0, Y0,0, Zsafe]

Motion loop 1

Read input

parameters

Start

Initialize

variables

154

Step 5: Move to the initial position, i.e. the first path point with Z offset by +200mm.

Step 6: Check if the Z coordinate in the first path point is greater than Zsafe.

- If true:

This means it is safe to lower the laser sensor to the defined Z coordinate. Thus,

proceed to Step 7

- Otherwise, replace the Z coordinate with Zsafe and proceed to Step 7.

Step 7: Start Motion loop 1.

4.2.1.2. Motion loop 1

Fig. 4.2-3 A general laser digitizing procedure – motion loop 1

Step 1: Check if i is greater than imax, the total number of sections that is required to be measured:

Lr > 19?

Acquire laser

reading Lr

Zcur = Zsafe?

Pi,j = [Xi,j, Yi,j, Zcur - 3]

j = j+1

N

Skipsection = false

Pi,j = [Xi,j, Yi,j, Zsafe] Zcur - 3 ≥ Zsafe?

Y Y

N

Y

Move to Pi,j

i > imax? Y

Start

End

Motion loop 2

N

Get Pcur = [Xcur, Ycur, Zcur]

N

155

- If true, terminate the algorithm as the last path point is visited.


Step 2: Move to path point Pi,j.

Step 3: Acquire robot current position, Pcur.

Step 4: Acquire a laser reading, Lr.

Step 5: Check if Lr is greater than 19:

- If true:

This implies the surface is outside laser measurement range6. Go to Step 8.


Step 6: Let j = j + 1.

Step 7: Start motion loop 2.

Step 8: Check if the Z coordinates, Zcur, of Pcur is equal to Zsafe.

- If true:

This means the point is unmeasurable. It is possibly outside the surface of the

turbine blade. Set Skipsection = false and go to step 7.


Step 9: Check if the Zcur – 3 is greater than Zsafe:

- If true:

This means it is safe to descend the laser sensor by 3mm. Set P i,j = [Xi,j, Yi,j, Zcur -

3] and go to Step 2.

- Otherwise,

Descend the laser sensor to the minimum height. Set Pi,j = [Xi,j, Yi,j, Zsafe] and go to

Step 2.

6 A proper laser reading is within the criterion [-2,18]. If the acquired value is outside this criterion,

it means the laser sensor is unable to measure the object. Here, it is also assumed that the user

defines a start point that is at a great distance above the surface which is beyond the upper limit of the measuring range.

156

4.2.1.3. Motion loop 2

Fig. 4.2-4 A general laser digitizing procedure – motion loop 2

N

Acquire laser

reading Lr

Skipsection

true?

Skipsection = true

Y

Y

Y Lr > 19?

N

Move to Pi,j

Lr ≥ 4?

Start

Pause 500ms

Acquire laser

reading Lr

Lr ≤ 10?

Zcur+Lr ≥

Zsafe? Pi,j

' = [Xi,j, Yi,j, Zcur+LR]

Pi,j' = [Xi,j, Yi,j, Zsafe]

Get Pcur = [Xcur, Ycur, Zcur]

Move to Pi,j' Get Pcur = [Xcur, Ycur, Zcur]

Output Pcur and Lr

Y

N

N

Y

i = i+1

Pi,j = [Xi,j, Yi,j, Zi,j+10]

Motion loop 1

Y

N

j > jmax?

N

j = j+1

j = j+1

157

Step 1: Move to path point Pi,j.

Step 2: Acquire robot current position, Pcur.

Step 3: Acquire a laser reading, Lr.

Step 4: Check if Lr is greater than 20:

- If true:

Further check if Skipsection is true:

If true:

This means the current path point is probably outside the

turbine blade or has a great curvature that the laser sensor

cannot measure. In this case, the remaining path points are

this section are likely unmeasurable too. Therefore, this section

is skipped. Go to Step 12.

If not true:

This means the starting path point in this section is outside the

turbine blade or has an unmeasurable curvature. In this case

the starting path point is replaced by the next point in

sequence. Thus, set j = j + 1 and go to Step 13.


Step 5: Set Skipsection = true.

Step 6: Check if Lr is greater than or equal to 47:

- If true, terminate the algorithm as the last path point is visited.


Step 7: Pause the thread for 500ms.

Step 8: Re-acquire a laser reading, Lr, after robot reaches a full stop.

Step 9: Check if Lr is smaller than or equal to 10.

- If true:

The laser reading is valid. Output current robot position Pcur and the latest laser

reading Lr, and go to Step 10.


7 For a laser sensor based on the principle of triangulation, the accuracy is the highest near the lower limit of its measurement range. The laser reading zero of our laser sensor is set to -8, which

is +2mm from the lower limit of the measurement range. For any reading greater than 4mm, i.e.

6mm away from the lower limit, the distance between the laser sensor and the surface is reduced and the measurement is repeated.

158

Step 10: Set j = j + 1.

Step 11: Check if j is greater than jmax, the total number of path points in this section:

- If true:

This means the last point in this scanning section has been visited. The next stripe

can be scanned. Go to Step 12.

- Otherwise,

There are still path points unvisited in this section. Go to Step 1.

Step 12: Set i = i + 1 and offset the Z coordinate of the next point Pi,j by +10mm.

Step 13: Start Motion loop 1.

Step 14: Check if Zcur + Lr is greater than Zsafe:

- If true:

This means the height of the laser sensor is safe to be lowered. Set Pi,j' = [Xi,j, Yi,j,

Zcur+Lr] and go to Step 15.

- Otherwise, lower the height of the laser sensor to the lowest limit. Set P i,j' = [Xi,j, Yi,j,

Zsafe] and go to Step 15.

Step 15: Move to Pi,j’.

Step 16: Acquire robot current position, Pcur and go to Step 7.

159

Ultrasonic measurement algorithm

4.2.2.1. Initialisation and Robot motion

Fig. 4.2-5 A general procedure of ultrasonic data acquisition – initialisation and robot motion

Start

Fill in water Water level

high?

Read input Initialize

variables

Probe

attached? Attach probe

Move to Pi

Rotation

required? Get Pcur

Pause 500ms

DAQdone =

true? Pause 50ms

i > imax?

Zcur >

Zsafe?

Rotate blade

Move to P =

[Xcur, Ycur, Zsafe]

End

N

Y

Y

Y

Y

N

Y

N

N

Y Y N

Start ultrasonic

data acquisition

i = i + 1

DAQdone =

false

160

Step 1: Read input parameters, such as gain settings and safe height etc., and probe path.

Step 2: Initialise variables, such as i=0.

Step 3: Check if the upper float switch is triggered:

- If true:

This means water level is upper the lower float switch. Go to Step 4.

- Otherwise

The water level is too low for ultrasonic testing. Fill in water, then go to Step 3.

Step 4: Check if the ultrasonic probe has already been attached to the robot:

- If true, there is no need to attach the probe. Thus proceed to Step 5.

- Otherwise, attach the ultrasonic probe and go to Step 5.

Step 5: Set Boolean DAQdone to false.

Step 6: Check if rotation is required:

- If true, Go to Step 13.

- Otherwise, go to Step 7

Step 7: Move to path point Pi and pause the thread for 500ms.

Step 8: Start a parallel thread for ultrasonic data acquisition (see the next section).

Step 9: Constantly check if DAQdone is true or false:

- If true, go to step 11

- Otherwise, pause 50ms and go to Step 10

Step 10: Set i = i + 1.

Step 11: Check if i is greater than imax:

- If true:

The last point in the probe path has been visited and the algorithm is terminated.


Step 12: Acquire the current robot position, Pcur.

Step 13: Check if Zcur > Zsafe:

- If true:

It means the it is safe to rotate the blade. Go to Step 16.

- Otherwise, the ultrasonic probe needs to be lifted from the surface before the blade

can be rotated. Go to step 15.

Step 14: Move to P= [Xcur, Ycur, Zsafe].

Step 15: Rotate the blade and go to Step 7.

161

4.2.2.2. Ultrasonic data acquisition

Fig. 4.2-6 A general procedure of ultrasonic data acquisition - Ultrasonic data acquisition

Step 1: Read input parameters, such as gain settings and sampling sizes.

Step 2: Initialise variables, such as flag8=1, m=0 and n=0.

Step 3: Reset memory in the ultrasonic card so new data can be loaded in.

Step 4: Set gain to a high value specified in the input parameter.

Step 5: Excite an ultrasonic wave.

Step 6: Check the returned value from the ultrasonic card whether indicates the excitation is

successful or not:

- If successful, go to Step 7.

8 When flag is equal to 1, the high gain defined by user is used; otherwise, the low gain is used.

Start

Ultrasound

excitation

Successful?

Reset ultrasonic

card memory

Read input Initialize

variables

Set gain (high)

Retrieve and

output data

m = m + 1

m > mmax?

Read data

status

Retrieve and

output data

n = n + 1

n > nmax?

Set gain (low)

flag = 0

Y

N

Y

N

N

N

N

Y

Y

Y

DAQdone =

true

Data ready?

End

Bit = 1?

162

- Otherwise, go back to Step 5 and re-excite an ultrasonic wave.

Step 7: Read data acquisition status from the ultrasonic card.

Step 8: Check if ultrasonic data is ready to be collected from the ultrasonic card memory:

- If the data is ready to be collected, proceed to Step 9.

- Otherwise, re-check data acquisition status, i.e. go to Step 7.

Step 9: Check if the flag value is 1:

- If true, the receiver is set to use a high gain. Go to Step 10.

- Otherwise, the receiver is set to use a low gain. Go to Step 14.

Step 10: Retrieve data from ultrasonic card memory and output to a text file.

Step 11: Set m = m + 1.

Step 12: Check if m equals mmax, which is the maximum number of ultrasonic data samples

required at one path point acquired with the high gain:

- If true, data acquisition with high gain is completed, now acquire data with low gain.

Go to Step 13.


Step 13: Set flat = 0 and receiver gain to the low value and go to Step 5.

Step 14: Retrieve data from ultrasonic card memory and output to a text file.

Step 15: Set n = n + 1.

Step 16: Check if n equals nmax, which is the maximum number of ultrasonic data samples required

at one path point acquired with the low gain:

- If true, data acquisition is completed. Go to Step 17.


Step 17: Set DAQdone = true.

Step 18: Terminate thread.

163

Theory

Ultrasonic testing involves many uncertainties that affect the accuracy of the result, such as

determination of time of flight, noise and angle of incidence. It was also found during experiment

that bubbles are also contributors to distortion of the shape of echoes and inaccurate testing

results. In this Chapter, related theories and methods to overcome these problems are first

discussed.

Apart from these uncertainties, the accuracy of ultrasonic testing is also highly dependent on the

accuracy of the probe path which has to be determined prior to ultrasonic testing. In the current

progress of this project, the probe path is calculated based on a B-spline surface representation of

the testing blade. In order to ensure the accuracy of the B-spline surface thereby the accuracy of

the probe path, the blade has to be digitized on a CMM. In turn, the probe path is computed in the

CMM coordinate system. A localisation method is therefore used to transform the probe path into

the coordinate system of the inspection machine. The accuracy of the localisation is crucial. In this

chapter, the theories and methods to solve these mathematical problems are also discussed.

164

Ultrasonics

Determination of thickness

Unlike a ruler or a caliper, which determines the dimensions of an object using a physical scale,

ultrasonic measurement is based on a velocity-time equation. In contact ultrasonic testing, a pulse

of ultrasound is generated from an ultrasonic probe. When the pulse reaches a reflector, it

bounces back and returns to the probe. The time interval, t, between when the pulse was emitted

and received is recorded. The distance, d, travelled from the ultrasonic probe to the reflector can

then be determined based on the velocity of sound v:

𝑑 = 𝑣 ∗ 𝑡/2 Eq. 5.1-1

This enables measurement of a subsurface feature which is impossible to measure with a physical

scale without destroying the material or obtaining an image inside the material. In ultrasonic

testing, the time interval is usually referred as the time of flight.

Fig. 5.1-1 A schematic drawing of the path of ultrasound for immersion ultrasonic testing

In our case, i.e. in immersion ultrasonic testing, the time of flight is determined in a slightly different

way. As the ultrasonic probe must be immersed in water during testing, the excited ultrasonic pulse

first travels through water before it reaches the test piece, as shown in Fig. 5.1-1 (a). The distance

between the lens of the ultrasonic probe and the test piece is called water path. On reaching the

interface between the water and test piece, part of the pulse is reflected back and received by the

probe, as shown in Fig. 5.1-1 (b) and (c). The received pulse is known as an interface echo. The rest

of the ultrasound continues to travel into the test piece and finally bounces off at the reflector, which

Ultrasonic Probe

Water path

Test piece

(a) Excitation (b) On reaching the interface

Red: reflected Purple: transmitted

(c) On receiving the interface echo

(d) On receiving the backwall echo

Excitation pulse

Interface echo

Backwall echo

Am

plit

ud

e

Time Time of flight

(e)

165

is the interface between the surface of the blade and the hole, and is received by the probe, known

as the backwall echo, as shown in Fig. 5.1-1 (b) and (d). In this case, the time of flight is the time

difference between the reception of the interface echo and backwall echo, as shown in Fig. 5.1-1 (e).

An accurate determination of the time of flight requires an analysis of the received ultrasonic pulse in

the time domain, where variations of the amplitude of received pulse are plotted against time, as

shown in Fig. 5.1-2.

As can be seen, there are three signals plotted in this time domain. They are the interface echo, first

backwall echo and the second backwall echo. For the interface echo, its pulse duration is

approximately 450 ns and across its entire wave lengths, there are two strong peaks (PI1 and PI2) and

three strong valleys (VI1, VI2 and VI3). The pulse duration of the backwall echo is approximately 300ns

and one strong peak (PB1) and two strong valleys (VB1 and VB2) can be found. Due to phase change

at the interface of water and metal, the actual time of flight is calculated between VI2 and PB1. In this

case, the distance can be evaluated with the velocity-time equation (Eq. 5.1-1) provided an accurate

value of velocity is determined with technique such as Laue X-ray diffraction [24]. The time of flight

can also be taken between any one of the peaks or valleys from each echo, for example PI1 and PB1.

In this case, Eq. 5.1-1 cannot be used and instead, a relationship between thicknesses and the time

of flight must be found. The establishment of this relationship is referred as calibration.

Calibration is a relatively more convenient method and therefore thickness calculations in this

project are all completed using calibration equations.

Fig. 5.1-2 Ultrasonic signals in time domain

VI1 VI2

VB1

Interface echo Backwall echo

VB2

PB1 PI1 PI2

VI3

166

Calibration

The purpose of calibration is to establish an accurate relationship between the calculated time of

flight and the actual wall thickness. As the time of flight can be calculated in many ways, a simple

linear velocity-time equation (Eq. 5.1-1) becomes inadequate for an accurate thickness

interpretation. Also, there are many other reasons that suggest the velocity-time equation

inapplicable, such as the variations in the acoustic velocity due to lack of uniformity in the test

material and lack of compensation for “the propagation time of electrical pulses through a long

cable” [8].

Calibration is usually defined by a linear equation [11]:

𝑑 = 𝑚𝐶𝑇 + 𝑐 Eq. 5.1-2

where 𝑑 is the distance, 𝑚𝐶 a multiplier, 𝑇 the time of flight and c a constant.

A calibration equation is established between a pair of points, one point on the interface echo and

the other on the backwall echo. The same equation can be used for another pair of points that are

positioned similarly. For example, if the calibration is performed between 𝑃𝐼2 and 𝑃𝐵1 , the

calibration can also be used between 𝑉𝐼2 and 𝑉𝐵1 or 𝑉𝐼3 and 𝑉𝐵2 . This provides alternative

calculation of ToF in the case that the echoes were distorted at one of the original pair of points.

To begin with, however, it is always suggested to select two strongest spikes for calibration. In our

system, from repeated experiments, it was found that PI1 and PB1 were in general the strongest

spikes. Therefore, calibration for this ultrasonic system should be established between 𝑃𝐼1 and 𝑃𝐵1.

As mentioned in the literature chapter, calibration should be performed for different thickness

ranges because one calibration is only accurate to a degree in the thickness range the calibration is

performed.

Resolution

The resolution of an ultrasonic system usually refers to the near surface resolution, i.e. the

minimum thickness that can be measured by an ultrasonic system. As mentioned earlier, the

interpretation of distance or thickness using an ultrasonic probe involves calculation of time of

flight which is evaluated from the interface echo and the backwall echo. When measuring a small

wall thickness, it is possible that the backwall echo overlaps the interface echo and the resultant

signal is usually distorted and makes determining time of flight very complex. This resolution is

greatly related to the frequency of the ultrasonic probe and the minimum pulse duration that can

be sent by the ultrasonic card.

With our system, it was found the minimum thickness that could be comfortably measured was

approximately 0.65mm. By upgrading the card with a lower minimum pulse duration, the near

surface resolution can be improved.

167

Despite the near surface resolution, it is also necessary to mention the resolution of thickness

measurement restricted by the sampling rate of the ultrasonic data acquisition/logging equipment,

in our case, the ultrasonic PCI card. This resolution ultimately leads to the sampling error ΔR𝜙 as

discussed in Chapter 2.1.4.3. The highest sampling rate is dependent on the time interval between

ticks of the internal clock in the ultrasonic card. The highest sampling rate available on our

ultrasonic card is 100MHz, which means the time difference Δ𝑇 between each data point, or

amplitude value, is 10ns. Substituting Δ𝑇 into Eq. 5.1-2, the distance is equal to Δ𝑇 times the

multiplier, i.e. Δ𝑇𝑚𝑐. This means any distance variation below Δ𝑇𝑚𝑐, or 10𝑚𝑐 in our case, cannot

be measured.

Noise

As discussed in the literature review chapter, some common sources of noise are [17]:

(e) probe noise

(f) weak echo due to material grain, texture and composite

(g) electronic noise due to amplifier, pulser reverberations and reflection in cable [8]

(h) interferences due to electro-magnetic

An important measure of noise level is signal-to-noise ratio. This ratio compares the power of a

signal with the power of background noise. A high ratio is usually desired. The signal-to-noise ratio

can be increased/decreased by adjusting the receiver gain, which is available in the ultrasonic card.

With a higher receiver gain, the strength of the ultrasonic signals is greatly increased at a cost of a

much smaller increase in the strength of background noise. However, a higher gain is not always

appreciated. An over amplified signal may exceed the detection threshold of signal strength and

thereby result in phase angle error. Thus, the required receiver gain should be obtained

experimentally by trial and error.

A very effective method of suppressing noise found during testing the ultrasonic probe was to

capture multiple sets of ultrasonic signals at the same place and take the average amplitudes. This

method works especially well against periodic noise.

However, one obvious drawback of this method is that the time cost for data acquisition is

increased. The average time for capturing 1000 data points is 2.24ms. Taking 100 sets of data

containing 1000 data points would require 224ms.

168

Bubbles

Air bubbles are known to affect ultrasonic testing

detrimentally in terms of accuracy of measurement [114].

There are two types of bubbles in this context, (a)

bubbles trapped on the lens of an ultrasonic probe and (b)

bubbles attached to the surface of inspection of the

specimen, as shown in Fig. 5.1-3.

The first type of bubbles is generated due to air trapped

on the concave-shaped focused lens at the instant when

the ultrasonic probe is immersed. These bubbles

significantly attenuate the ultrasonic signal and greatly

distort echoes. Bubbles that are big as the one shown in

the picture can have a devastating effect to the testing.

An example of a signal captured in the presence of these

bubbles is shown in Fig. 5.1-4 (c), where the interface

echo cannot be detected, compared with Fig. 5.1-4 (a),

captured after the bubbles were removed. However, this

type of bubbles can be easily removed by wiping across

the lens with one’s finger after the probe is immersed

[115].

The second type of bubbles is formed by air dissolved in water on surfaces that have temperature

differences with water. This type of bubbles has less influence on ultrasonic testing results, but still

attenuate the ultrasound as well as add bubble echoes and noise [115]. An example signal affected

by these bubbles is shown in Fig. 5.1-4 (b). Compared with Fig. 5.1-4 (a), as can be seen, a

bubble echo is captured before the interface echo and generally, the amplitude of the backwall

echoes is reduced. However, in this example, the backwall echoes are strong enough and even

with reduced amplitude, they are still detectable. Fig. 5.1-5 (a) shows a weak backwall echo

captured at a surface without bubbles and the backwall echo was captured again at the same

place after bubbles were gathered on the surface (see Fig. 5.1-5 (b)). It can be seen the amplitude

of the backwall echo was reduced to near noise level. At a receiver gain of 70db, the bubble echo

was as strong as the interface echo which may cause incorrect detection of the interface echo and

the added noise became significant which could be mistakenly detected as a backwall echo.

Fig. 5.1-3 Two types of bubbles that affect ultrasonic testing

Surface of

specimen with

small bubbles

Surface of

specimen

without bubbles

(b)

A bubble got

trapped on the

lens

(a)

169

Fig. 5.1-4 Effect of having bubbles on surface of inspection and probe lens

Bubbles attached to the surface of the specimen are difficult to avoid as they grow gradually

temporally as long as there is a temperature difference. Nakanishi et al. [114] developed a device

that sprays high-pressure water onto the surface of inspection to remove these bubbles. Lumsden

[115] suggests adding chemical solutions such as surfactants to reduce the surface tension of

water. However, as both techniques are not available here, the surface bubbles are removed

periodically, typically every 5 minutes, with hands. These bubbles usually stop growing after

several hours.

It is noted that as the probe lens has an anti-bubble coating, this type of bubble cannot

accumulate on the probe lens.

170

Fig. 5.1-5 Nose caused by surface bubbles at receiver gain = 70

Angle of incidence

When an ultrasonic wave acts on the interface of two different media at an oblique angle 𝜃1, i.e.

when the tested surface is not normal to the sound wave, both refracted and reflected waves are

produced. The extent of refraction and reflection are each correlated to the velocity of sound

within the medium through which the signal passes [6] [116] [117].

As shown in Fig. 5.1-6, when a sound wave is incident at an angle 𝜃1 to the interface, a portion of

this wave is reflected back into the medium at the same angle, because the two waves are

travelling in the same medium and therefore have the same sound velocity. The remaining part of

the incident wave penetrates the tested surface and is refracted at a different angle, 𝜃2. The value

of this refraction angle depends upon the different sound velocities within the two media [116] or

their mutual wave resistance [6]. Moreover, the greater the sound velocity in the tested material,

171

the greater will be the refraction angle. Snell’s Law, reproduced below, is a well-known way to

describe this phenomenon [6] [116]:

𝑠𝑖𝑛𝜃1

𝑠𝑖𝑛𝜃2

=𝐶1

𝐶2

Eq. 5.1-3

The refraction of ultrasonic wave should be

avoided because any refraction would affect the

accuracy of measurement. As shown in Fig. 5.1-6

(a), when the angle of incidence (𝜃1) is equal to

0° the wall thickness is given by half the time

taken to travel from A to B and back. However,

when 𝜃1 ≠ 0, the ultrasound is diffracted at the

interface and the material path of the ultrasound,

i.e. CDE, is increased (Fig. 5.1-6 (b)). The

increased thickness can be evaluated by Eq.

5.1-4, where 𝜃2 can be obtained with Eq. 5.1-5

based on Snell’s law.

It should be noted that although the central axis

of the ultrasonic signal seems to pass beyond the width of the ultrasonic probe at a certain angle,

the probe can still acquire a proportion of the echo, because the returned ultrasonic wave is

already defocused and the width of the wave is dependent on the distance travelled beyond the

focal point, acoustic velocity, angle of incidence, etc. Depending on the proportion captured and

overall strength of the echo, the signal may be still sufficiently strong to determine the wall

thickness.

𝐶𝐷 = 𝐷𝐸 =𝐴𝐵

cos(𝜃2) Eq. 5.1-4

sin 𝜃2 =𝑉𝑖 . sin 𝜃1

𝑉𝑤 Eq. 5.1-5

where Vi and Vw are the velocities of sound in Inconel (6130 m/s) and water (1480 m/s)

respectively at ambient temperature.

Fig. 5.1-6 Refraction and reflection of ultrasonic signal

172

Reverse engineering

Generation of the path for an ultrasonic probe when it is required to measure the wall thicknesses in

turbine blade, is similar to generating an NC tool path to mill a free-form surface. This requires the

surface to be modelled mathematically and surface normals to be calculated. As discussed in Chapter

2.2, reverse engineering involves digitizing, registration, triangulation, segmentation and surface

fitting.

The following reverse engineering procedures have been implemented in this project.

1. A CMM with a touch-trigger probe is used for digitizing.

2. Triangulation is done with 2D Delaunay triangulation and some pre-processing and post-

processing procedures.

3. Surface fitting is achieved with shape preservation parameterisation and B-spline surfaces

which model the low pressure and high pressure surfaces separately.

It is noted that the use of a touch-trigger probe is because this is the only type of probe available in

the current CMM. Also noted that registration is avoided because turbine blades are fixed during

digitizing and the coordinate system of the CMM is kept constant. Given that the surface of a turbine

blade can be modelled as one smooth and continuous surface, segmentation is also not needed.

In this section, procedures and methodology of digitizing turbine blades are introduced first, then

methods and algorithms for surface fitting tested in the early stage of this project are discussed, and

finally procedures and mathematics of triangulation, parameterisation and surface fitting are

presented.

Digitizing turbine blades

The decision to digitizing turbine blades on a CMM was made based on two concerns. The first

concern is due to accuracy of the robot. It is not suitable to use the laser sensor for an accurate

digitization because the accuracy of the result is significantly limited by the accuracy of the robot,

which is typically around 50 to 200 µm. The second concern is time requirement for the measuring

process. If digitization of a turbine blade is performed on a CMM, it is possible to digitize a second

blade and prepare the probe path whilst the first blade is still being measured on the inspection

machine. This approach then requires a localisation i.e. an (ICP) algorithm to transform the B-spline

representation and probe path from the CMM to the inspection machine, which is discussed later in

this chapter.

Due to aerodynamic requirements, the surface of a turbine blade is always a smooth and continuous

surface without corners or flat faces. The surface of the turbine blade must be divided into several

173

regions depending on the curvatures of the cross sections to allow a

correct angle for the touch probe to make contact with the surface of

the blade. An example of the division of the blade into regions is

shown in Fig. 5.2-1. Manually digitizing such surfaces accurately with

a CMM and a touch-trigger probe can be very time-consuming

depending on the size and variation in the curvature of the blade.

Therefore, a two-stage scanning strategy is adopted where in the

first stage a coarse scan is obtained with manual operation for

automating a more detailed scan in the second stage.

In the first stage, only a few cross-sectional profiles of the turbine

blade are scanned with a reasonable amount of detail. The acquired

data are collected and fitted with a B-spline surface (see Chapter

5.2.5) individually for each scan region. With these B-spline surfaces, it is possible to compute a large

number of points and generate a mesh to represent the surface of the turbine blade. Undoubtedly

the precision of this mesh is lacking and cannot be used for probe path calculation. Therefore, based

on this mesh, a CMM program is generated for a second-stage scan. This CMM program enables

automatic surface data acquisition by visiting all points on the mesh. The number of data points to be

collected can be easily adjust by increasing or decreasing the density of the mesh.

(a) 47 surface points acquired on one region in the first stage

(b) 1404 points calculated on the B-spline surface

Fig. 5.2-2 Acquired surface points and calculated points on the B-spline surface

Fig. 5.2-2 (a) shows 47 surface points acquired manually in one region of the blade in the first-stage

scan using the CMM and the touch-trigger probe. Fig. 5.2-2 (b) shows 1404 points calculated on the

B-spline surface which is fitted to the 47 surface points. Fig. 5.2-3 shows the CMM probe path

calculated for the second-stage scan based on the calculated 1404 points. One scan of these points

Fig. 5.2-1 The five regions

defined on the surface of the blade

174

takes approximately one and a half hour and this is only one quarter of the surface area of the blade.

In the context of testing and experimenting, this time may not be crucial but on the factory floor,

where this inspection rig will be eventually installed, the scanning time could add to the production

costs.

When the blade is scanned, it is positioned such that its longitudinal axis is vertical. This vertical

position is ideal for locating all the sections of the blade to be inspected.

Fig. 5.2-3 Generated CMM path based on the calculated 1404 points

Fitting methods tested in the early stages.

Before surface fitting methods are tested, it is useful to investigate curve fitting methods, where

cross sections of turbine blades are reverse engineered.

175

The Bezier curve is a good method for curve fitting problems and it is relatively easy to be program

and differentiate, although in the literature reviewed [118] [119] it was not employed in representing

cross sections of turbine blades. It was soon found that the Bezier curve is not ideal for modelling

cross sections of turbine blades due to oscillations found in high degree curve and difficulties in

maintaining continuity between segments. Next a B-spline curve was tested and it was found that the

goodness of fitting was much better than the Bezier curve. Therefore, it was decided to extend the

B-spline curve to surface fitting, i.e. B-spline surface was adopted for modelling the surfaces of the

blade.

Before a B-spline surface representation can be calculated, the surface has to be parameterized. The

most convenient parameterisation method, i.e. chord length method, was tested first. The virtue of

this method is that a triangulated surface mesh is not needed and algorithms for implementation of

this method required very little effort. However, due to the linearity of the formula, the

parameterisation was inaccurate and in turn modelled surfaces were of poor accuracy.

Shape-preserving parameterization developed by Floater [100] was tested next. This method

requires a triangulation mesh of the surface and the Delaunay triangulation was therefore used. In

Matlab, 3D Delaunay triangulation can be easily implemented with a built-in function t =

Delaunay(x,y,z). However, the triangulation generated with this built-in function includes

tetrahedrons through the thickness of the blade, which have to be removed. Crust method [120] was

adopted in this case to extract the surface triangulation. Although the theory introduced in the

literature seems to work, the practical implementation of the theory sometimes failed. Fig. 5.2-4

shows a failed extraction result where some triangular elements are deleted mistakenly.

Fig. 5.2-4 Failed surface triangulation extraction result

176

In order to obtain a correct surface triangulation, 3D Delaunay triangulation was replaced by 2D

Delaunay triangulation, which is supposed to generate surface triangulation only and thus the

extraction algorithm is not needed. This strategy worked well and the surface fitting results were

promising. Therefore, this method is adopted for the remainder of the project.

Triangulation

5.2.3.1. 2D Delaunay triangulation

A brief description of the steps of generating a 3D triangulation mesh using 2D Delaunay

triangulation is described below.

1. Map 3D points into a 2D coordinate system, for example, u and w coordinate system.

2. Compute a 2D Delaunay triangulation for the 2D point set. Once the 2D Delaunay

triangulation is computed, the connections among points are obtained.

3. Map these connections to 3D points and a 3D triangulation mesh can be obtained.

2D triangulation requires the point set defined in a 2D space. Mapping 3D points into 2D can be

achieved with various parameterisation methods. In this context, accuracy is not important and

because surfaces are scanned on a CMM, data are always ordered by the z coordinates. In this

case, the chord length method9 is the most convenient and thus is selected. As shown in Fig. 5.2-5,

a sphere surface model (Fig. 5.2-5 (a)) is parameterised into u and w coordinates (Fig. 5.2-5 (b)).

By now, each xyz point has a unique point in u-w coordinate system. Next, 2D Delaunay

triangulation is generated using the Matlab built-in function t = delaunay(u, w) [121]. Output t is a

matrix that contains the connectivity information of each points10. This matrix is then mapped onto

the 3D surface and finally a triangulation of the surface is produced (Fig. 5.2-5 (d)).

The example shown in Fig. 5.2-5 (a)-(d) presents a good result when this triangulation method is

applied to a set of uniformly distributed surface points. However, for a set of non-uniformly

distributed surface points, direct application of this method may generate ill triangles when 2D

triangulation mesh is mapped to 3D space. An example of an ill triangle found in the 3D mesh is

shown in Fig. 5.2-5 (f), although in 2D (Fig. 5.2-5 (e)) the triangle is good. This is because, when 3D

points are mapped onto a 2D surface, the u coordinates of the end points of the cross sections are

always set to 0 or 1 as shown in Fig. 5.2-6 (a), which means the cross sections are perfectly aligned

in the w direction. In cases where the points in 3D are non-uniformly distributed, although the start

or the end of the cross sections do not necessarily line up in 3D, as shown in Fig. 5.2-6 (b), they are

9 More details of the chord length method can be found in Chapter 5.2.4.1 10 More detailed explanation of the Matlab function t=delaunay(u,w) can be found in Chapter 5.2.3.3.

177

Fig. 5.2-5 Triangulation of a sphere surface

(a) a sphere surface model (b) parameterised points

(c) 2D Delaunay triangulation (d) 2D Delaunay triangulation mapped onto 3D surface

(e) 2D Delaunay triangulation for non-uniformly distributed points (f) an ill triangle

178

Fig. 5.2-6 Starting points of each cross section in 2D and 3D

lined up in 2D. Therefore, when the mesh calculated in 2D is mapped onto 3D, the two boundaries

of the mesh, where u=0 and u=1, are greatly distorted and so are the triangles in the mesh.

Therefore, pre-processing is required to trim the point set and line up the start and end of the

cross sections.

Because points are non-uniformly distributed, it is not possible to line up the cross sections by

deleting points or shifting the end points. One possible solution is to fit a B-spline curve to each

cross section and generate large numbers of points along each section. With enough point density,

it is possible to trim the cross sections without greatly shortening the length of the curve. If the

shape is closed, the end points can be shifted along the cross section without trimming. The

mathematics and algorithm employed for B-spline curve fitting are introduced in the next section.

The result of the spherical surface and the end points of each section after B-spline curve fitting

are shown in Fig. 5.2-7 and Fig. 5.2-8. An example of a triangulated turbine blade surface is shown

in Fig. 5.2-9. Procedures for this Delaunay triangulation algorithm are shown in Fig. 5.2-10.

(a) (b)

179

Fig. 5.2-7 Spherical surface after B-spline curve fitting and the line connecting the end points of the cross sections

180

Fig. 5.2-8 Triangulation result based on points generated by B-spline curves

181

Fig. 5.2-9 Triangulated surface of a turbine blade

182

Fig. 5.2-10 Calculation procedures in the triangulation algorithm

5.2.3.2. B-spline curve

The general equation

The general equation of B-spline curve is defined as [87][18]:

𝑷(𝑢) = ∑�̅�𝑖𝑁𝑖,𝑘(𝑢)

𝑛

𝑖=0

, 𝑡𝑘−1 < 𝑢 ≤ 𝑡𝑛+1 Eq. 5.2-1

where {�̅�𝑖} is a set of control points, 𝑘 is the order of the curve and 𝑘 − 1 gives the degree of the

curve, 𝑛 + 1 is the total number of control points and 𝑁𝑖,𝑘(𝑢) are the basis equations or blending

functions given in Eq. 5.2-2.

𝐹𝑜𝑟 𝑘 = 1

𝑁𝑖,1(𝑢) = {1, 𝑡𝑖 < 𝑢 < 𝑡𝑖+1

0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Eq. 5.2-2 𝐹𝑜𝑟 𝑘 ≠ 1

𝑁𝑖,𝑘(𝑢) =(𝑢 − 𝑡𝑖)𝑁𝑖,𝑘−1(𝑢)

𝑡𝑖+𝑘−1 − 𝑡𝑖+

(𝑡𝑖+𝑘 − 𝑢)𝑁𝑖+1,𝑘−1(𝑢)

𝑡𝑖+𝑘 − 𝑡𝑖+1

where 𝑖 = 0,1, … , 𝑛 + 𝑘 − 1

{𝑡𝑖} are values of the knots which join the segments, their values can be obtained

from Eq. 5.2-3:

𝑡𝑖 = {0, 0 ≤ 𝑖 < 𝑘

𝑖 − 𝑘 + 1, 𝑘 ≤ 𝑖 ≤ 𝑛𝑛 − 𝑘 + 2, 𝑛 < 𝑖 ≤ 𝑛 + 𝑘

Eq. 5.2-3

CMM point data B-spline curve

fitting uniformly

distributed points

2D Delaunay

triangulation

2D Triangulation

mesh

Input Output

Input Output Uniform

parameterisation

u and w

coordinates

Input Output

Remap 2D mesh

to 3D

3D Triangulation

mesh Input Input Output

183

The implementation of a B-spline curve is done in three general steps: (i) determination of the

curve parameters, such as 𝑘 and 𝑛, (ii) calculation of the control points �̅� and (iii) generation of

the fitted points. Usually, there is another step in which the fitted curve is examined in various

ways, such as deviations from the measured points and rate of change in slope. If the result is not

of the required accuracy, the curve parameters should be adjusted and steps (ii) and (iii) repeated.

Determination of the curve parameters

Parameters need to be determined are the order of the curve (𝑘) and the number of control points

(𝑛 + 1).

The number of control points must satisfy the follow condition:

𝑘 ≤ 𝑛 + 1 ≤ 𝑟, 𝑜𝑟 𝑘 − 1 ≤ 𝑛 ≤ 𝑟 − 1

where 𝑟 is the total number of points in 𝑷𝐶 , which is a collection of the point data acquired in

digitizing process sorted in form of a column vector (𝑷𝐶,1, 𝑷𝐶,2, … , 𝑷𝐶,𝑟)𝑇.

According to Eq. 5.2-3, when 𝑛 = 𝑘 − 2, all knot vectors are equal to zero and when 𝑛 is even

smaller, the knot vectors (𝑡0, 𝑡1, … , 𝑡𝑘−1) are zeros and the rest become negative. This means that

all terms, except for the first term, in the blending functions are zero and the fitted points will have

only two different coordinates, the first being the coordinates of the control point and the second

being the origin 𝑥 = 0, 𝑦 = 0, 𝑧 = 0. When 𝑛 > 𝑚 − 1, i.e. the number of control points is greater

than the number of measured data points, the control points cannot be calculated accurately. This

will be discussed in the next section.

Depending on the fluctuation of the curve and point density of the measured point set, the optimal

values of 𝑘 and 𝑛 vary. Normally, with high point density, a 4th order curve is accurate enough to

define complex shapes, and the value of 𝑛 should be adjusted carefully. A higher value of 𝑛 often

gives a closer approximation to the measured points. However, excessive number of control points

as well as an unnecessarily high definition of the order of the curve introduce undesirable

oscillations, especially at the two ends of the curve.

In addition, it is not always true to obtain the best approximation to the CMM measured points.

Because of various factors, such as roughness of the blade surface and inaccuracy of the CMM, the

points do not lie on a smooth curve. Fig. 5.2-11 shows parts of two B-spline curves fitted to the

same set of CMM points. As shown, the point in the centre of the CMM curve tends to be away

from the overall tendency of the points. The B-spline curve shown in Fig. 5.2-11 (b), because it

was defined by more control points and a much higher order curve than the one in Fig. 5.2-11 (a),

presents a better approximation to the CMM points but replicates the departure and causes an

oscillation in its vicinity.

184

Fig. 5.2-11 (a) number of control points = 50, degree of curve = 10; (b) number of control points = 65, degree of curve = 45

Calculation of the control points

Coordinates of the control point �̅�𝑖 can be obtained by solving the set of equations defined by

solving Eq. 5.2-1. First we substitute the left part of the equation, i.e. 𝑷(𝑢), by 𝑷𝐶(𝑢), which is the

point data acquired during the digitizing process:

𝑷𝐶(𝑢) = ∑ �̅�𝑖𝑁𝑖,𝑘(𝑢)

𝑛

𝑖=0

Eq. 5.2-4

The next step is to solve the blending functions, i.e. Eq. 5.2-2. Each point in 𝑷𝐶 needs a

corresponding 𝑢 ∈ {𝑢𝑗}, which can be obtained conveniently using chord length method11:

𝑢𝑗 = {

0 , 𝑗 = 1

𝐷(𝑷𝐶,𝑗)

𝐷(𝑷𝐶,𝑟) , 1 < 𝑗 ≤ 𝑚

Eq. 5.2-5

where 𝑟 is the total number of points in 𝑷𝐶 and 𝐷(𝑷𝐶,𝑗) is the summation of the lengths of all

chords up to 𝑷𝐶,𝑗:

𝐷(𝑷𝐶,𝑗) = ∑|𝑷𝐶,𝑖 − 𝑷𝐶,𝑖−1|

𝑗

𝑖=1

11 More details of the chord length method can be found in Chapter 5.2.4.1

185

Once the u coordinates are obtained, the blending functions for each u coordinate can be

determined.

It is now convenient to re-write Eq. 5.2-4 in a matrix form:

[

𝑷𝑐,1

𝑷𝑐,2

⋮𝑷𝑐,𝑟

] =

[ 𝑁1,𝑘(𝑢1) 𝑁2,𝑘(𝑢1) ⋯ 𝑁𝑛,𝑘(𝑢1)

𝑁1,𝑘(𝑢2) 𝑁2,𝑘(𝑢2) ⋯ 𝑁𝑛,𝑘(𝑢2)

⋮𝑁1,𝑘(𝑢𝑟) 𝑁2,𝑘(𝑢𝑟) ⋯ 𝑁𝑛,𝑘(𝑢𝑟)]

[ �̅�0

�̅�1

⋮�̅�𝑛]

or

𝑷𝐶 = [𝑁] ∙ [�̅�]

Eq. 5.2-6

where [𝑁] is an 𝑟 × 𝑛 matrix of all the blending functions and [�̅�] = (�̅�0, �̅�1 … , �̅�𝑛)𝑇

The final step is to solve the above overdetermined system, which can be easily achieved in Matlab

[122]:

[�̅�] = [𝑁]\𝑷𝐶

An example of the calculated control points is shown in Fig. 5.2-12, where the sphere with non-

uniformly distributed data points are used as the input model for calculation.

(a) Cross section at z = -0.2588 (b) 3D space Fig. 5.2-12 Measured points and control points

Generation of the fitted points

Fitted points can be generated by multiplying the control points, which are calculated in the

previous step, with blending functions calculated from a set of u coordinates. This set of u

coordinates can be obtained from the coordinates of any number of points. The density of the

fitted points is determined by the density of the u coordinates. Obviously, it is always wiser to

choose a set of u coordinates of higher density, which is the purpose of curve fitting.

186

Firstly, we define a uniform set of 𝑢 coordinates of 𝑚 number of points. It is also possible to use

non-uniformed u coordinates, only if necessary.

𝑢𝑓 = (0,1

𝑚 − 1,… ,

𝑚 − 2

𝑚 − 1, 1 )

Recalling Eq. 5.2-2 and Eq. 5.2-6, the new matrix of blending functions can be calculated from 𝑢𝑓:

𝑁𝑓 =

[

𝑁1,𝑘(𝑢𝑓,0) 𝑁2,𝑘(𝑢𝑓,0) ⋯ 𝑁𝑛+𝑘,𝑘(𝑢𝑓,0)

𝑁1,𝑘(𝑢𝑓,1) 𝑁2,𝑘(𝑢𝑓,1) ⋯ 𝑁𝑛+𝑘,𝑘(𝑢𝑓,1)

⋮𝑁1,𝑘(𝑢𝑓,𝑚−1) 𝑁2,𝑘(𝑢𝑓,𝑚−1) ⋯ 𝑁𝑛+𝑘,𝑘(𝑢𝑓,𝑚−1)]

Eq. 5.2-7

Finally, fitted points 𝑷𝑓 can be generated:

𝑷𝑓 = 𝑁𝑓 ∙ [�̅�]

An example of the fitted results is shown in Fig. 5.2-13, where the non-uniformly distributed data

points for the sphere are used as the input model for calculation.

(a) Cross section at z = -0.2588 (b) 3D space

Fig. 5.2-13 Cross-sections of the sphere fitted B-spline curves

5.2.3.3. Miscellaneous mathematics and algorithms

Input and output data structure of t=Delaunay(u,w) in Matlab

The output t is a nx3 matrix containing the index of the vertices of n number of triangles that

structure the triangulation mesh. As shown in Table 5.2-1, the input data are two variables

consisting of u and w coordinates of the points respectively and the output is a matrix of 9x3. Each

B-spline curves Measured points Control points

187

row of the output represents the node numbers of the vertices of a triangle in the mesh. For

example, row 1 is 1, 4, 2 and this means, P1, P4 and P4 make up one triangle.

Table 5.2-1 Example input and output of t=Delaunay(u,w) [121] in Matlab Index Input data (u, w) Output data (t)

- u w P1 index P2 index P3 index

P1 0 0 1 4 2

P2 0 1 4 5 2

P3 0 2 2 5 3

P4 1 0 5 8 6

P5 1 1 3 5 6

P6 1 2 4 7 5

P7 2 0 6 8 9

P8 2 1 5 7 8

P9 2 2 1 4 2

Fig. 5.2-14 Triangulation results with above input and output

Parameterisation

Two parameterisation methods are implemented in this project. The first method is the chord

length method and the second method is Floater’s [100] shape preserving method.

The chord length method is simple, efficient and easy to program. It works well for a point set with

high point density and relatively flat surface or linear curve and has some use in this project, such

P7

P8

P9

P4

P3

P2

P1

P5

P6

188

as pre-processing CMM data points for 2D Delaunay triangulation, as mentioned in the previous

chapters. The problem with this method, however, is that its accuracy is not guaranteed. Therefore,

the second method, i.e. shape preserving parameterisation, is adopted when calculating B-spline

surfaces.

5.2.4.1. Chord length method for parameterisation

A simple parameterisation of a point 𝑢(𝑝) on a linear curve can be obtained by calculating the

proportion of the length of the segment from the start point 𝑝0 up to 𝑝 in the entire curve length 𝐿,

i.e. 𝑢(𝑝) = |𝑝 − 𝑝0|/𝐿 . If we do the same for each point 𝑝𝑖 on this curve, we then obtain a

parameterisation of this linear curve:

𝑢(𝑝𝑖) =|𝑝𝑖 − 𝑝0|

𝐿 , 𝑖 = 0,1,2,3, … , 𝑛

Eq. 5.2-8

where 𝑛 is the total number of points, and 𝐿 = |𝑝𝑛 − 𝑝0|.

It is noticed that at the boundaries, i.e. when 𝑖 = 0, 𝑢(𝑝0) = 0 and when 𝑖 = 𝑛, 𝑢(𝑝𝑖) = 1.

If Eq. 5.2-5 were adopted for parameterising a non-linear curve, the results would be rather

inaccurate and problematic. When the curve is linear, Eq. 5.2-5 presents a simplified calculation for

the chord length method, but in the case of a non-linear curve, the actual chord lengths can only

be estimated by adding all small chord lengths between two near points from the start point up to

the point being parameterised [123]:

𝑢(𝑝𝑖) = {

0 , 𝑖 = 0𝐿(𝑝𝑖)

𝐿(𝑝𝑛) , 0 < 𝑖 < 𝑛

Eq. 5.2-9

where 𝐿(𝑝𝑖) is the summation of the lengths of all previous chords in sequence up to 𝑝𝑖:

𝐿(𝑝𝑖) = ∑|𝑝𝑗 − 𝑝𝑗−1|

𝑖

𝑗=1

The same boundary conditions are obtained here: 𝑢(𝑝0) = 0 and 𝑢(𝑝𝑖) = 1.

Due to the fact that the chord length calculation is dependent on the sequence of the points, the

results of the chord length parameterisation will be different if the point sequence is altered. This

also presents a huge problem if the points along the curve are not sorted in the correct order and

in this case, pre-processing to re-arrange the points is necessary.

Another problem with this method is when the points are sparsely arranged and the surface or the

curve has a great variation in curvatures, approximation of the chord lengths become less accurate

and consequently the accuracy of parameterisation results is reduced.

189

5.2.4.2. Shape preserving parameterisation

Floater [100] suggested a much better method, known as shape preserving parameterisation. This

method assumes that the surface of the object has been triangulated. Floater’s method preserves

the shape (curvature) by calculating the solid angle subtended at each node. There are three

major steps to achieve the parameterisation:

1. Map 3D points onto a 2D plane

2. Calculate barycentric coordinates

3. Calculate coordinates of the parameters

3D to 2D mapping

Floater incorporated a method due to Welch and Witkin [124] for local parameterisation to

preserve the arc length adopting the construction of the geodesic polar map. For a complete

surface triangulation of a point set, take one point 𝒙𝑖 and extract all its neighbouring triangles from

the triangulation as shown in Fig. 5.2-15 (a). For this extracted sub-triangulation S, there are six

boundary vertices, 𝒙𝑗1 … 𝒙𝑗6. The local parameterisation of S is denoted by P and 𝒙𝑖, 𝒙𝑗1 … 𝒙𝑗6 ∈ ℝ3

are transformed into 𝒑𝒊, 𝒑1 … 𝒑6 ∈ ℝ2. 𝒑𝑖 is defined as the centre of mass of this polygon, referred

as the barycentre, and 𝒑1 …𝒑6 are boundary points in P in an anticlockwise sequence.

Fig. 5.2-15 Local parameterisation of a sub-triangulation. Reproduced from Floater (1997) [100]

This transformation satisfies the equations in Eq. 5.2-10 and Eq. 5.2-11 proposed by Floater [100].

‖𝒑𝑘 − 𝒑𝒊‖ = ‖𝒙𝑗𝑘 − 𝒙𝑖‖ Eq. 5.2-10

∠(𝒑𝑘 , 𝒑, 𝒑𝑘+1) = 2𝜋∠(𝒙𝑗𝑘, 𝒙𝑖 , 𝒙𝑗𝑘+1) ∕ 𝜃𝑖 Eq. 5.2-11

where 𝜃𝑖 = ∑ ∠(𝒙𝑗𝑘 , 𝒙𝑖 , 𝒙𝑗𝑘+1)𝑑𝑖𝑘=1 , 𝒙𝑗𝑑𝑖+1 = 𝒙𝑗1, 𝑘 = 1,… , 𝑑𝑖 and 𝑑𝑖 = total number of boundary

points.

(a)

xj5 xj

4

xj

3

xj

2 x

j

1

xj

6

x

i p

p

4 p

3

P

2

p

1

p

6

pi

(b)

190

In practice, by letting 𝑝 be the origin, i.e. 𝑝 = 0 , Eq. 5.2-10 can be simplified into ‖𝒑𝑘‖ =

‖𝒙𝑗𝑘 − 𝒙𝑖‖, and 𝒑1, 𝒑2, 𝒑3 … 𝒑𝑑𝑖 can then be computed in sequence.

Calculation of barycentric coordinates

Barycentric coordinates 𝜆𝑖,𝑗 > 0 must satisfy Eq. 5.2-12, which defines an affine combination

between neighbouring points [100].

𝒑𝒊 = ∑ 𝜆𝑖,𝑗𝑘𝒑𝑘

𝑑𝑖

𝑘=1

, ∑ 𝜆𝑖,𝑗𝑘

𝑑𝑖

𝑘=1

= 1 Eq. 5.2-12

For 𝑑𝑖 = 3 , there is only one unique triangle subtended at each 𝒑𝑘 . Therefore, 𝜆𝑖,𝑗𝑘 can be

obtained easily by dividing the area of the triangle subtended at 𝒑𝑘 by the area of the polygon:

𝜆𝑖,𝑗1 =𝐴(𝒑𝑖, 𝒑2, 𝒑3)

𝐴(𝒑1, 𝒑2, 𝒑3), 𝜆𝑖,𝑗2 =

𝐴(𝒑𝑖 , 𝒑1, 𝒑3)

𝐴(𝒑1, 𝒑2, 𝒑3), 𝜆𝑖,𝑗3 =

𝐴(𝒑𝑖, 𝒑1, 𝒑2)

𝐴(𝒑1, 𝒑2, 𝒑3)

For 𝑑𝑖 > 3, it is not possible to easily select the triangle subtended at each 𝒑𝑘 . A method for

selecting the unique triangle is suggested by Floater [100]. For each 𝒑𝑙 ∶= 𝒑𝑘, 𝑙 ∈ {1, … , 𝑑𝑖}, plot a

straight line passing through 𝒑𝑙 and 𝒑 as is done in Fig. 5.2-16. There is a unique second point

where this straight line intersects the polygon. This point can either be a vertex 𝒑𝑟(𝑙) or lie on the

chord connecting 𝒑𝑟(𝑙) and 𝒑𝑟(𝑙)+1, where 𝑟(𝑙) ∈ {1, … , 𝑑𝑖} and 𝑟(𝑑𝑖) + 1 = 𝑟(1).

Fig. 5.2-16 The straight line 𝑙 passing through 𝑝𝑙 and 𝑝𝑖 and intersects the polygon at a second point.

In the case that the point lies on the chord, a unique triangle is found subtended at 𝒑𝑙 which is

defined by 𝒑, 𝒑𝑟(𝑙) and 𝒑𝑟(𝑙)+1 and the relationship between 𝒑𝑖, 𝒑𝑟(𝑙) and 𝒑𝑟(𝑙)+1 can be defined by:

𝒑𝑖 = 𝜇𝑙,𝑙𝒑𝑙 + 𝜇𝑟(𝑙),𝑙𝒑𝑟(𝑙) + 𝜇𝑟(𝑙)+1,𝑙𝒑𝑟(𝑙)+1 Eq. 5.2-13

where

𝜇𝑙,𝑙 =𝐴(𝒑𝑖 , 𝒑𝑟(𝑙), 𝒑𝑟(𝑙)+1)

𝐴(𝒑𝑙 , 𝒑𝑟(𝑙), 𝒑𝑟(𝑙)+1), 𝜇𝑟(𝑙),𝑙 =

𝐴(𝒑𝑖 , 𝒑𝑙, 𝒑𝑟(𝑙)+1)

𝐴(𝒑𝑙, 𝒑𝑟(𝑙), 𝒑𝑟(𝑙)+1), 𝜇𝑟(𝑙)+1,𝑙 =

𝐴(𝒑𝑖, 𝒑𝑙 , 𝒑𝑟(𝑙))

𝐴(𝒑𝑙 , 𝒑𝑟(𝑙), 𝒑𝑟(𝑙)+1)

In case the point is a vertex 𝒑𝑟(𝑙), Eq. 5.2-13 is still valid.

pr(l)+1

p

p

i

pr(l)

l

191

𝜇𝑙,𝑙 =‖𝒑𝑖 − 𝒑𝑟(𝑙)‖

‖𝒑𝑙 − 𝒑𝑟(𝑙)‖, 𝜇𝑟(𝑙),𝑙 =

‖𝒑𝑖 − 𝒑𝑙‖

‖𝒑𝑙 − 𝒑𝑟(𝑙)‖, 𝜇𝑟(𝑙)+1,𝑙 = 0

Thus, for each 𝑙, an equation for 𝒑 is given by:

𝒑𝑖 = ∑ 𝜇𝑘,𝑙𝒑𝑘

𝑑𝑖

𝑘=1

Eq. 5.2-14

where 𝑘 = 1,… , 𝑑𝑖 and for 𝑘 ∉ {𝑙, 𝑟(𝑙), 𝑟(𝑙) + 1}, 𝜇𝑘,𝑙 = 0

Taking the average of the summation of all the 𝒑𝑖 calculated for each individual 𝑙 using Eq. 5.2-14

gives 𝒑𝑖 weighted over the entire polygon:

𝒑𝑖 =1

𝑑𝑖

∑ ∑ 𝜇𝑘,𝑙𝒑𝑘

𝑑𝑖

𝑘=1

𝑑𝑖

𝑙=1

Eq. 5.2-15

Thus, the barycentric coordinates 𝜆𝑖,𝑗𝑘 are defined by:

𝜆𝑖,𝑗𝑘 =1

𝑑𝑖

∑𝜇𝑘,𝑙

𝑑𝑖

𝑙=1

, 𝑘 = 1,… , 𝑑𝑖

for 𝑘 ∉ {𝑙, 𝑟(𝑙), 𝑟(𝑙) + 1}, 𝜇𝑘,𝑙 = 0

Eq. 5.2-16

Calculation of the parameter coordinates

The third step is to solve Eq. 5.2-12. The method of solving the parameterisation equation based

on affine combination is well described by Kai et al. [101]. First, the internal points 𝐼 of the entire

triangulation mesh are separated from boundary points 𝐵. Therefore, in 𝑃, define {𝒑1, 𝒑2, … , 𝒑𝑛𝑖} ∈

𝐼 and {𝒑𝑛𝑖+1, 𝒑𝑛𝑖+2, … , 𝒑𝑁𝑖} ∈ 𝐵. Eq. 5.2-12 can be re-written as:

𝒑𝑖 − ∑ 𝜆𝑖,𝑗𝑘𝒑𝑘

𝑛𝑖

𝑘=1

= ∑ 𝜆𝑖,𝑗𝑘𝒑𝑘

𝑁𝑖

𝑘=𝑛𝑖+1

Eq. 5.2-17

Representing 𝒑𝑖 with two components 𝑢𝑖 and 𝑤𝑖 , the above equation is equivalent to two linear

systems:

𝐴𝑢 = �̅�, 𝐴𝑤 = �̅� Eq. 5.2-18

where 𝑢 = (𝑢1, 𝑢2, … , 𝑢𝑛𝑖)𝑇, 𝑣 = (𝑣1, 𝑣2, … , 𝑣𝑛𝑖

)𝑇 and 𝐴 is a 𝑛𝑖 × 𝑛𝑖 matrix with elements:

𝑎𝑖,𝑗 = 1, 𝑎𝑖,𝑗 = −𝜆𝑖,𝑗 , 𝑗 ≠ 𝑖

�̅� = (�̅�1, �̅�2, … , �̅�𝑛𝑖)𝑇 and �̅� = (�̅�1, �̅�2, … , �̅�𝑛𝑖

)𝑇 are coefficients:

192

�̅�𝑖 = ∑ 𝜆𝑖,𝑗𝑘𝑢𝑘

𝑁𝑖

𝑘=𝑛𝑖+1

, �̅�𝑖 = ∑ 𝜆𝑖,𝑗𝑘𝑤𝑘

𝑁𝑖

𝑘=𝑛𝑖+1

Eq. 5.2-19

Now the boundary points need to be fixed, so that �̅� and �̅� can be calculated. Here an artificial

boundary is defined by chord length method as suggested by Floater [100].

Some examples of parameterisation results are shown here:

Fig. 5.2-17 shows the mapping of a polyhedron from a spherical surface to a 2D plane.

Fig. 5.2-18 shows the parameterisation results for the spherical surface using the same

triangular mesh.

Fig. 5.2-19 shows the parameterisation results for the spherical surface using a refined

triangular mesh.

Fig. 5.2-20 shows a parameterised turbine blade surface whose triangulation result is

shown in Fig. 5.2-9.

(a) (b)

Fig. 5.2-17 Mapping a Polyhedron onto a 2D plane

193

Fig. 5.2-18 Parameterised spherical surface based on a coarse triangular mesh

194

Fig. 5.2-19 Parameterised spherical surface based on a refined triangular mesh

Fig. 5.2-20 Parameterised turbine blade surface (see Fig. 5.2-9 for the triangular mesh)

195

B-spline surface fitting

The B-spline surface shares a similar general equation with the B-spline curve but extends it in a

second orthogonal direction:

𝑷(𝑢, 𝑤) = ∑∑�̅�𝑖𝑗𝑁𝑖,𝑘(𝑢)𝑁𝑗,𝑙(𝑤)

𝑚

𝑗=0

𝑛

𝑖=0

, 𝑡𝑘−1 < 𝑢 ≤ 𝑡𝑛+1, 𝑠𝑙−1 < 𝑤 ≤ 𝑠𝑚+1 Eq. 5.2-20

where 𝑘 and 𝑙 are the order of the surface in the 𝑢 and 𝑤 directions respectively and the knot

vectors, 𝑡 and 𝑠 are constant in both 𝑢 and 𝑤 directions, but not necessarily equal.

The calculation of B-spline surface also follows the major steps used in calculating the B-spline

curve: (i) determination of the surface parameters, (ii)calculation of the control points �̅� and (iii)

generation of the fitted points.

Determination of the surface parameters

The number of control points and the order of the surface can be defined separately in 𝑢 and 𝑤

directions. The logic of determining these parameters is the same as that of for the B-spline curve

described in Chapter 5.2.3.2.

For a turbine blade surface usually there are more points scanned in the 𝑢 direction, which is the

direction of the cross section, and there is a greater variation in the curvature in this direction than

that in the longitudinal direction (i.e. w direction). Therefore, in most situations the values of both

parameters in the 𝑢 direction are higher than their values in the 𝑤 direction.

Calculation of the control points

The control points of a B-spline surface are calculated in a similar way as they are calculated in a

B-spline curve.

First we substitute the left part of Eq. 5.2-20, i.e. 𝑷(𝑢, 𝑤), by 𝑷𝐶(𝑢, 𝑤), the point data acquired in

digitizing process sorted:

𝑷𝐶(𝑢, 𝑤) = ∑∑ �̅�𝑖𝑗𝑁𝑖,𝑘(𝑢)𝑁𝑗,𝑙(𝑤)

𝑚

𝑗=0

𝑛

𝑖=0

Eq. 5.2-21

Then we can calculate the blending function for 𝑢 and 𝑤 separately with Eq. 5.2-2. The 𝑢 and 𝑤

used here are obtained from shape preserving parameterisation (see Chapter 5.2.4.2).

Re-write Eq. 5.2-4 in a matrix form:

[𝑷𝐶] = [𝑁𝑢] ∙ [�̅�] ∙ [𝑁𝑤] Eq. 5.2-22

where

196

[𝑷𝐶] =

[ 𝑃𝐶(𝑢1, 𝑤1) 𝑃𝐶(𝑢1, 𝑤2) ⋯ 𝑃𝐶(𝑢1, 𝑤𝑞)

𝑃𝐶(𝑢2, 𝑤1) 𝑃𝐶(𝑢2, 𝑤2) ⋯ 𝑃𝐶(𝑢2, 𝑤𝑞)

⋮𝑃𝐶(𝑢𝑟 , 𝑤1) 𝑃𝐶(𝑢𝑟 , 𝑤2) ⋯ 𝑃𝐶(𝑢𝑟 , 𝑤𝑞)]

𝑟 is the number of points in 𝑃𝐶 whose 𝑤 are the same and 𝑞 is the number of points in 𝑃𝐶 whose 𝑢

coordinates are the same. [𝑁𝑢] is an 𝑟 × (𝑛 + 1) matrix of all blending functions in the 𝑢 direction,

[𝑁𝑤] is an (𝑚 + 1) × 𝑞 matrix of all the blending functions in the 𝑤 direction and [�̅�] is an (𝑛 +

1) × (𝑚 + 1) matrix of all control points that are currently unknown.

In order to solve Eq. 5.2-6, we need to re-write the matrix in form of 𝐴 = 𝐵𝑥 so that 𝑥 can be

solved in Matlab by 𝑥 = 𝐵\𝐴.

Given

[𝑁𝑢] = [

𝑎1,1 ⋯ 𝑎1,𝑛+1

⋮ ⋱ ⋮𝑎𝑟,1 ⋯ 𝑎𝑟,𝑛+1

] , [𝑁𝑤] = (

𝑏1,1 ⋯ 𝑏1,𝑚+1

⋮ ⋱ ⋮𝑏𝑞,1 ⋯ 𝑏𝑞,𝑚+1

)

Define

𝒩 =

[ 𝑎1,1𝑏1,1 𝑎1,1𝑏1,2 ⋯ 𝑎1,1𝑏1,𝑚+1 𝑎1,2𝑏1,1 ⋯ 𝑎1,2𝑏1,𝑚+1 ⋯ 𝑎1,𝑛+1𝑏1,𝑚+1

𝑎2,1𝑏2,1 𝑎2,1𝑏2,2 ⋯ 𝑎2,1𝑏2,𝑚+1 𝑎2,2𝑏2,1 ⋯ 𝑎2,2𝑏2,𝑚+1 ⋯ 𝑎2,𝑛+1𝑏1,𝑚+1

⋮𝑎𝑟,1𝑏𝑞,1 𝑎𝑟,1𝑏𝑞,2 ⋯ 𝑎𝑟,1𝑏𝑞,𝑚+1 𝑎𝑟,2𝑏𝑞,1 ⋯ 𝑎𝑟,2𝑏𝑞,𝑚+1 ⋯ 𝑎𝑟,𝑛+1𝑏𝑞,𝑚+1]

Eq. 5.2-23

Also we arrange all points in 𝑷𝐶 as a column vector:

𝒫 = [𝑃𝐶(𝑢1, 𝑤1) 𝑃𝐶(𝑢1, 𝑤2) ⋯ 𝑃𝐶(𝑢1, 𝑤𝑞) 𝑃𝐶(𝑢2, 𝑤1) ⋯ 𝑃𝐶(𝑢2, 𝑤𝑞) ⋯ 𝑃𝐶(𝑢𝑟 , 𝑤𝑞)]𝑇

Eq. 5.2-24

Now we have

𝒫 = 𝒩 ∙ �̅�

Finally, control points can now be computed in Matlab:

�̅� = 𝒩\𝒫

The output is in the form of a column vector:

�̅� = [𝑷0,0 𝑷0,1 ⋯ 𝑷0,𝑚 𝑷1,0 ⋯ 𝑷1,𝑚 ⋯ 𝑷𝑛,𝑚]𝑇

Two examples of calculated control points are shown in Fig. 5.2-21. The control points calculated

for the spherical surface were based on the parameterisation results shown in Fig. 5.2-19. The

197

control points calculated for the blade surface were based on the parameterisation result shown in

Fig. 5.2-20.

Fig. 5.2-21 Control points calculated for (a) the spherical surface and (b) the surface of the blade

Generation of fitted points

The 𝑢 and 𝑤 used in the previous step can now be discarded. Here, we generate a new set of 𝑢

and 𝑤 with uniform spacing:

𝑢′ = (0,1

𝑐 − 1,… ,

𝑐 − 2

𝑐 − 1, 1 ) , 𝑤′ = (0,

1

𝑐′ − 1,… ,

𝑐′ − 2

𝑐′ − 1, 1 )

where 𝑐 and 𝑐′ are the numbers of points in 𝑢′ and 𝑤′ respectively.

Repeating 𝑢′ for 𝑐′ number of rows and 𝑤′ for 𝑐 number of rows give and 𝑢𝑓 which is a 𝑐′ × 𝑐

matrix and 𝑤𝑓 which is a 𝑐 × 𝑐′ matrix:

𝑢𝑓 = [𝑢1′

𝑢2′⋮

] , 𝑤𝑓 = [𝑤1′

𝑤2′⋮

]

(a)

(b)

198

Recalling Eq. 5.2-2 and Eq. 5.2-6, the new blending functions 𝑁(𝑢𝑓) and 𝑁(𝑤𝑓) can be calculated.

𝑁(𝑢𝑓) and 𝑁(𝑤𝑓) can also be rearranged to the form of Eq. 5.2-23, 𝒩𝑓, so that fitted points can be

generated in form of a column vector 𝒫𝑓 with 𝑐 × 𝑐′ number of elements:

𝒫𝑓 = 𝒩𝑓 ∙ �̅�

Otherwise, �̅� should be re-ordered to a (𝑛 + 1) × (𝑚 + 1) matrix [�̅�]. In this case, fitted points are

generated in form of a 𝑐′ × 𝑐 matrix 𝑷𝑓:

𝑷𝑓 = [𝑁𝑢𝑓] ∙ �̅� ∙ [𝑁𝑤𝑓

]

Fig. 5.2-22 shows two surfaces calculated with the control points shown in Fig. 5.2-21.

Fig. 5.2-22 Surfaces calculated with B-spline surface for (a) the sphere and (b) the turbine blade

(a)

(b)

199

Localisation

Localisation is very similar to registration. Both problems are aimed at obtaining a transformation

matrix that transforms the coordinates of one set of data into the coordinate system used in

another set of data, based on the common points or meshes shared between the two data sets.

Localisation has two uses in this project. The first application is to compare geometric deviations

between turbine blades. The second application is to transform the probe path calculated based on

CMM coordinate system into the coordinate system of the inspection machine.

The localisation algorithm chosen in this project is the iterative closest point (ICP) algorithm. The

reason for this is that it is well established and documented. Because of time constraints in this

investigation, orientation independent algorithms were not considered.

The ICP algorithm starts with finding the point on the target surface which is closest to a given

measured point. After the closest point is found for each point contained in the measured point set,

the distances between each pair of the closest points are calculated. The next step is to solve for

the transformation matrix that minimises the summed squared error of the distances.

In this chapter, the closest point problem will be first discussed, followed by the theory of solving

the minimisation problem.

Closest point problem

For the closest point problem, three methods were tested in this project.

The first method is referred as brute force. In this method, the whole measured point set is taken

and compared with the target surface. The distance between each two of the points in both set is

calculated and the minima can then be found. The weakness of this method is that the points

representing a surface are finite, which means that there are spaces between the points on the

target surface, which cannot be used as a closest point, even though a measured point could lie

there. To minimise this error, the number of points used for the surface representation should be

maximised but this obviously increases the calculations. In the second method, the surface is a

parametric description of a B-spline surface, which is virtually an infinite point set. However, this

complicates the problem with finding the parametric transformation. The last method is k-

dimensional binary search tree (k-d tree) algorithm, which is included in Matlab already as a Matlab

function.

All three methods were tested in Matlab. The accuracy of all methods were found to be equally

good. However, in terms of computing time, it is found that the k-d tree algorithm is significantly

faster for a large point set, for example a point set containing 25,000,000 points.

200

The implementation of k-d tree algorithm in Matlab is documented in [125]. The output of the k-d

tree algorithm consists of two components. The first component is the indices of the closest points

and the second component is the distances between the enquiry points and the corresponding

closest points.

Least square transformation

After the corresponding closest points are found on the target surface 𝑃 for all points on the

measured surface 𝑆, they are used as a target for a transformation of the measured points. The

goal is to find the transformation matrix 𝑇 which satisfies Eq. 5.3-1:

min (𝑒) = min(∑‖𝑇𝒑𝑖 − 𝒔𝑖‖2

𝑛

𝑖=1

) Eq. 5.3-1

where 𝑘 = 1,2,3… representing the number of iteration, 𝒑 ∈ 𝑃 = {𝒑𝑖}, 𝒔 ∈ 𝑆 = {𝒔𝑗}, and 𝑛 is the

total number of points in 𝑆. The transformation matrix 𝑇 includes both rotation and translation in a

3D space, which means the matrix consists of six unknowns 𝑡𝑥, 𝑡𝑦 , 𝑡𝑧, 𝛼, 𝛽, 𝛾.

5.3.2.1. Pseudoinverse method

In the papers presented in the literature review (see Chapter 2.2.1.2), the pseudoinverse approach

[59] [60] [126] is one of the simplest and fastest one. However, during the testing of this

approach, the quality of the localisation results is found highly dependent of the initial alignment

error between the two surfaces. When the angular alignment error is greater than 5° and linear

alignment error is over 1/10 of the length scale of the model, the localisation result is likely to be

inaccurate.

5.3.2.2. Quaternion method

Quaternion representation

In the second approach [62] [63] tested, the transformation matrix is represented by quaternions,

where the rotation component and the translational component are separated. Therefore, the

objective function, which is shown in Eq. 5.3-2, is slightly different from the objective function of

Eq. 5.3-1.

𝑓(�̅�) =1

𝑛∑‖𝑅(�̅�𝑅)𝒑𝑖 − �̅�𝑇 − 𝒔𝑖‖

2

𝑛

𝑖=1

Eq. 5.3-2

where 𝑅(�̅�𝑅) , given in Eq. 5.3-3, is the rotation matrix based on the unit quaternion:

201

�̅�𝑅 = [𝑞0, 𝑞1, 𝑞2, 𝑞3]𝑇

𝑞0 ≥ 0, 𝑞02 + 𝑞1

2 + 𝑞22 + 𝑞3

2 = 1

and �̅�𝑇 = [𝑞4, 𝑞5, 𝑞6]𝑇 is the translation vector.

𝑹(�̅�𝑅) = [

𝑞02 + 𝑞1

2 − 𝑞22 − 𝑞3

2 2(𝑞1𝑞2 − 𝑞0𝑞3) 2(𝑞1𝑞3 + 𝑞0𝑞2)

2(𝑞1𝑞2 + 𝑞0𝑞3) 𝑞02 + 𝑞2

2 − 𝑞12 − 𝑞3

2 2(𝑞2𝑞3 − 𝑞0𝑞1)

2(𝑞1𝑞3 − 𝑞0𝑞2) 2(𝑞2𝑞3 + 𝑞0𝑞1) 𝑞02 + 𝑞3

2 − 𝑞12 − 𝑞2

2

] Eq. 5.3-3

Calculation of an optimal transformation

The unit quaternion �̅�𝑅 that represents the optimal rotation can be found by selecting the

eigenvector that corresponds to the maximum eigenvalue of the 4 × 4 matrix 𝑀(Σ𝑝𝑠):

𝑀(Σ𝑝𝑠) = [𝑡𝑟(Σ𝑝𝑠) Δ𝑇

Δ Σ𝑝𝑠 + Σ𝑝𝑠𝑇 − 𝑡𝑟(Σ𝑝𝑠)𝐼3

] Eq. 5.3-4

where 𝐼3 is a 3x3 identity matrix, Σ𝑝𝑠 is the cross-covariance matrix obtained with Eq. 5.3-6,

𝑡𝑟(Σ𝑝𝑠) is the trace of Σ𝑝𝑠, and Δ = [𝐴23 𝐴31 𝐴12]𝑇 in which 𝐴 is the cyclic component of the anti-

symmetric matrix Σ𝑝𝑠 − Σ𝑝𝑠𝑇 :

𝐴𝑖𝑗 = (Σ𝑝𝑠 − Σ𝑝𝑠𝑇 )

𝑖𝑗, 𝑖 = 1,2,3, 𝑗 = 1,2,3 Eq. 5.3-5

Σ𝑝𝑠 =1

𝑛∑(𝒑𝑖 − 𝜇𝑝)(𝒔𝑖 − 𝜇𝑠)

𝑡

𝑛

𝑖=1

Eq. 5.3-6

𝜇𝑝 and 𝜇𝑠 are centres of mass of point set 𝑃 and 𝑆 respectively, given by:

𝜇𝑝 =1

𝑛∑𝒑𝑖

𝑛

𝑖=1

, 𝜇𝑠 =1

𝑛∑ 𝒔𝑖

𝑛

𝑖=1

Eq. 5.3-7

The optimal translation vector �̅�𝑇 can be calculated with:

�̅�𝑇 = 𝜇𝑠 − 𝑹(�̅�𝑅)𝜇𝑝 Eq. 5.3-8

Implementation

The implementation of the theory starts with Eq. 5.3-7, where the centres of mass of both point

sets are calculated. Next, the cross-covariance matrix Σ𝑝𝑠 can be obtained using Eq. 5.3-6,

followed by the anti-symmetric matrix Σ𝑝𝑠 − Σ𝑝𝑠𝑇 . Now the cyclic components of the anti-symmetric

matrix 𝐴𝑖𝑗 can be extracted and thereby vector Δ can be constructed. With all elements calculated,

the matrix 𝑀(Σ𝑝𝑠) can be formed.

The eigenvectors, 𝑣, and the corresponding eigenvalues, 𝜆, of 𝑀(Σ𝑝𝑠) is related as:

202

(𝑀(Σ𝑝𝑠) − 𝜆𝐼4) ∙ 𝑣 = 0 Eq. 5.3-9

where 𝐼4 is a 4 × 4 identity matrix.

Horn [62] demonstrated a non-iterative solution for 𝜆 and 𝑣. Here in Matlab, the equation can be

easily solved with a built-in solver [𝑣, 𝜆] = 𝑒𝑖𝑔(𝑀).

The maximum eigenvalue can be then found as well as the corresponding eigenvector which gives

the unit quaternion vector �̅�𝑅 . With 𝑞0, … , 𝑞3 determined, the rotation matrix 𝑹(�̅�𝑅) can be

constructed. Finally, the translation vector, �̅�𝑇, can be calculated using Eq. 5.3-8. emphasis

5.3.2.3. Single value decomposition method

The rotation matrix 𝑹(�̅�𝑅) in Eq. 5.3-3 can also be solved with single value decomposition (SVD) of

the cross-covariance matrix Σ𝑝𝑠 [66]:

𝑈Λ𝑉𝑇 = SVD(Σ𝑝𝑠)

𝑹(�̅�𝑅) = 𝑉 ∗ 𝑈𝑇 Eq. 5.3-10

In Matlab, 𝑈 and 𝑉 can be easily solved with the built-in method [𝑈, Λ, 𝑉] = 𝑠𝑣𝑑(Σ𝑝𝑠)

The rotation matrices calculated using either quaternion or SVD method are identical. However, a

series tests show that the time cost of SVD method varies extensively and Freeman and Herbert

[66] mentioned that SVD method may generate noise points and reflection when det(𝑹(�̅�𝑅)) =

−1. Therefore, quaternion method is used in this project.

ICP with initial alignment error correction

A common problem found in most of the ICP algorithms is the mean square error converges to a

local minimum instead of a global minimum. This problem is illustrated in Fig. 5.3-1, where the

blue curve is the localisation target of the orange curve. The localisation scenario shown at the top

is when the mean square error converges at a local minimum as well as a global minimum.

However, in the scenario when the measured curve is introduced with an initial rotation of 180°, as

shown in the bottom of the figure, the convergence is due to a local minimum and the algorithm

will never figure out that the correct transformation requires a further rotation about the centre of

gravity by 180°.

ICP algorithms are essentially minimisation algorithms that searches for the local minimum. For

minor alignment errors, the local minimum is usually the same as the global minimum, which

makes ICP algorithms very useful for minor initial alignment errors. For major initial alignment

203

errors, such as a rotation between 90° and 270°, the global minimum cannot be solved directly

without an initial correction for such errors.

Fig. 5.3-1 Two conditions of convergence

In our ICP algorithm, a routine is incorporated to loop the entire ICP algorithm several times.

Before each time the ICP algorithm starts, a unique initial rotation is applied to the measured

points. We call each application of an initial rotation as one approach. For the first approach, the

initial rotation is zero. In this way, the initial rotational alignment error is changed systematically

from the second approach and onwards.

Obviously, running an ICP algorithm for multiple times multiplies the time cost. It is important to

select a combination of the initial rotations wisely. Ideally, for each approach, the initial rotation

should enable the ICP algorithm to reach a convergence in different conditions, i.e. the orientation

of the measured point set should be unique. With the quaternion method, we found experimentally

that 180° is a good increment value for the initial rotations. This means, for example, the

measured point set is rotated by 180° about the x axis for the second approach, by 180° about the

y axis for the third approach and by 180° about the z axis for the fourth approach which is the last

approach. For all the tests we have conducted, especially for turbine blades, a global convergence

is always reached within these four approaches.

In our case, we can also escape the problem caused by the initial alignment error easily by

introducing a fixed initial transformation to the measured point set, or specifically, the surface

where probe paths are calculated. Knowing that neither the axis of the CMM nor the axis of the

robot change, we can use a fixed initial transformation to correct any substantial alignment errors,

provided that the poses of the blades are maintained well for each scan in the CMM, for example

always have the low pressure surface roughly parallel to the XZ plane of the CMM, and for each

measurement on the inspection machine.

The final ICP algorithm is shown in Fig. 5.3-2

(a) 1st iteration (b) 2nd iteration (c) Convergence

204

Performance test

The performance of the ICP algorithm is checked with two surfaces. The first surface is produced

with a peak function, as shown in Fig. 5.3-3. The target surface was represented by 250,000

points and the measured surface was represented by 484 points. The deviations between the two

Fig. 5.3-2 Flowchart of the ICP algorithm

Start

Solve transformation matrix 𝑇

Transform 𝑃 with 𝑇

Calculate the sum of mean

squared deviation

Transform 𝑃 with initial

transformation matrix

Find closest points for 𝒑𝑖 in 𝑆

End

Y

N

Y

Min. mean

squared error

reached?

Initial

transformation?

Converged?

Max. number of

iterations reached?

Max. number of

approaches

reached?

Transform 𝑃 with an artifitial


Output the latest


Output the optimal


N

N

N

N

Y Y

Y

205

sample surfaces was approximately 0.00589. In order to simulate the situation where a substantial

initial alignment error exists, the measured surface was rotated by 45° about the x-axis and -110°

about the y axis. The surface was further transformed by a translation vector [2,3, −4]𝑇. The final

pose of the measured surface is shown in Fig. 5.3-4.

Fig. 5.3-3 The surface created with a peak function used for testing the ICP algorithm

The turbine blade surface, which is shown in Fig. 5.2-22 (b), was also used for testing the

algorithm. The target surface contains 30,000 points. 340 points were extracted from the target

surface to represent the measured surface. This means the deviation between the two surfaces is

zero. The measured surface was then introduced with a 126° rotation about the x-axis and -35°

about the y-axis, as well as a translation vector [33,77, −44]𝑇.

Table 5.3-1 ICP configurations and results

N.O.P.12(𝑆) N.O.P.12(𝑃)

Sample

Deviation

Residual

Deviation

Time per

iteration

Convergence

condition

Peak 250,000 484 0.00589 0.00590 0.39878 s Global minimum

Blade 30,000 340 0 0.2198 0.0393 s Local minimum

The results of the localisations are shown in Table 5.3-1, Fig. 5.3-5 and Fig. 5.3-8. As can be seen,

global minimum was found for the B-spline surface. According to the convergence plot (see Fig.

5.3-6), it was found in the third approach where the measured surface was rotated by 180° about

the y-axis. For the turbine blade surfaces, local minimum was found with a residual deviation of

0.2198mm. According to Fig. 5.3-9, the error converged at the local minimum in the second

approach, in which the surface was rotated by 180° about the x-axis. As can be seen from Fig.

5.3-8, the error was mainly caused by the misalignment in the z direction. The surface of the

turbine blade varied slowly in the vertical direction, which caused difficulty to accurately locate the

12 N.O.P. stands for number of points. N.O.P.(S) means number of points in S.

206

surface patch. A possible solution is to scan a few points on the fir-tree root and force matching

surfaces in the z direction.

It can be seen that the iteration time was increased by ten times when the number of points on

the target surface was increased by approximately 8.33 times. Even though, the total iteration time

was 93.95s, which was acceptable.

Fig. 5.3-4 B-spline surfaces for localisation

207

Fig. 5.3-5 B-spline surfaces matched using the ICP algorithm

Fig. 5.3-6 Convergence plot for matching the B-spline surfaces

208

Fig. 5.3-7 Turbine blade surfaces for localisation

Fig. 5.3-8 Blade surfaces matched using the ICP algorithm

209

Fig. 5.3-9 Convergence plot for matching the turbine blade surfaces

210

Probe path

Definition of a probe path

In immersion ultrasonic testing, one of the most important factors that contributes to the accuracy

of the testing is the normality of the ultrasonic probe to the surface of inspection, which ensures

ultrasound is transmitted through the surface with minimum refraction. In our case, the ultrasonic

probe is carried by a Fanuc robot during inspection and the alignment of the probe is determined

by the motion of the robot.

The inspection process is similar to 5-axis machining, where a tool is carried by the spindle of a 5-

axis machined and moved to various places according a list of commands, which consists of such

as feed, motion mode and more importantly the coordinates and orientations of the tip of the tool.

For a 6-axis robot, moving an end effector, e.g. the ultrasonic probe, also requires a series of

commands, the most important components of which are the coordinates and orientations. The

coordinates defined in the command herein are referred to as path points and the orientations are

referred to as path orientations. Each path point must be defined together with a path orientation

and a probe path is a collection of one or more path point(s) and the corresponding path

orientation(s) organised in sequence.

5.4.1.1. Coordinate system

Path points and path orientations are defined with respect to a certain coordinate system, such as

the robot base coordinate system (RBCS) or a user defined coordinate system that is related to the

Y

X

Fig. 5.4-1 Coordinate systems and axes in the inspection machine

X

Z

Y

Axis of rotation

Robot base coordinate system

User coordinate system / coordinate system of the inspection machine

Z

211

RBCS. In this project, a user coordinate system is used which is almost identical to the RBCS but

has a slight orientation so that the y-axis is parallel to the rotary axis, i.e. the axis of the shaft

which carries the turbine blade. The three coordinate systems or axis are shown in Fig. 5.4-1. The

user coordinate system is also referred as the coordinate system of the inspection machine.

5.4.1.2. Path points and path orientations

A path point 𝑃 consists of three parameters (𝑥, 𝑦, 𝑧), which define the 𝑥, 𝑦 and 𝑧 coordinates of the

tip of the end effector respectively. A path orientation 𝐴 also consists of three parameters (𝜔, 𝜌, 𝛾),

which define the angles of rotations about the X-, Y- and Z-axes in degrees respectively. Note that

the required path orientation at a particular point must be achieved by performing the rotations in

a definite sequence, i.e. rotation about the X-axis first, followed by that about the Y-axis and finally

about the Z-axis. Note that the initial path orientation, i.e. 𝐴(𝜔, 𝜌, 𝛾) = (0,0,0), is defined by a unit

vector �⃑� co-axial with the Z-axis, i.e. �⃑�(0,0,1), and a torsion of zero.

Calculation of a probe path

5.4.2.1. Path points and tool length

Once the matrix equation for a B-spline surface is determined, it is possible to generate a point

cloud of any density. In our case, the path points do not lie on the surface of the B-spline surface.

In 5-axis machining, the coordinates in a tool path are associated with the tool’s length and

diameter. In our case, the diameter of the probe has no significance, as the transmitter and

receiver are located at the centre of the probe; the tool length can also be simply defined by the

physical length of the ultrasonic probe plus the length of the probe holder and the length of

Schunck’s tool change adaptor. Considering that the probe makes no contact with the surface of

inspection, points generated on a B-spline surface cannot be directly used as path points. They

must be offset by the offset distance of the probe from the surface, i.e. the water path.

In order to reduce complexity, the preferred definition of the tool length is the sum of water path

and the total length added on to the face plate of the robot. In this way, there is no need for

offsetting the surface points and path points can be defined directly on the surface.

5.4.2.2. Path orientations and surface normals

Path orientations are defined with three rotations. In 3-D space, two rotations are adequate to

define the orientation of a vector, a third rotation is only employed for the purpose of defining the

torsion about the axis of the tool, which is not needed in our case. To simplify the problem, we

212

assume the third rotation 𝛾, i.e. rotation about the Z-axis, is equal to 0. Now a path orientation can

be represented by a unit vector. Because the ultrasonic probe must be kept normal to the surface,

normal vectors of the B-spline surface are used to represent path orientations.

The normal vector at a point on a B-spline surface can be obtained by taking the cross product of

the two tangent vectors in both parametric directions, i.e. 𝑢 and 𝑤 directions:

𝒗𝑛⃑⃑ ⃑⃑ ⃑(𝑢, 𝑤) = �⃑⃑⃑�(𝑢) × �⃑⃑⃑�(𝑤) Eq. 5.4-1

By differentiating the B-spline surface with respect to 𝑢 and 𝑤 directions separately, tangent

vectors in both directions can be calculated:

�⃑⃑⃑�(𝑢) =𝜕𝑃(𝑢, 𝑤)

𝜕𝑢= ∑

𝑑

𝑑𝑢[∑�̅�𝑖𝑗𝑁𝑖,𝑘(𝑢)

𝑛

𝑖=0

]𝑁𝑗,𝑙(𝑤)

𝑚

𝑗=0

Eq. 5.4-2

�⃑⃑⃑�(𝑤)𝜕𝑃(𝑢, 𝑤)

𝜕𝑤= ∑

𝑑

𝑑𝑤[∑ �̅�𝑖𝑗𝑁𝑗,𝑙(𝑤)

𝑚

𝑗=0

]𝑁𝑖,𝑘(𝑢)

𝑛

𝑖=0

Eq. 5.4-3

Fig. 5.4-2 shows an example of the surface normals evaluated on a B-spline surface where 600

points are generated.

Fig. 5.4-2 B-spline surface representation of a blade and evaluated surface normals

213

Note that the values of 𝜔 and 𝜌 are the angles of rotation about the X- and Y-axis, respectively,

surface normals, which are defined by �⃑�(𝑥, 𝑦, 𝑧), cannot be directly input as path orientations. The

conversion from �⃑�(𝑥, 𝑦, 𝑧) to 𝐴(𝜔, 𝜌, 0) can be achieved with the aid of rotation matrices.

Knowing that the corresponding path orientation for �⃑�0 = (0,0,1) is 𝐴0 = (0,0,0), and the rotations

have to follow the sequence of X, Y and Z, for any arbitrary unit vector, �⃑�(𝑥, 𝑦, 𝑧), the conversion

to 𝐴(𝜔, 𝜌, 0) can be achieved by:

(i) rotating �⃑�0 by 𝜔° about the X-axis

(ii) rotating �⃑�0 further by 𝜌° about the Y-axis.

Mathematically, these two steps can be represented as:

�⃑�(𝑥, 𝑦, 𝑧) = �⃑�0 ∙ 𝑅𝑥(𝜔°) ∙ 𝑅𝑦(𝜌°) Eq. 5.4-4

where 𝑅𝑥(𝛼) is the rotation matrix about the X-axis:

𝑅𝑥(𝛼) = [

1 0 00 cos(𝛼) sin(𝛼)

0 − sin(𝛼) cos(𝛼)] Eq. 5.4-5

and 𝑅𝑦(𝛼) is the rotation matrix about the Y-axis:

𝑅𝑥(𝛼) = [cos(𝛼) 0 − sin(𝛼)

0 1 0sin(𝛼) 0 cos(𝛼)

] Eq. 5.4-6

Expanding and simplifying Eq. 5.4-4 gives:

�⃑�(𝑥, 𝑦, 𝑧) = [cos(𝜔°) sin(𝜌°) , − sin(𝜔°), cos(𝜔°) cos(𝜌°)] Eq. 5.4-7

Obviously, there is no unique solution to Eq. 5.4-7. Nevertheless, any of the solutions can be

accepted by the robot.

It is also possible to specify a torsion for the probe, i.e. a value for 𝛾. This can be done with a

slight modification Eq. 5.4-4:

�⃑�(𝑥, 𝑦, 𝑧)

𝑅𝑧(𝛾°)= �⃑�0 ∙ 𝑅𝑥(𝜔°) ∙ 𝑅𝑦(𝜌°) Eq. 5.4-8

where 𝑅𝑧(𝛼) is the rotation matrix about the Z-axis:

𝑅𝑧(𝛼) = [cos(𝛼) sin (𝛼) 0−sin (𝛼) cos (𝛼) 0

0 0 1

] Eq. 5.4-9

214

Regions of inspection

Inspecting a complete cross section curve in a point-to-point manner can take enormous amount

of time and inspecting regions where holes are non-existent, only adds unnecessary time for both

inspection and data processing. Therefore, inspection should only take place in the vicinity of a

hole, herein referred as region of inspection, and fast travel can be enabled between each region

of inspection.

However, as it is impossible to acquire the positions of the holes with a CMM and a touch probe, at

this stage, this information is absent from the B-spline surface model. There are some methods for

obtaining the hole positions, such as CT scanning [46]. At this stage, the only feasible method was

to obtain the position of the holes from the CAD model of the turbine blade.

Fig. 5.4-3 Acquiring points from a CAD model

Fig. 5.4-3 shows a sectional view of a CAD model of a turbine blade. 24 points are taken from the

convex side of the cross section as well as the centres of the holes. In the example shown in Fig.

5.4-4 (a), points are obtained on five different cross sections of the CAD model and the centres of

the holes are only taken on the section where ultrasonic inspection is required. These points are

then localised into the coordinate system of the B-spline surface using the ICP algorithm shown in

Chapter 5.3.3. The result of the localisation is shown in Fig. 5.4-4 (b).

215

(a) CAD points and hole positions (b) CAD points and hole positions localised on the B-spline surface

Fig. 5.4-4 Positions of holes

The next step is to find an appropriate “window” located on either side of the hole to be inspected.

Wall thicknesses are defined by the shortest distances between the hole centre and surface of the

blade. In most situations, there is one unique point on the section curve that is closest to a hole,

as indicated by the squares in Fig. 5.4-5 (a). Regions of inspection or ‘windows” are defined by

with making the centre of the window coincide with the blue squares i.e. points on the surface

closest to the hole centres as shown in Fig. 5.4-5 (a). The width of the window has to take into

account the possible differences between the CAD model and the actual manufactured blade. One

must ensure that the hole is inspected. It was found a span of 2mm on both sides of the closest

point was sufficient tolerance to ensure that the holes were detected by the probe (see Fig. 5.4-5

(b). Finally, the path points and path orientations for the windows are shown in Fig. 5.4-5 and

Fig. 5.4-6.

216

Fig. 5.4-5 Regions of inspection

(a) The points closest to the centres of holes on a section curve

(b) Regions of inspection defined near the closest points

(c) Extracted surface normals

217

Fig. 5.4-6 A complete probe path for the convex side of a cross section

Dividing and grouping of a probe path

A complete probe path has to be divided into

several sections and grouped according to the

curvature and size of the cross section. The

reason for this is because the movement of the

robot arm is bounded by the water tank, as

can be seen in Fig. 5.4-8, and it is not possible

for the robot to complete the entire probe path

without having to rotate the turbine blade. The

required number and angles of rotations can

be identified and calculated from the probe

path but only after knowing the maximum

angle of swing 𝜙 (see Fig. 5.4-7), the

coordinates of the turbine blade in the inspection machine and localising the probe path in the

coordinate system of the inspection machine.

The localisation can be achieved using the ICP algorithm. This requires digitization of the surface of

the turbine blade with respect to the coordinate system of the inspection machine, which can be

done with the laser sensor. Fig. 5.4-9 (a) shows the localised probe path.

ϕ

Fig. 5.4-7 Maximum angle of swing

Blade section curve

Water tank wall

218

Fig. 5.4-8 Robot arm is restricted by the water tank

After the probe path is localised, the probe path can now be divided into groups. The positive

angle 𝜃 between the Y-Z plane and each extracted surface normal is calculated and compared with

𝜙. This comparison is conducted in a sequence starting from the first path point in the probe path.

If there is a surface normal at which 𝜃 > 𝜙/2, this means a rotation is needed for the inspection

region that this surface normal is affiliated to. The angle of rotation 𝛼 is calculated by either

positive or negative 𝜃𝑚𝑎𝑥 + 𝜙/2 , where 𝜃𝑚𝑎𝑥 is the maximum positive angle in this inspection

region. From this region and onwards, the surface normals are transformed by 𝛼 with respect to

the rotary axis and the positive angles of the transformed normals are calculated and compared.

The probe path in the above example is divided into three groups and therefore, requires three

rotations of the turbine blade. The path groups in the probe path are shown in Fig. 5.4-9 (b) – (c).

219

Fig. 5.4-9 probe path grouping

(a) Localisation of the probe path in the coordinate system of the inspection machine

(a) First path group of the probe path

(a) Second path group of the probe path (a) Third path group of the probe path

220

Experiments, Results and Discussions

The results have been obtained on two rigs, an OKK 4-axis milling machine (see Fig. 6-1) and the

prototype inspection machine. The earlier tests were obtained on this 4-axis machine and a few of

these tests were repeated on the prototype inspection machine. Repeating the results on the

inspection machine only serves to confirm the accuracy and reliability of the results.

The specimens that have been tested include a stepped component, a “curved” component, a

“disc” blade (i.e. a blade with no fir tree and the aerofoil section is welded on to a circular disc)

and three full size blades from the same batch. The main aim of the tests on the stepped and

curved components was to assess the capabilities of the Olympus V316-SU ultrasonic probe,

calibrate the probe, investigate the effect of varying the length of the water path, and angle of

incidence.

As mentioned earlier, the wall thicknesses of three presumably identical turbine blades from one

batch were measured and compared. The aim of these experiments was to determine the accuracy

of the prototype cell, establish the geometric differences amongst blades from the same batch, and

ascertain whether the same probe path could be used for them.

221

Fig. 6-1 The OKK 4-axis milling machine

Spindle

Rotary axis

222

Effect of varying water paths

Background, aim and methodology

As the ultrasonic probe is a focused-lens probe, its performance may be affected by different water

paths. Theoretically, the water path should be adjusted so that the reflector is placed at the focal

point of the ultrasound where the intensity of the ultrasound is at its maximum and so is the power

or amplitude of the echo. This water path can be calculated using Eq. 2.1-4. However, this

equation requires the knowledge of material paths, i.e. wall thicknesses. In our case, these values

are the subject of measurement and thus are unknown. Also, depending on the curvature of the

surface of inspection, ultrasonic waves may be further refracted, which may either accelerate or

decelerate the focusing effect. The amplitude of an echo is also related to the value of the receiver

gain, which amplifies the signals as well as the noise.

The aim of this experiment was to analyse the effect of the water paths on the signal strength and

to determine an optimal setting for the receiver gain.

The test specimen, shown in Fig. 6.1-1 (a), was used for calibration; it is made of Inconel, the

same material as the turbine blades. The specimen consists of several steps and the thicknesses of

the steps are 0.65mm, 0.95mm, 1.99mm, 2.98mm, 3.98mm, 5.87mm, 8.01mm and 10mm. These

thicknesses were measured with a vernier caliper.

Fig. 6.1-1 (a) The Inconel stepped specimen and (b) the clamping of the stepped component

Experiment setup and procedures

The specimen was clamped on the shaft with the flat surface facing upwards, as shown in Fig.

6.1-1 (b). The surface was made to lie in the X-Y plane (of the robot axes, see Fig. 5.4-1) using

the laser sensor and the stepper motor.

Ultrasonic probe attached to the robot

Stepped component

223

Firstly, laser readings were taken at 20 different points on the surface along the length of the

specimen. The inclination of the specimen was then evaluated by taking the slope, s, of the linear

curve that best fits these points. Next the stepper motor was rotated by tan-1(s) degrees. Finally,

the surface was measured again by the laser sensor to verify whether the required level had been

achieved.

Once the specimen was levelled, the tank was filled with water to submerge the specimen to a

depth of at least 30mm. The robot was moved until the ultrasonic probe was at the centre of each

step of the test component. Next, for each step, the water path was varied in non-uniform

increments from 4 mm to 32 mm (see Table I1 – Table I32). For each water path length, the robot

was paused and one hundred ultrasonic data points were collected at receiver gains varying from

30 to 80, in steps of 5.

It was observed that once the ultrasonic probe is immersed, bubbles accumulated on the probe

lens and they had to be removed; therefore, the inspection process was paused approximately

every 5 minutes to remove all the bubbles. This was done for all the following experiments

presented in this chapter.

The program routine used for instructing the robot and acquiring ultrasonic data is described in

Chapter 4.2.

The collected data were processed with Matlab. The water paths were determined by calculating

the product of the acoustic velocity in water at 20°C, i.e. 1482m/s, and half the time of flight

between the first interface echoes and the second bounce of the interface echoes. The values are

rounded to the nearest integers for easier comparison between different sets of results.

224

Results and discussions

The complete results of this experiment are shown in Appendix I.

Varying the water paths, in theory, has no effect on the accuracy of the thickness measurements,

because the TOF or acoustic velocity does not vary with the water path. This was also confirmed

experimentally here. As shown in Table 6.1-1, the standard deviations of the TOF was less than

6ns and this is much less than the sampling rate of the ultrasonic card, i.e. 10ns.

Table 6.1-1 Standard deviations of the evaluated time of flight at each step

Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8

S.D. (10ns) 0.53 0.45 0.51 0.49 0.46 0.53 0.60 0.60

In spite of the theory suggesting that the signal strength is related to the water path, it was found

experimentally that varying water paths had minimum impact on signal strength as long as it is

kept above 15mm, which is approximately the starting point of the focal zone of the ultrasonic

probe. Table 6.1-2 shows the theoretical optimal water path calculated with Eq. 2.1-4. The speeds

of sound in water and Inconel used in the equation were 1482m/s and 5700m/s respectively. For

steps 6, 7 and 8, the values are negative, thus they are not shown in the table.

Table 6.1-2 Theoretical optimal water path for each steps

Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8

Water path (mm) 17.82 16.67 12.67 8.89 5.01 - - -

The experiments are presented in Fig. 6.1-2, where the variations of the amplitudes of backwall

echoes are plotted in colour contours with respect to different gains and water paths. The colour

scale used is shown at the bottom of the figure. As can be seen, the amplitudes of the backwall

echoes increase with water path below approximately 15mm for the same gain. This was more

obvious at low gains. The theoretical increases in amplitudes at the water paths specified in Table

6.1-2 cannot be observed from the experimental results. For example, at Step 5 (Thickness =

4.161mm), at a water path near 5.01mm, the amplitudes of backwall echoes are obviously lower

than the amplitudes found at greater water paths. In general, as the water path was increased,

the amplitudes gradually stabilised.

225

Fig. 6.1-2 Amplitudes of the first backwall echoes

226

Also shown in these figures are the variations

in the amplitudes at different receiver gain

values. It appears that above a gain of 70db,

the amplitude of a backwall echo usually reach

the maximum value, i.e. 255. However, as the

gain is increased, the noise also increases at

the same time. As shown in Fig. 6.1-4 (a), the

difference between high and low limits (see

Fig. 6.1-3) of noise increased exponentially

with receiver gain until 75db, after which the

increase in the difference slows down. The

purpose of increasing the receiver gain is

usually to increase signal-to-noise ratio (S/N). As shown in Fig. 6.1-4 (b), for second backwall

echoes, which are weaker signals, the S/N ratio always increases with gain values, but for strong

signals, i.e. first backwall echoes, as the amplitudes are capped at 255 at a gain of 65db, any

increase of gain beyond 65db only increases the power of noise.

Fig. 6.1-4 Effect of varying gain regarding noise

It can be argued that the receiver gain should always be set at 80db to ensure detection of any

weak echoes. However, excessive gain could introduce extra efforts when determining the location

of a strong echo, such as interface echoes. Fig. 6.1-5 shows three signals acquired with gains set

at 80db, 55db and 35db.

At a gain of 80db (see Fig. 6.1-5 (a)), it is apparent that both the interface echo and the backwall

echo are over amplified, which introduces phase angle error in wall thickness evaluation. Apart

from the amplitudes of the first peak in the interface echo and the second peak in the backwall

(a) Variations of amplitudes of noise (b) Variations of S/N

Fig. 6.1-3 Low limit and high limit of noise

227

echo being capped at 255, the power of other peaks, which are not of any interest in the thickness

evaluation, in the echoes are also increased. In this case, to locate the peaks of interest, either a

filter is needed to bypass other peaks or a more complex logic must be developed to identify the

correct peaks. In order to reduce the phase angle error, the locations of the peaks should be

assumed to be at the mid of the flattened area; otherwise, curve fitting is required for more

accurate estimations.

Fig. 6.1-5 Signals captured with different receiver gains

At a gain of 55db (see Fig. 6.1-5 (b)), the signals are clearer with less excessively amplified peaks.

The peaks of interest can be identified easily. Also the peak in the backwall echo is now a sharp

peak whose location can then be determined precisely. Further reducing the gain to 35db, causes

(a) Receiver gain = 80 db

(b) Receiver gain = 55 db

(c) Receiver gain = 35 db

228

the peak in the interface echo to become sharp and the precise location of the interface echo can

be determined.

Since the interface echo is much stronger than a backwall echo, it is recommended to acquire

signals with a relative low receiver gain for determining the interface echo and increase gain

afterwards for detecting backwall echoes. By browsing through all logged data in this experiment,

it was found signals captured at a gain of 35db were most appropriate for interface echo

interpretation and for backwall echo, a gain of 60db was the best setting overall, or use Table

6.1-3 for more detailed control.

Table 6.1-3 Optimum receiver gain found for different thickness range

Thickness range t <= 2.0mm 2.0mm < t <= 6.2mm t > 6.2mm

Optimum gain (db) 55 60 65

However, in real blade tests or experiments in other situations, since the wall thicknesses and

surface conditions such as roughness and curvature may differ and other uncontrollable variations

may exist, the above recommended gain values may have to be adjusted.

Conclusion

This experiment shows that the water path does not affect the accuracy of the measurement of

wall thicknesses and it has a limited influence on the power of signals, as long as the water path is

kept approximately greater than 15mm. Regarding the receiver gain, it is recommended to use a

low gain, around 35db, to determine interface echoes and use a high gain, typically around 60db,

to determine the backwall echoes.

229

Calibration


As mentioned in Chapter 4, before ultrasound data can be analysed or used for thickness

interpretation, the probe has to be calibrated. Calibration is done by establishing the relationship

between known thicknesses and the time taken for sound to travel through materials of these

dimensions. This relationship is linear in the form of 𝑡 = 𝑚𝑇 + 𝑐 , where 𝑡 is thickness, 𝑚 is a

multiplier, 𝑇 is time of flight and c is a constant or a zero offset [8] [11]. Depending on the

definition of time of flight, the multiplier and constant vary. In this calibration, the time of flight is

taken between the first peak in the interface echo and the second peak in the backwall echo in unit

of 10ns. Fig. 6.2-1 shows an example of the peaks that are used to determine the location of

either echo. Note that this is also equivalent to the TOF between the second valley in the interface

echo and the second valley in the second backwall echo.

Fig. 6.2-1 Peak-to-peak calibration was used in the experiment

Calibration of an ultrasonic probe is usually done for various thickness ranges. In this experiment,

the stepped component, used in the previous experiment as shown in Fig. 6.1-1 (a), was employed

as the calibration test piece and hence seven thickness ranges were calibrated (Calibration sets 1

to 7) in Table 6.2-1. Calibration set 8 is a general calibration, which enables an approximate

interpretation for thicknesses outside the specifically calibrated ranges.

230

Table 6.2-1 Planned calibration set

Calibration set 1 2 3 4 5 6 7 8

Thickness

range (mm)

0.65

0.95

0.95

1.99

1.99

2.98

2.98

3.98

3.98

5.87

5.97

8.01

8.01

10

All

thicknesses

Experiment setup and procedures

The experiment setup was exactly the same as the previous experiment. The procedures were,

however, slightly different.

The ultrasonic probe was carried by the robot and moved in the plane parallel to the test specimen

surface and offset from it by 20 mm, the focal length of the probe. The ultrasonic probe was

stopped at twenty random positions above each step of the specimen to acquire data. At each

position, one hundred ultrasonic data samples were captured at a receiver gain of 65 for detection

of backwall echoes and for determining interface echo, additionally, twenty ultrasonic data samples

were captured at a receiver gain of 33.9.

Fig. 6.2-2 A linear curve fitted to the ultrasonic data acquired at Step 1 and Step2

The acquired data were processed using Matlab. Thicknesses were evaluated for all twenty

positions on each step. Calibration results were obtained by fitting a linear curve to the thickness

against time of flight plot for each calibration set. One example of the best straight line fitted is

shown in Fig. 6.2-2, where the data acquired above Steps 1 and 2 were fitted using the Matlab

Curve Fitting Toolbox version 3.5. The results and goodness of fit are shown next to the plot.

Calibration set 8 was established by fitting a linear curve through data acquired for all the steps.

231


Table 6.2-2 Calibration results for seven different thickness sets

Calibration

set # 1 2 3 4 5 6 7 8

Thickness

range (mm)

0.65

0.95

0.95

1.99

1.99

2.98

2.98

3.98

3.98

5.87

5.97

8.01

8.01

10 -

TOF range

(10ns)

23.3

35.8

35.8

67.4

67.4

100.9

100.9

128.1

128.1

197.6

197.6

260.8

260.8

334.9 -

Multiplier, 𝑚 0.0240 0.0329 0.0289 0.0354 0.0269 0.0341 0.0267 0.0304

Zero-offset, 𝑐 0.0889 -0.2244 0.0661 -0.5598 0.5634 -0.8885 1.0750 -0.0645

SSE 0.0055 0.0329 0.0241 0.0366 0.0845 0.0128 0.0736 2.483

Calibration results are tabulated in Table 6.2-2. The sum of squared errors (SSE) shows that the

calibration results for specified thickness ranges are quite acceptable, although the results for Set 5

and 7 are not as good as the other sets as their SSEs exceed 0.05. This may be due to the surface

roughness of the stepped component, for example the ultrasonic probe could be measuring a

valley or a hill yet the result was assumed to represent the common thickness of the step.

Calibration set 8 presents a much higher error, which suggests this calibration set can only be used

as estimation for thicknesses that are outside the specifically calibrated ranges.

Regarding the sampling resolution as discussed in Chapter 5.1.1, since the unit of TOF used in the

calibration equation is 10ns, i.e. the tick interval of the ultrasonic card, the sampling rate is directly

given by the multiplier, 𝑚.

232

Effect of varying angle of incidence


As mentioned in literature review, one of the factors which affects the accuracy of the results is the

angle of incidence of sound waves, 𝜃1, on an oblique planar surface; in other words, the angle of

incidence of an inclined sound signal on a planar surface. Snell’s law for refraction and reflection of

sound waves has to be understood very carefully in this situation. One of the concepts to be

understood is that the sound signal will be reflected at an angle equal to the angle of incidence,

with respect to a line perpendicular to the surface of the material, while when it penetrates the

material it will be refracted. The refraction will depend upon the velocity ratio between the

couplant, e.g. water in our case, and the tested material. The greater the sound velocity in the

tested material, the greater will be the refraction angle.

The aim of this experiment was to determine the extent to which the wall thickness is affected by

the angle of incidence of the ultrasonic signal.

Fig. 6.3-1 (a) The curved component and (b) dimensions of the component (units in mm)

The specimen used in this experiment was a curved component, made from Inconel, the same

material as the turbine blades used herein. A picture of the test workpiece is shown in Fig. 6.3-1

(a). The component has twenty-four holes with diameters of 3mm, 1.5mm, and 1mm, at different

distances from the curved face. The wall thickness variations are shown in Fig. 6.3-1 (b). The

accurate measurement of the actual wall thicknesses is not critical, as the aim of this experiment is

to compare the deviation in thicknesses measured at different angles of incidence. Therefore, the

wall thicknesses were measured with a height gauge and cylindrical measuring pins. This was done

by, firstly, testing the diameter with the measuring pins and once the diameter was found, placing

the specimen on a flat cast iron surface with the pin inserted in the hole; then the height of the pin

was measured with the height gauge and finally the wall thickness was calculated by subtracting

the diameter from the height.

To reduce the complexity, the wall thicknesses were measured from the flat surface side. With the

specimen attached to the shaft, the specimen was rotated through various angles using the

stepper motor. However, because of the resolution of the stepper motor and the gearing, it was

233

not possible to rotate the stepper motor by exactly 0.5° but 0.495° was possible. Therefore,

fourteen different angles of incidence, varying from 0.495° to 6.435°, in increments of 0.495°,

were used for this experiment.

Experimental setup and procedures

As shown in Fig. 6.3-2, the component was clamped on the shaft and levelled in the same way as

the stepped component in Chapter 6.2.2.

Fig. 6.3-2 Clamp of the curved component

Once the component was levelled, the tank was filled with water sufficient to submerge the top

surface of the component by approximately 50mm. The robot was programmed to move the

ultrasonic probe from one end of the specimen to the other along a line parallel to the surface and

at an offset distance of 20.3 mm from it. The probe was also moved as close as possible to the

edge, where the wall thicknesses were measured with the height gauge. The movement was

paused every 0.2 mm along the line to acquire the ultrasonic data. At each point, 100 ultrasonic

signals were captured at a receiver gain of 70 for intercepting the backwall echoes and for

interpreting the interface echoes, 20 ultrasonic signals were captured at a receiver gain of 33.9.

Once the robot reached the other end of the specimen, the specimen was rotated clockwise by

0.495°. Then, the robot returned to the starting position and the measurements were repeated.

The results obtained at all the above-mentioned tilt angles were processed in Matlab. Thicknesses

were evaluated based on the TOF and compared. If multiple consecutive thicknesses were

captured, the minimum was taken.

234


The wall thicknesses measured by the ultrasonic probe at different angles of incidence (𝜃1) are

compared with the thicknesses measured by a height gauge. Fig. 6.3-3 shows an image of

interpreted wall thicknesses at 𝜃1 = 0° and the reference locations of the holes (measured by the

height gauge). Images of other angles of incidence are included in Appendix II.

Fig. 6.3-3 Ultrasonic inspection image interpreted from experiment results obtained at 𝜃1 = 0°

It can be seen that the wall thickness measured at Hole 2 overlaps the wall thickness measured at

Hole 1 and it is difficult to accurately determine a value for Hole 2. It is because the wall thickness

at Hole 2 is slightly greater than that at Hole 1 by 0.27mm, and Hole 1 is a relatively big hole. Due

to the diameter of the ultrasonic beam, even the probe as it leaves Hole 1 and measures at a

location above the space between Hole 1 and Hole 2, it is still able to detect the circumference of

Hole 1, but it is a slightly increased wall thickness because of the curvature. When the probe

detects Hole 2, the wall thickness measured is almost identical to the wall thickness measured at

the circumference of Hole 1. Thus, there is no significant edge to separate the two wall

thicknesses. Therefore, in the following discussion, this hole is omitted. The rest of the holes are

detected. The absolute deviations are plotted against wall thickness in Fig. 6.3-4.

Fig. 6.3-4 Errors of measured wall thickness at 𝜃1 = 0

235

The results are good for wall thicknesses below 10mm, with the error mostly being less than

0.1mm. The sources of error can be

(i) the resolution of the acquired ultrasonic data, and

(ii) the error in thicknesses measured with the height gauge and calibration equation.

Above 10mm, the absolute errors show a big deviation between the two sets of measured

thicknesses. For thicknesses greater than 10mm, the general calibration coefficients are used.

Therefore, the results should not be considered as accurate interpretations and this suggests that

calibration maybe one of the biggest source for errors for thicknesses above 10mm.

The wall thicknesses measured by the ultrasonic probe at different angles of incidence were

compared with the thicknesses measured at 𝜃1 = 0°. Fig. 6.3-5 shows the deviation, 𝛥𝑇, at each

angle of incidence for each wall thickness, 𝑇𝑖,𝜃1,𝑗. ΔT, i.e. the y coordinates, are evaluated from:

𝛥𝑇 = 𝑇𝑖,𝜃1,𝑗− 𝑇𝑖,𝜃1,1

Eq. 6.3-1

where 𝑖 = 1, 2, … , 𝑛, 𝑗 = 1, 2,… ,𝑚, 𝑛 is the total number of measured wall thicknesses (23) and 𝑛 is

the total number of angles of incidence (12), and 𝜃1,1 = 0.

Fig. 6.3-5 ΔT against angle of incidence for each wall thickness

It is noted that the experiment results obtained at 𝜃1 = 6.435° are not included in the discussion as

the wall thicknesses were almost impossible to be evaluated with reasonable accuracy. Explanation

is given later in this section.

236

As the angle of incidence increases the average deviation ΔT varies non-linearly. Below 2.5° there

is a slight decrease in the measured wall thicknesses, as can be seen from the mean ΔT curve,

which is calculated by averaging the deviations at each angle of incidence. While the mean ΔT is

not significant below 2.5°, i.e. it is less than 0.06mm, at 1.485° the maximum ΔT is over 0.1mm

with a standard deviation of 0.043, as clearly shown in Table 6.3-1, which is considered as

noticeable error. Beyond an angle of incidence of 2.5°, the tendency to increase becomes very

obvious as indicated by the positive slope of the mean deviation curve. At and beyond 5.445°,

deviations greater than 1mm are shown.

Table 6.3-1 Maximum ΔT and standard deviations of ΔT

𝜃1 (°) 0.495 0.99 1.485 1.98 2.475 2.97 3.465

ΔTmax (mm) 0.034 0.068 0.102 0.171 0.205 0.396 0.746

S.D. (mm) 0.017 0.028 0.043 0.058 0.089 0.118 0.187

𝜃1 (°) 3.96 4.455 4.95 5.445 5.94

ΔTmax (mm) 0.640 0.960 0.991 1.957 1.626

S.D. (mm) 0.159 0.227 0.231 0.515 0.573

It was also noticed that with an increase in the angle of incidence, automatic detection of the

thicknesses using Matlab scripts became increasingly difficult. At 𝜃1= 5.445° and beyond, Matlab

scripts either calculated incorrectly or missed the feature completely; therefore, in such situations,

the ultrasonic data had to be analysed manually.

One reason for this problem can be traced back to the attenuation of the backwall echo. As shown

in Fig. 6.3-6, in general, the mean S/N of the backwall echoes decreases gradually with an increase

in the angle of incidence. The variations of S/N are also plotted in separate figures for each wall

thicknesses in Fig. IV-1 and Fig. IV-2 in Appendix IV. Note that the maximum achievable S/N in

these experiments was approximately 1.56. At several angles of incidence, e.g. from 𝜃1 = 3.465°

to 5.94°, the attenuation of some backwall echoes was extreme that these backwall echoes were

completely buried in noise, shown as S/N = 1 in the figure.

In Table 6.3-2, the holes that were undetected are listed, where T is the reference wall

thicknesses, ∅ is the diameter of the hole, Tm is the interpreted wall thicknesses from ultrasonic

measurement and “-“ indicates the wall thickness was not measureable. It can be seen that for T

= 6.89mm and 13.79mm, although the wall thicknesses were measured after it was missed at a

smaller angle of incidence, either these measured values are incorrect or the S/N of the backwall

echo is rather low. For T = 7.54mm, the S/N of the backwall echoes are generally low which may

suggest that the surface of backwall is rough and thereby causes noticeable amount of diffusion at

the backwall which in turn reduces the amplitude of the backwall echo.

237

Fig. 6.3-6 Variation of signal-to-noise ratio of the backwall echoes with angle of incidence

Table 6.3-2 Wall thicknesses and signal-to-noise ratio of the backwall echoes measured at different angles of incidence at five holes (units in mm otherwise specified)

T 6.86mm 7.54mm 13.79mm 10.66mm 9.09mm

∅ 0.99mm 1.48mm 1.48mm 1.48mm 2.97mm

𝜃1(°) Tm S/N Tm S/N Tm S/N Tm S/N Tm S/N

0 6.754 1.46 7.471 1.13 13.264 1.49 10.343 1.42 8.963 1.22

0.495 6.754 1.37 7.505 1.05 13.294 1.32 10.343 1.38 8.963 1.27

0.990 6.720 1.17 - - 13.264 1.22 10.343 1.41 8.937 1.42

1.485 6.720 1.06 7.505 1.06 13.264 1.19 10.373 1.27 8.963 1.27

1.980 6.720 1.16 7.505 1.18 13.294 1.18 10.373 1.19 8.937 1.24

2.475 6.754 1.08 7.539 1.01 13.355 1.13 10.373 1.13 8.963 1.27

2.970 6.789 1.08 7.573 1.05 13.659 1.05 10.434 1.11 9.017 1.33

3.465 6.891 1.17 8.217 1.02 - - 10.556 1.13 9.097 1.30

3.960 7.061 1.08 7.949 1.02 - - 10.586 1.09 9.230 1.24

4.455 7.198 1.03 8.404 1.02 - - 10.890 1.02 9.177 1.16

4.950 7.573 1.03 - - - - 11.286 1.01 9.470 1.17

5.445 - - 9.177 1.03 12.716 1.18 11.164 1.01 10.921 1.15

5.940 5.558 1.27 9.097 1.07 14.207 1.00 - - - - -

238

However, it is difficult to conclude whether a deeper or a shallower, bigger or smaller hole is more

prone to such attenuation in backwall echo. Apart from the depth and size of the subsurface

feature, attenuation of the ultrasonic wave can also be affected by many other factors, such as

previously mentioned surface finish as well as uniformity of the alloy and proximity of other

subsurface feature.

Fig. 6.3-7 Distorted interface echoes

The attenuation of the backwall echo is not the only cause of incorrect measurement or inability to

detect a feature. Starting at 4.455°, the first interface echo gets progressively distorted. As shown

in Fig. 6.3-7 (a), starting from 𝜃1= 4.455°, occasionally there is a small peak in the strongest valley

of the first interface echo. However, this does not affect determining the correct time of the

interface echo by Matlab script as valleys are ignored by the script and the small peak in the valley

is probably filtered because of its low amplitude. Starting from 𝜃1= 4.95°, as shown in Fig. 6.3-7

(b), a valley of low amplitude is present in the first peak of the interface echo. This can hinder the

correct detection of the interface echo using the current Matlab script, as the first peak in the

(a) 𝜃1= 4.455°, gain = 70 (b) 𝜃1= 4.95°, gain = 70

(c) 𝜃1= 6.435°, gain = 70

239

interface echo is then defined by two peaks and a valley. A way around can be developed by

filtering out the small valley between two strong peaks that are very close to each other in terms

of time and similar amplitudes. However, this might bring other unseen problems. As the angle of

incidence is increased, the amplitudes of the valley and peak also increase. At 𝜃1= 6.395°, as

shown in Fig. 6.3-7 (c), the first peak and the valley in the interface echo are significantly distorted

by the two valleys and peak that were previously quite small. This makes automatic as well as

manual determination of the location of the interface echo very difficult. One hypothesis is that the

distorted interface echo is possibly caused by the interference during reflection of the ultrasonic

wave. When an ultrasonic wave is reflected from an inclined surface, the entire width of the wave

is not reflected at the same instant; the portion of the wave that is reflected first travels across the

proportion that has not yet reached the interface and hence the interference.

Apart from having difficulty to correctly detect echoes, at high angle of incidence, it also brings

problems regarding extracting the correct thickness values for each hole. As can be seen in Fig.

6.3-8, the wall thicknesses plotted are significantly inclined and shifted. This makes determination

of correct wall thicknesses challenging. For example, for Holes from 7 to 10, as there are multiple

continuous wall thicknesses detected in vicinity, it is difficult to justify as to which wall thickness

corresponds to each one of these holes.

Fig. 6.3-8 Ultrasonic inspection image interpreted from experiment results obtained at 𝜃1 = 5.94°

Moreover, it was also observed that the width of the interface echo grew gradually with an increase

in the angle of incidence, as shown in Fig. 6.3-9. The time difference between the two peaks in an

interface echo at 𝜃1 = 0° is, as shown in Table 6.3-3, 90ns and this figure increases gradually with an

increase in the angle of incidence. At 𝜃1=5.445°, the time difference is increased by almost threefold.

Beyond this angle, as the interface echoes are substantially distorted, it was difficult to accurately

locate the peaks in the interface echoes and the time differences are only rough estimations.

Table 6.3-3 Comparison of time differences between peaks in interface echoes at various angles of incidence

𝜃1 (°) 0 0.495 0.99 1.485 1.98 2.475 2.97

Δt (10ns) 9 9.5 9.5 10 10 11 12

𝜃1 (°) 3.465 3.96 4.455 4.95 5.445 5.94 6.435

Δt (10ns) 14 16 19 22 26 27 29

240

Fig. 6.3-9 Time differences between peaks in interface echoes increase with angles of incidence

All the evaluated thicknesses and amplitudes are given in Table III-1, Table III-2 and Table III-3 in

Appendix III.

Conclusion

The results from these experiments suggest that the Olympus V316-SU ultrasonic probe is very

sensitive to the angle of incidence which should be kept within 3.465° to avoid excessively

attenuated backwall echo that may result in failure of feature recognition. For angles greater than

3.465°, in addition to the attenuation of the backwall echo, the interface and backwall echo get

distorted and in some cases, recognition of the appropriate peaks/valleys become difficult. The

analysis shows that it is preferable to keep the angle within 1° to ensure that the angle of

incidence has a minimum effect on the measured wall thicknesses.

Regarding the accuracy of the measured wall thicknesses at 𝜃1 = 1°, the average error is 0.159mm

with a standard deviation of 0.174mm. The cause of this big error is the inaccuracy of the general

calibration equation. Excluding the wall thicknesses evaluated using the general calibration

equations, i.e. thickness > 10mm, the mean error is 0.081mm with a standard deviation of

0.078mm. These errors are well within the accuracy requirement, which is 0.3mm.

241

Measuring a curved component from curved surface


The aim of this experiment was to test the capability of the ultrasonic probe when measuring wall

thicknesses from curved surfaces.

The test was carried out on the OKK 4-axis milling machine, which is shown in Fig. 6-1. The

specimen used in this experiment is the curved component as shown in Fig. 6.4-1, slightly different

from the previously introduced one. This curved component is also made of Inconel but the

number of holes was reduced to 16 to simplify the analysis. The geometry of the specimen was

measured on a CMM at ELE. The acquired surface points were fitted with a B-spline curve which

was then differentiated to calculate the probe path. The probe path was determined such that the

ultrasonic probe was positioned always perpendicular to the surface and 20mm above the blade.

Fig. 6.4-2 Experimental setup for measuring the curved component on the OKK milling machine

y

z

x

1 2

3 4

5 6

7 8

9 10

11

12 13

14

15 16

Fig. 6.4-1 The curved component

Data cable

Water tank

Ultrasonic probe

Fixture and rubber seal

Specimen

Machine table

Spindle

Computer Rotary axis

242

An underwater environment was provided by a Perspex water tank, which had a hole in one of its

side walls to allow the fixture to be fixed on the rotary axis. The gap between the hole and fixture

was sealed with a rubber seal.


The water tank was placed and clamped on the machine table and a fixture with jaws was bolted

onto the rotary axis. The specimen was then clamped in the fixture, with the curved surface facing

upwards and the workpiece aligned along the machine Y axis. The two side faces were made

vertical and this was checked by a dial gauge. The specimen datum was set at the centre of one of

the edges of the component as shown in Fig. 6.4-1.

Next, the calculated probe path was loaded into the milling machine’s controller and the ultrasonic

probe was connected to the computer. Once the probe was initialised and started to acquire data,

the milling machine was started.

The collected ultrasonic data were processed with Matlab script and wall thicknesses were

evaluated. The results were also checked manually to ensure the evaluation was accurate.


Table 6.4-1 shows the reference wall thicknesses as measured by the CMM machine, the ultrasonic

measured results and the calculated deviations between the two sets of wall thicknesses.

Table 6.4-1 Comparison between CMM results and Ultrasonic results

Hole # 1 2 3 4 5 6 7 8

CMM (mm) 1.193 1.179 5.715 5.689 1.146 1.158 5.674 5.660

Ultrasonics (mm) 1.201 1.186 5.982 5.890 1.125 1.186 5.692 5.493

Deviation (mm) 0.008 0.006 0.267 0.201 0.021 0.027 0.017 0.167

Hole # 9 10 11 12 13 14 15 16

CMM (mm) 1.191 1.206 5.653 5.656 1.192 1.115 5.679 5.687

Ultrasonics (mm) 1.186 1.201 5.738 5.553 1.125 1.155 - 5.738

Deviation (mm) 0.006 0.005 0.084 0.104 0.068 0.040 - 0.050

The timestamp of each ultrasonic signal was processed and combined with the interpreted

thickness values to create a 2D image, as shown in Fig. 6.4-3, which shows the surface of the test

component and the detected subsurface features. Also shown in this figure is the position and size

of the holes measured by the CMM. It is noted that starting from hole 9, the thicknesses indicating

holes were displaced from the position measured by CMM. This was possibly because the actual

machine feedrate was slower than the feedrate specified in the NC program and therefore, the

calculated distance was greater. This was reasonable because the spindle had to wait for the 4th

243

axis of the machine to finish its rotation and at hole 9 and beyond the angle of rotation was much

greater and the wait time was increased.

Fig. 6.4-3 Processed ultrasonic thickness data

Generally, the wall thicknesses measured by the ultrasonic probe are very similar to those

measured on the CMM, especially for holes that are close to the surface, i.e. wall thicknesses

around 1.2mm such as at holes 1 and 2 The maximum deviation of 0.267mm occurs at hole 3

where the wall thickness is 5.714 mm. It is not the magnitude of the wall thickness because at

hole 7 with a similar wall thickness the error is 0.0017 mm. One probable cause of this was that

the ultrasonic probe was not exactly normal to the surface, leading to refraction of the ultrasonic

waves at the interface and resulting in increased value for the wall thickness. At Hole 15, the

ultrasonic probe failed to detect the correct wall thickness. From Fig. 6.4-3, it can be seen that the

thicknesses measured near X = 90 was approximately the thickness of the block, which means the

hole was not detected.

Also, it was noticed during the experiment that the milling machine jerked heavily which could

cause the ultrasonic probe being positioned at a wrong direction.

Conclusion

The wall thicknesses as measured by the ultrasonic probe were close to the actual wall

thicknesses, with the average error for 12 of the holes being 0.036mm, whilst for remaining three

holes, except for Hole 15, (Hole 3, 4 and 8) the average error was substantially more (0.212mm),

probably due to jerking of the machine or the inaccurate probe direction.

244

Measuring the disc blade on a 4-axis milling machine


Previous experiments conducted with the stepped and curved components13 have shown that the

ultrasonic probe is capable of measuring wall thicknesses accurately, even if the component has

curved surfaces. However, before the prototype machine could be designed, it was still important

to test the capability of the probe on measuring a real turbine blade.

The aim of this experiment was to examine the accuracy of the probe when measuring wall

thicknesses of holes in a turbine blade.

Tests on the disc blade were carried out on the OKK 4-axis milling machine, as shown previously in

Fig. 6-1. The disc blade, as mentioned earlier, has no fir tree roots. Instead the blade is welded on

to a circular disc, as shown in Fig. 6.5-1 (a). There is a step machined on the disc which is useful

for program datum setup. The aerofoil surfaces of this blade were measured on a CMM at ELE. The

acquired surface points were fitted with Bezier curves and differentiated to calculate the probe

path. The probe path allowed the ultrasonic probe to be positioned perpendicular to the cross

section and 20mm above the blade. The machined step on the disc was chosen as a datum for the

CMM points. A 10mm hole was drilled in the centre of the disc so that the specimen could be

mounted on the rotary axis.

(a) (b)

Fig. 6.5-1 The long blade and wall thicknesses from both convex and concave surfaces (units in mm)

13 These experiments were also conducted on the OKK 4-axis milling machine before they

were repeated in the prototype machine.

x

y Step for datum setup

245

The cross section tested in this experiment was the section at the top of the blade, where the wall

thicknesses could be measured with a vernier caliper. The measured thicknesses are shown in Fig.

6.5-1 (b).


The experimental setup was similar to the one shown in Fig. 6.4-2. The water tank was placed and

clamped on the machine table and the fixture was bolted onto the rotary axis. The long blade was

then bolted on the fixture. The rotary axis was adjusted so that the surface of the step on the

circular disc was vertical and facing outwards. The position was checked by running a dial gauge

which was held in the spindle of the milling machine; the dial gauge was moved up and down and

across the entire length of the step. The specimen datum was set to the surface of the step as

shown in Fig. 6.5-1 (a). In this way, the part program zero was synchronised with that on the

CMM.

Next, the calculated probe path was loaded into the milling machine’s controller and the ultrasonic

probe was connected to the computer. Once the probe was initialised and started to acquire data,

the milling machine was started. The collected ultrasonic data were processed with Matlab scripts

and wall thicknesses were evaluated.


Table 6.5-1 Wall thicknesses measured with ultrasonic probe compared with CMM results

Convex Concave

Hole #

Vernier

Caliper

(mm)

Ultrasonics (mm)

dt (mm)

α1

(°)

Vernier

Caliper

(mm)

Ultrasonics (mm)

dt (mm)

α1

(°)

1 0.870 - - -5.82 1.960 - - 9.88

2 1.020 1.139 0.119 -3.00 2.270 - - 7.58

3 1.490 1.500 0.010 -1.20 2.350 - - 5.60

4 1.550 1.566 0.016 -0.12 2.100 2.256 0.156 4.00

5 1.380 1.402 0.022 0.33 1.930 2.092 0.162 2.86

6 1.200 1.188 -0.012 0.71 1.820 1.927 0.107 1.20

7 1.400 1.402 0.002 1.11 1.610 1.697 0.087 0.03

8 1.680 1.796 0.116 1.51 1.420 1.517 0.097 0.12

9 1.500 1.566 0.066 1.93 1.370 1.320 -0.050 0.30

10 1.680 1.697 0.017 2.41 1.150 1.122 -0.028 0.55

11 1.550 - - 3.34 0.970 0.925 -0.045 0.78

12 1.370 - - 4.21 0.580 - - 1.02 1 α represents the longitudinal inclination of the surface

The evaluated wall thicknesses are compared with CMM measurements in Table 6.5-1. The twelve

holes are numbered starting from the leading edge to trailing edge.

246

The first thing to note is that the ultrasonic probe failed to detect seven wall thicknesses. For Hole

12 from the concave side, the wall thickness, which is 0.58mm is outside the measurement range

of the ultrasonic probe. For the rest of the holes, the failure of detection was likely due to the

inability to rotate the tool about the Y-axis, which meant that it was not possible to cater for the

slope of the blade in the longitudinal direction. As shown in Table 6.5-1, the longitudinal

inclinations (α) of the surfaces above these holes are substantial, these inclinations being

equivalent to the angles of incidence of ultrasound. As discussed in Chapter 6.3, at an angle of

incidence higher than 3.465°, it is possible that the backwall echo is greatly attenuated making the

signal undetectable. Significant errors have also been introduced due to the angle of incidence not

being normal to the blade surface. According to the CMM data, the longitudinal inclinations are

determined at the surface above each hole from both surfaces. Interface echoes captured above

these holes are distorted in a similar way as shown previously in Fig. 6.3-7 (c). Fig. 6.5-2 (a) and

(b) shows two examples of the distorted interface echo captured above Hole 1 from the convex

and concave surfaces respectively, compared with a healthy interface echo shown in Fig. 6.5-2 (c).

The first peak of the interface echo in Fig. 6.5-2 (a) was separated into two peaks by a valley and

both peaks in the interface echo are absent in Fig. 6.5-2 (b).

(a) (b)

(c)

Fig. 6.5-2 Distorted interface echoes captured above Hole 1 from (a) the convex surface and (b) the concave surface, gain = 60 compared with (c) a healthy interface echo

247

The absence of a wall thickness for Hole 12 from the concave surface could not be attributed to

the out-of-normality of the probe which for this hole was only 1.02°. The reason for this is the

limitation of the ultrasonic probe; because the wall thickness was only 0.6 mm, the backwall echo

overlaid the interface echo and it was difficult to detect the time difference between the two

peaks.

Apart from the undetected wall thicknesses, some of the measured wall thicknesses are not

accurate, such as those for holes 2 and 8 from the convex surface and for holes 4, 5 and 6 from

the concave surface. These surfaces, in the vicinity of the holes, have a significant inclination in the

longitudinal direction and this is possibly the biggest source of error. Other possible sources of

error include the resolution of the acquired data, accuracy of calibration and error in measuring

reference wall thicknesses.

Conclusion

The results of the experiment suggest a 4-axis machine is definitely inadequate for the job, as the

machine lacks an additional rotary axis to keep the probe normal to the blade in the longitudinal

direction. This experiment also reveals the difficulty of obtaining reference values with which the

ultrasonic measured wall thicknesses can be compared. Because of this difficulty, the wall

thicknesses were measured and compared at the top section of the disc blade.

On the other hand, these experiments show promise that when the ultrasonic probe is positioned

correctly, the results can be good. Therefore, if a 5-axis machine or a 6-axis robot is deployed as

the actuator of the probe, the test results could be improved.

248

Measuring the disc blade on the inspection machine


In this experiment, the disc blade, which was tested on the OKK milling machine, is re-tested on the

prototype inspection machine. The major problem found previously when testing this blade on the

milling machine was lack of an additional axis to tilt the ultrasonic probe in the longitudinal direction of

the blade. With a 6-axis robot, the ultrasonic probe can be positioned normal to the surface of the

blade.

The aim of this experiment was to test the capability of the robot and compare the results obtained

with those obtained previously with the OKK machine.

The probe path for this experiment was generated from the surface data acquired at ELE during the

previous experiment. The same section i.e. section at the top of the blade, was selected so that the

previously obtained results could be compared. The probe path generation algorithm was slightly

different from the one discussed in Chapter 5.4, which was developed after this experiment. Instead of

having a scanning window above each hole, the robot was paused at 500 different positions over the

entire cross section. The distance between each two path points was approximately 0.15mm. Four

rotations of the blade were required for a complete scan.


Fig. 6.6-1 Clamp of the disc blade on the inspection machine

The blade was bolted on the shaft through the hole on the circular disc, as shown in Fig. 6.6-1.

The shaft was rotated until the majority of the convex surface of the blade was approximately

horizontal. The blade was then measured by the laser sensor, which was held in the robot, at 50

different locations on the convex surface. The point data were loaded in Matlab and the previously

calculated probe path was localised with the help of these points, thus transforming the probe path

into the robot co-ordinate system. The probe path was automatically divided into several sections

249

based on the inclination of the surface at each path point. For each section, the angles of rotations

of the shaft, which were required to bring the section inside the boundary of scan, were calculated.

The shaft was then rotated by these angles and for each rotation of the shaft, the surface was

brought within the boundary of the scan and was measured with the laser sensor. These laser

points were used to localise the corresponding section of the probe path.

After all the sections of the probe path were localised, the laser sensor was returned to the tool

magazine and the ultrasonic probe was attached. In the meantime, the tank was filled with water,

until the water was sufficient to submerge the blade by approximately 50mm. Ultrasonic testing

was then started. After all path points defined in the probe path for convex surface were visited,

the above procedures were repeated for measuring the concave surface.


Fig. 6.6-2 shows the results of reverse engineered models of the blade. The convex and concave

surfaces were scanned at different times (i.e. with different set-ups) with the CMM and therefore it

was not possible to stitch them together. Therefore, the two surfaces had to be modelled separately.

Fig. 6.6-2 Fitted B-spline surfaces (units in mm)

The aerofoil section of the blade, which was measured with ultrasonics in this experiment, is

shown in Fig. 6.6-3. Also shown in this figure are the approximate hole positions and the calculated

(a) Convex (b) Concave

250

surface normals. These surface normals represent the directions of ultrasound and were used to

construct the probe path. As can be seen in Fig. 6.6-3 (c) and (d), the curves extracted from the


(c) Convex

(d) Concave

Fig. 6.6-3 Surface normals at the top cross section (units in mm)

251

B-spline surfaces accurately fit the CMM points and the directions of the surface normals are mostly

uniform along the curvatures of the cross section. This confirms the accuracy of the B-spline fitting

procedure as well as the probe path calculations.

The results of this experiment are compared with those obtained from the experiment conducted

on the OKK machine. The comparison is shown in Table 6.6-1. In the table, 𝑑𝑡 denotes the

differences between the thickness values measured with the ultrasonic probe and the CMM. The

subscripts 𝑂𝐾𝐾 and 𝐼.𝑀. indicate the experiment in which the thickness values were obtained;

specifically, 𝑂𝐾𝐾 refers to the experiment conducted on the OKK machine and 𝐼.𝑀. refers to this

experiment. The values in column ∆𝑑𝑡 were evaluated by |𝑑𝑡𝑂𝐾𝐾| − |𝑑𝑡𝐼.𝑀.| ; literally, negative

values indicate worse results and positive values indicate improved results, all in comparison with

the OKK experiment from the perspective of this experiment. Also the thicknesses obtained from

these sources, caliper (as the reference thickness), experiment on OKK and this experiment were

plotted in Fig. 6.6-4.

Table 6.6-1 Comparison between errors of evaluated thicknesses from two experiments

Hole # Convex Concave

𝑑𝑡𝑂𝐾𝐾 (mm) 𝑑𝑡𝐼.𝑀. (mm) ∆𝑑𝑡 (mm) 𝑑𝑡𝑂𝐾𝐾 (mm) 𝑑𝑡𝐼.𝑀. (mm) ∆𝑑𝑡 (mm)

1 - -0.022 - - 0.115 -

2 0.119 0.102 0.017 - 0.068 -

3 0.01 0.092 -0.082 - 0.119 -

4 0.016 0.098 -0.082 0.156 0.074 0.082

5 0.022 0.005 0.017 0.162 0.014 0.148

6 -0.012 0.021 -0.009 0.107 -0.073 0.034

7 0.002 -0.015 -0.013 0.087 0.038 0.049

8 0.116 0.034 0.082 0.097 0.097 0

9 0.066 -0.016 0.050 -0.05 0.015 0.035

10 0.017 -0.016 0.001 -0.028 -0.060 -0.032

11 - -0.033 - -0.045 -0.045 0

12 - -0.050 - - - -

It can be seen that out of 24 holes, 23 holes were detected in this experiment. The hole that could

not be detected had a wall thickness of 0.58mm which was outside the capability range of the

probe. Six holes that were not detected in the previous experiment, possibly due to the inclination

in the longitudinal direction, were detected in this experiment and the accuracy at these holes,

except for Hole 1 and 3 from the concave side, is good. As for the other wall thicknesses, the

accuracy was, in general, improved.

However, note that significant differences were observed between the thicknesses evaluated in this

experiment and the reference thicknesses at holes closer to the leading edge, as for example in

the case of holes 1-4. It was also found that the interface echoes in this region were slightly

distorted and the echoes did not exhibit the expected – i.e. the wall thicknesses approaching a

minimum value as the probe travels towards the hole.

252

Fig. 6.6-4 Comparison between thicknesses obtained from difference sources (units in mm)

Conclusion

The mean error of the measured wall thicknesses is 0.053mm with a standard deviation of

0.037mm and the maximum error is 0.119mm. In this experiment, the probe was positioned

normal to the surface and the improvement in the wall thickness can be largely attributed to the

probe being normal.


253

Reverse engineering of the PSM104 turbine blade


With a 6-axis robot, the ultrasonic probe can be positioned normal to the surface of the blade.

Therefore, when positioning the probe at the required position, one must ensure that the axis of

the probe makes the appropriate angles with the X- and Y-axes (see Fig. 5.4-1). In order to

calculate probe paths for a surface, the surface should be, firstly, reverse engineered and then

represented as a B-spline surface. The B-spline surface is, next, differentiated with respect to u

and w, to evaluate the direction of the normal vector at a point on the surface.

The aim of this experiment was to calculate a probe path based on the theory introduced in

Chapter 5.4 and measure the turbine blade with the ultrasonic probe using the probe path.

The method for reverse engineering used in this experiment was discussed in Chapter 5.2, which

involves digitization of the surface, B-spline curve fitting, Delaunay’s triangulation, shape

preserving parameterisation and B-spline surface fitting. The cross section of the aerofoil selected

for calculating the probe paths is 60mm from the top of the blade.

Fig. 6.7-1 (a) A PSM104 turbine blade with the fixture; (b) the turbine blade being measured on the CMM

In this experiment, the aerofoil surface of a PSM104 turbine blade (see Fig. 6.7-1 (a)) was digitized

with a Nikon LK G90C CMM with a 2mm ruby stylus.

(a) (b)

254

Start

End of probe path reached

Ultrasonic testing initialisation

Go to the next path point

Data acquisition

Laser measurement and localisation of probe path

Blade clamping

End

Drain water

Y

N

Fig. 6.7-3 Procedures of measuring blades in the prototype cell


The turbine blade fixture which was introduced in Chapter 3.8 was

bolted on the CMM granite table and the turbine blade was clamped

in the fixture, as shown in Fig. 6.7-1. As only the aerofoil section is

of interest, the root section was not measured. During inspection,

each cross section of the aerofoil surface was divided into five

regions, which are shown in Fig. 6.7-2. The reason for doing is that

for each region, the A and B axes of the CMM, i.e. the orientation of

the stylus, could be kept stationary and roughly perpendicular to

the surface in the middle of this region. When one region was

completely scanned, the orientation of the stylus was adjusted to

suit the next region. The measurement took place between the

aerofoil section

approximately 1mm and 87.5mm from the top edge.

The CMM measurement involved a coarse

measurement and a detailed measurement. During the

coarse measurement, approximately 200 points were

measured manually with the CMM using the joystick.

Based on these 200 points, five coarse meshes, one

representing each region of the aerofoil part of the

blade, were generated and fitted with B-spline

surfaces in Matlab. Next, approximately 3500 points

were generated on the fitted surface. These 3500

points were then used to create a CMM tool path

which measured the surfaces automatically at these

3500 coordinates.

The measured data points were processed using

Matlab scripts. These data points were triangulated

using Delaunay’s rule, parameterised with shape-

preserving method, and finally fitted with B-spline

surfaces.

Next, the probe paths were calculated based on the

theory described in Chapter 5.4. The generated B-

spline surfaces were differentiated and thereby, the

tangent vectors at each data point were found. The

Fig. 6.7-2 Five regions defined on the surface of

the blade

255

positions of the holes at the section 51 mm from the top face of the blade were extracted from the

CAD model of the blade and were localised in the CMM coordinate system with the ICP algorithm.

Then, the closest points to each hole on both the concave and convex surfaces were found. A scan

window of approximately 2mm wide on each side of every closest point was created and in each

scan window, twenty tool paths points were defined.

Fig. 6.7-4 Turbine blade fixed on the shaft of the inspection machine

The fixture was then fixed on to the shaft and the turbine blade was clamped in the fixture as

shown in Fig. 6.7-4. The stepper motor was started and turned the turbine blade so that region A

was roughly in the X-Y plane. The surface was first measured with the laser sensor, which was

carried by the robot. For each rotation of the blade, point data were acquired at 40 different

locations on the aerofoil surface. At the end of each laser measurement session, the blade was

rotated clockwise by the angle specified in the probe path data file. The acquired laser points were

imported into Matlab for localising the probe path, i.e. transforming the probe path to the

coordinate system of the inspection machine.

After the path was localised, the laser sensor was returned to the tool magazine and the ultrasonic

probe was attached. In the meantime, the tank was filled with water until the water level was

approximately 50mm above the turbine blade. The localised probe path was then loaded into the

control software and the ultrasonic testing was started. At each path point defined in the probe

path, the movement of the robot was paused for ultrasonic data acquisition. For each path point,

100 ultrasonic signals were acquired at a gain of 70 for interpreting the backwall echoes and

additionally 20 ultrasonic signals were acquired at a gain of 56 for interpreting the interface

echoes.

After all the path points were visited and the data acquired, the probe was returned to the

magazine.

256


6.7.3.1. Reverse engineering and probe path generation

In Fig. 6.7-5 (a), data points acquired from the CMM are plotted in 3D. Blue, orange, yellow, green

and purple points represent regions A, B, C, D and E (see Fig. 6.7-2) respectively. As can be seen,

on the concave surface, i.e. the CMM points on parts D and E are not connected to their adjacent

regions. This was because at the time of measurement, the CMM was only calibrated for four

stylus orientations and the missed area14 required an additional calibration.

Fig. 6.7-5 (a) CMM data points collected on Blade 1, (b) generated Model 1 and (c) Model 2 (units in mm)

Two aerofoil surface models, Models 1 and 2, were generated. Each model contains 500,000 points.

Model 1, as shown in Fig. 6.7-5 (b), was generated by fitting the concave and convex surfaces

separately, as a result of which, the generated surfaces are disconnected and each surface

contains 250,000 points. Model 2, as shown in Fig. 6.7-5 (c), was generated by fitting a B-spline

surface to the complete set of digitized data and this avoided the discontinuity at the leading edge

seen in the first model. Both surface models are visually smooth and both B-spline models closed

the gap on the concave surface.

Table 6.7-1 Linear errors of surface fitting of B1 (units in mm)

M1 M2

Mean Max Min S.D. Mean Max Min S.D.

Convex 0.062 0.191 0.001 0.029

0.064 0.353 0.002 0.034

Concave 0.054 0.181 0.001 0.025 0.062 0.163 0.002 0.026

Overall 0.059 0.191 0.001 0.028 0.063 0.353 0.002 0.031

The goodness of the fittings was assessed by calculating the linear deviations between the CMM

points and the corresponding closest points in the fitted point sets. Table 6.7-1 shows the mean,

14 The maximum gap distance of the missed area is 9.64mm and minimum is 5.58mm.

257

maximum and minimum errors and standard deviation, where M1 stands for Model 1 and M2

stands for Model 2. Overall, both models are accurate representations of the aerofoil surface. The

goodness of the fitting on the concave surfaces for both models is slightly better than that for the

convex surfaces. This is more obvious in Model 2, as the maximum error on the convex surface is

nearly twice as much as that on the concave surface and the standard deviation is also greater on

the convex surface. The less accurate fitting of the convex surface also makes Model 2 slightly

inferior to Model 1.

Fig. 6.7-6 Surface fitting error of (a) the convex surface and (b) the concave surface of Model 1, and (a) the convex surface and (b) the concave surface of Model 2 (units in mm)

Fig. 6.7-6 shows the deviations at each data point. The maximum errors were found near the end

of a scan. This is especially the case for Model 2, in the area close to the leading edge. One reason

behind this is likely to be the inaccuracy of the CMM calibration. It must be mentioned that each

scan required the probe on the CMM to be tilted to a different position. Fig. 6.7-7 clearly shows the

mismatch between two sets of CMM points; ideally, the two sets should overlap in the area

(a) (b)

(c) (d)

258

indicated by the green box, if the CMM had been precisely calibrated. This can also be seen in Fig.

6.7-5 (a), where there is a mismatch between the orange and blue data points. Before fitting the

B-spline curve, these points were identified, extracted and the blue points were discarded. This,

however, resulted in discontinuity in the CMM points, as seen in Fig. 6.7-7 (c). In the later B-spline

curve fitting, these discontinuities were erased, as seen in Fig. 6.7-7 (d).

Fig. 6.7-7 (a) CMM points measured at section A and B; (b) Mismatch between two sets of data points when the same surface was measured but with different CMM orientations of the probe on the CMM; (c) Unmatched points on the convex surface have been removed; (d) B-spline curve smoothed out the displacement found in CMM data after unmatched points were removed. (units in mm)

(a) (b)

(c) (d)

259

Another reason, which could apply to Model 2, is that the leading edge was not completely

digitized and the gap was filled by a curve with continuity at its ends.

Model 1 is slightly closer to the CMM data points, but Model 2 includes the leading edge. However,

for some turbine blades, such as this one, PSM104, the leading edge is of no consequence and

therefore Model 1 is sufficient for the calculation of probe paths. For blades whose leading edge is

required to be tested, the leading edge must be included in the digitization to improve the

accuracy of the B-spline surface around the leading edge.

Fig. 6.7-8 shows the calculated probe paths using Model 1. The green segments indicate the

orientation of the probe. This path was later tested on the prototype cell and the results are

presented in the next section.

Fig. 6.7-8 Probe path for measuring from the convex surface ((a) and (b)); probe path for measuring from the

concave surface ((c) and (d)) (units in mm)

(a) (b)

(d) (c)

260

6.7.3.2. Ultrasonic testing

Wall thicknesses of this turbine blade were obtained from three sources: ultrasonic data acquired

on the inspection machine, ultrasonic data acquired manually using a touch probe at ELE and a CT

scan image (see Fig. 6.7-9). However, due to the limited penetration ability of the CT scanner, the

edges of the holes are not clearly defined and thus the confidence bounds of the estimated

thicknesses shown in the image is around ±0.08mm. Also it was not possible to define the concave

edge from the CT image. Thus the section curve of the blade was extracted from the B-spline

surface and plotted on the CT image. The wall thickness values measured on the concave side may

be less accurate.

Fig. 6.7-9 Wall thicknesses obtained from a CT image of the blade cross section (units in mm)

H 1 4 2 . 2 2 9

T 1 5 - 1 . 6 3 0

T 1 6 - 1 . 5 2 8

T 1 7 - 2 . 0 2 0

T 1 8 - 3 . 7 6 2

T 1 9 - 3 . 5 8 9

T 2 0 - 3 . 8 5 0

T 2 1 - 3 . 7 2 9

T 2 2 - 3 . 2 2 2

T 2 3 - 3 . 4 0 1

T 2 4 - 1 . 3 9 6

T 1 3 - 2 . 6 5 4

T 1 - 0 . 5 0 1

T 2 - 1 . 8 7 0

T 3 - 1 . 6 1 0

T 4 - 2 . 2 5 5

T 5 - 3 . 6 2 4

T 6 - 4 . 3 3 4

T 7 - 3 . 3 6 7

T 1 0 - 4 . 6 1 6

T 8 - 3 . 5 3 4

T 9 - 5 . 0 4 0

T 1 1 - 4 . 0 7 5

T 1 2 - 4 . 4 9 1

261

Fig. 6.7-10 Wall thicknesses measured using the inspection machine and touch probe compared with the reference values

Nevertheless, values interpreted from the CT scan image are used as references for comparing the

accuracy of wall thicknesses obtained from other two sources as shown in Fig. 6.7-10. The mean

errors and standard deviations (S.D.) are compared in Table 6.7-2. It is noted that the touch probe

failed to measure wall thicknesses at T20, T21 and T22 and the inspection machine was not able

to measure wall thickness at T1 which is smaller than 0.6mm, i.e. it is outside the measurement

range of our ultrasonic probe. In addition, at T8, the error was over 3mm. It is likely that instead

of measuring T8, the inspection machine was measuring the hole which corresponds to T20 from

the convex side. Scanning windows were determined based on the hole positions in the CAD model

and when the actual position of the hole is very different from the CAD model, which was probably

the case at T8, detection of the hole may fail. This suggests the scanning windows should be wider

to tolerate such inaccuracy in hole positions. These wall thicknesses are not involved in the

calculation in Table 6.7-2.

Table 6.7-2 Mean errors and standard deviations of wall thicknesses measured on the inspection machine and using the touch probe

ΔTI.M. ΔTELE

Mean absolute error (mm) 0.1385 0.3362

S.D. (mm) 0.1821 0.3206

In general, the accuracy of wall thicknesses measured on the inspection machine is better than

they were measured using the touch probe at ELE. Mean absolute error was reduced by 58.8%.

However, wall thicknesses measured at T5 and T18 using both the inspection machine and the

touch probe are significantly deviated from the reference values negatively and it is noted that at

these two thicknesses, the same hole was measured. This is possibly due to the surface

262

roughness of the hole that the ultrasonic probes measured a depression on the surface which was

not captured by the CT scanner.

Summary

A B-spline model has been developed for the aerofoil section of the PSM104 turbine blade; two

representations were obtained one of which did not include the leading edge. The first model

which included the leading edge had sufficient information to generate the probe paths.

The probe path was tested by measuring the turbine blade. Results shows the average accuracy of

wall thicknesses measured by the inspection machine is 0.1385mm which is 58.8% more accurate

than the wall thicknesses measured using touch probes at ELE.

263

Measuring three PSM104 turbine blades with a common

probe path


If each and every blade in a batch has to be reverse engineered and its probe path determined,

then the automated process of inspection is likely to be equally time-consuming as the manual

process and one of the main advantages of automating the procedure will be lost.

The aim of this experiment is to investigate whether a common probe path can be used for all the

blades in a batch. This aim can be achieved by meeting two objectives: (i) quantify the geometric

differences between blades and (ii) determine the effect of these differences on measured wall

thicknesses.

To meet these objectives, three turbine blades of Model PSM104 were selected from a batch for

the experiment. Let the three blades be denoted as B1, B2 and B3. To save some effort, the blade

described in the previous sections was selected as one of the blades (i.e. blade B1).

In order to determine the geometric differences between B1, B2 and B3, all three turbine blades

must be first reverse engineered. Of course, blade B1 has already been reverse engineered and

was described in the previous section. Thus only blades B2 and B3 had to be reverse engineered.

They were measured again using the CMM and their B-spline models created; the B-spline models

of B1, B2 and B3 were then compared geometrically both for linear and slope differences.

Let the probe path calculated from blade B1 in the previous section be referred to as P1. Two more

probe paths (P2 and P3) were calculated from the B-spline models of B2 and B3 respectively. Each

probe path was used to measure the wall thicknesses of holes in the three blades; these holes lie

in a cross-section 51 mm from the top of the blade. Since the holes in one blade have three probe

paths associated with it, it meant that, Hole 1, in blade B1, has three wall thickness values

associated with it, i.e. B1-P1, B1-P2 and B1-P3. The same hole

in blade B2 has three wall thicknesses and a further three

when blade B3 is considered.


The setup and procedures for measuring B2 and B3 on the

CMM were similar to the setup and procedures for measuring

B1 described in Chapter 6.7.2. The fixture was bolted on the

CMM table and the blade was then clamped in the fixture. In

this experiment, the surfaces of the blades were divided into Fig. 6.8-1 The four regions A, B, C and D defined on the surface

of the blade

264

Start

End of current probe path?

Another probe path to test?

Ultrasonic testing initialisation

Go to the next path point

Data acquisition

Laser measurement and localisation of probe path

Blade selection and clamping

End

Drain water

Remove current blade

Another blade

to test?

Y

N

N

N

Y

Y

Fig. 6.8-2 Procedures of measuring blades in the prototype cell

four regions. The four regions are shown in Fig.

6.8-1. The measurement took place between the

aerofoil sections at 1.8mm and 61mm from the top.

This was about 26.5mm shorter than the

measurement of B1.

B2 was used for coarse measurement and

approximately 250 point data were acquired. Based

on these 250 points, a refined mesh containing

approximately 2000 data points were generated

with B-spline surface fitting. The CMM was then

programed to touch and measure the aerofoil

surfaces of B2 at these 2000 points. The same

procedure was used to acquire 2000 data points on

B3.

After the blades were measured, the collected point

data were processed with Matlab scripts. Examining

the results, which are discussed later in this

chapter, the CMM point data collected on the

concave surfaces were inaccurate. Therefore, it was

decided that only the convex surfaces were to be

analysed. Two probe paths, P2 and P3, based on

the convex surfaces of B2 and B3 respectively, were

generated for measuring the convex surfaces of B1,

B2 and B3 in the prototype cell.

The fixture was removed from the CMM table and

fixed on the shaft in the prototype cell. B1, B2 and

B3 were clamped in the fixture and measured in

sequence. The clamping of the blades was similar

to the clamping shown in Fig. 6.7-4. B2 and B3

were tested with PP1 (the probe path generated

previously from the convex surface of B1), P2 and

P3 and B1 was tested with P2 and P3. The

procedure for the rest of the experiment is

described in Fig. 6.8-2.

The test blade was first measured with the laser

sensor at approximately 40 different locations on the surface of the blade for each rotation defined

265

in the selected probe path. With these laser point data, the probe path was localised to the

coordinate system of the inspection cell. The tank was next filled with water and the ultrasonic

probe was attached to the robot face plate, and the ultrasonic testing was started for this blade. At

each path point defined in the probe path, the robot was paused to allow 100 ultrasonic signals to

be acquired at a gain 70 for interpreting backwall echoes and 20 ultrasonic signals at a gain of 56

for interpreting interface echoes.

After all the path points were visited, water was drained from the tank and the blade was rotated

back to its initial state. The next probe path was selected and the surface of the blade was

measured again at 40 points with the laser sensor for each rotation defined in the path to allow

path to be localised. And the above described measurement procedures were repeated. After the

blade was tested with all probe paths, the next blade was selected and the test procedures were

repeated.

It is noted that the wall thicknesses measured on B1 with P1 in the previous experiment were

imported into this experiment, and thus B1 was measured with P2 and P3 only.

266


6.8.3.1. Reverse engineering

In Fig. 6.8-3 (a), the acquired CMM point data for each scan region (A, B, C and D) of B2 are

plotted in blue, orange, yellow and violet respectively and the generated B-spline surfaces are

shown next to it, i.e. Fig. 6.8-3 (b). Similarly, the acquired data and the B-spline representations

for blade B3 are shown in Fig. 6.8-3 (c) and (d). On each surface, 250,000 points were generated.

Fig. 6.8-3 (a) CMM data points measured on B2; (b) Fitted B-spline surfaces of B2; (c) CMM data points measured on B3; (d) Fitted B-spline surfaces of B3 (units in mm)

The B-spline surfaces fitted to the data points are fairly accurate, with the errors shown in Table

6.8-1. These errors are in fact the linear differences between the CMM data points and the

corresponding closest points on the B-spline surface. Compared with Table 6.7-1, the B-spline

representations of B2 and B3 on the concave side are slightly worse. The deviation at each CMM

(a) (b)

(c) (d)

267

point is shown in Fig. 6.8-4. The maximum linear errors on both surfaces are near the junction of the

two scan regions, i.e. regions A and B, and C and D. This is more obvious on the concave surface.

The rate of change in slope, as shown in Fig. 6.8-5, indicates the there are several noticeable

depressions near the junction of regions C and D on the concave surfaces. However, these

depressions were not found on B1 (see Fig. 6.8-5 (e) and (f)).

Table 6.8-1 Linear errors of surface fittings of B2 and B3 (units in mm)

B2 B3

Mean Max S.D. Mean Max S.D.

Convex 0.056 0.149 0.023

0.056 0.127 0.022

Concave 0.053 0.387 0.036 0.055 0.437 0.042

Fig. 6.8-4 Linear deviation between the CMM points and the fitted (a) convex and (b) concave surface of B2, and the fitted (c) convex and (d) concave surface of B3 (units in mm)

(a) (b)

(c) (d)

268

Fig. 6.8-5 Rate of change in slopes of the (a) convex and (b) concave B-spline surfaces of B2, (c) convex and (d) concave B-spline surfaces of B3 and (e) convex and (f) concave B-spline surfaces of B1 (units in mm)

(a) (b)

(c) (d)

(e) (f)

269

Sections of the concave surfaces were extracted at Z ≈ -101 mm from both the fitted B-spline

surfaces and CMM points of all three blades and plotted in Fig. 6.8-6. It is clear that the depression

is caused by inaccurate data points acquired with the CMM, and this inaccuracy probably originates

from the inaccurate calibration of CMM orientations. The x coordinates of the two end points at the

junction of regions C and D were misaligned by approximately 1.6mm. The generated B-spline

surfaces for B2 and B3 modelled these misaligned points accurately. However, in the case of blade

B1, as surface data was not collected in this area, this part of the fitted surface was filled in

smoothly by the B-spline surface.

Fig. 6.8-6 Blade surface section profiles and CMM points on the concave surface, at Z ≈ -101 mm (all point data were localised to B1 CMM points and units in mm)

A hill caused by inaccurate

CMM point data

B1, B-spline section curve

B2, B-spline section curve B3, B-spline section curve

B1, CMM points B2, CMM points B3, CMM points

270

6.8.3.2. Comparison of the three blades

To facilitate the comparison, B2 and B3 were both localised to B1. The localised models were

compared with each other in terms of both linear and slope deviations. The results are shown in

Table 6.8-2, Fig. 6.8-7 and Fig. 6.8-8.

Table 6.8-2 Comparison of the three turbine blades

Linear deviation (mm) Slope deviation (°)

Mean Max S.D. Mean Max S.D. %>1° %>3.5°

B1 - B2 Convex 0.219 1.136 0.144 1.937 10.591 1.346 75.26% 8.19%

Concave 0.364 1.394 0.243 4.608 26.994 3.687 82.82% 44.66%

B1 - B3 Convex 0.226 1.135 0.143 1.932 11.727 1.364 73.80% 7.24%

Concave 0.425 1.335 0.279 4.968 23.445 3.651 84.21% 47.95%

B2 - B3 Convex 0.075 0.527 0.037 0.391 7.202 0.487 5.38% 0.50%

Concave 0.059 0.496 0.048 0.978 10.990 1.337 26.81% 0.63%

B2 and B3 are, in general, similar geometrically. The linear deviations between the two blades are

insignificant. The mean linear deviations are lower than 0.1 mm and the maximum deviations

occur along one of the edges (see Fig. 6.8-7 (e) and (f)), which is probably caused by errors in

localisation. Note that near the junction of regions C and D on the concave surface, the linear

deviations are much greater than the surrounding area. The slope deviations between the convex

surfaces of the blades are acceptable. The maximum slope deviations are at the edge (see Fig.

6.8-8 (e)) and again this is likely to be due to errors in localisation. Fig. 6.8-8 (e), as well as the

standard deviation, shows that the slope deviations are uniform on the convex surface and only

5.4% of the 250,000 data points have a slope deviation greater than 1°. For the concave surfaces,

on the other hand, the mean deviation is near the allowable limit of angle of incidence, i.e. 1°, and

26.8% of the points have slope deviation exceeding 1°. Fig. 6.8-8 (f) shows that, except for the

area at the junction of regions C and D, the slope deviations are generally acceptable.

Furthermore, slope deviations greater than 3.5° are almost non-existent.

When B1 is compared with B2 and B3, the linear deviations are acceptable for the convex surfaces.

The maximum linear deviations are near one of the bottom corner of the surfaces (see Fig. 6.8-7 (a)

and (c)). When the concave surface of B1 is compared with that of B2 (or B3), although the mean

deviations are not significant, the majority of the large deviations (indicated by green, yellow and

red) are in the middle of the surface (see Fig. 6.8-7 (b) and (d)). The slope deviations suggest

significant dissimilarity between the blades. The mean slope deviations between the convex surfaces

are nearly 2° whilst the mean deviations between the concave surfaces are more than 4.5°. The

number of slope deviations greater than 1° is over 70% for the convex surfaces and around 7-8%

of the slope deviations are greater than 3.5°. For the concave surfaces, this is worse. According to

271

Fig. 6.8-7 Linear deviations compared between each two of the three blades (units in mm)

(a) B1 and B2 convex (b) B1 and B2 concave

(c) B1 and B3 convex (d) B1 and B3 concave

(e) B2 and B3 convex (f) B2 and B3 concave

272

Fig. 6.8-8 (b) and (d), major slope deviations occur on one of the edges of the surface and at the

junction area of regions C and D as well.

By comparing the cross sections extracted at various z coordinates of the blades, it was found that

the majority of the greatest slope deviations between the concave surfaces are due to the

depressions shown in Fig. 6.8-6.

Fig. 6.8-9 (a) shows the cross sections of B1 and B3 with the surface normals at Z ≈ -118 mm; the

reason for choosing this section is because the linear and slope deviations between the concave

surfaces of these blades are near their maximum values. At x = 155 and y = -235, the depression

on B2 caused a linear deviation of approximately 1.3mm and a slope deviation of approximately

23°. There is also a depression at x = 144 and y = -237, which causes slightly smaller deviations.

Fig. 6.8-9 (b) shows the cross sections of B1 and B3 with surface normals at Z ≈ -92mm, where the

deviations are also near their maximum values. Both the hill and depression were found here. The

edge near the depression on B2 is deviated from B1 by 1.3mm. The major deviations between the

convex surfaces shown in these two figures are near the two ends of the curves.

Fig. 6.8-9 (c) and (d) shows the cross sections of B2 and B3 with surface normals at Z ≈ -105 mm,

where the slope deviations between the concave surfaces are over 9°. The deviations are clearly

shown in Fig. 6.8-9 (d). Apart from this area, there is a good match between the two cross

sections.

At this stage, because of the poorly calibrated CMM, it is difficult to conclude the true amount of

deviations caused by the geometric difference in blade. It is seen that between B2 and B3, apart

from the junction area of region C and D, both linear and slope deviations are acceptable.

However, between B1 and B2 or B1 and B3, the slope deviations were found greater than the

upper limit (1°) on over 70% of the surfaces. It is possible that B1 is geometrically different from

B2 and B3, but it is also possible that these deviations can be attributed to the different settings

and CMM programs when measuring B1.

273

Fig. 6.8-8 Slope deviations compared between each two of the three blades (units in mm)

(a) B1 and B2 convex (b) B1 and B2 concave

(c) B1 and B3 convex (d) B1 and B3 concave

(e) B2 and B3 convex (f) B2 and B3 concave

274

Fig. 6.8-9 Cross sections of the localised B-spline surfaces and surface normals (units in mm)

(a) B1 and B3 at Z ≈ -118 mm (b) B1 and B3 at Z ≈ -118 mm

(c) B2 and B3 at Z ≈ -105 mm (d) B2 and B3 at Z ≈ -105 mm

275

6.8.3.3. Ultrasonic testing

As there are significant differences between the concave surfaces of B2 and B3, it was decided not

to perform any ultrasonic tests on these surfaces. Therefore, only the convex surfaces were tested

using the ultrasonic probe. Two probe paths, P2 and P3 were generated based on the reverse

engineered models of B2 and B3. And P1, the probe path generated from B1, was imported from

the previous experiment. These probe paths are compared in Fig. 6.8-10. It can be seen in Fig.

6.8-10 (b) that the curves and normals of P2 and P3 match very closely whilst there are some

differences between the normals for P1 and P2, as can be seen from Fig. 6.8-10 (a); the two sets

of normals mostly overlap except at Hole 12 (x ≈ 141, y ≈ -222).

Fig. 6.8-10 Comparison between different probe paths (units in mm)

The results from the ultrasonic testing are compared in Table 6.8-3. The complete results of the tests

are shown in Table V-1, Table V-2 and Table V-3 in Appendix V. The values shown in row B2-P3, for

example, refer to the differences in the wall thicknesses (Δ𝑡) of the holes in blade B2 measured with

probe paths P3 and P2. Also shown in this table are the differences in the angles (Δ𝜃) between the

normals to the modelled blade surface at the path points where the thickness values were evaluated.

For B2 and B3, the wall thicknesses measured using hand-held touch probes at ELE are also included

in the table in Appendix V. As the touch probes were unable to measure wall thicknesses greater

than approximately 4 mm, 30% of the wall thicknesses are absent. Most of the remaining results do

not show much agreement with the wall thickness values obtained using the inspection machine.

In general, the slope deviations between the normals of P2 and P3 are very small and the

differences in thicknesses measured on B2 and B3 using P2 or P3 are minor (see row B2-P3 and

(a) P1 and P2 (b) P2 and P3

276

B3-P2). However, the differences in the measured thicknesses as shown in row B1-P2 and B1-P3

are substantially greater and it is also noticed that the magnitudes of these deviations are very

similar, which agrees with the fact that P2 and P3 match closely.

Table 6.8-3 Differences in measured wall thickness

Hole 1 Hole 2 Hole 3 Hole 4 Hole 5 Hole 6 Hole 7

B1-P2 Δ𝑡 (mm) 0.115 -0.017 0.082 0.101 0.158 0.094 1.502

Δ𝜃 (°) 2.256 0.359 0.933 1.643 0.898 0.999 4.638

B1-P3 Δ𝑡 (mm) 0.115 -0.017 0.082 0.087 0.158 0.081 1.515

Δ𝜃 (°) 2.294 0.414 1.081 1.539 1.065 0.865 4.640

B2-P1 Δ𝑡 (mm) 0.148 -0.099 0.082 0.043 0.105 0 -1.538

Δ𝜃 (°) 2.797 0.616 1.611 1.245 1.683 0.997 4.221

B3-P1 Δ𝑡 (mm) 0.162 -0.066 0.148 0.101 0.177 0.202 0.349

Δ𝜃 (°) 2.624 0.570 1.642 1.430 1.173 2.19 4.592

B2-P3 Δ𝑡 (mm) 0 0.016 0 0 0 0.013 -0.027

Δ𝜃 (°) 0.035 0.026 0.042 0.062 0.086 0.067 0.060

B3-P2 Δ𝑡 (mm) 0 0 0 0 0 0.035 0.013

Δ𝜃 (°) 0.035 0.026 0.042 0.062 0.086 0.067 0.060

Hole 8 Hole 9 Hole 10 Hole 11 Hole 12 Hole 13

B1-P2 Δ𝑡 (mm) 0.068 0.108 0.094 -0.027 -0.067 -0.057

Δ𝜃 (°) 0.148 2.743 0.927 1.988 6.640 1.281

B1-P3 Δ𝑡 (mm) 0.137 0.108 0.094 -0.027 -0.053 -0.057

Δ𝜃 (°) 1.228 2.201 0.631 1.677 6.290 1.301

B2-P1 Δ𝑡 (mm) 0.102 1.495 0 0.040 0.135 0

Δ𝜃 (°) 1.577 3.389 0.976 1.289 6.5 0.263

B3-P1 Δ𝑡 (mm) 0.103 -0.068 -0.015 -0.067 - -0.087

Δ𝜃 (°) 0.986 2.535 1.073 1.122 - 0.023

B2-P3 Δ𝑡 (mm) -0.051 0 0 0 0 0

Δ𝜃 (°) 0.024 0.096 0.034 0.113 0.059 0.025

B3-P2 Δ𝑡 (mm) 0 0.131 0 -0.027 -0.027 0

Δ𝜃 (°) 0.024 0.096 0.034 0.113 0.059 0.025

Although it can be argued that on B1 the differences in measured thicknesses using P2/P3 and its

own probe path were caused by the Δ𝜃, some of these differences do not agree with experimental

results discussed in Chapter 6.3. For example, at Hole 12, where the differences between the

normals of P1 and P2/P3 are maximum, the differences between the measured thicknesses are in

fact small. Comparing the thicknesses obtained using P2 and P3 with the CT scan, it was found

that the differences are only around 0.036mm, while the thickness measured using P1 differs from

the CT scan by 0.103mm. Similarly, at Hole 11 and Hole 13, results obtained using P2 and P3 are

closer to the CT scan results. This suggests P2 and P3 are more accurate in this region.

277

When blades B2 and B3 were measured using P1, the results are also very different from the

results obtained using their own probe paths and the value of Δ𝑡 do not appear to be justified by

the difference between the values of the two normals, i.e. Δ𝜃. It is noted that at Hole 12, when B3

was measured with P1, it was not possible to measure the thickness.

This problem is probably caused by inaccurate localisation result when the probe path is localised

from CMM to the inspection machine. Most likely a shift along the axis of the turbine blades. If this

were true, the probe would be measuring holes at different cross sections. In Table 6.8-3, the

calculation of Δ𝜃 is based on the assumption that the probe was measuring at the correct cross

section, i.e. 51mm from the top face. Thus Δ𝜃 was calculated between the path orientation and

the normal vectors at the supposed cross section. However, because the probe path files have

been lost, it is not possible to compute the actual Δ𝜃.

Summary

Two more PSM104 turbine blades were reverse engineered and their B-spline models suggest that

the point data acquired on the concave surfaces of both models contain significant errors which

are probably due to errors in the calibration of the CMM.

The geometric differences between the three blades are quantified with linear deviations and slope

deviations. The mean linear deviations between the convex surfaces of B1 and B2 and B1 and B3

are approximately 0.2mm whilst the mean slope deviations are about 1.9°, which is greater than

the upper allowable limit of 1°. Also note that 75.26% of the surface has slope deviations of 1°.

When the convex surfaces of B2 and B3 were compared, there was good geometric similarity

between them. The mean linear deviations are 0.075mm and the mean slope deviations are

0.391°. In addition, only 5.38% of the surface has a slope deviation greater than 1°. As the

concave surfaces were modelled from problematic CMM point data, the deviations between the

surfaces are much greater and this may not reflect the actual geometric deviations.

The ultrasonic tests also confirmed the geometric similarity between the convex surfaces of B2 and

B3. When B2 was measured with P3 and B3 was measured with P2, the results were almost

identical to the results obtained with their own probe path. However, when both surfaces were

measured with P1, the results were noticeably different. Similarly, when B1 was measured with P2

and P3, the deviations between measured thicknesses were substantial. However, this is probably

due to inaccurate localisation of probe paths.

However, with problematic CMM calibration, and considering the fact that B1 was measured at a

different location in the CMM space using a separate CMM program, it is difficult to conclude that

B1 was very different from the other two blades, geometrically. There was also insufficient proof to

conclude that the concave surfaces of the blades were dissimilar.

278

Conclusions

In this thesis, an affordable automated system has been designed and built for measuring wall

thicknesses in gas turbine blades and the following conclusions are made:

In ultrasonic testing, the water path does not appear to affect the wall thicknesses

determined. However, when the water path is lower than the starting point of the focal

zone, the amplitude of the backwall echo is reduced.

Bubbles accumulated on both surface of inspection and probe lens negatively affect the

accuracy and detection of backwall echoes.

Angle of incidence of ultrasonic wave should be maintained within ±1° to ensure the

accuracy of the results.

In order to reduce phase angle error or the effect of pulse amplitude cropping, receiver

gain should be adjusted to avoid over amplifying the returned echo. One working strategy

is to use a lower gain value to acquire signals for determining interface echoes and then

increase the gain to detect backwall echoes.

Averaging multiple signals acquired at the same location is a feasible method to improve

the signal-to-noise ratio but at a cost of increased time.

Calibration of an ultrasonic probe for a specific material should be performed separately for

different thickness ranges. A general calibration across the entire thickness range is

inaccurate.

It is possible to represent cross sectional curves of turbine blades using both Bezier curve

and B-spline curve. However, the quality of the curve approximated using the B-spline

curve is better than the curve approximated using the Bezier curve.

The quality of a 3D surface triangular mesh generated using 2D Delaunay triangulation

based on uniformly distributed data points is good. The procedure is much less

problematic than a 3D Delaunay triangulation with surface extraction algorithms.

Turbine blade surfaces can be smoothly represented by B-spline surfaces constructed

based on shape-preserving parameterisation.

A 2-step localisation is not needed for our application since with a normal ICP algorithm,

convergence can be usually reached in a very short time. However, due to limited variation

279

along the axis of a turbine blade, it is sometimes challenging for the ICP algorithm to

converge at a global minimum with surface patches of the aerofoil section solely.

The motion accuracy of the robot is not maintained during linear motion and therefore,

accuracy dependant tasks, such as distance gauging, should only be carried out when the

robot has reached its destination.

The sixth axis of a robot was of no use during measurement of a turbine blade. On the

contrary, the additional axis introduces complexity in control of the robot using software.

Even though the average motion accuracy of the robot is greater than 0.1mm, the wall

thicknesses measured by the ultrasonic probe are generally close to the reference values.

The use of a scanning window, nullifies, to some extent, the positioning error of the robot

and errors introduced by the ICP algorithm.

The mean error of the wall thicknesses measured on the curved component (excluding

when the wall thickness > 10mm), disc blade and the PSM104 turbine blade is below 0.1

mm and the maximum error is around 0.15mm.

There is considerable similarity in geometry between two blades digitized in a CMM with

the mean linear deviation 0.067mm and the mean slope deviation 0.685°.

The wall thicknesses measured on one blade using the probe path generated based on the

geometrical model of the other blade are almost identical to the wall thicknesses measured

using its own probe path. The mean deviation is 0.013mm, which shows that a common

probe path can be used. More tests need to be conducted to confirm the results from

these initial tests.

280

Suggestions for Further Work

In order to improve the performance of the inspection machine and deploy the inspection machine

in production, the following work still remains to be completed:

i. Improve the localisation algorithm for localising probe paths in the coordinate system of

the inspection machine.

ii. Improve signal/noise ratio to reduce the number of samples of ultrasonic data has to be

acquired and thus reduce the overall the time cost of the inspection process.

iii. Measure more turbine blades from one batch and confirm whether a common probe path

can be used.

iv. Calibrate the robot and investigate the feasibility of using a 2D laser scanner for local

reverse engineering turbine blades on the inspection machine.

v. If a common probe path is feasible, construct a probe path library for various turbine blade

models.

vi. Improve the feature recognition and thickness evaluation algorithm to adopt distorted

echoes.

vii. Develop a real-time feature recognition algorithm. Therefore, it is possible to identify any

detection failure and adjust the probe path intelligently according to information acquired

from interface echoes.

viii. Integrate all Matlab scripts and control software and develop a user interface for

production use.

281

References

[1] L. K. Bhagi, P. Gupta and V. Rastogi, “Fractographic investigations of the failure of L-1 low

pressure steam turbine blade,” Case Studies in Engineering Failure Analysis, vol. 1, no. 2,

pp. 72-78, 2013.

[2] J. Pattavanitch and S. Hinduja, “Machining of turbulated cooling channel holes in turbine

blades,” CIRP Annals-Manufacturing Technology, vol. 61, no. 1, pp. 199-202, 2012.

[3] Ndt-ed.org, “Automated Scanning,” unknown. [Online]. Available: https://www.nde-

ed.org/EducationResources/CommunityCollege/Ultrasonics/MeasurementTech/automatedsca

nning.htm. [Accessed 20 January 2014].

[4] S. Pilli, P. Bhunia, S. Yan, R. J. LeBlanc, R. D. Tyagi and R. Y. Surampalli, “Ultrasonic

pretreatment of sludge: A review.,” Ultrasonics Sonochemistry, vol. 18, no. 1, pp. 1-18,

2011.

[5] “Basic Principles of Ultrasonic Testing,” NDT Education, [Online]. Available: http://www.ndt-

ed.org/EducationResources/CommunityCollege/Ultrasonics/Introduction/description.htm.

[Accessed 23 9 2012].

[6] Š. Kočiš and Z. Figura, Ultrasonic Measurements and Technologies First Edition, London:

Chapman & Hall, 1996.

[7] P. Cawley, “Non-destructive testing—current capabilities and future directions,” Proceedings

of the Institution of Mechanical Engineers, Part L: Journal of Materials Design and

Applications, vol. 215, no. 4, pp. 213-223, 2001.

[8] K. A. Fowler, G. M. Elfbaum, K. A. Smith and T. J. Nelligan, “Theory and application of

precision ultrasonic thickness gaging,” Insight, vol. 2, no. 10, 1997.

[9] J. Blitz and G. Simpson, Ultrasonic Methods of Non-destructive Testing, London: Champman

& Hall, 1996.

[10] R. Thompson, “NDT Techniques: Ultrasonic,” in Encyclopedia of Materials: Science and

Technology, Oxford, Elsevier Science Ltd, 2001, pp. 6039-6043.

[11] OLYMPUS NDT, “Ultrasonic Transducers Technical Notes,” 2011.

282

[12] T. H. University, “Introduction to Non-Destructive Testing Techniques,” The Hashemite

University, Zarqa.

[13] K. Foweler, F. Hotchkiss, T. Yamartino and T. Nelligan, “Important Characteristics of Sound

Fields of Ultrasonic Transducers,” Olympus Inc., 2012.

[14] B. M. Lempriere, Ultrasound and Elastic Waves, Burlington: Academic Press, 2003.

[15] M. Berke, “Nondestructive material testing with ultrasonics - introduction to the basic

principles,” The E-Journal of Nondestructive Testing & Ultrasonics, vol. 5, no. 9, 2000.

[16] P. Hammond, “On Resolution, Accuracy and Calibration,” NDTnet, vol. 2, no. 10, 1997.

[17] R. Diederichs, “Analog Characteristics of Ultrasonic Flaw Detectors,” NDTnet, vol. 3, no. 5,

1998.

[18] T. J. Mason, “Developments in ultrasound--Non-medical,” Progress in Biophysics and

Molecular Biology, vol. 93, no. 1-3, pp. 166-175, 2007.

[19] K. R. Erikson, F. J. Fry and J. P. Jones, “Ultrasound in Medicine-A Review,” IEEE

Transactions on Sonics and Ultrasonics, vol. 21, no. 3, pp. 144 - 170, 1974.

[20] P. D. Wall, D. Tucker, F. J. Fry and W. H. M. Jr., “The Use of High Intensity Ultrasound in

experimental neurosurgery,” The Journal of the Acoustical Society of America, vol. 25, pp.

281-285, 1953.

[21] D. H. Evans, J. A. Jensen and M. B. Nielsen, “Ultrasonic colour Doppler imaging,” Interface

Focus, vol. 1, no. 4, p. 490–502, 2011.

[22] B. E. Polat, D. Hart, R. Langer and D. Blankschtein, “Ultrasound-mediated transdermal drug

delivery: Mechanisms, scope, and emerging trends,” Journal of Controlled Release, vol. 152,

no. 3, pp. 330-348, 2011.

[23] Krautkrämer GmbH Corporation, “Ultrasonic Applications Highlights - Part 1, 2 and 3,”

NDTnet, vol. 2, no. 2-4, 1997.

[24] G. M. Amulele, A. G. Every and S. C. Yates, “Acoustic Microscopy Wall Thickness

Measurements on Nickel Based Superalloy Gas Turbine Blades,” Review of Progress in

Quantitative Nondestructive Evaluation, vol. 18, pp. 2001-2007, 1999.

[25] V. Raja and K. J. Fernandes, “Introduction to reverse engineer,” in Reverse engineering - an

283

industrial perspective, London, Springer, 2008.

[26] B. V. Chowdary, A. D. Noon, F. Ali and C. A. Imbert, “An investigation for improvement of

the 3D‐digitization process: a reverse engineering approach,” Journal of Manufacturing

Technology Management, vol. 22, no. 1, pp. 131-147, 2011.

[27] S. Hinduja, “Lecture notes - Reverse engineering overview,” Manchester, 2015.

[28] P. Benkő, R. R. Martin and T. Várady, “Algorithms for reverse engineering boundary

representation models,” Computer-Aided Design, vol. 33, no. 11, p. 839–851, 2001.

[29] J. Hoschek and R. Muller, “Turbine blade design by lofted B-spline surfaces,” Journal of

Computational and Applied Mathematics, vol. 119, pp. 235-248, 2000.

[30] T. Varady, R. R. Martin and J. Cox, “Reverse engineering ofgeometric models - an

introduction,” Computer-Aided Design, vol. 29, no. 4, pp. 255-268, 1997.

[31] M. Salman and A. Mansor, “Free-Form Surface Models Generation Using Reverse

Engineering,” 04 11 2008. [Online]. Available: http://eprints.usm.my/4902/. [Accessed 22

10 2015].

[32] A. Kumar, P. K. Jain and P. M. Pathak, “Industrial Application of Point Cloud/STL Data for

Reverse Engineering,” in DAAAM International Scientific Book, Vienna, DAAAM International

Publishing, 2012, pp. 445-462.

[33] M. Bern and D. Eppstein, “Mesh Generation and Optimal Triangulation,” in Computing in

Euclidean Geometry, vol. 1, Singapore, World Scientific, 1995, pp. 47-123.

[34] Renishaw, “Renishaw,” 2005. [Online]. Available: http://www.renishaw.com. [Accessed 20

April 2013].

[35] Nikon, “LK CMM Techonology,” 2015. [Online]. Available:

http://www.nikonmetrology.com/en_EU/content/download/11063/228870/version/14/file/LK

+CMM_EN.pdf. [Accessed 22 November 2015].

[36] A. Joubair and I. A. Bonev, “Non-kinematic calibration of a six-axis serial robot using planar

constraints,” Precision Engineering, vol. 40, pp. 325-333, 2015.

[37] FARO, “FARO Gage,” 2013. [Online]. Available: http://www.faro.com/en-GB/download-

centre/search-results/search-item?document=30da3207-4dec-4dff-a02e-47335d1c281a.

[Accessed 22 November 2015].

284

[38] Fanuc, “LR Mate 200iC Series,” 2009. [Online]. Available:

http://www.fanucrobotics.com/cmsmedia/datasheets/LR%20Mate%20200iC%20Series_10.p

df. [Accessed 23 November 2015].

[39] K. Fan, “A non-contact automatic measurement for free-form surface profiles,” Computer

Integrated Manufacturing Systems, vol. 10, no. 4, pp. 277-285, 1997.

[40] V. Carbone, M. Carocci, E. Savio, G. Sansoni and L. D. Chiffre, “Combination of a Vision

System and a Coordinate Measuring Machine for the Reverse Engineering of Freeform

Surfaces,” The International Journal of Advanced Manufacturing Technology, vol. 17, no. 4,

pp. 263-271, 2001.

[41] A. Modjarrad, “Non-Contact Measurement Using A Laser Scanning Probe,” in SPIE,

Hamburg, 1989.

[42] Nikon, “K-Scan MMDx walkaround scanning,” Nikon, 2015. [Online]. Available:

http://www.nikonmetrology.com/en_EU/Products/Laser-Scanning/Handheld-scanning/K-

Scan-MMDx-walkaround-scanning/(key_features). [Accessed 23 November 2015].

[43] M. J. Milroy, D. J. Weir, C. Bradley and G. W. Vickers, “Reverse engineering employing a 3D

laser scanner: a case study,” International Journal of Advance Manufacturing Technology,

vol. 12, pp. 111-121, 1996.

[44] V. H. Chan, C. H. Bradley and G. W. Vickers, “Automating laser scanning of 3D surfaces for

reverse engineering,” in SPIE, Pittsburgh, 1997.

[45] S. Son, H. Park and K. H. Lee, “Automated laser scanning system for reverse engineering

and inspection,” International Journal of Machine Tools & Manufacture, vol. 42, pp. 889-897,

2002.

[46] A. Gameros, L. De Chiffre, H. R. Siller, J. Hiller and G. Genta, “A reverse engineering

methodology for nickel alloy turbine blades with internal features,” CIRP Journal of

Manufacturing Science and Technology, vol. 9, pp. 116-124, 2015.

[47] Keyence, “Keyence UK & Ireland,” Keyence, 2015. [Online]. Available:

http://www.keyence.co.uk/index.jsp. [Accessed 23 November 2015].

[48] L. Chen and G. Lin, “Reverse engineering in the design of turbine blades - a case study in

applying the MAMDP,” Robotics and Computer Integrated Manufacturing, vol. 16, pp. 161-

167, 2000.

285

[49] 3Shape, “3D Scanning Q700 Series,” 3Shape, 2015. [Online]. Available:

www.3shape.com/our-products/quality-control/3d-scanning.aspx. [Accessed 23 November

2015].

[50] D. Hüser-Teuchert, E. Trapet, A. Garces, F. Torres-Leza, T. Pfeifer and P. Scharsich,

“Performance Test Procedures for Optical Coordinate Measuring Probes,” European

Commission, Hannover, 1994.

[51] A. Contri, P. Bourdet and C. Lartigue, “Quality of 3D digitised points obtained with non-

contact optical sensors,” CIRP Annals - Manufacturing Technology, vol. 51, no. 1, pp. 443-

446, 2002.

[52] H. Schwenke, U. Neuschaefer-Rube, T. Pfeifer and H. Kunzmann, “Optical Methods for

Dimensional Metrology in Production Engineering,” CIRP Annals - Manufacturing Technology,

vol. 51, no. 2, pp. 685-699, 2002.

[53] N. Vukašinović, M. Korošec and J. Duhovnik, “The Influence of Surface Topology on the

Accuracy of Laser,” Strojniski Vestnik - Journal of Mechanical Engineering, vol. 56, no. 1, pp.

23-30, 2010.

[54] H. Woo, E. Kang, S. Wang and K. H. Lee, “A new segmentation method for point cloud

data,” International Journal of Machine Tools & Manufacture, vol. 42, p. 167–178, 2002.

[55] P. Fu, “Reverse Engineering in Aerospace Industry,” in Springer Series in Advanced

Manufacturing, London, Springer, 2008, pp. 157-175.

[56] J. McDonald, C. Ryall and D. Wimpenny, Rapid Prototyping Casebook, Suffolk: Professional

Engineering Publishing, 2001.

[57] J. Tao and K. Jiyong, “A 3-D point sets registration method in reverse engineering,”

Computers & Industrial Engineering, vol. 53, no. 2, pp. 270-276, 2007.

[58] C. H. Menq and K. C. Sahoo, “Localization of 3D objects using surface representation and

tactile sensing,” in Symp. Computer Aided Design Manufact. of Dies and Molds, Chicago,

1988.

[59] C. H. Menq, H. T. Yau and G. Y. Lai, “Automated precision measurement of surface profile in

CAD-directed inspection,” Transactions on Robotics and Automation, vol. 8, no. 2, pp. 268-

278, 1992.

286

[60] X. Huang, P. Gu and R. Zernicke, “Localization and comparison of two free-form surfaces,”

Computer-Aided Design, vol. 26, no. 12, pp. 1017-1022, 1996.

[61] O. Faugeras and M. Hebert, “The Representation, Recognition, and Locating of 3-D Objects,”

The International Journal of Robotics Research, vol. 5, no. 3, pp. 27-52, 1986.

[62] B. K. P. Horn, “Closed-form solution of absolute orientation using unit quaternions,” Journal

of the Optical Society of America A, vol. 4, no. 4, pp. 629-642, 1987.

[63] P. J. Besl and N. D. McKay, “A method for registration of 3-D shapes,” IEEE Transactions on

Pattern Analysis and Machine Intelligence, vol. 14, no. 2, pp. 239-256, 1992.

[64] K. S. Arun, T. S. Huang and S. D. Blostein, “Least-Squares Fitting of Two 3-D Point Sets,”

IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 9, no. 5, pp. 698-700,

1987.

[65] R. M. Haralick, H. Joo, C. N. Lee, X. Zhuang, V. G. Vaidya and M. Bae Kim, “Pose Estimation

from Corresponding Point Data,” IEEE Transactions on Systems, Man and Cybernetics, vol.

19, no. 6, pp. 1426-1446, 1989.

[66] H. Freeman, Machine Vision for Three-Dimensional Scenes, London: Academic Press Limited,

1990.

[67] Z. Li, J. Gou and Y. Chu, “Geometric algorithms for workpiece localization,” IEEE

Transactions on Robotics and Automation, vol. 14, no. 6, pp. 864-878, 1998.

[68] X. Li, M. Yeung and Z. Li, “An Algebraic Algorithm for Workpiece Localization,” in IEEE,

Minneapolis, 1998.

[69] J. Hong and X. Tan, “Method and apparatus for determining position and orientation of

mechanical objects”. US Patent US005208763A, 4 mAY 1992.

[70] Y. Xu, J. Jiang and Z. Li, “Cyclic optimisation for localisation in freeform surface inspection,”

International Journal of Production Research, vol. 49, no. 2, pp. 361-374, 2001.

[71] R. J. Campbell and P. J. Flynn, “A survey of free-form object representation and recognition

techniques,” Computer Vision and Image Understanding, vol. 81, no. 2, pp. 166-201, 2001.

[72] Y. Li and P. Gu, “Automatic localization and comparison for free-form surface inspection,”

Journal of Manufacturing Systems, vol. 25, no. 4, pp. 251-268, 2006.

287

[73] S. M. Yamany and A. A. Farag, “Surface signatures: an orientation independent free-form

surface representation scheme for the purpose of objects registration and matching,” IEEE

Transactions on Pattern and Analysis and Machine Intelligence, vol. 24, no. 8, pp. 1105-

1120, 2002.

[74] L. M. Galantucci, G. Percoco and R. Spina, “An artificial intelligence approach to registration

of free-form shapes,” CIRP Annals - Manufacturing Technology, vol. 53, no. 1, pp. 139-142,

2004.

[75] B. N. Delaunay, “Sur la sphere vide,” Bulletin of Academy of Sciences of the USSR, no. 6, pp.

793-800, 1934.

[76] D. Lee and B. Schachter, “Two algorithms for constructing a Delaunay triangulation,”

International Journal of Computer and Information Sciences, vol. 9, no. 3, pp. 219-242,

1980.

[77] L. P. Chew, “Constrained delaunay triangulations,” Algorithmica, vol. 4, no. 1, pp. 97-108,

1989.

[78] J. C. Cavendish, D. A. Field and W. H. Frey, “An apporach to automatic three-dimensional

finite element mesh generation,” International Journal for Numerical Methods in

Engineering, vol. 21, no. 2, pp. 329-347, 1985.

[79] F. Aurenhammer, “Voronoi diagrams - a survey of a fundamental geometric,” ACM

Computing Surveys, vol. 23, no. 3, pp. 345-405, 1991.

[80] C. Lawson, “Software for C1 surface interpolation,” Mathematical Software III, pp. 161-194,

1977.

[81] B. A. Lewis and J. S. Robinson, “Triangulation of planar regions with applications,” The

Computer Journal, vol. 21, no. 4, pp. 324-332, 1978.

[82] L. Guibas and J. Stolfi, “Primitives for the manipulation of general subdivisions and the

computations of Voronoi diagrams,” ACM Tmns. Graph, vol. 4, no. 2, p. 74–123, 1985.

[83] N. Golias and R. Dutton, “Delaunay triangulation and 3D adaptive mesh,” Finite elements in

analysis and design, vol. 25, no. 3-4, pp. 331-341, 1997.

[84] C. Dyken and M. S. Floater, “Preferred directions for resolving the non-uniqueness of

Delaunay triangulations,” Computational Geometry, vol. 34, no. 2, pp. 96-101, 2006.

288

[85] D. F. Watson, “Computing the n-dimensional Delaunay tessellation with application to

Voronoi polytopes,” The computer journal, vol. 24, no. 2, pp. 167-172, 1981.

[86] L. D. Angelo, P. D. Stefano and L. Giaccari, “A new mesh-growing algorithm for fast surface

reconstruction,” Computer-Aided Design, vol. 43, no. 6, pp. 639-650, 2011.

[87] K. Lee, Principles of CAD/CAM/CAE Systems, Addison-Wesley, 1999.

[88] E. Kreyszig, Advanced Engineering Mathematics, 9th ed., Hoboken: John Wiley & Sons,

2005, p. 816.

[89] I. Zeid, CAD/CAM Theory and Practice, New York: McGraw-Hill, 1991.

[90] P. E. Bezier, The Mathematical Basis of the UNIURF CAD System, London: Butterworth & Co,

1986.

[91] G. M. Sturgeon, “Surface Reconstruction from Medical Imaging for Use in a Computer-Aided

Design (CAD) Environment,” Grand Valley State University, Allendale, 2005.

[92] C. Loop, “Smooth spline surfaces over irregular meshes,” in Computer Graphics and

Interactive Techniques, New York, 1994.

[93] M. Eck and H. Hoppe, “Automatic reconstruction of B-spline Surfaces of arbitrary topological

type,” in Computer graphics and interactive techniques, New York, 1996.

[94] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald and W. Stuetzle, “Surface reconstruction

from unorganized,” in Computer graphics and interactive techniques, New York, 1992.

[95] H. Hoppe, T. DeRose, T. Duchamp, M. J. and W. Stuetzle, “Mesh optimization,” in Computer

graphics and interactive techniques, New York, 1993.

[96] Y. L. a, X. Huang, C. Gong and K. Wang, “An Engineering Rules based Parameterization

Approach for Turbine Blade Reverse Engineering,” in Geometric Modeling and Processing,

Beijing, 2004.

[97] C.Y. Lin, C.S. Liou and J.Y. Lai, “A surface-lofting approach for smooth-surface

reconstruction from 3D measurement data,” Computers in Industry, vol. 34, pp. 73-85 ,

1997.

[98] H. Haron, A. Rehman, D. I. S. Adi, S. P. Lim and T. Saba, “Parameterization method on B-

spline curve,” Mathematical Problems in Engineering, vol. 2012, p. 22, 2012.

289

[99] J. Fang and C. Huang, “An improved parameterization method for B-spline curve and surface

interpolation,” Computer-aided design, vol. 45, no. 6, pp. 1005-1028, 2013.

[100] M. Floater, “Parameterization and smooth approximation of surface,” Computer Aided

Geometric Design, vol. 14, no. 3, pp. 231-250, 1997.

[101] K. Hormann, B. Levy and A. Sheffer, “Mesh Parameterization: Theory and Practice,”

Siggraph, 2007.

[102] T. Ju, “Barycentric Coordinates with Applications in Mesh Deformation,” Washington

University in St. Louis, 2007. [Online]. Available:

http://www.cs.wustl.edu/~taoju/research/bary.htm. [Accessed 22 February 2016].

[103] M. Eck, T. D. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery and W. Stuetzle,

“Multiresolution analysis of arbitrary meshes,” in Computer graphics and interactive

techniques, New York, 1995.

[104] M. S. Floater, “Mean value coordinates,” Computer Aided Geometric Design, vol. 20, no. 1,

pp. 19-27, 2003.

[105] V. Paquin, X. Maldague and M. Akhloufi, “A vision-based method for improving absolute

positioning accuracy of industrial robots,” in Applied Vision and Robotics Workshop,

Montreal, 2012.

[106] A. Joubair and I. A. Bonev, “Kinematic calibration of a six-axis serial robot using distance

and sphere constraints,” Int J Adv Manuf Technol, vol. 77, no. 1, p. 515–523, 2015.

[107] SKF Group, “Recommended fits,” [Online]. Available: www.skf.com/sg/products/bearings-

units-housings/roller-bearings/principles/design-considerations/radial-location-

bearings/recommended-fits/index.html. [Accessed 24 January 2016].

[108] Parker Hannifin Corporation, “Rotatry Seal Design Guide,” 2006. [Online]. Available:

http://www.parker.com/literature/Engineered%20Polymer%20Systems/5350.pdf. [Accessed

25 January 2016].

[109] Parker Hannifin Corporation, “Parker O-Ring Handbook,” 2007. [Online]. Available:

https://www.parker.com/literature/ORD%205700%20Parker_O-Ring_Handbook.pdf.

[Accessed 25 January 2016].

[110] The International Nickel Company, Inc., “Properties of Some Metal and Alloys,” 1982.

[Online]. Available: http://www.nickelinstitute.org/~/media/files/technicalliterature/

290

propertiesofsomemetalsandalloys_297_.pdf. [Accessed 26 January 2016].

[111] Special Metals Corporation, “Inconel Alloy,” 7 September 2007. [Online]. Available:

http://www.specialmetals.com/documents/Inconel%20alloy%20718.pdf. [Accessed 26

January 2016].

[112] FANUC Corporation, “FANUC LR Mate 200iD Operator's Manual,” 2012.

[113] FANUC Corporation, “FANUC Robot LR Mate 200iD,” UK, 2012.

[114] A. Nakanishi, H. Nakazawa, K. Yamashima, T. Shiraiwa and H. Yamaguchi, “Immersion

ultrasonic inspection system of the whole surface of rolled flat bar”. Patent US3850027A, 26

November 1974.

[115] R. H. Lumsden, “Passive bubble minimization in ultrasonic testing”. Patent

WO2014153669A1, 2 October 2014.

[116] NDT Education, “Refraction and Snell's Law,” [Online]. Available: www.ndt-

ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/refractionsnells.htm.

[Accessed 18 February 2016].

[117] Columbia College, “Physical attributes of acoustic waves - Part I,” Audio Arts & Acoustics,

Columbia College Chicago, [Online]. Available:

acousticslab.org/psychoacoustics/PMFiles/Module02.htm. [Accessed 18 February 2016].

[118] J. Hoschek and R. Muller, “Turbine blade design by lofted B-spline surfaces,” Journal of

Computational and Applied Mathematics, vol. 119, pp. 235-248, 2000.

[119] Y. Liu, S. Zhao and X. Dong, “Constructing section profile curve of turbine blade,” in 2010

International Conference on Wavelet Analysis and Pattern Recognition, Qingdao, 2010.

[120] N. Amenta, S. Choi and R. Kolluri, “The power crust,” in ACM symposium on Solid modeling

and applications, New York, 2001.

[121] Mathworks, “Delaunay triangulation,” Mathworks, 2016. [Online]. Available:

http://uk.mathworks.com/help/matlab/ref/delaunay.html. [Accessed 25 February 2016].

[122] Mathworks, “Solve systems of linear equations Ax = B for x,” Mathworks, 2016. [Online].

Available: http://uk.mathworks.com/help/matlab/ref/mldivide.html. [Accessed 23 February

2016].

291

[123] W. Lü, “Curves with chord length parameterization,” Computer Aided Geometric Design, vol.

26, no. 3, pp. 342-350, 2009.

[124] W. Welch and A. Witkin, “Free-form shape design using triangulated surfaces,” in 21st

annual conference on Computer graphics and interactive techniques, Orlando, 1994.

[125] Mathworks, “k-nearest neighbors search using Kd-tree or exhaustive search,” Mathworks,

2016. [Online]. Available: http://uk.mathworks.com/help/stats/searcher.knnsearch.html.

[Accessed 22 Feb 2016].

[126] K. T. Gunnarson and P. F. B, “CAD model based localization of parts in manufacturing,”

Computer, vol. 20, no. 8, pp. 66-74, 1987.

[127]

J. Dexclaux and J. Serre, “M88-2 E4: Advanced New Generation Engine for Rafale Multirole

Fighter,” in AIAA International Air and Space Symposium and Exposition: The Next 100

Years, Dayton, 2003.

292

Ultrasonic testing results for Chapter 6.1 “Effect of varying water path” are presented here.

Thickness = 0.666mm

Table I-1 Variations of amplitudes of the first backwall echo

WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 144 153 162 182 208 252 255 255 255 255 255

30 147 153 163 182 209 254 249 255 255 255 255

28 147 153 164 185 213 255 255 255 255 255 255

26 146 153 163 184 210 248 255 255 255 255 255

25 147 153 163 185 214 254 255 255 255 255 255

24 147 154 164 186 214 253 255 255 255 255 255

23 147 154 163 186 215 253 255 255 255 255 255

22 147 154 165 187 217 255 255 255 255 255 255

21 147 154 164 187 215 255 255 255 255 255 255

20 147 154 164 185 213 255 255 255 255 255 255

19 147 154 164 186 215 255 255 255 255 255 255

18 147 154 164 185 214 255 255 255 255 255 255

17 147 153 163 184 212 253 255 254 255 255 255

16 145 152 161 181 205 251 255 255 255 255 255

15 145 151 160 179 205 252 255 255 255 255 255

14 145 151 159 177 200 251 255 255 255 255 255

12 144 148 155 170 192 235 255 255 255 255 255

10 143 147 153 162 182 220 255 255 255 255 255

8 144 148 154 167 188 226 255 255 255 255 255

6 143 147 154 168 188 229 255 255 255 255 255

4 141 143 146 154 165 192 234 255 255 255 255

Table I-2 Variations of amplitudes of the second backwall echo

WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 142 149 156 168 188 226 255 255 255 255 255

30 145 149 156 168 188 227 249 255 255 255 255

28 145 149 156 169 189 229 255 255 255 255 255

26 145 149 156 169 188 222 255 255 255 255 255

25 145 150 157 169 191 230 255 255 255 255 255

24 145 150 157 172 192 229 254 255 255 255 255

23 145 150 157 171 194 233 255 255 255 255 255

22 145 150 158 172 195 239 255 255 255 255 255

21 145 150 157 171 193 235 255 255 255 255 255

20 145 150 157 171 192 236 255 255 255 255 255

19 145 150 157 172 194 237 255 255 255 255 255

18 145 150 158 173 194 237 255 255 255 255 255

293

17 146 150 158 173 194 234 255 254 255 255 255

16 144 150 156 171 189 229 255 255 255 255 255

15 145 149 156 171 190 232 254 255 255 255 255

14 145 149 157 171 188 232 255 255 255 254 255

12 144 148 154 166 184 222 255 255 255 255 255

10 143 146 151 159 175 205 252 255 255 255 255

8 142 144 148 156 169 190 233 255 255 255 255

6 141 143 146 153 162 182 218 253 255 255 255

4 139 140 142 147 154 170 194 241 255 255 255

Table I-3 Variations of amplitudes of the interface echo

WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 182 255 255 255 255 254 255 255 255 255 255

30 211 254 255 255 255 255 245 255 255 255 255

28 214 255 255 255 255 255 255 255 254 255 255

26 206 254 254 255 254 250 255 255 253 254 255

25 215 255 255 255 255 255 255 255 255 255 255

24 218 255 255 255 255 255 253 254 254 255 255

23 221 255 255 255 255 255 250 252 255 255 255

22 220 255 255 255 255 255 255 255 255 255 255

21 221 255 255 255 255 255 255 255 255 255 255

20 212 255 255 255 255 255 255 255 255 255 255

19 221 255 255 255 255 255 255 255 255 255 255

18 223 255 255 255 255 255 255 255 255 255 255

17 220 255 255 255 255 255 255 254 255 255 255

16 206 255 255 255 255 255 255 255 255 254 255

15 213 255 255 255 255 255 255 255 255 255 255

14 213 255 255 255 255 255 255 255 255 254 255

12 203 248 255 255 255 255 255 254 255 255 255

10 202 249 255 253 255 255 255 255 252 255 255

8 191 233 255 255 255 255 255 255 255 254 255

6 184 223 255 255 255 255 255 255 255 255 255

4 177 207 254 255 255 255 255 255 255 255 255

Table I-4 Variations of interpreted time of flight

WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 24 24 24 24 24 24 24 24 24 24 24

30 23 24 24 23 23 23 24 23 23 24 24

28 23 23 23 23 23 23 23 23 24 23 24

26 23 23 23 23 23 23 23 24 23 24 23

25 23 24 23 23 23 23 23 24 24 24 24

24 23 23 23 23 23 23 23 23 24 24 24

23 23 23 23 23 23 23 23 23 23 23 23

22 24 24 24 24 24 24 24 24 24 24 24

21 23 23 23 23 23 23 23 23 23 23 24

294

20 24 24 24 23 24 23 24 24 24 24 24

19 23 23 23 23 23 23 23 23 23 23 23

18 24 24 24 24 24 24 24 24 24 24 24

17 24 24 24 24 24 24 24 24 25 24 24

16 22 23 23 23 23 23 23 23 23 23 23

15 23 24 23 23 23 23 24 24 24 24 24

14 24 24 24 24 24 24 24 24 24 25 24

12 24 24 24 24 24 24 23 24 24 24 24

10 23 23 23 23 23 23 23 23 23 23 23

8 23 23 23 23 23 23 23 23 23 24 23

6 23 23 23 23 23 23 23 24 24 23 24

4 23 23 24 24 24 24 24 23 24 23 23

Thickness = 1.024mm


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 146 151 160 177 203 252 255 255 255 255 255

30 146 152 161 178 200 243 255 255 255 255 255

28 146 151 160 178 205 249 255 255 255 254 253

26 144 151 154 177 182 243 243 238 255 255 255

25 146 153 160 182 206 254 255 254 254 255 252

24 147 153 162 182 210 254 255 255 254 254 255

23 146 152 162 184 199 240 255 255 255 255 255

22 147 153 163 184 212 255 238 255 255 255 252

21 147 154 163 183 210 254 255 255 255 255 255

20 147 154 163 182 210 255 255 255 255 255 255

19 147 154 163 184 213 255 255 255 255 255 255

18 148 154 163 183 213 255 255 255 255 255 255

17 147 154 163 183 212 255 255 255 255 255 255

16 147 153 162 181 208 254 255 255 255 255 255

15 147 153 163 182 210 254 255 255 255 255 255

14 147 153 162 180 207 255 255 255 255 255 255

12 146 151 160 177 202 251 255 255 255 255 255

10 145 149 157 171 191 233 255 255 255 255 255

8 144 148 154 166 184 219 255 255 255 255 255

6 142 145 150 159 173 202 250 255 255 255 255

4 140 142 146 153 163 187 228 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 145 150 158 174 197 242 255 255 255 255 255

30 145 150 157 173 192 234 255 255 255 255 255

28 145 150 158 173 198 242 255 255 255 254 250

26 143 150 152 171 178 234 249 245 255 255 255

295

25 145 150 156 173 192 238 255 255 255 255 252

24 145 150 158 174 198 243 255 255 255 255 255

23 145 149 157 174 186 224 255 255 255 253 255

22 146 151 159 174 198 245 244 255 255 255 251

21 146 151 159 175 199 247 255 255 255 255 255

20 146 151 159 175 198 246 255 255 255 255 255

19 145 151 158 175 197 243 255 255 255 255 255

18 145 150 158 174 196 242 255 255 255 255 255

17 145 151 158 174 197 245 255 255 255 253 252

16 145 151 158 174 195 241 255 255 255 255 255

15 145 150 158 173 195 241 255 255 255 254 255

14 145 150 158 173 194 237 255 255 255 255 251

12 145 149 156 170 189 228 255 255 255 255 255

10 144 148 155 167 186 221 254 255 255 255 255

8 143 146 152 164 180 211 254 255 255 255 255

6 142 145 149 158 170 198 242 255 255 255 255

4 140 142 145 150 159 179 213 254 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 204 249 255 255 255 255 254 255 255 253 255

30 209 254 255 255 249 248 254 255 252 251 252

28 205 245 254 255 255 255 255 255 255 249 239

26 186 244 241 253 237 243 234 232 253 255 255

25 206 255 251 255 254 255 255 254 253 254 243

24 215 255 255 255 255 255 255 255 254 253 255

23 209 244 254 255 253 247 255 255 254 255 255

22 222 255 255 255 255 255 231 255 255 255 243

21 223 255 255 255 255 255 255 255 255 255 255

20 221 255 255 255 255 255 255 255 255 255 255

19 217 255 255 255 255 255 255 255 255 255 255

18 217 255 255 255 255 255 255 255 255 255 255

17 214 255 255 255 255 255 255 255 255 255 255

16 215 255 255 255 255 255 255 255 255 255 255

15 210 255 255 255 255 255 255 255 255 255 255

14 209 254 255 255 255 255 255 255 255 255 255

12 206 253 255 255 255 255 255 255 255 255 255

10 201 247 255 255 255 255 255 255 255 255 255

8 195 236 255 255 255 255 255 255 255 255 255

6 187 224 255 255 255 255 255 255 255 255 255

4 177 205 254 255 255 255 255 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 39 38 38 38 38 38 38 38 38 38 38

296

30 38 38 38 38 38 38 38 38 38 38 38

28 38 38 37 37 37 37 37 37 38 38 38

26 38 38 37 37 37 37 38 38 38 37 37

25 38 38 38 38 38 38 38 38 39 38 38

24 38 38 38 38 38 38 38 38 38 38 38

23 38 38 38 38 38 38 38 38 38 38 38

22 38 38 38 38 38 38 39 39 38 38 39

21 39 39 39 38 38 38 39 38 39 38 38

20 39 39 39 39 38 39 38 39 39 38 38

19 38 38 38 38 38 38 38 38 38 38 38

18 38 38 38 38 38 38 38 38 38 38 38

17 38 38 38 38 38 38 38 38 38 38 38

16 37 38 37 37 37 37 37 38 37 38 38

15 37 38 38 38 38 38 38 38 38 38 38

14 38 38 38 38 38 38 38 38 38 38 38

12 37 37 37 37 37 37 37 37 37 37 37

10 38 38 38 38 38 38 38 38 38 38 38

8 38 38 38 38 38 38 38 38 38 38 38

6 38 38 38 38 38 38 38 38 38 38 38

4 38 38 38 38 38 38 38 38 38 38 38

Thickness = 2.031mm


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 145 150 158 174 196 242 255 255 255 255 255

30 145 151 158 174 198 244 255 255 255 255 255

28 146 151 159 175 198 247 255 255 255 255 255

26 146 152 161 178 203 253 255 255 255 255 255

25 146 152 160 177 202 250 255 255 255 255 255

24 146 152 160 177 201 251 255 255 255 255 255

23 146 152 160 177 202 252 255 255 255 255 255

22 146 152 160 178 203 251 255 255 255 255 255

21 146 152 161 179 205 254 255 255 255 255 255

20 146 152 160 178 200 252 255 255 255 255 255

19 146 153 162 180 206 254 255 255 255 255 255

18 146 152 161 179 205 253 255 255 255 255 255

17 147 153 162 179 206 253 255 255 255 255 255

16 146 152 161 178 203 252 255 255 255 255 255

15 146 152 161 179 205 253 255 255 255 255 255

14 145 151 160 176 201 248 255 255 255 255 255

12 145 150 159 175 197 244 255 255 255 255 255

10 144 149 157 172 193 232 255 255 255 255 255

8 144 148 155 168 187 226 255 255 255 255 255

6 142 145 150 160 174 204 252 255 255 255 255

4 140 142 145 152 162 184 223 255 255 255 255

297


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 143 147 153 164 181 215 255 255 255 255 255

30 144 148 153 165 182 217 254 255 255 255 255

28 144 148 154 166 185 220 255 255 255 255 255

26 144 148 154 167 186 225 255 255 255 255 255

25 144 148 155 167 186 225 255 255 255 255 255

24 144 148 154 167 186 224 255 255 255 255 255

23 144 149 155 167 187 227 255 255 255 255 255

22 144 149 155 168 186 223 255 255 255 255 255

21 144 149 155 168 188 227 255 255 255 255 255

20 144 149 155 168 185 226 255 255 255 255 255

19 144 149 155 169 188 227 255 255 255 255 255

18 144 149 155 169 188 228 255 255 255 255 255

17 144 149 155 168 188 227 255 255 255 255 255

16 144 149 156 168 187 225 255 255 255 255 255

15 145 149 155 169 188 226 255 255 255 255 255

14 144 148 155 168 186 225 255 255 255 255 255

12 144 148 155 167 186 223 255 255 255 255 255

10 144 147 154 165 182 216 255 255 255 255 255

8 143 146 152 164 180 214 255 255 255 255 255

6 142 145 149 159 172 201 248 255 255 255 255

4 141 142 146 153 164 187 227 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 209 254 255 255 255 255 255 255 255 255 255

30 213 255 255 255 255 255 255 255 255 255 255

28 215 255 255 255 255 255 255 255 255 255 255

26 214 255 255 255 255 255 255 255 255 255 255

25 217 255 255 255 255 255 255 255 255 255 255

24 216 255 255 255 255 255 255 255 255 255 255

23 221 255 255 255 255 255 255 255 255 255 255

22 220 255 255 255 255 255 255 255 255 255 255

21 217 255 255 255 255 255 255 255 255 255 255

20 219 255 255 255 250 255 255 255 255 255 255

19 219 255 255 255 255 255 255 255 255 255 255

18 216 255 255 255 255 255 255 255 255 255 255

17 220 255 255 255 255 255 255 255 255 255 255

16 213 255 255 255 255 255 255 255 255 255 255

15 215 255 255 255 255 255 255 255 255 255 255

14 203 255 255 255 255 255 255 255 255 255 255

12 205 255 255 255 255 255 255 255 255 255 255

10 199 247 255 255 255 255 255 255 255 255 255

298

8 193 233 255 255 255 255 255 255 255 255 255

6 186 223 255 255 255 255 255 255 255 255 255

4 177 206 251 255 255 255 255 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 68 68 68 68 68 68 67 68 68 68 68

30 68 69 69 69 68 68 69 68 69 69 69

28 67 68 68 67 68 67 67 68 68 68 68

26 68 68 68 68 68 68 68 68 68 69 69

25 68 68 68 68 68 68 67 68 68 68 68

24 68 68 68 67 67 67 67 68 68 68 68

23 67 68 68 68 68 68 68 68 68 68 68

22 67 68 68 68 68 67 67 67 68 68 68

21 68 68 68 68 68 68 68 68 68 68 68

20 67 68 68 68 68 68 67 68 68 68 68

19 67 68 68 68 68 68 68 68 68 68 68

18 67 68 68 68 68 68 67 68 68 68 68

17 68 68 68 68 68 68 68 68 68 68 68

16 68 68 68 68 68 68 67 68 68 68 68

15 68 68 68 68 68 68 68 68 69 69 69

14 68 69 68 68 68 68 68 69 69 69 68

12 69 68 69 68 68 68 68 69 69 69 69

10 68 68 68 68 68 67 67 67 68 68 68

8 67 67 67 67 67 67 67 67 67 68 67

6 68 69 68 68 68 68 68 68 69 69 69

4 68 68 68 68 68 68 68 68 68 68 68

Thickness = 2.955mm


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 145 149 156 169 190 231 255 255 255 255 255

30 145 149 156 171 192 233 255 255 255 255 255

28 145 150 157 171 193 234 255 255 255 255 255

26 145 150 158 173 196 241 255 255 255 255 255

25 145 150 158 173 196 241 255 255 255 255 255

24 145 150 157 173 195 240 255 255 255 255 255

23 146 151 158 174 197 243 255 255 255 255 255

22 146 150 158 174 197 242 255 255 255 255 255

21 146 151 158 173 195 240 255 255 255 255 255

20 145 150 158 174 197 242 255 255 255 255 255

19 145 151 159 174 198 244 255 255 255 255 255

18 145 151 158 174 197 242 255 255 255 255 255

17 146 150 158 173 197 241 255 255 255 255 255

299

16 145 150 158 173 196 241 255 255 255 255 255

15 145 150 158 173 195 238 255 255 255 255 255

14 145 150 158 176 199 246 255 255 255 255 255

12 146 150 158 174 197 242 255 255 255 255 255

10 145 150 158 173 195 237 255 255 255 255 255

8 144 148 155 168 187 225 255 255 255 255 255

6 143 146 151 163 178 212 255 255 255 255 255

4 141 143 147 155 168 193 238 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 143 146 151 161 177 208 253 255 255 255 255

30 143 146 151 162 177 208 254 255 255 255 255

28 143 146 152 162 179 211 255 255 255 255 255

26 143 147 152 164 179 212 254 255 255 255 255

25 143 147 152 164 180 214 254 255 255 255 255

24 143 147 152 163 180 211 255 255 255 255 255

23 143 147 152 164 181 215 255 255 255 255 255

22 142 147 152 164 179 212 254 255 255 255 255

21 143 147 152 164 181 215 254 255 255 255 255

20 143 147 152 164 181 215 255 255 255 255 255

19 144 147 153 164 181 214 254 255 255 255 255

18 143 147 152 164 180 213 255 255 255 255 255

17 143 147 152 164 180 214 255 255 255 255 255

16 143 147 152 163 179 212 254 255 255 255 255

15 143 147 152 163 179 212 254 255 255 255 255

14 143 147 153 165 182 217 255 255 255 255 255

12 144 147 153 165 181 216 255 255 255 255 255

10 143 147 153 164 181 215 255 255 255 255 255

8 143 146 151 162 178 209 254 255 255 255 255

6 142 145 149 159 172 200 248 255 255 255 255

4 141 143 146 153 164 188 227 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 204 255 255 255 255 255 255 255 255 255 255

30 209 255 255 255 255 255 255 255 255 255 255

28 209 255 255 255 255 255 255 255 255 255 255

26 203 255 255 255 255 255 255 255 255 255 255

25 210 255 255 255 255 255 255 255 255 255 255

24 214 255 255 255 255 255 255 255 255 255 255

23 217 255 255 255 255 255 255 255 255 255 255

22 217 255 255 255 255 255 255 255 255 255 255

21 218 255 255 255 255 255 255 255 255 255 255

20 215 255 255 255 255 255 255 255 255 255 255

300

19 214 255 255 255 255 255 255 255 255 255 255

18 211 255 255 255 255 255 255 255 255 255 255

17 214 255 255 255 255 255 255 255 255 255 255

16 209 255 255 255 255 255 255 255 255 255 255

15 208 255 255 255 255 255 255 255 255 255 255

14 204 254 255 255 255 255 255 255 255 255 255

12 208 254 255 255 255 255 255 255 255 255 255

10 204 251 255 255 255 255 255 255 255 255 255

8 197 240 255 255 255 255 255 255 255 255 255

6 189 227 255 255 255 255 255 255 255 255 255

4 177 210 255 255 255 255 255 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 100 100 99 99 99 99 99 99 100 100 100

30 100 100 100 100 100 100 100 100 100 100 100

28 99 99 99 99 99 99 99 99 99 99 99

26 99 100 100 100 100 100 99 100 100 100 100

25 100 100 100 100 100 100 99 100 100 100 100

24 99 99 99 99 99 99 99 99 100 100 100

23 100 100 100 100 100 100 100 100 100 100 100

22 100 100 99 99 99 99 99 100 100 100 100

21 100 100 100 100 100 100 99 100 100 100 100

20 99 99 99 99 99 99 99 99 100 100 100

19 100 100 100 100 100 100 100 100 100 100 100

18 99 99 99 99 99 99 99 99 100 100 100

17 100 100 100 100 100 100 100 100 100 100 100

16 99 99 99 99 99 99 99 99 100 100 100

15 100 100 100 100 100 100 100 100 100 100 100

14 99 99 99 99 100 100 99 100 100 100 100

12 99 100 100 99 100 99 99 100 100 100 100

10 100 100 100 100 100 100 100 100 100 100 100

8 100 100 100 100 100 100 100 101 101 100 100

6 100 100 99 99 99 99 99 99 100 100 100

4 100 100 100 99 99 99 99 99 100 100 100

Thickness = 4.161mm


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 144 149 156 171 192 234 255 255 255 255 255

30 145 150 157 172 194 237 255 255 255 255 255

28 145 150 157 172 194 238 255 255 255 255 255

26 145 150 157 172 194 237 255 255 255 255 255

25 145 150 157 172 195 238 255 255 255 255 255

301

24 145 150 157 173 196 240 255 255 255 255 255

23 145 150 157 172 195 239 255 255 255 255 255

22 145 150 158 174 196 241 255 255 255 255 255

21 145 150 157 173 195 239 255 255 255 255 255

20 145 151 158 173 195 239 255 255 255 255 255

19 145 150 157 172 195 238 255 255 255 255 255

18 145 151 158 173 195 238 255 255 255 255 255

17 145 151 158 174 196 242 255 255 255 255 255

16 145 151 158 174 196 242 255 255 255 255 255

15 145 150 157 172 194 235 255 255 255 255 255

14 145 150 158 173 195 238 255 255 255 255 255

12 144 150 157 172 193 234 255 255 255 255 255

10 144 149 157 171 192 232 255 255 255 255 255

8 144 148 154 167 186 223 255 255 255 255 255

6 143 147 152 164 180 212 255 255 255 255 255

4 142 144 148 157 170 197 245 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 144 147 153 165 183 219 255 255 255 255 255

30 143 147 154 165 183 220 255 255 255 255 255

28 144 147 153 165 182 218 255 255 255 255 255

26 144 148 153 166 183 217 255 255 255 255 255

25 143 147 153 165 181 217 254 255 255 255 255

24 143 148 153 165 183 219 255 255 255 255 255

23 144 148 153 165 183 219 255 255 255 255 255

22 144 148 153 165 183 218 255 255 255 255 255

21 143 147 153 165 182 216 254 255 255 255 255

20 144 147 153 165 182 218 255 255 255 255 255

19 144 147 153 164 180 214 255 255 255 255 255

18 143 147 153 165 181 217 255 255 255 255 255

17 144 147 153 164 181 216 254 255 255 255 255

16 143 147 153 164 180 213 254 255 255 255 255

15 143 147 152 163 178 211 253 255 255 255 255

14 143 146 152 163 178 209 254 253 255 255 255

12 143 146 151 161 176 206 252 255 255 255 255

10 143 146 151 161 174 204 251 255 255 255 255

8 142 145 149 158 171 196 240 255 255 255 255

6 142 144 148 156 167 190 230 255 255 255 255

4 140 142 146 152 162 183 218 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 210 255 255 255 255 255 255 255 255 255 255

30 208 255 255 255 255 255 255 255 255 255 255

302

28 215 255 255 255 255 255 255 255 255 255 255

26 215 255 255 255 255 255 255 255 255 255 255

25 218 255 255 255 255 255 255 255 255 255 255

24 215 255 255 255 255 255 255 255 255 255 255

23 217 255 255 255 255 255 255 255 255 255 255

22 224 255 255 255 255 255 255 255 255 255 255

21 219 255 255 255 255 255 255 255 255 255 255

20 220 255 255 255 255 255 255 255 255 255 255

19 220 255 255 255 255 255 255 255 255 255 255

18 222 255 255 255 255 255 255 255 255 255 255

17 220 255 255 255 255 255 255 255 255 255 255

16 216 255 255 255 255 255 255 255 255 255 255

15 213 255 255 255 255 255 255 255 255 255 255

14 212 255 255 255 255 255 255 255 255 255 255

12 203 254 255 255 255 255 255 255 255 255 255

10 200 248 255 255 255 255 255 255 255 255 255

8 192 235 255 255 255 255 255 255 255 255 255

6 185 220 255 255 255 255 255 255 255 255 255

4 178 209 255 255 255 255 255 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 134 134 134 134 134 134 134 134 134 134 134

30 134 134 134 134 134 134 134 134 134 134 134

28 134 134 134 134 134 134 134 134 135 134 134

26 134 134 134 134 134 134 133 134 134 134 134

25 134 134 134 134 134 134 134 134 135 134 135

24 134 134 134 134 134 134 134 134 134 134 134

23 134 134 134 134 134 134 133 134 134 134 134

22 134 134 134 134 134 134 133 134 134 134 134

21 133 134 133 133 133 133 133 133 134 134 134

20 134 134 134 134 134 134 133 134 134 134 134

19 133 133 133 133 133 133 133 133 134 134 134

18 134 134 134 134 134 134 133 134 134 134 134

17 134 134 134 134 134 134 134 134 134 134 134

16 133 133 133 133 133 133 133 133 134 133 133

15 133 134 134 134 133 133 134 133 134 134 134

14 134 134 134 134 134 134 134 134 134 135 135

12 133 133 133 133 133 133 133 133 134 134 134

10 134 134 134 134 134 134 134 134 134 134 134

8 133 134 134 134 133 133 133 133 134 134 133

6 134 134 134 134 134 134 134 134 134 134 134

4 133 133 134 133 133 133 133 133 134 134 134

303

Thickness = 6.174mm


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 144 147 153 165 182 217 255 255 255 255 255

30 144 147 153 165 183 218 255 255 255 255 255

28 144 148 154 165 182 218 255 255 255 255 255

26 144 148 153 165 183 218 255 255 255 255 255

25 144 148 153 165 182 218 255 255 255 255 255

24 144 147 153 164 181 215 254 255 255 255 255

23 144 147 153 165 182 216 255 255 255 255 255

22 144 148 153 165 181 216 255 255 255 255 255

21 144 147 153 164 181 216 254 255 255 255 255

20 143 147 153 165 181 217 254 255 255 255 255

19 144 147 152 164 180 214 255 255 255 255 255

18 143 147 153 164 181 216 255 255 255 255 255

17 143 147 153 164 180 215 254 255 255 255 255

16 143 147 153 164 180 215 255 255 255 255 255

15 144 147 153 163 180 215 254 255 255 255 255

14 143 147 152 163 178 211 255 255 255 255 255

12 143 146 151 161 176 206 253 255 255 255 255

10 143 146 150 160 174 203 250 255 255 255 255

8 142 145 150 159 172 198 245 255 255 255 255

6 142 144 148 156 169 192 233 255 255 255 255

4 140 142 145 152 161 182 218 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 141 143 146 153 163 183 216 254 255 255 255

30 141 144 147 154 163 185 216 253 255 255 255

28 142 144 147 154 164 185 219 254 255 255 255

26 142 144 147 154 164 184 218 254 255 255 255

25 141 144 147 154 164 184 220 253 255 255 255

24 142 144 147 153 164 183 219 255 255 255 255

23 141 144 147 154 164 185 219 254 255 255 255

22 142 144 147 153 163 184 219 254 255 255 255

21 142 144 147 153 163 185 219 253 255 255 255

20 141 144 147 153 163 182 216 253 255 255 255

19 141 144 147 153 163 184 219 254 255 255 255

18 141 144 147 153 163 184 221 254 255 255 255

17 141 143 147 153 163 183 219 255 255 255 255

16 141 144 147 153 162 182 216 253 255 255 255

15 141 144 147 153 163 183 218 252 255 255 255

14 141 143 147 152 161 180 213 252 255 255 255

12 141 143 146 152 161 179 213 253 255 255 255

304

10 141 143 146 151 160 176 206 250 255 255 255

8 140 142 145 150 158 175 201 243 254 255 255

6 139 142 144 148 155 168 193 229 255 255 255

4 139 141 143 148 155 168 193 228 254 254 254


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 206 255 255 255 255 255 255 255 255 255 255

30 211 255 255 255 255 255 255 255 255 255 255

28 211 255 255 255 255 255 255 255 255 255 255

26 214 255 255 255 255 255 255 255 255 255 255

25 219 255 255 255 255 255 255 255 255 255 255

24 215 255 255 255 255 255 255 255 255 255 255

23 218 255 255 255 255 255 255 255 255 255 255

22 219 255 255 255 255 255 255 255 255 255 255

21 220 255 255 255 255 255 255 255 255 255 255

20 221 255 255 255 255 255 255 255 255 255 255

19 221 255 255 255 255 255 255 255 255 255 255

18 217 255 255 255 255 255 255 255 255 255 255

17 216 255 255 255 255 255 255 255 255 255 255

16 221 255 255 255 255 255 255 255 255 255 255

15 214 255 255 255 255 255 255 255 255 255 255

14 215 255 255 255 255 255 255 255 255 255 255

12 206 254 255 255 255 255 255 255 255 255 255

10 201 247 255 255 255 255 255 255 255 255 255

8 196 239 255 255 255 255 255 255 255 255 255

6 188 226 255 255 255 255 255 255 255 255 255

4 179 210 255 255 255 255 255 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 208 207 207 207 207 207 207 207 208 208 207

30 207 207 207 207 207 207 207 207 207 208 208

28 207 207 207 207 207 207 207 207 207 207 207

26 207 207 207 207 207 207 207 207 207 207 207

25 207 207 207 207 207 207 207 207 208 208 208

24 207 207 207 207 207 207 206 207 207 207 207

23 206 206 206 206 206 206 206 206 207 207 207

22 207 207 207 207 207 207 207 206 207 207 207

21 206 206 206 206 206 206 206 206 207 207 207

20 206 207 207 207 207 207 207 206 207 207 207

19 206 206 206 206 206 206 206 206 207 207 207

18 207 206 206 206 206 206 206 206 207 207 207

17 207 207 207 207 207 207 206 207 207 207 207

16 207 207 207 207 207 207 207 206 207 207 207

305

15 206 206 206 206 206 206 206 206 206 207 207

14 207 207 207 207 207 207 207 206 207 207 207

12 207 207 206 206 206 206 206 206 206 207 207

10 207 207 207 206 206 206 206 206 207 207 207

8 207 207 207 207 207 207 207 207 207 207 207

6 206 206 206 206 206 206 206 206 206 206 206

4 206 206 206 206 206 206 206 206 206 207 207

Thickness = 8.271mm


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 141 144 147 153 164 184 222 254 255 255 255

30 141 143 147 153 164 184 220 253 255 255 255

28 141 144 147 153 164 185 222 253 255 255 255

26 141 144 147 154 164 186 222 254 255 255 255

25 141 144 147 153 163 184 220 254 255 255 255

24 141 144 147 153 163 183 218 254 255 255 255

23 141 144 147 154 163 184 219 254 255 255 255

22 141 143 146 152 162 181 215 253 255 255 255

21 141 144 146 152 161 181 211 253 255 255 255

20 141 143 146 152 161 179 212 253 255 255 255

19 141 143 146 152 161 178 211 253 255 255 255

18 141 143 146 152 161 180 212 252 255 255 255

17 141 144 146 152 161 179 211 252 255 255 255

16 141 143 146 151 160 178 209 251 255 255 255

15 141 143 146 152 161 178 210 253 255 255 255

14 141 143 146 151 160 178 207 250 255 255 255

12 141 143 145 151 158 176 205 247 255 255 255

10 141 142 145 151 159 174 201 244 255 255 255

8 140 142 144 149 157 171 197 236 255 255 255

6 140 141 143 148 155 168 193 231 255 255 255

4 139 140 142 145 151 162 182 216 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 140 140 141 143 146 153 164 184 226 251 253

30 139 140 141 143 146 152 164 183 221 248 251

28 140 140 141 143 146 153 165 184 221 253 253

26 140 140 141 143 145 153 163 182 223 248 248

25 139 140 141 143 146 153 163 179 218 249 251

24 140 140 141 143 146 152 165 183 216 246 247

23 140 140 141 143 146 153 163 182 212 239 249

22 140 140 141 142 144 150 160 179 211 245 251

21 139 140 140 142 145 149 161 173 210 237 247

306

20 139 140 140 142 145 150 159 175 209 241 245

19 139 140 141 142 145 150 160 175 210 238 243

18 140 140 141 142 144 149 159 173 209 237 243

17 140 140 141 142 144 149 157 175 205 236 245

16 139 140 141 142 144 149 157 175 208 240 244

15 139 140 140 142 143 149 160 173 195 232 243

14 139 140 141 142 144 149 156 171 205 237 243

12 139 140 140 141 144 149 156 169 198 225 235

10 139 140 140 141 143 147 155 168 194 218 233

8 139 139 140 141 143 147 155 168 194 218 231

6 139 139 139 140 142 145 152 163 181 200 217

4 138 139 139 140 141 144 151 162 181 200 216


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 208 255 255 255 255 255 255 255 255 255 255

30 211 255 255 255 255 255 255 255 255 255 255

28 214 255 255 255 255 255 255 255 255 255 255

26 215 255 255 255 255 255 255 255 255 255 255

25 214 255 255 255 255 255 255 255 255 255 255

24 215 255 255 255 255 255 255 255 255 255 255

23 217 255 255 255 255 255 255 255 255 255 255

22 214 255 255 255 255 255 255 255 255 255 255

21 217 255 255 255 255 255 255 255 255 255 255

20 217 255 255 255 255 255 255 255 255 255 255

19 215 255 255 255 255 255 255 255 255 255 255

18 213 255 255 255 255 255 255 255 255 255 255

17 210 255 255 255 255 255 255 255 255 255 255

16 215 255 255 255 255 255 255 255 255 255 255

15 214 255 255 255 255 255 255 255 255 255 255

14 209 255 255 255 255 255 255 255 255 255 255

12 205 254 255 255 255 255 255 255 255 255 255

10 200 246 255 255 255 255 255 255 255 255 255

8 190 232 255 255 255 255 255 255 255 255 255

6 184 223 255 255 255 255 255 255 255 255 255

4 175 203 248 255 255 255 255 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 271 270 270 270 270 270 270 270 270 270 270

30 270 270 270 270 270 270 270 270 270 270 270

28 269 270 269 269 269 269 269 269 269 269 269

26 271 270 270 270 270 270 270 270 270 270 270

25 269 270 270 270 270 270 270 270 270 270 270

24 269 269 269 269 269 269 269 269 269 270 270

307

23 269 269 269 269 269 269 269 270 269 269 269

22 269 269 269 269 269 269 269 269 269 269 269

21 270 270 270 270 270 270 270 270 269 270 270

20 269 270 270 270 270 270 270 270 270 270 270

19 269 269 269 269 269 269 269 269 269 269 269

18 269 269 269 269 269 269 269 269 268 269 269

17 269 269 269 269 269 269 269 269 269 269 269

16 270 270 270 270 270 269 269 269 270 270 270

15 269 269 269 269 269 269 269 269 269 269 269

14 269 270 270 270 269 269 269 270 269 270 270

12 270 270 270 270 269 269 269 269 269 269 269

10 270 270 270 269 269 269 269 269 270 270 270

8 269 269 269 269 269 269 269 269 269 268 269

6 268 269 268 268 268 268 268 268 268 268 268

4 268 269 269 269 269 269 269 269 269 269 269

Thickness = 10.16mm


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 142 144 148 155 167 189 228 254 255 255 255

30 142 144 148 155 165 188 226 254 255 255 255

28 142 144 148 155 166 189 229 254 255 255 255

26 142 144 148 155 166 187 226 254 255 255 255

25 142 144 148 156 167 192 232 255 255 255 255

24 142 145 148 156 167 191 231 254 255 255 255

23 141 144 148 156 168 192 233 255 255 255 255

22 142 145 148 156 168 191 234 255 255 255 255

21 142 145 149 156 168 192 233 255 255 255 255

20 142 145 148 155 167 191 233 254 255 255 255

19 142 145 148 156 169 192 233 255 255 255 255

18 142 144 148 156 167 191 233 255 255 255 255

17 142 145 148 156 167 191 229 254 255 255 255

16 142 145 149 156 167 192 229 254 255 255 255

15 142 145 149 157 169 193 234 254 255 255 255

14 142 145 149 157 169 193 234 255 255 255 255

12 142 144 148 156 167 188 226 254 255 255 255

10 142 144 148 156 166 189 228 254 255 255 255

8 142 144 148 155 166 187 223 255 255 255 255

6 142 143 146 153 162 181 212 253 255 255 255

4 141 142 145 150 158 175 204 249 255 255 255

308


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 139 140 141 142 145 152 163 181 216 246 249

30 139 140 141 143 146 153 163 180 216 249 248

28 139 141 141 143 146 153 163 182 217 246 249

26 139 140 141 143 146 154 165 186 221 249 250

25 139 140 142 144 147 153 166 184 222 248 252

24 139 140 141 143 147 154 167 184 224 248 252

23 137 140 141 143 146 154 164 183 220 248 253

22 140 141 141 144 147 153 166 185 222 248 248

21 139 140 141 143 146 152 163 181 218 247 251

20 139 140 141 144 147 155 166 186 228 253 252

19 139 140 141 143 147 153 167 184 228 246 251

18 139 140 141 143 147 154 167 185 222 246 252

17 139 140 141 144 147 153 165 184 220 250 250

16 139 140 141 144 147 153 165 186 225 250 252

15 139 140 141 143 146 153 165 184 225 248 246

14 139 140 141 143 146 152 166 184 225 250 252

12 140 140 141 143 147 153 165 183 225 249 253

10 139 140 141 143 146 152 164 180 218 247 247

8 139 140 141 143 146 152 163 181 218 248 249

6 138 140 141 143 145 152 163 180 218 247 248

4 137 139 140 142 144 151 161 179 216 245 247


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 202 246 255 255 255 255 255 255 255 255 255

30 205 254 255 255 255 255 255 255 255 255 255

28 208 255 255 255 255 255 255 255 255 255 255

26 207 255 255 255 255 255 255 255 255 255 255

25 212 255 255 255 255 255 255 255 255 255 255

24 208 255 255 255 255 255 255 255 255 255 255

23 211 255 255 255 255 255 255 255 255 255 255

22 211 255 255 255 255 255 255 255 255 255 255

21 210 255 255 255 255 255 255 255 255 255 255

20 212 255 255 255 255 255 255 255 255 255 255

19 212 255 255 255 255 255 255 255 255 255 255

18 208 255 255 255 255 255 255 255 255 255 255

17 211 255 255 255 255 255 255 255 255 255 255

16 206 255 255 255 255 255 255 255 255 255 255

15 203 253 255 255 255 255 255 255 255 255 255

14 203 249 255 255 255 255 255 255 255 255 255

12 199 243 255 255 255 255 255 255 255 255 255

309

10 193 233 255 255 255 255 255 255 255 255 255

8 185 220 255 255 255 255 255 255 255 255 255

6 180 212 255 255 255 255 255 255 255 255 255

4 173 198 239 255 255 255 255 255 255 255 255


WP Gain

30 35 40 45 50 55 60 65 70 75 80

32 337 337 337 337 337 337 337 337 337 337 337

30 336 337 337 336 336 336 336 336 336 336 336

28 337 337 337 337 337 337 337 337 337 337 337

26 337 337 337 337 337 336 337 337 336 337 337

25 337 337 337 337 337 337 337 337 337 337 337

24 336 336 336 336 336 336 336 336 336 337 336

23 337 337 337 337 337 337 337 337 337 337 337

22 336 337 336 336 336 336 336 336 336 336 337

21 337 337 337 337 337 337 337 337 337 337 337

20 337 337 337 336 336 336 336 336 336 337 337

19 336 336 336 336 336 336 336 336 336 336 336

18 336 337 337 337 336 336 336 336 336 336 337

17 337 337 337 337 336 336 336 337 336 337 337

16 337 337 336 336 337 336 336 336 336 337 337

15 336 336 336 336 336 336 336 336 335 335 335

14 335 336 336 336 336 336 336 336 336 336 336

12 336 336 336 336 336 336 337 336 336 336 337

10 335 336 335 335 335 335 335 335 335 335 335

8 336 336 336 336 336 336 336 336 336 336 336

6 336 335 336 336 336 336 336 336 336 336 335

4 336 336 336 336 336 336 336 336 336 336 336

310

Ultrasonic image interpreted from the results obtained in the experiments discussed in Chapter 6.3

Effect of varying angle of incidence.

Fig. II-1 Ultrasonic image for angle of incidence from 0° to 1.485°

311

Fig. II-2 Ultrasonic image for angle of incidence from 1.98° to 3.96°

312

Fig. II-3 Ultrasonic image for angle of incidence from 4.4455° to 5.94°

313

Ultrasonic testing results for Chapter 6.3 “Effect of varying angle of incidence” are presented here.

T and A in the tables represent thickness and amplitude of backwall echoes respectively.

Table III-1 Wall thicknesses measured on the curved component with angles of incidence from 0° to 1.98°

Hole

#

θ1 = 0° θ1 = 0.495° θ1 = 0.99° θ1 = 1.485° θ1 = 1.98°

T A T A T A T A T A

1 9.603 243 9.603 245 9.576 246 9.550 249 9.576 245

2 - - - - - - - - - -

3 9.230 204 9.230 211 9.230 193 9.203 199 9.283 189

4 5.101 253 5.101 255 5.047 253 5.047 253 5.021 253

5 4.322 237 4.322 220 4.296 212 4.296 195 4.242 215

6 1.845 253 1.845 253 1.845 253 1.812 253 1.812 253

7 0.882 253 0.882 253 0.882 253 0.834 253 0.858 253

8 2.695 253 2.695 253 2.666 253 2.666 253 2.666 253

9 2.753 253 2.753 253 2.753 253 2.724 253 2.695 253

10 6.754 252 6.754 247 6.720 243 6.720 230 6.720 235

11 7.471 192 7.505 197 - - 7.505 185 7.505 197

12 7.403 253 7.403 253 7.369 253 7.369 253 7.369 253

13 10.343 252 10.343 252 10.312 250 10.312 243 10.312 246

14 13.264 252 13.294 248 13.264 238 13.264 216 13.294 203

15 14.146 212 14.146 201 14.116 204 14.146 197 14.116 192

16 10.890 250 10.921 253 10.890 253 10.860 253 10.829 250

17 10.343 251 10.343 249 10.343 245 10.373 245 10.373 234

18 7.334 235 7.334 228 7.403 233 7.437 228 7.505 229

19 3.161 253 3.161 253 3.126 253 3.091 252 3.126 253

20 4.349 253 4.349 252 4.296 251 4.296 246 4.296 243

21 4.054 253 4.027 253 4.027 252 3.977 251 3.977 252

22 6.959 250 6.925 250 6.925 247 6.891 243 6.857 249

23 7.607 253 7.573 253 7.539 253 7.505 253 7.539 253

24 8.963 246 8.963 249 8.937 236 8.963 232 8.937 234

Table III-2 Wall thicknesses measured on the curved component with angles of incidence from 2.475° to 4.455°

Hole

#

θ1 = 2.475° θ1 = 2.975° θ1 = 3.465° θ1 = 3.96° θ1 = 4.455°

T A T A T A T A T A

1 9.576 250 9.630 245 9.710 239 9.923 230 10.130 214

2 - - - - - - - - - -

3 9.337 191 9.416 196 9.763 217 9.870 214 10.190 227

4 5.021 253 5.074 251 5.155 253 5.235 251 5.343 251

5 4.296 228 4.322 239 4.403 250 4.484 248 4.645 240

6 1.878 253 1.944 253 2.088 255 2.233 255 2.406 255

314

7 0.906 253 0.991 253 1.122 255 1.320 255 1.517 255

8 2.695 253 2.782 253 2.897 255 3.055 255 3.303 255

9 2.724 253 2.753 253 2.840 255 2.868 255 2.955 255

10 6.754 224 6.789 224 6.891 222 7.061 201 7.198 185

11 7.539 203 7.573 176 8.217 185 7.949 176 8.404 168

12 7.334 253 7.369 253 7.437 255 7.573 255 7.710 255

13 10.312 238 10.373 219 10.464 219 10.556 232 10.677 247

14 13.355 194 13.659 178 - - - - - -

15 13.872 198 13.994 183 14.146 172 14.298 190 14.451 222

16 10.829 253 10.921 251 10.951 251 11.012 248 11.195 230

17 10.373 233 10.434 228 10.556 207 10.586 205 10.890 191

18 7.539 204 7.607 211 7.710 226 7.778 239 7.880 243

19 3.161 250 3.232 247 3.339 248 3.551 246 3.764 240

20 4.296 248 4.322 250 4.376 252 4.671 253 4.725 253

21 3.977 253 3.941 252 3.941 255 4.027 255 4.134 255

22 6.925 244 6.993 245 7.130 246 7.266 235 7.505 244

23 7.539 253 7.539 253 7.642 255 7.642 255 7.812 255

24 8.963 235 9.017 230 9.097 214 9.230 211 9.177 199

Table III-3 Wall thicknesses measured on the curved component with angles of incidence from 4.95° to 5.94°

Hole # θ1 = 4.95° θ1 = 5.445° θ1 = 5.94°

T A T A T A

1 10.251 196 10.343 183 10.373 172

2 - - - - - -

3 10.221 234 10.221 239 10.464 241

4 5.504 247 5.531 237 5.719 228

5 4.725 247 4.779 237 4.833 226

6 2.637 255 2.695 255 2.897 255

7 1.779 254 1.878 254 2.175 254

8 3.551 255 3.622 255 3.906 255

9 3.161 255 2.897 255 3.126 255

10 7.573 175 - - 5.558 207

11 - - 9.177 180 9.097 185

12 7.880 254 7.846 254 7.983 253

13 10.829 252 10.799 253 10.982 253

14 - - 12.716 192 14.207 174

15 14.846 226 14.816 224 14.816 232

16 11.377 201 11.864 191 12.168 170

17 11.286 181 11.164 176 - -

18 8.137 246 8.164 251 8.324 251

19 4.027 227 4.108 219 4.349 223

20 4.833 206 4.913 255 4.994 254

21 4.161 254 4.188 255 4.349 255

22 8.164 221 8.495 209 8.644 233

315

23 8.777 251 9.150 250 - -

24 9.790 185 10.312 187 10.403 181

316

Variations of amplitude of backwall echoes at each individual holes for Chapter 6.3.3

Fig. IV-1 Variations of amplitude of backwall echoes at the first 12 holes (excluding hole 2)

317

Fig. IV-2 Variations of amplitude of backwall echoes at the last 11 holes

318

The results for Chapter 6.8 “Measuring three PSM104 turbine blades with a common probe path”

are presented here.

Table V-1 Thicknesses measured on B1 using P1, P2, P3 and a touch probe at ELE

Hole # Probe path P1 Probe path P2 Probe path P3

ELE touch probe

Thickness Amplitude Thickness Thickness Thickness Amplitude Thickness

1 1.533 255 1.648 254 1.648 254 0.8

2 1.763 255 1.746 254 1.746 254 1.8

3 1.648 255 1.730 255 1.730 254 1.55

4 2.334 253 2.435 254 2.421 253 2.15

5 2.897 254 3.055 254 3.055 254 2.45

6 4.067 216 4.161 208 4.148 204 3.725

7 3.250 189 4.752 181 4.765 186 3.075

8 6.959 162 7.027 164 7.096 162 3.125

9 4.886 223 4.994 183 4.994 173 4.275

10 4.604 202 4.698 192 4.698 189 4.15

11 4.322 173 4.295 178 4.295 181 3.65

12 4.443 219 4.376 183 4.390 187 3.85

13 2.666 255 2.609 255 2.609 254 2.425

Table V-2 Thickness measured on B2 using P1, P2, P3 and a touch probe at ELE

Hole

#

Probe path P2 Probe path P1 Probe path P3 ELE touch

probe

Thickness Amplitude Thickness Amplitude Thickness Amplitude Thickness

1 1.402 254 1.550 255 1.402 254 1.43

2 1.862 254 1.763 250 1.878 254 1.73

3 1.599 254 1.681 254 1.599 255 1.56

4 2.421 242 2.464 251 2.421 246 2.22

5 2.912 254 3.017 238 2.912 254 2.64

6 4.296 171 4.296 223 4.309 169 no reading

7 4.806 185 3.268 178 4.779 188 no reading

8 7.966 177 8.068 173 7.915 172 no reading

9 5.208 216 6.703 190 5.208 202 no reading

10 4.865 216 4.865 190 4.865 202 4.17

11 4.524 200 4.564 217 4.524 198 3.29

12 3.906 223 4.041 182 3.906 171 2.66

13 2.869 255 2.869 255 2.869 255 2.51

Table V-3 Thickness measured on B3 using P1, P2, P3 and a touch probe at ELE

Hole Probe path P3 Probe path P1 Probe path P2 ELE touch

319

# probe

Thickness Amplitude Thickness Amplitude Thickness Amplitude Thickness

1 1.388 253 1.550 254 1.388 254 1.34

2 1.796 253 1.730 254 1.796 254 1.69

3 1.632 254 1.780 250 1.632 254 1.54

4 2.262 254 2.363 255 2.262 254 2

5 3.498 254 3.675 211 3.498 253 3.02

6 3.906 215 4.108 175 3.941 207 3.32

7 4.806 197 5.155 196 4.819 192 no reading

8 6.959 160 7.062 161 6.959 164 no reading

9 7.062 178 6.993 174 7.192 179 no reading

10 4.667 178 4.652 174 4.667 179 no reading

11 4.376 218 4.309 173 4.349 183 3.39

12 4.403 171 Difficult to be interpreted 4.376 171 3.22

13 2.840 253 2.753 245 2.840 255 2.51

DESIGN, DEVELOPMENT AND TESTING OF AN

AUTOMATED SYSTEM FOR MEASURING WALL

THICKNESSES IN TURBINE BLADES WITH COOLING

CHANNELS

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

PhD

in the Faculty of Faculty of Engineering and Physical Sciences

2016

ZHENGYI JIANG

SCHOOL OF MECHANICAL, AEROSPACE AND CIVIL ENGINEERING

VOLUME II OF II

321

Contents

CONTENTS 321

CHAPTER 1 C# CODES 324

1.1 Robot control 325

1.1.1 Connect to the robot 325

1.1.2 Number register 328

1.1.3 Position register 330

1.1.4 Robot program 333

1.1.5 Robot program execution 335

1.1.6 File header fix 337


1.1.8 Advanced robot position enquiry 339

1.1.9 Advanced robot motion control 346

1.2 Ultrasonic control 352

1.3 DAQ device 363

1.3.1 Connect to the DAQ device 363

1.3.2 Data transmission 364

1.3.3 Error message handling 368

1.3.4 Special function 369


1.3.6 Advanced Digital IO control 370

322

1.3.7 Advanced analog IO control 370

1.4 Stepper motor control 372

1.4.1 Connect to the stepper motor 372

1.4.2 Stepper motor instructions 373


1.4.4 Advanced stepper motor control 376

1.5 Matlab interaction 381

1.6 Miscellaneous classes 383

1.6.1 Extended type conversions 383

1.7 Demo software 385

1.7.1 Initilisation 385

1.7.2 Connect to equipment 386

1.7.3 Private Methods 388

1.7.4 Laser digitization 391

1.7.5 Probe path localisation 395

1.7.6 Ultrasonic data acquisition 397

1.7.7 Wall thickness evaluation 405

CHAPTER 2 MATLAB CODES 407

2.1 Reverse engineering 408

2.1.1 The main Matlab function 408

2.1.2 B-spline curve 410

2.1.3 Shape-preserving parameterisation 412

2.1.4 B-spline surface 415

2.2 Probe path calculation 421

2.2.1 Data preparation 421

2.2.2 The main path calculation function 422

2.2.3 Tangent vectors in u direction 428

2.2.4 Tangent vectors in w direction 430

2.3 Localisation 434

2.3.1 Initialisation 434

2.3.2 Multi-approach algorithm 435

2.3.3 Quaternion method 438

2.3.4 Closest point 438

323

2.4 Path grouping 440


2.4.2 Path grouping sub-function 445

2.4.3 Probe path transformation sub-function 447

2.4.4 Path ordering sub-function 448

2.4.5 Robot rotation parameter calculation 449

2.5 Thickness evaluation 451


2.5.2 Interface echo detection 452

2.5.3 Backwall echo detection and thickness calculation 456

324

Chapter 1

C# Codes

It was decided to use a programming language from the C family for control software to control all

aspects of data transmission between the PC and controllers of other equipment including the robot

controller, the ultrasonic PCI card, the USB-1208FS DAQ device the RS232 controller for the stepper

motor. The dynamic-link library (DLL) of these controllers provided by their manufacture are available

in both C\C++ and C# language. Considering that C# language is an advanced language which

means it is easier to learn and to program, the control software in this project are development in

C# language.

Since all mathematical calculations are completed using Matlab scripts, it is also necessary to develop

a port or a link via which users can execute Matlab scripts using the software developed in C#

language.

In this chapter, C# classes developed for all controllers are presented. The classes are in general

categorised into two: basic classes and advanced classes. The basic classes provide the most basic

methods for transmitting data between the PC and the controllers. A lengthy block of codes is usually

needed to perform a simple action; for example, for instructing the robot to move to one point in

linear motion, a series of codes need to be written including specifying the motion type, defining the

coordinates, specifying the speed, specifying CNT, selecting the robot program for point-to-point

movement and finally instructing the robot to execute the robot program. Since linear motion as well

as many more actions are frequently used, it is not possible to write a block of codes each time. The

advanced classes make it possible to perform these actions using one line of code only; for example,

for a linear motion, it is now possible to write LMove(coordinate, speed, cnt).

At the end of this chapter, a demo software is presented which can be used for automated wall

thickness measurement on the inspection machine.

325

1.1 Robot control

1.1.1 Connect to the robot

Codes listed in this section are used for initialising a robot software interface and connecting to or

disconnecting from the robot controller.

namespace ELE_Application.Class.FANUC { public class ConnectRobot { ErrorHandling errorHandling = new ErrorHandling(); //Fanuc core instance public static FRRJIf.Core fanucCore; //Fanuc data table public static FRRJIf.DataTable fanucDataTable; public static FRRJIf.DataCurPos fanucCurPos; //current position public static FRRJIf.DataCurPos fanucCurPosUF1; //current user frame 1 position public static FRRJIf.DataCurPos fanucCurPosUF2; //current user frame 2 position public static FRRJIf.DataCurPos fanucCurPosUF3; //current user frame 3 position public static FRRJIf.DataCurPos fanucCurPosUF4; //current user frame 4 position public static FRRJIf.DataCurPos fanucCurPosUF5; //current user frame 5 position public static FRRJIf.DataCurPos fanucCurPosUF6; //current user frame 6 position public static FRRJIf.DataCurPos fanucCurPosUF7; //current user frame 7 position public static FRRJIf.DataCurPos fanucCurPosUF8; //current user frame 8 position public static FRRJIf.DataCurPos fanucCurPosUF9; //current user frame 9 position public static FRRJIf.DataSysVar fanucSysVarString_selectProg; //select program public static FRRJIf.DataSysVar fanucSysVarInt_startProg; //start program public static FRRJIf.DataSysVar fanucSysVarInt_progNum; //current program number public static FRRJIf.DataSysVar fanucSysVarInt_cyctskNum; //current cycle task number public static FRRJIf.DataSysVar fanucSysVarString_activeProg; //active program public static FRRJIf.DataSysVar fanucSysVarUAlarm; //user alarm public static FRRJIf.DataNumReg fanucNumReg100_speed; //number register 100 - speed public static FRRJIf.DataNumReg fanucNumReg120_cnt; //number register 120 - cnt public static FRRJIf.DataPosReg fanucPosReg51; //position register 51

326

public static FRRJIf.DataNumReg fanucNumReg; //unspecified number register public static FRRJIf.DataPosReg fanucPosReg; //unspecified position register public static FRRJIf.DataSysVar fanucSysVarString; public static FRRJIf.DataSysVar fanucSysVarInt; //Connect status; true for connected, otherwise disconnected. public static bool isConnected = false; #region initialization private void InitializeCommu() { //Initiate Fanuc core instance fanucCore = new FRRJIf.Core(); fanucCore.set_TimeOutValue(10000); errorHandling.catchError(); //Set Fanuc data table fanucDataTable = fanucCore.get_DataTable(); //Add item to data table fanucSysVarInt_startProg = fanucDataTable.AddSysVar(FRRJIf.FRIF_DATA_TYPE.SYSVAR_INT, "$SHELL_WRK.$CUST_START"); //Start Prog fanucSysVarString_selectProg = fanucDataTable.AddSysVar(FRRJIf.FRIF_DATA_TYPE.SYSVAR_STRING, "$SHELL_WRK.$CUST_NAME"); //Select Program fanucSysVarInt_progNum = fanucDataTable.AddSysVar(FRRJIf.FRIF_DATA_TYPE.SYSVAR_INT, "$SHELL_WRK.$TASK_NUM"); //Get current task number fanucSysVarInt_cyctskNum = fanucDataTable.AddSysVar(FRRJIf.FRIF_DATA_TYPE.SYSVAR_INT, "$SHELL_WRK.$CYCTSK_NUM"); //Get current cycle task number fanucSysVarString_activeProg = fanucDataTable.AddSysVar(FRRJIf.FRIF_DATA_TYPE.SYSVAR_STRING, "$SHELL_WRK.$ACTIVEPROG"); //Get active program fanucSysVarUAlarm = fanucDataTable.AddSysVar(FRRJIf.FRIF_DATA_TYPE.SYSVAR_STRING, "$UALRM_SEV"); fanucSysVarInt = fanucDataTable.AddSysVar(FRRJIf.FRIF_DATA_TYPE.SYSVAR_INT, "$MNUFRAMENUM");//Get user alarm fanucCurPos = fanucDataTable.AddCurPos(FRRJIf.FRIF_DATA_TYPE.CURPOS, 1); fanucCurPosUF1 = fanucDataTable.AddCurPosUF(FRRJIf.FRIF_DATA_TYPE.CURPOS, 1, 1); fanucCurPosUF2 = fanucDataTable.AddCurPosUF(FRRJIf.FRIF_DATA_TYPE.CURPOS, 1, 2); fanucCurPosUF3 = fanucDataTable.AddCurPosUF(FRRJIf.FRIF_DATA_TYPE.CURPOS, 1, 3); fanucCurPosUF4 = fanucDataTable.AddCurPosUF(FRRJIf.FRIF_DATA_TYPE.CURPOS, 1, 4); fanucCurPosUF5 = fanucDataTable.AddCurPosUF(FRRJIf.FRIF_DATA_TYPE.CURPOS, 1, 5); fanucCurPosUF6 = fanucDataTable.AddCurPosUF(FRRJIf.FRIF_DATA_TYPE.CURPOS, 1, 6); fanucCurPosUF7 = fanucDataTable.AddCurPosUF(FRRJIf.FRIF_DATA_TYPE.CURPOS, 1, 7);

327

fanucCurPosUF8 = fanucDataTable.AddCurPosUF(FRRJIf.FRIF_DATA_TYPE.CURPOS, 1, 8); fanucCurPosUF9 = fanucDataTable.AddCurPosUF(FRRJIf.FRIF_DATA_TYPE.CURPOS, 1, 9); fanucNumReg100_speed = fanucDataTable.AddNumReg(FRRJIf.FRIF_DATA_TYPE.NUMREG_INT, 100, 100); //Set number register 100 - speed fanucNumReg120_cnt = fanucDataTable.AddNumReg(FRRJIf.FRIF_DATA_TYPE.NUMREG_INT, 120, 120); //Set number register 120 - cnt fanucPosReg51 = fanucDataTable.AddPosReg(FRRJIf.FRIF_DATA_TYPE.POSREG, 1, 51, 51); //Set position register 51 fanucNumReg = fanucDataTable.AddNumReg(FRRJIf.FRIF_DATA_TYPE.NUMREG_INT, 1, 200); //Set number register 1-200 fanucPosReg = fanucDataTable.AddPosReg(FRRJIf.FRIF_DATA_TYPE.POSREG, 1, 1, 100); //Set position register 1-100 } //Reset varibles private void InitializeVaribles() { isConnected = false; } #endregion #region Connection public bool Disconnect() { try { fanucCore.Disconnect(); InitializeCommu(); //Reset Fanuc core instance and data table InitializeVaribles(); //Reset variables } catch { errorHandling.catchError(); return true; } return false; } public bool Connect(string ipAddress) { bool isConn = false; //In case the robot has been connected already, disconnect from it and return; //otherwise, connect. if (isConnected) Disconnect(); else { InitializeCommu(); try { isConn = fanucCore.Connect(ipAddress); } catch

328

{ errorHandling.catchError(); } //In case of failure, disconnect. if (!isConn) Disconnect(); } isConnected = isConn; return isConnected; } #endregion #region Set system varibles public bool SetSysVarString(string varible, string value) { fanucSysVarString = fanucDataTable.AddSysVar(FRRJIf.FRIF_DATA_TYPE.SYSVAR_STRING, "$SHELL_WRK.$CUST_NAME"); string Str = null; fanucSysVarString.SetValue(Str); //Clear Selection bool isSet = fanucSysVarString.SetValue(value); fanucDataTable.Refresh(); return isSet; } public bool SetSysVarInt(string varible, int value) { fanucSysVarInt = fanucDataTable.AddSysVar(FRRJIf.FRIF_DATA_TYPE.SYSVAR_INT, varible); bool isSet = fanucSysVarInt.SetValue(value); fanucDataTable.Refresh(); return isSet; } #endregion } }

1.1.2 Number register

Codes listed in this section are used for specifying number registers in the robot controller.

using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace ELE_Application.Class.FANUC.Programs { public class SetRobotNumReg { //1. index, value

329

//2. index, value, type //3. type, value //4. type, value, movetype //1. public void setNumReg(int index, int value) { ConnectRobot.fanucNumReg.SetValue(index, value); } /// <summary> /// 2. index, value, type /// </summary> /// <param name="index">index</param> /// <param name="value">value</param> /// <param name="type">speed/cnt</param> public void setNumReg(int index, float value, FanucConstants.NumRegType numRegtype) { switch (numRegtype) { case FanucConstants.NumRegType.Speed: if (value > 2000) value = 2000; else if (value < 1) value = 1; break; case FanucConstants.NumRegType.Cnt: if (value > 2000) value = 2000; else if (value < 0) value = 0; break; } ConnectRobot.fanucNumReg.SetValue(index, value); } /// <summary> /// 3. type, value /// </summary> /// <param name="value">value</param> /// <param name="type">speed/cnt/joint/linear</param> public void setNumReg(FanucConstants.NumRegType numRegtype, int value) { int index = 0; switch (numRegtype) { case FanucConstants.NumRegType.Speed: index = FanucConstants.indexNumReg_speed; break; case FanucConstants.NumRegType.Cnt: index = FanucConstants.indexNumReg_cnt; break; } setNumReg(index, value, numRegtype); } /// <summary> /// 4. type, value, moveType

330

/// </summary> /// <param name="value">value</param> /// <param name="type">speed/cnt</param> /// <param name="moveType">joint/linear</param> public void setNumReg(FanucConstants.NumRegType numRegType, int value, FanucConstants.MoveType moveType) { if (moveType == FanucConstants.MoveType.Joint) { if (value > 100) value = 100; else if (value < 1) value = 1; } setNumReg(numRegType, value); } public void setNumReg(FanucConstants.NumRegType numRegtype) { int value = 1; int index = 0; switch (numRegtype) { case FanucConstants.NumRegType.JointBit: value = FanucConstants.intNumRegBit_JMoveBit; index = FanucConstants.indexNumRegBit_moveType; break; case FanucConstants.NumRegType.LinearBit: value = FanucConstants.intNumRegBit_LMoveBit; index = FanucConstants.indexNumRegBit_moveType; break; } ConnectRobot.fanucNumReg.SetValue(index, value); } } }

1.1.3 Position register

Codes listed in this section are used for specifying position registers in the robot controller.

using System; namespace ELE_Application.Class.FANUC.Programs { public class SetRobotPosReg { public static Array intConfig = new short[7]; /// <summary> /// Index, Value, LinearMove /// </summary> /// <param name="index">index</param> /// <param name="value">posReg</param> public float[] SetPosReg(int index, float[] value, short UF, short UT) { Array sngArray = new float[6]; //Array intConfig = new short[7];

331

float[] finalPos = new float[6]; // Copy contents of Reg22 to sngArray value.CopyTo(sngArray, 0); value.CopyTo(finalPos, 0); // Config, this sets to (NUT 000) - Needs Editing to be alterable // NUT 000 - 0 1 1 0 0 0 // FUT 000 - 1 1 1 0 0 0 if (Convert.ToInt32(intConfig.GetValue(2)) != 1) { intConfig = new short[7]; intConfig.SetValue((short)1, 0); intConfig.SetValue((short)1, 2); intConfig.SetValue((short)1, 3); intConfig.SetValue((short)0, 4); intConfig.SetValue((short)0, 5); intConfig.SetValue((short)0, 6); } //UT = 2; //Validity check for UT & UF if (UT > 10 | UT < 0) return finalPos; if (UF > 9 | UF < 0) return finalPos; // Transfer the data ConnectRobot.fanucPosReg.SetValueXyzwpr(index, ref sngArray, ref intConfig, UF, UT); ConnectRobot.fanucNumReg.SetValue(FanucConstants.indexNumReg_UFSelection, UF); ConnectRobot.fanucNumReg.SetValue(FanucConstants.indexNumReg_UTSelection, UT); return finalPos; } /// <summary> /// Index, Value, Config, LinearMove /// </summary> /// <param name="index">index</param> /// <param name="value">posReg</param> /// <param name="config">intConfig</param> public float[] SetPosReg(int index, float[] value, short[] config, short UF, short UT) { Array sngArray = new float[6]; Array intConfig = new short[7]; float[] finalPos = new float[6]; // Copy contents of Reg22 to sngArray value.CopyTo(sngArray, 0); value.CopyTo(finalPos, 0); config.CopyTo(intConfig, 0); // Transfer the data ConnectRobot.fanucPosReg.SetValueXyzwpr(index, ref sngArray, ref intConfig, UF, UT); return finalPos;

332

} /// <summary> /// Index, Value, [Linear/Joint] /// </summary> /// <param name="index">index</param> /// <param name="value">posReg</param> /// <param name="moveType">linear/joint</param> public float[] SetPosReg(int index, float[] value, FanucConstants.MoveType moveType, short UF, short UT) { float[] finalPos = new float[6]; value.CopyTo(finalPos, 0); if (moveType == FanucConstants.MoveType.Joint) { ConnectRobot.fanucPosReg.SetValueJoint(index, value, UF, UT); } else { finalPos = SetPosReg(index, value, UF, UT); } return finalPos; } /// <summary> /// Index, Value, [Relative/Absolute], [Linear/Joint] /// </summary> /// <param name="index">index</param> /// <param name="value">posReg</param> /// <param name="coorType">relative/absolute</param> /// <param name="moveType">linear/joint</param> public float[] SetPosReg(int index, float[] value, FanucConstants.MoveType moveType, FanucConstants.CoorType coorType, short UF, short UT) { RobotPosition robotPosition = new RobotPosition(); float[] sngArray = new float[6] { 0, 0, 0, 0, 0, 0}; value.CopyTo(sngArray, 0); if (coorType == FanucConstants.CoorType.Relative) { float[] curPos = new float[9] { 0, 0, 0, 0, 0, 0, 0, 0, 0 }; string posTime; robotPosition.GetPosition(out curPos, out posTime, moveType, UF); sngArray[0] = value[0] + curPos[0]; sngArray[1] = value[1] + curPos[1]; sngArray[2] = value[2] + curPos[2]; sngArray[3] = value[3] + curPos[3]; sngArray[4] = value[4] + curPos[4]; sngArray[5] = value[5] + curPos[5]; } return SetPosReg(index, sngArray, moveType, UF, UT); } } }

333

1.1.4 Robot program

Codes listed in this section are used for retrieving robot programs from the robot controller.

using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.IO; using System.Net; using System.Text.RegularExpressions; using ELE_Application.Class.FANUC; namespace ELE_Application.Class.FANUC.Programs { public class GetRobotProgram { public static string CurProg = null; public List<string> ProgList = new List<string>(); public static string CurDirectory = Directory.GetCurrentDirectory(); public string PosTime = ""; public static string RobotProgramList = CurDirectory + "\\RobPrograms\\RobotProgramList"; //Get robot's current position in xyzwqr coordinates. public void getCurProgram() { CurProg = null; object vntValue = null; ConnectRobot.fanucDataTable.Refresh(); if (ConnectRobot.fanucSysVarString_selectProg.GetValue(ref vntValue) == true) { CurProg += vntValue; } else { CurProg += ConnectRobot.fanucSysVarString_selectProg.SysVarName + " : Error!!! \r\n"; } } //Get a list of programs stored in the robot. public void getPorgramList(string ipAddress) { string link = "http://" + ipAddress + "/MD/INDEX_TP.HTM"; // Get the website, save to file WebClient Client = new WebClient(); Client.DownloadFile(link, RobotProgramList); readProgramList(); } //Read the saved file public List<string> readProgramList() {

334

//clear ProgList ProgList.Clear(); string line; string segment; // Array List to store program names. int pos; FileInfo theSourceFile = new FileInfo(RobotProgramList); StreamReader reader = theSourceFile.OpenText(); // Create regular expression. Regex theReg = new Regex("/MD/.*.TP"); // Read every line in file. while ((line = reader.ReadLine()) != null) { // Check if it is a line containing a program. if (line.Contains(".TP")) { if (!line.Contains("-BCKED") & !line.Contains("GETDATA.TP") & !line.Contains("REQMENU.TP") & !line.Contains("SENDDATA.TP") & !line.Contains("SENDEVNT.TP") & !line.Contains("SENDSYSV.TP")) { // Run Reg Ex on line. Match mat = theReg.Match(line); segment = mat.ToString(); // Find position of first instance of program extension. pos = segment.IndexOf(".TP"); // strip out all characters except program name. segment = segment.Substring(4, (pos - 4)); // Add to array list. ProgList.Add(segment); } } } reader.Close(); return ProgList; } public void ReadLSFile(string ipAddress, string LSFileName) { string link = "http://" + ipAddress + "/MD/" + LSFileName + ".LS"; string filepath = CurDirectory + "\\RobPrograms\\" + LSFileName + ".html"; // Get the website, save to file WebClient ClientLS = new WebClient(); ClientLS.DownloadFile(link, filepath); System.Diagnostics.Process.Start(filepath);

335

} } }

1.1.5 Robot program execution

Codes listed in this section are used for selecting a specified robot program and instructing the robot

to execute the selected robot program.

using System; using System.Windows.Forms; namespace ELE_Application.Class.FANUC.Programs { public class SetRobotProgram { //Set seleted program to robot current selection for execution. public void SetProg(string prog) { string StrProg = null; ConnectRobot.fanucSysVarString_selectProg.SetValue(StrProg); //Clear Selection StrProg = prog; // PROGRAM NAME HERE (CUST_NAME) ConnectRobot.fanucSysVarString_selectProg.SetValue(StrProg); //(STYLE) //Com.fanucSysVarSeleProg.SetValue(1); //(PNS) ConnectRobot.fanucDataTable.Refresh(); GetRobotProgram getRobotProgram = new GetRobotProgram(); getRobotProgram.getCurProgram(); } //Execute seleted program. public void RunProg() { int startNew = 1; try { // Sets "$SHELL_WRK.$CUST_START" to run the program selected in "$SHELL_WRK.$CUST_NAME" ConnectRobot.fanucSysVarInt_startProg.SetValue(startNew); return; } catch (Exception ex) { MessageBox.Show(ex.Message); } } public void RunProg(string prog, bool doCheckRunning) { int startNew = 1;

336

try { SetProg(prog); // Sets "$SHELL_WRK.$CUST_START" to run the program selected in "$SHELL_WRK.$CUST_NAME" ConnectRobot.fanucSysVarInt_startProg.SetValue(startNew); if(doCheckRunning) { int task_num = 999; System.Threading.Thread.Sleep(1000); while (task_num!=0) { task_num = isRunning(); } } return; } catch (Exception ex) { MessageBox.Show(ex.Message); } } public int isRunning() { int task_num = 0; object vntValue = 0; ConnectRobot.fanucDataTable.Refresh(); if (ConnectRobot.fanucSysVarInt_progNum.GetValue(ref vntValue) == true) { task_num = (int)vntValue; } else { Console.WriteLine("Error getting task number"); } return task_num; } public void isRunning(out int task_num, out int cyc_num, out string active_prog) { object vntValue = 0; task_num = 999; cyc_num = 999; active_prog = "Error"; ConnectRobot.fanucDataTable.Refresh(); if (ConnectRobot.fanucSysVarInt_progNum.GetValue(ref vntValue) == true) { task_num = (int)vntValue;

337

} else { Console.WriteLine("Error getting task number"); } if (ConnectRobot.fanucSysVarInt_cyctskNum.GetValue(ref vntValue) == true) { cyc_num = (int)vntValue; } else { Console.WriteLine("Error getting task number"); } if (ConnectRobot.fanucSysVarString_activeProg.GetValue(ref vntValue) == true) { active_prog = vntValue.ToString(); } else { Console.WriteLine("Error getting task number"); } } } }

1.1.6 File header fix

Codes listed in this section are used for preparing files that are downloaded from the robot controller

to be read by the software.

using System; using System.Reflection; namespace ELE_Application.Class.FANUC.Programs { public class UnsafeHeaderParsing { // Method added to allow non-standard HTML headers to be read // http://o2platform.wordpress.com/2010/10/20/dealing-with-the-server-committed-a-protocol-violation-sectionresponsestatusline/ public static bool SetAllowUnsafeHeaderParsing20() { //Get the assembly that contains the internal class Assembly aNetAssembly = Assembly.GetAssembly(typeof(System.Net.Configuration.SettingsSection)); if (aNetAssembly != null) { //Use the assembly in order to get the internal type for the internal class Type aSettingsType = aNetAssembly.GetType("System.Net.Configuration.SettingsSectionInternal"); if (aSettingsType != null) {

338

//Use the internal static property to get an instance of the internal settings class. //If the static instance isn't created allready the property will create it for us. object anInstance = aSettingsType.InvokeMember("Section", BindingFlags.Static | BindingFlags.GetProperty | BindingFlags.NonPublic, null, null, new object[] { }); if (anInstance != null) { //Locate the private bool field that tells the framework is unsafe header parsing should be allowed or not FieldInfo aUseUnsafeHeaderParsing = aSettingsType.GetField("useUnsafeHeaderParsing", BindingFlags.NonPublic | BindingFlags.Instance); if (aUseUnsafeHeaderParsing != null) { aUseUnsafeHeaderParsing.SetValue(anInstance, true); return true; } } } } return false; } } }

1.1.7 Variables and configurations

Codes listed in this section defines variables related to robot control. These variables are constantly

used in the software and can be configured by the user.

using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace ELE_Application.Class.FANUC { public class FanucConstants { public static int indexNumRegBit_moveType = 130; //set R(130) to intNumRegBit_LMoveBit for LMove, intNumRegBit_JMoveBit for JMove. public static int intNumRegBit_LMoveBit = 1; public static int intNumRegBit_JMoveBit = 2; public static int indexPosReg_generalL = 50; public static int indexPosReg_generalJ = 60; public static int indexPosReg_toolOffset = 70; public static int indexNumReg_speed = 100; public static int indexNumReg_cnt = 120; public static int indexNumReg_UFSelection = 110; public static int indexNumReg_UTSelection = 111;

339

public static float positionTolerance = 0.005f; public static string ipAddress = "192.168.100.5"; public static string progMoveToPosRegProgName = "MOVETOPOSREG"; public static string progAttachLaser = "AttachLaser"; public static string progDettachLaser = "DettachLaser"; public static string progAttachUltra = "AttachUltrasonic"; public static string progDettachUltra = "DettachUltrasonic"; public enum MoveType { Linear, Joint }; public enum CoorType { Relative, Absolute }; public enum NumRegType { Speed, Cnt, JointBit, LinearBit }; public enum Coordinate { X, Y, Z, W, P, R, Xy, Xz, Yz, Xyz, Xyzwpr }; public enum Tool { None, Laser, Ultrasonic } public static float[] laserOffset = { 0, 0, -117.835f, 0, 0, 0 }; public static float[] ultrasonicOffset = { 0, 0, -197.823f, 0, 0, 0 }; #region program settings public static int moveToTimeout = 60; //Timeout value in s public static int moveToMaxAttempt = 5; //Max number of attempts for a move, after which the move is aborted. #endregion } }

1.1.8 Advanced robot position enquiry

Codes listed in this section are used for enquiring the location of the end effector in a coordinate

system specified by user. Returned location type can be configured between xyzwpr location and

joint location.

using System; using System.Linq; namespace ELE_Application.Class.FANUC { public class RobotPosition { ErrorHandling errorHandling = new ErrorHandling(); #region get robot position /// <summary> /// Get current position of the robot in the form of either xyzwpr coordinates or joint positions /// </summary> /// <param name="curPos">current position (linear/joint): float[]{x,y,z,w,p,r} / float[]{j1,j2,j3,j4,j5,j6}</param> /// <param name="posTime">time in s when robot reached the position: hh:mm:ss.milisecond</param> public void GetPosition(out float[] curPos, out string posTime, FanucConstants.MoveType type, short UF) { UFNo = UF;

340

posTime = ""; Array xyzwpr = new float[9]; Array config = new short[7]; Array joint = new float[9]; short intUF = 0; short intUT = 0; short intValidC = 0; short intValidJ = 0; float[] cacheCurPos = { 0, 0, 0, 0, 0, 0, 0, 0, 0 }; DateTime PosTimeNow = new DateTime(); //Refresh Fanuc data table to update robot position information. try { ConnectRobot.fanucDataTable.Refresh(); } catch { errorHandling.catchError(); } PosTimeNow = DateTime.Now; //recording time if (ConnectRobot.fanucCurPos.Valid) { //Read position information from the table switch (UFNo) { case 1: ConnectRobot.fanucCurPosUF1.GetValue(ref xyzwpr, ref config, ref joint, ref intUF, ref intUT, ref intValidC, ref intValidJ); break; case 2: ConnectRobot.fanucCurPosUF2.GetValue(ref xyzwpr, ref config, ref joint, ref intUF, ref intUT, ref intValidC, ref intValidJ); break; case 3: ConnectRobot.fanucCurPosUF3.GetValue(ref xyzwpr, ref config, ref joint, ref intUF, ref intUT, ref intValidC, ref intValidJ); break; case 4: ConnectRobot.fanucCurPosUF4.GetValue(ref xyzwpr, ref config, ref joint, ref intUF, ref intUT, ref intValidC, ref intValidJ); break; case 5: ConnectRobot.fanucCurPosUF5.GetValue(ref xyzwpr, ref config, ref joint, ref intUF, ref intUT, ref intValidC, ref intValidJ); break; case 6: ConnectRobot.fanucCurPosUF6.GetValue(ref xyzwpr, ref config, ref joint, ref intUF, ref intUT, ref intValidC, ref intValidJ); break;

341

case 7: ConnectRobot.fanucCurPosUF7.GetValue(ref xyzwpr, ref config, ref joint, ref intUF, ref intUT, ref intValidC, ref intValidJ); break; case 8: ConnectRobot.fanucCurPosUF8.GetValue(ref xyzwpr, ref config, ref joint, ref intUF, ref intUT, ref intValidC, ref intValidJ); break; case 9: ConnectRobot.fanucCurPosUF9.GetValue(ref xyzwpr, ref config, ref joint, ref intUF, ref intUT, ref intValidC, ref intValidJ); break; default: ConnectRobot.fanucCurPos.GetValue(ref xyzwpr, ref config, ref joint, ref intUF, ref intUT, ref intValidC, ref intValidJ); break; } //Format time string posTime = PosTimeNow.ToLongTimeString(); //time in the form of hh:mm:ss posTime += PosTimeNow.Millisecond.ToString(); //add milisecond if (type == FanucConstants.MoveType.Linear) xyzwpr.CopyTo(cacheCurPos, 0); else joint.CopyTo(cacheCurPos, 0); } curPos = cacheCurPos; } /// <summary> /// Get current xyzwpr position of the robot and current time /// </summary> /// <param name="curPos">current position (linear): float[]{x,y,z,w,p,r}</param> /// <param name="posTime">time in s when robot reached the position: hh:mm:ss.milisecond</param> public void GetXyzwprPosition(out float[] curPos, out string posTime, short UF) { GetPosition(out curPos, out posTime, FanucConstants.MoveType.Linear, UF); } ///// <summary> ///// Get current xyzwpr position of the robot ///// </summary> ///// <returns>current xyzwpr position</returns> //public float[] GetXyzwprPosition() //{ // float[] curPos; // string posTime; // GetXyzwprPosition(out curPos, out posTime); // return curPos; //} /// <summary> /// Get current joint position of the robot and current time /// </summary>

342

/// <param name="curPos">current position (joint): float[]{j1,j2,j3,j4,j5,j6}</param> /// <param name="posTime">time in s when robot reached the position: hh:mm:ss.milisecond</param> public void GetJointPosition(out float[] curPos, out string posTime, short UF) { GetPosition(out curPos, out posTime, FanucConstants.MoveType.Joint, UF); } ///// <summary> ///// Get current joint position of the robot ///// </summary> ///// <returns>current joint position</returns> //public float[] GetJointPosition() //{ // float[] curPos; // string posTime; // GetJointPosition(out curPos, out posTime); // return curPos; //} #endregion #region check if at position //Difference method /// <summary> /// The most basic method, with a develop option. /// This method checks whether or not the current position of robot = the target position. /// However, the two positions cannot be exactly identical due to precision. Therefore, a parameter, positionTolerance is introduced. /// positionTolerance can be sepcified by user in FanucConstants Class. /// Develop option: (output)position accuracy, which returns differences bettween the target position and the position where the method returns true. /// </summary> /// <param name="targetPos">targe position (linear): float[]{x,y,z,w,p,r}</param> /// <param name="moveType">Move type: linear / joint (joint not implemented)</param> /// <param name="coordinate">Coordinate(s) to check: {x}, {y}, {z}, {w}, {p}, {r}, {x,y}, {x,z}, {y,z}, {x,y,z}, {x,y,z,w,p,r}</param> /// <param name="positionAcc">position accuracy, for develop use</param> /// <returns>true if at the target position within tolerance; false if not</returns> public bool CheckIfAtPosition(float[] targetPos, FanucConstants.MoveType moveType, FanucConstants.Coordinate coordinate, out float[] positionAcc, short UF) { float[] curPos; int[] index; string posTime; bool[] isWithinAllowance; //Get current robot position GetPosition(out curPos, out posTime, moveType, UF); if (moveType == FanucConstants.MoveType.Linear) { //if any coordinate is negative, correct it to possitive.

343

if (curPos[3] < 0) curPos[3] = 360 + curPos[3]; if (curPos[4] < 0) curPos[4] = 360 + curPos[4]; if (curPos[5] < 0) curPos[5] = 360 + curPos[5]; if (targetPos[3] < 0) targetPos[3] = 360 + targetPos[3]; if (targetPos[4] < 0) targetPos[4] = 360 + targetPos[4]; if (targetPos[5] < 0) targetPos[5] = 360 + targetPos[5]; } switch (coordinate) { case FanucConstants.Coordinate.X: index = new int[1] { 0 }; break; case FanucConstants.Coordinate.Y: index = new int[1] { 1 }; break; case FanucConstants.Coordinate.Z: index = new int[1] { 2 }; break; case FanucConstants.Coordinate.W: index = new int[1] { 3 }; break; case FanucConstants.Coordinate.P: index = new int[1] { 4 }; break; case FanucConstants.Coordinate.R: index = new int[1] { 5 }; break; case FanucConstants.Coordinate.Xy: index = new int[2] { 0, 1 }; break; case FanucConstants.Coordinate.Xz: index = new int[2] { 0, 2 }; break; case FanucConstants.Coordinate.Yz: index = new int[2] { 1, 2 }; break; case FanucConstants.Coordinate.Xyz: index = new int[3] { 0, 1, 2 }; break; case FanucConstants.Coordinate.Xyzwpr: index = new int[6] { 0, 1, 2, 3, 4, 5 }; break; default: index = new int[6] { 0, 1, 2, 3, 4, 5 }; break; } positionAcc = new float[index.Length]; isWithinAllowance = new bool[index.Length]; for (int i = 0; i < index.Length; i++) { positionAcc[i] = Math.Abs(curPos[i] - targetPos[i]);

344

if (positionAcc[i] < FanucConstants.positionTolerance) isWithinAllowance[i] = true; } if (isWithinAllowance.All(x => x)) return true; return false; } /// <summary> /// This method checks whether or not the current position of robot = the target position. /// However, the two positions cannot be exactly identical due to precision. Therefore, a parameter, positionTolerance is introduced. /// positionTolerance can be sepcified by user in FanucConstants Class. /// </summary> /// <param name="targetPos">targe position (linear): float[]{x,y,z,w,p,r}</param> /// <param name="moveType">Move type: linear / joint (joint not implemented)</param> /// <returns>true if at the target position within tolerance; false if not</returns> public bool CheckIfAtPosition(float[] targetPos, FanucConstants.MoveType moveType, short UF) { return CheckIfAtPosition(targetPos, moveType, FanucConstants.Coordinate.Xyzwpr, UF); } /// <summary> /// This method checks whether or not the current position of robot = the target position. /// However, the two positions cannot be exactly identical due to precision. Therefore, a parameter, positionTolerance is introduced. /// positionTolerance can be sepcified by user in FanucConstants Class. /// </summary> /// <param name="targetPos">targe position (linear): float[]{x,y,z,w,p,r}</param> /// <param name="moveType">Move type: linear / joint (joint not implemented)</param> /// <param name="coordinate">Coordinate(s) to check: {x}, {y}, {z}, {w}, {p}, {r}, {x,y}, {x,z}, {y,z}, {x,y,z}, {x,y,z,w,p,r}</param> /// <returns>true if at the target position within tolerance; false if not</returns> public bool CheckIfAtPosition(float[] targetPos, FanucConstants.MoveType type, FanucConstants.Coordinate coordinate, short UF) { float[] delta; return CheckIfAtPosition(targetPos, type, coordinate, out delta, UF); } #endregion #region position properties private short UFNo = 0;

345

/// <summary> /// Set/get current user frame number for robot position check. /// </summary> public short UFNum { get { return UFNo; } set { UFNo = value; } } private float[] _curPos; private string _posTime; /// <summary> /// Get current xyz coordinates of the robot. /// <para>By default this property returns robot position in world frame. </para> /// <para>To request position in a specific user frame, the UF number must be set by calling property UFNum. </para> /// </summary> public float[] CurXYZPosition { get { GetPosition(out _curPos, out _posTime, FanucConstants.MoveType.Linear, UFNo); return _curPos; } } /// <summary> /// Get current joint coordinates of the robot. /// <para>By default this property returns robot position in world frame. </para> /// <para>To request position in a specific user frame, the UF number must be set by calling property UFNum. </para> /// </summary> public float[] CurJointPosition { get { GetPosition(out _curPos, out _posTime, FanucConstants.MoveType.Joint, UFNo); return _curPos; } } public string LastPosReportTime { get { return _posTime; } } #endregion } }

346

1.1.9 Advanced robot motion control

Codes listed in this section are used for instructing the robot to move to a certain coordinate in a

user specified coordinate system. Motion types can be configured between linear motion and joint

motion.

using System; using ELE_Application.Class.FANUC.Programs; using System.IO; namespace ELE_Application.Class.FANUC { public class MoveToPos { ErrorHandling errorHandling = new ErrorHandling(); #region developer methods //Load basic method libraries SetRobotPosReg setPosReg = new SetRobotPosReg(); SetRobotNumReg setNumReg = new SetRobotNumReg(); SetRobotProgram setProgram = new SetRobotProgram(); RobotPosition position = new RobotPosition(); /// <summary> /// The most basic MoveTo method, with develop options. /// Develop option: (output)position accuracy, which write differences bettween the target positions and the positions where the robot is considered completing the move. /// </summary> /// <param name="targetPos">target position (linear/joint): float[] = {x,y,z,w,p,r} / float[] = {j1,j2,j3,j4,j5,j6}</param> /// <param name="moveType">move type: linear / joint </param> /// <param name="coorType">coordinate type: absolute / relative</param> /// <param name="speed">speed</param> /// <param name="cnt">cnt</param> /// <param name="attemptCount">number of attempts; for general use, set 1</param> /// <param name="logAccuracy">true / false; used only for software developing; for general use, set false</param> public bool MoveTo(float[] targetPos, FanucConstants.MoveType moveType, FanucConstants.CoorType coorType, int speed, int cnt, int attemptCount, bool logAccuracy, bool doPositionCheck, FanucConstants.Tool tool, short UF, short UT) { if (targetPos == null) return false; TargetPos = targetPos; UserFrame = UF; MoveType = moveType; CoorType = coorType; int moveTypeBit = FanucConstants.intNumRegBit_LMoveBit; int posRegIndex = FanucConstants.indexPosReg_generalL; if (moveType == FanucConstants.MoveType.Joint) { moveTypeBit = FanucConstants.intNumRegBit_JMoveBit; posRegIndex = FanucConstants.indexPosReg_generalJ;

347

} //for accuracy logging only float[] positionAcc; //Move to target position float[] finalPos = setPosReg.SetPosReg(posRegIndex, targetPos, moveType, coorType, UF, UT); //Set position setNumReg.setNumReg(FanucConstants.indexNumRegBit_moveType, moveTypeBit); //Set moveType bit info (index, value) setNumReg.setNumReg(FanucConstants.NumRegType.Speed, speed, moveType); //Set speed (numRegType, value, moveType) setNumReg.setNumReg(FanucConstants.NumRegType.Cnt, cnt); //Set cnt (numRegType, value) setProgram.RunProg(FanucConstants.progMoveToPosRegProgName, doPositionCheck);//Execute if (doPositionCheck) { PositionCheck(finalPos, moveType, FanucConstants.Coordinate.Xyz, out positionAcc, coorType, speed, cnt, attemptCount, logAccuracy, tool, UF, UT); //accuracy logging, for develop use only if (logAccuracy) { try { using (StreamWriter write = File.AppendText(@"C:\PositionAcc.txt")) { write.WriteLine(string.Join(" ", positionAcc)); } } catch { errorHandling.catchError(); } } } if (IsAtTargetPos == true) return true; return false; } private void RepeatMoveTo(float[] targetPos, FanucConstants.MoveType moveType, FanucConstants.CoorType coorType, int speed, int cnt, int attemptCount, bool logAccuracy, FanucConstants.Tool tool, short UF, short UT) { attemptCount += 1; MoveTo(targetPos, moveType, coorType, speed, cnt, attemptCount, logAccuracy, true, tool, UF, UT); } private void PositionCheck(float[] targetPos, FanucConstants.MoveType moveType, FanucConstants.Coordinate coordinate, out float[] positionAcc, FanucConstants.CoorType coorType, int speed, int cnt, int attemptCount, bool logAccuracy, FanucConstants.Tool tool, short UF, short UT) { //While target position not reached:

348

//keep thread in loop unless target position is reached or time runs out, at which instance another attempt for this move will be initiated until maximum number of attempts reached. double time0 = DateTime.Now.Hour * 3600 + DateTime.Now.Minute * 60 + DateTime.Now.Second + DateTime.Now.Millisecond * 0.001; double time1; while (!position.CheckIfAtPosition(targetPos, moveType, FanucConstants.Coordinate.Xyz, out positionAcc, UF)) { time1 = DateTime.Now.Hour * 3600 + DateTime.Now.Minute * 60 + DateTime.Now.Second + DateTime.Now.Millisecond * 0.001; if (attemptCount <= FanucConstants.moveToMaxAttempt) { //If maximum number of attempts not reached if (Math.Abs(time1 - time0) > FanucConstants.moveToTimeout) //If time out RepeatMoveTo(targetPos, moveType, coorType, speed, cnt, attemptCount, logAccuracy, tool, UF, UT); else continue; } else { IsAtTargetPos = false; return; } } IsAtTargetPos = true; } #endregion #region user methods /// <summary> /// Basic MoveTo method. /// </summary> /// <param name="targetPos">target position (linear/joint): float[] = {x,y,z,w,p,r} / float[] = {j1,j2,j3,j4,j5,j6}</param> /// <param name="moveType">move type: linear / joint </param> /// <param name="coorType">coordinate type: absolute / relative</param> /// <param name="speed">speed</param> /// <param name="cnt">cnt</param> public bool MoveTo(float[] targetPos, FanucConstants.MoveType moveType, FanucConstants.CoorType coorType, int speed, int cnt, FanucConstants.Tool tool, bool doPositionCheck, short UF, short UT) { return MoveTo(targetPos, moveType, coorType, speed, cnt, 1, false, doPositionCheck, tool, UF, UT); } /// <summary> /// Linear move to an absolute position /// </summary> /// <param name="targetPos">target position (linear): float[] = {x,y,z,w,p,r}</param> /// <param name="speed">speed</param> /// <param name="cnt">cnt</param> public bool LMove(float[] targetPos, int speed, int cnt, FanucConstants.Tool tool, bool doPositionCheck, short UF, short UT) {

349

return MoveTo(targetPos, FanucConstants.MoveType.Linear, FanucConstants.CoorType.Absolute, speed, cnt, tool, doPositionCheck, UF, UT); } /// <summary> /// Linear move to a relative position /// </summary> /// <param name="targetPos">target position (linear): float[] = {x,y,z,w,p,r}</param> /// <param name="speed">speed</param> /// <param name="cnt">cnt</param> public bool LMoveRel(float[] targetPos, int speed, int cnt, FanucConstants.Tool tool, bool doPositionCheck, short UF, short UT) { return MoveTo(targetPos, FanucConstants.MoveType.Linear, FanucConstants.CoorType.Relative, speed, cnt, tool, doPositionCheck, UF, UT); } /// <summary> /// Joint move to an absolute position /// </summary> /// <param name="targetPos">target position (joint): float[] = {j1,j2,j3,j4,j5,j6}</param> /// <param name="speed">speed</param> /// <param name="cnt">cnt</param> public bool JMove(float[] targetPos, int speed, int cnt, FanucConstants.Tool tool, bool doPositionCheck, short UF, short UT) { return MoveTo(targetPos, FanucConstants.MoveType.Joint, FanucConstants.CoorType.Absolute, speed, cnt, tool, doPositionCheck, UF, UT); } /// <summary> /// Joint move to a relative position /// </summary> /// <param name="targetPos">target position (joint): float[] = {j1,j2,j3,j4,j5,j6}</param> /// <param name="speed">speed</param> /// <param name="cnt">cnt</param> public bool JMoveRel(float[] targetPos, int speed, int cnt, FanucConstants.Tool tool, bool doPositionCheck, short UF, short UT) { return MoveTo(targetPos, FanucConstants.MoveType.Joint, FanucConstants.CoorType.Relative, speed, cnt, tool, doPositionCheck, UF, UT); } #endregion #region properties private float[] _targetPos = { 0, 0, 0, 0, 0, 0 }; public float[] TargetPos { get { return _targetPos; } private set { _targetPos = value;

350

} } private short _UF = 0; public short UserFrame { get { return _UF; } private set { _UF = value; } } private bool? _isAtTargetPos = null; public bool? IsAtTargetPos { get { IsAtTargetPos = position.CheckIfAtPosition(TargetPos, MoveType, FanucConstants.Coordinate.Xyz, 0); return _isAtTargetPos; } private set { _isAtTargetPos = value; } } public bool? IsAtTargetPosUF { get { IsAtTargetPosUF = position.CheckIfAtPosition(TargetPos, MoveType, FanucConstants.Coordinate.Xyz, 1); return _isAtTargetPos; } private set { _isAtTargetPos = value; } } private FanucConstants.MoveType _moveType; public FanucConstants.MoveType MoveType { get { return _moveType; } private set { _moveType = value; } } private FanucConstants.CoorType _coorType;

351

public FanucConstants.CoorType CoorType { get { return _coorType; } private set { _coorType = value; } } #endregion } }

352

1.2 Ultrasonic control

Codes listed in this section are used for data transmission between the PC and the ultrasonic PCI

card.

using System; using System.Runtime.InteropServices; // DllImport using ELE_Application.Class.General; namespace ELE_Application.Class.Ultrasonics { public class DLink { #region core methods /// <summary> /// Get the status of the data acquisition process /// </summary> /// <returns>0 if no data in the memory yet; Otherwise there are data in the memory.</returns> public int IsDataReady() { return Class_PCIUT.PCIUTParms(1000, 0, 0, 0); } /// <summary> /// Generate a software trigger. After this method call the board will generate a pulse from the PULSE OUT /// connector, and the analogue to digital converter will start converting analogue signal to digital data with the /// user-specified parameters. /// </summary> /// <returns>1 if successful.</returns> public int SetSoftwareTrigger() { return Class_PCIUT.PCIUTParms(1001, 0, 0, 0); } /// <summary> /// Set sampling rate. /// </summary> /// <param name="wParam">Index of the settings. /// <para>0 - 100MHz</para> /// <para>1 - 50MHz</para> /// <para>2 - 25MHz</para> /// <para>3 - 12.5 MHz</para> /// <para>4 - 6.25 MHz</para> /// <para>5 - 3.125 MHz</para> /// <para>6 - 1.5725 MHz</para> /// <para>7 - External clock</para></param> /// <returns>1 if successful.</returns> public int SetSamplingRate(uint wParam) { switch (wParam) { case 0: SamplingRate = 100; break;

353

case 1: SamplingRate = 50; break; case 2: SamplingRate = 25; break; case 3: SamplingRate = 12.5; break; case 4: SamplingRate = 6.25; break; case 5: SamplingRate = 3.125; break; case 6: SamplingRate = 1.5725; break; case 7: SamplingRate = 0; break; } return Class_PCIUT.PCIUTParms(1002, 0, wParam, 0); } private double _samplingR; public double SamplingRate { get { return _samplingR; } private set { _samplingR = value; } } /// <summary> /// Set receiver low pass filter. /// </summary> /// <param name="wParam">Index of the settings. /// <para>0 - No filter</para> /// <para>1 - 148 MHz</para> /// <para>2 - 28 MHz</para> /// <para>3 - 18 MHz</para> /// <para>4 - 8.8 MHz</para> /// <para>5 - 7.5 MHz</para> /// <para>6 - 6.7 MHz</para> /// <para>7 - 5.9 MHz</para></param> /// <returns>1 if successful.</returns> public int SetLowPassFilter(uint wParam) { switch (wParam) { case 0: LowPassFilter = 0; break; case 1:

354

LowPassFilter = 148; break; case 2: LowPassFilter = 28; break; case 3: LowPassFilter = 18; break; case 4: LowPassFilter = 8.8; break; case 5: LowPassFilter = 7.5; break; case 6: LowPassFilter = 6.7; break; case 7: LowPassFilter = 5.9; break; default: LowPassFilter = 5.9; wParam = 7; break; } return Class_PCIUT.PCIUTParms(1004, 0, wParam, 0); } private double _lowPassF; public double LowPassFilter { get { return _lowPassF; } private set { _lowPassF = value; } } /// <summary> /// Set receiver high pass filter. /// </summary> /// <param name="wParam">Index of the settings. /// <para>0 - 4.8 kHz</para> /// <para>1 - 1.8 kHz</para> /// <para>2 - 0.8 kHz</para> /// <para>3 - 0.6 kHz</para></param> /// <returns>1 if successful.</returns> public int SetHighPassFilter(uint wParam) { switch (wParam) { case 0: HighPassFilter = 4.8; break; case 1: HighPassFilter = 1.8;

355

break; case 2: HighPassFilter = 0.8; break; case 3: HighPassFilter = 0.6; break; default: HighPassFilter = 4.8; wParam = 0; break; } return Class_PCIUT.PCIUTParms(1005, 0, wParam, 0); } private double _highPassF; public double HighPassFilter { get { return _highPassF; } private set { _highPassF = value; } } /// <summary> /// Set receiver signal type. /// </summary> /// <param name="wParam">Index of the settings. /// <para>0 - Full wave rectify</para> /// <para>1 - positive half rectify</para> /// <para>2 - negative half rectify</para> /// <para>3 - RF signal (no rectification)</para></param> /// <returns>1 if successful.</returns> public int SetRectifier(uint wParam) { return Class_PCIUT.PCIUTParms(1006, 0, wParam, 0); } /// <summary> /// Set the pulser damping resistor value on a single channel PCIUT3100 card. /// </summary> /// <param name="wParam">Index of the settings. /// <para>0 – 620 ohms</para> /// <para>1 – 339 ohms</para> /// <para>2 – 202 ohms</para> /// <para>3 – 159 ohms</para> /// <para>4 – 60 ohms</para> /// <para>5 – 55 ohms</para> /// <para>6 – 50 ohms</para> /// <para>7 – 47 ohms</para></param> /// <returns>1 if successful.</returns> public int SetDamping(uint wParam) { return Class_PCIUT.PCIUTParms(1007, 0, wParam, 0); }

356

/// <summary> /// Set the transducer mode, pulse/echo or through transmission on single channel PCIUT3100 card. /// </summary> /// <param name="wParam">0 – pulse/echo /// <para>1 – through transmission</para></param> /// <returns>1 if successful.</returns> public int SetTransducerMode(uint wParam) { return Class_PCIUT.PCIUTParms(1008, 0, wParam, 0); } /// <summary> /// Set the buffer length that specifies how many data samples that the next acquisition will collect data. /// </summary> /// <param name="wParam">number of samples to take. It ranges from 16 to 16382 in step of 4 samples.</param> /// <returns>1 if successful.</returns> public int SetBufferLength(uint wParam) { _bufferL = (int)wParam; return Class_PCIUT.PCIUTParms(1009, 0, wParam, 0); } private int _bufferL; public int BufferLength { get { return _bufferL; } set { _bufferL = value; SetBufferLength((uint)value); } } /// <summary> /// Set the trigger delay that specifies how many samples that the next acquisition will skip before collecting data. /// </summary> /// <param name="wParam">number of samples to skip. It ranges from 2 to 32764 samples in step of 2 samples.</param> /// <returns>1 if successful.</returns> public int SetTriggerDelay(uint wParam) { return Class_PCIUT.PCIUTParms(1010, 0, wParam, 0); } /// <summary> /// Set pulse voltage. /// </summary> /// <param name="value">Voltage of pulse in V, from 40V to 300V.</param> /// <returns>1 if successful.</returns> public int SetPulseVoltage(int value) {

357

uint wParam; double vMin = 40; double vMax = 300; wParam = Convert.ToUInt32((value - vMin)*255/(vMax-vMin)); if (wParam > 255) wParam = 255; if (wParam < 0) wParam = 0; return Class_PCIUT.PCIUTParms(1011, 0, wParam, 0); } /// <summary> /// Set pulse width. /// </summary> /// <param name="value">Width of pulse in ns, up to 80dB.</param> /// <returns>1 if successful.</returns> public int SetPulseWidth(double value) { uint wParam; double wMin = GetMinPulseWidth(); wParam = Convert.ToUInt32(161.67*(wMin - value)/(value - wMin - 760.8)); if (wParam > 255) wParam = 255; if (wParam < 0) wParam = 0; return Class_PCIUT.PCIUTParms(1012, 0, wParam, 0); } /// <summary> /// Set the receiver gain. /// </summary> /// <param name="value">Receiver gain in dB, from -20dB to 80dB with about 0.1 dB resolution</param> /// <returns>1 if successful.</returns> public int SetGain(double value) { uint wParam; wParam = Convert.ToUInt32(value/0.0978 + 204); if (wParam > 1023) wParam = 1023; if (wParam < 0) wParam = 0; return Class_PCIUT.PCIUTParms(1013, 0, wParam, 0); } /// <summary> /// Set the receiver DC offset. /// </summary> /// <param name="value">DC offset in V, from –2.5V to 2.5V with 0.005V resolution.</param> /// <returns>1 if successful.</returns> public int SetDCOffset(double value) { uint wParam; wParam = Convert.ToUInt32(value/0.005 + 511); if (wParam > 1023) wParam = 1023; if (wParam < 0) wParam = 0;

358

return Class_PCIUT.PCIUTParms(1014, 0, wParam, 0); } /// <summary> /// Set the trigger source of the analogue to digital converter. /// </summary> /// <param name="wParam">Index of the settings. /// <para>0 – +External trigger. The board will take data when a transit of 0 to 5V (rising edge) signal appears at the EXT TRIG connector.</para> /// <para>1 - Software trigger</para> /// <para>2 – -External trigger. The board will take data when a transit of 5 to 0V (falling edge) signal appears at the EXT TRIG connector.</para></param> /// <returns>1 if successful.</returns> public int SetADTriggerSource(uint wParam) { return Class_PCIUT.PCIUTParms(1016, 0, wParam, 0); } /// <summary> /// Get the encoder counter from one of the counters. /// </summary> /// <param name="wParam">Index of the counter. /// <para>0 – first encoder (X axis)</para> /// <para>1 – second encoder (Y axis)</para> /// <para>2 – third encoder (Z axis)</para> /// <para>3 – forth encoder (W axis)</para></param> /// <returns>Counter value from -8388608 to 8388607.</returns> public int GetEncoderCounter(uint wParam) { return Class_PCIUT.PCIUTParms(1017, 0, wParam, 0); } /// <summary> /// Set the value of an encoder counter. /// </summary> /// <param name="wParam">Index of the counter. /// <para>0 – first encoder (X axis)</para> /// <para>1 – second encoder (Y axis)</para> /// <para>2 – third encoder (Z axis)</para> /// <para>3 – forth encoder (W axis)</para></param> /// <param name="lParam">Counter value from -8388608 to 8388607.</param> /// <returns>1 if successful.</returns> public int SetEncoderCounter(uint wParam, int lParam) { return Class_PCIUT.PCIUTParms(1018, 0, wParam, lParam); } /// <summary> /// Get the digitized data from the memory on the board after the data acquisition. /// </summary> /// <param name="wParam">Pointer of the receiving buffer.</param> /// <param name="lParam">Number of bytes to move from the board memory to the buffer. It should be multiple of 4.</param> /// <returns>-2 if wParam is NULL or 1 if successful.</returns> public int GetData(out byte[] data, int lParam) { if (lParam/4 % 1 != 0)

359

lParam = Convert.ToInt32(lParam/4)*4; data = new byte[lParam]; return Class_PCIUT.PCIUTParms(1019, 0, data, lParam); } /// <summary> /// Reset the analogue to digital converter before acquiring data. /// </summary> /// <returns>1 if successful.</returns> public int ResetCounter() { return Class_PCIUT.PCIUTParms(1020, 0, 0, 0); } /// <summary> /// Clean up any data in the memory. It should be called before acquiring data. /// </summary> /// <returns>1 if successful.</returns> public int ResetMemory() { return Class_PCIUT.PCIUTParms(1021, 0, 0, 0); } /// <summary> /// Set DC offset adjustment which can make the signal smoother. /// </summary> /// <param name="wParam">0 - change the adjustment value and download it to the board /// <para>1 – do the task above and save the adjustment value in the Non-Volatile memory on the board.</para> /// </param> /// <param name="lParam">Adjustment value from –127 to 127.</param> /// <returns>1 if successful.</returns> public int SetOffsetAdjustment(uint wParam, int lParam) { return Class_PCIUT.PCIUTParms(1022, 0, wParam, lParam); } #endregion #region other methods /// <summary> /// Turn on or off the distance amplitude correction. /// </summary> /// <param name="wParam">0 - off /// <para>1 - on</para></param> /// <returns>1 if successful.</returns> public int SetDACEnable(uint wParam) { return Class_PCIUT.PCIUTParms(1003, 0, wParam, 0); } /* /// <summary> /// Set the gain table of the distance amplitude correction (DAC). /// </summary> /// <param name="value">DC offset in V, from –2.5V to 2.5V with 0.005V resolution.</param> /// <returns>-2 if wParam is NULL or 1 if successful.</returns> public int SetDACTable(double value) {

360

uint wParam; wParam = Convert.ToUInt32(value/0.005 + 511); if (wParam > 1023) wParam = 1023; if (wParam < 0) wParam = 0; return Class_PCIUT.PCIUTParms(1015, 0, wParam, 0); } */ /// <summary> /// Get the model number of the board. Normally it is PCIUT3100. /// </summary> /// <param name="modelNumber">Pointer of the receiving buffer: (char *). It should have enough room for at least 20 characters.</param> /// <returns>-2 if modelNumber is NULL /// <para>-3 if the specified board is not valid</para> /// <para>1 if successful</para></returns> public int GetModelNumber(out char[] modelNumber) { byte[] m = new byte[20]; int check = Class_PCIUT.PCIUTParms(1023, 0, m, 0); modelNumber = ConvertExt.ToCharArray(m); return check; } /// <summary> /// Get the serial number of the board. The serial number can be used to verify which board you are talking to. /// </summary> /// <param name="serialNumber">Pointer of the receiving buffer: (char *). It should have enough room for at least 20 characters.</param> /// <returns>-2 if serialNumber is NULL /// <para>-3 if the specified board is not valid</para> /// <para>1 if successful</para></returns> public int GetSerialNumber(out char[] serialNumber) { byte[] m = new byte[20]; int check = Class_PCIUT.PCIUTParms(1024, 0, m, 0); serialNumber = ConvertExt.ToCharArray(m); return check; } /// <summary> /// Get the size of the memory. The returned value could be 16384 or 262144. /// </summary> /// <returns>Size of the memory.</returns> public int GetMemorySize() { return Class_PCIUT.PCIUTParms(1025, 0, 0, 0); } /// <summary> /// Get the minimum pulse width in nanosecond. /// </summary> /// <remark> /// It is used to calculate the index of the pulse width. /// </remark> /// <returns>Minimum pulse width in ns</returns> public double GetMinPulseWidth()

361

{ return Class_PCIUT.PCIUTParms(1026, 0, 0, 0); } /// <summary> /// Get the option byte 1 which tells the user what kind of options are installed on the board. /// </summary> /// <remark> /// Bit7 DAC /// <para>Bit6 X encoder</para> /// <para>Bit5 Y encoder</para> /// <para>Bit4 External clock connector</para> /// <para>Bit3 Sync out connector</para> /// <para>Bit2 -350V pulse voltage</para> /// <para>Bit1 Wide pulse</para> /// <para>Bit0 Encoder line receiver</para> /// </remark> /// <param name="wParam"> Pointer of array /// <returns>1=Option was installed /// <para>0=options was not installed.</para> /// </returns> public int GetOptionByte1(uint wParam) { return Class_PCIUT.PCIUTParms(1034, 0, wParam, 0); } /// <summary> /// Get the option byte 2 which tells the user what kind of options are installed on the board. /// </summary> /// <remark> /// Bit7 1st 14-bit A/D converter /// <para>Bit6 2nd 14-bit A/D converter</para> /// <para>Bit5 Log Amplifier</para> /// <para>Bit4 Z encoder counter</para> /// <para>Bit3 W encoder counter</para> /// <para>Bit2 9-bit resolution</para> /// <para>Bit1 reserved </para> /// <para>Bit0 Tone burst pulser</para> /// </remark> /// <returns>1=Option was installed /// <para>0=options was not installed.</para> /// </returns> public int GetOptionByte2(uint wParam) { return Class_PCIUT.PCIUTParms(1035, 0, wParam, 0); } /// <summary> /// Get the revision number of the driver software. /// </summary> /// <returns>Driver software revision number.</returns> public int GetRevNumber() { return Class_PCIUT.PCIUTParms(1036, 0, 0, 0); } /// <summary>

362

/// Turn logarithmic amplifier on or off. /// </summary> /// <param name="wParam"> 1=on, or 0=off.</param> /// <returns>1 if successful.</returns> public int SetLogAMP(uint wParam) { return Class_PCIUT.PCIUTParms(1037, 0, wParam, 0); } #endregion } class Class_PCIUT { // for mode = 1019, 1023, or 1024 [DllImport("PCIUTDLL.dll", CallingConvention = CallingConvention.Cdecl)] public static extern int PCIUTParms(int mode, int card, byte[] wParam, int lParam); // for rest of the modes [DllImport("PCIUTDLL.dll", CallingConvention = CallingConvention.Cdecl)] public static extern int PCIUTParms(int mode, int card, uint wParam, int lParam); } }

363

1.3 DAQ device

1.3.1 Connect to the DAQ device

Codes listed in this section are used as root class modules for connecting to, disconnecting from and

initialising the USB1208FS DAQ device.

using System.Windows.Forms; namespace ELE_Application.Class.USB1208FS { public class ConnectUSB1208FS { #region Initialize MccBoard // Create new MccDAQ instance. public static MccDaq.MccBoard DaqBoard; public void Connect() { DaqBoard = new MccDaq.MccBoard(); DAQIO IO = new DAQIO(); IO.AnalogIn(); } #endregion #region Initialize DigitalPort private MccDaq.DigitalPortType PortNumA = MccDaq.DigitalPortType.FirstPortA; private MccDaq.DigitalPortType PortNumB = MccDaq.DigitalPortType.FirstPortB; //private int NumPorts, NumBits, FirstBit; //private int PortType, ProgAbility; //private string PortName; /// <summary> /// set digital port type as input/output according to user config. /// </summary> /// <param name="DPortA">Digital Port A type</param> /// <param name="DPortAType">Static Digital Port A type</param> public static string DPortAType = "null"; public enum DPortATypeEnum { DIn, DOut }; public void SetDigitalPortType(DPortATypeEnum DPortAInOrOut) { if (DPortAInOrOut == DPortATypeEnum.DIn) { DaqBoard.DConfigPort(PortNumA, MccDaq.DigitalPortDirection.DigitalIn); DaqBoard.DConfigPort(PortNumB, MccDaq.DigitalPortDirection.DigitalOut); DPortAType = "in"; } else if (DPortAInOrOut == DPortATypeEnum.DOut) { DaqBoard.DConfigPort(PortNumA, MccDaq.DigitalPortDirection.DigitalOut); DaqBoard.DConfigPort(PortNumB, MccDaq.DigitalPortDirection.DigitalIn); DPortAType = "out";

364

} else { MessageBox.Show("Please select a digital input port"); DPortAType = "null"; } } #endregion } }

1.3.2 Data transmission

Codes listed in this section are used as root class modules for transmitting data between the PC and

the DAQ device.

using System; using System.IO; namespace ELE_Application.Class.USB1208FS { public class DAQIO { #region Digital IO public MccDaq.DigitalPortType PortNumA = MccDaq.DigitalPortType.FirstPortA; public MccDaq.DigitalPortType PortNumB = MccDaq.DigitalPortType.FirstPortB; /// <summary> /// For every set time interval, read data from digital input ports. /// </summary> /// <param name="ULStat_Message">Error message from DAQ if any, otherwise return Null</param> /// <param name="DataValue">Received data</param> public void DigitalIn(out string ULStat_Message, out short DataValue) { MccDaq.ErrorInfo ULStat = new MccDaq.ErrorInfo(0); if (ConnectUSB1208FS.DPortAType == "in") { ULStat = ConnectUSB1208FS.DaqBoard.DIn(PortNumA, out DataValue); } else if (ConnectUSB1208FS.DPortAType == "out") { ULStat = ConnectUSB1208FS.DaqBoard.DIn(PortNumB, out DataValue); } else { ULStat_Message = "Please select a digital input port"; DataValue = 0; } if (ULStat.Value != MccDaq.ErrorInfo.ErrorCode.NoErrors) { ULStat_Message = ULStat.Message; }

365

else { ULStat_Message = "null"; } } /// <summary> /// Send bit information to digital output ports to enable/disable devices. /// </summary> /// <param name="DODataValue">Data to be sent to DAQ</param> /// <returns>Error message from DAQ if any, otherwise return Null</returns> public string DigitalOut(short DODataValue) { MccDaq.ErrorInfo ULStat = new MccDaq.ErrorInfo(0); string ULStat_Message = "null"; if (ConnectUSB1208FS.DPortAType == "out ") { ULStat = ConnectUSB1208FS.DaqBoard.DOut(PortNumA, DODataValue); } else if (ConnectUSB1208FS.DPortAType == "in") { ULStat = ConnectUSB1208FS.DaqBoard.DOut(PortNumB, DODataValue); } else { ULStat_Message = "Please select a digital output port"; return ULStat_Message; } if (ULStat.Value != MccDaq.ErrorInfo.ErrorCode.NoErrors) { ULStat_Message = ULStat.Message; } else { ULStat_Message = "null"; } return ULStat_Message; } #endregion #region Digital data processing public int[] DIchannel = new int[8]; public int[] DOchannel = new int[8]; /// <summary> /// Convert received decimal data into binary channel info. /// </summary> /// <param name="DataValue">decimal data received from DAQ</param> /// <returns>channel info</returns> public int[] DDataValue2Channel(int DataValue) { /*================================= * For USB-1208FS, there are 8 channels on each port. For each port, USB-1208FS creates a binary numeral containing 8 digits, * where each digit stands for the status of a channel: * 0 means the channel is idle and 1 means the channel is receiving data. * And the binary digits are arranged in a such order:

366

* * the 1st digit is the status of the 28th channel; * the 2nd digit ................ the 27th channel; * the 3rd digit ................ the 26th channel; * ...; * the 8th digit ................ the 21st channel. * * For example 0000101 means both channel 21 and 23 are receiving data and the rests are idle. * * However, instead of sending a binary numeral to the computer, the USB-1208FS converts the binary numeral into a decimal numeral * and sends the decimal numeral. * For example, instead of sending 0000101, it sends 5 (i.e. 101 in binary format). =================================*/ /* Input: decimal info * Output: channel info * This method will: 1 convert the Input, decimal info, into a binary number; 2 store each digit in the binary number into an array which reprecents the channel info; */ int[] channel; channel = new int[8]; string binary = Convert.ToString(DataValue, 2); //1 for (int i = 0; i < binary.Length; i++) //2 { channel[i] = binary[binary.Length - i - 1] - '0'; } return channel; } /// <summary> /// Convert binary channel info into decimal data. /// </summary> /// <param name="channel">binary channel info</param> /// <returns>decimal data for output to DAQ</returns> public short DChannel2DataValue(int[] channel) { /* Input: channel info * Output: short DataValue which can be sent to the I/O box * This method will: 1 convert the Input, channel info, into text for editting; 2 convert the text yielded in step 2 into a number in long format, decimal info; 3 convert the number into short format and Output this value, decimal info; */ short DOutDataValue = 0; string S_DOchannel = string.Join("", channel); //1 long value = Convert.ToInt32(S_DOchannel, 2); //2 DOutDataValue = (short)value; //3 return DOutDataValue; } #endregion #region Analog input

367

/// <summary> /// For every certain time interval, the code reads data from the digital input ports. /// </summary> /// <param name="ULStat_Message">Error message from DAQ if any, otherwise return Null</param> /// <param name="HighResEngUnits">Value returned from DAQ</param> /// <param name="time">time</param> public void AnalogIn(out string ULStat_Message, out double HighResEngUnits, out string time) { MccDaq.ErrorInfo ULStat = new MccDaq.ErrorInfo(0); MccDaq.Range Range = new MccDaq.Range(); DateTime timetick = new DateTime(); timetick = DateTime.Now; int Chan = 0; int Options = 0; System.UInt32 DataValue32; ULStat = ConnectUSB1208FS.DaqBoard.AIn32(Chan, Range, out DataValue32, Options); // Convert raw data to Volts by calling ToEngUnits // (member method of MccBoard class) ULStat = ConnectUSB1208FS.DaqBoard.ToEngUnits32(Range, DataValue32, out HighResEngUnits); time = timetick.ToLongTimeString(); time += timetick.Millisecond.ToString(); if (ULStat.Value != MccDaq.ErrorInfo.ErrorCode.NoErrors) { ULStat_Message = ULStat.Message; } else { ULStat_Message = "null"; } } //Preserved method for special purposes, such as establish initial communication. public void AnalogIn() { MccDaq.ErrorInfo ULStat = new MccDaq.ErrorInfo(0); MccDaq.Range Range = new MccDaq.Range(); int Chan = 0; int Options = 0; System.UInt32 DataValue32; ULStat = ConnectUSB1208FS.DaqBoard.AIn32(Chan, Range, out DataValue32, Options); } #endregion #region Analog data processing /// <summary> /// Translate received voltage signal into distance in mm.

368

/// </summary> /// <param name="curDisVol">Current voltage signal reading</param> /// <returns>Distance in mm</returns> public double AVoltageToDistance(double curDisVol) { double minDis = USB1208FSConstants.analogMinDis; double minDisVol = USB1208FSConstants.analogMinDisVol; double maxDis = USB1208FSConstants.analogMaxDis; double maxDisVol = USB1208FSConstants.analogMaxDisVol; double DisPerVol = (maxDis - minDis) / (maxDisVol - minDisVol); double curDis = (curDisVol - minDisVol) * DisPerVol + minDis; return curDis; } #endregion #region Log data //Log time + data public void LogData(string path, string time, double logData) { using (StreamWriter write = File.AppendText(@path)) { write.WriteLine(time + "\t" + logData.ToString()); } } //Log data only public void LogData(string path, double logData) { using (StreamWriter write = File.AppendText(@path)) { write.WriteLine(logData.ToString()); } } #endregion } }

1.3.3 Error message handling

Codes listed in this section are used for showing error message received from the DAQ device on

the PC screen.

using System.Windows.Forms; namespace ELE_Application.Class.USB1208FS { public class ULStatMsg { public bool ULStatMsgAna(string ULStat_Message) { bool isError = true; switch (ULStat_Message) { case "null": isError = false;

369

break; default: MessageBox.Show(ULStat_Message); isError = true; break; } return isError; } } }

1.3.4 Special function

Codes listed in this section are used for utilising useful but not frequently used functions provided

with the DAQ device. Currently, only one function is available, i.e. flash the LED light, which is useful

for checking whether the PC is connected to the DAQ device.

namespace ELE_Application.Class.USB1208FS { public class Functions { /// <summary> /// flash LED /// </summary> public void flashLED() { ConnectUSB1208FS.DaqBoard.FlashLED(); } } }


Codes listed in this section are used for defining variables related to the DAQ device. These variables

are constantly used in the software and can be configured by the user.

namespace ELE_Application.Class.USB1208FS { public class USB1208FSConstants { //Analog voltage-distance correction public static double analogMinDis = -10; public static double analogMinDisVol = -3.9266021; public static double analogMaxDis = 10; public static double analogMaxDisVol = 1.0747929; //Digital channel public static int valveChannel = 6; public static int pumpChannel = 7; public static int lowerFloatSWChannel = 1; public static int upperFloatSWChannel = 0; } }

370

1.3.6 Advanced Digital IO control

Codes listed in this section are used for digital data transmission between the PC and the DAQ device.

namespace ELE_Application.Class.USB1208FS { public class DigitalAdv { public int[] GetChannelInfo() { DAQIO daqIO = new DAQIO(); ULStatMsg ulStatMsg = new ULStatMsg(); int[] channel = {9,9,9,9,9,9,9,9}; string message; short value; bool isError = false; daqIO.DigitalIn(out message, out value); isError = ulStatMsg.ULStatMsgAna(message); if (!isError) channel = daqIO.DDataValue2Channel(value); return channel; } public void SendChannelInfo(int[] channel) { DAQIO daqIO = new DAQIO(); DigitalSignal_NotInUse digitalSignal = new DigitalSignal_NotInUse(); ULStatMsg ulStatMsg = new ULStatMsg(); string message; short value; bool isError = false; value = daqIO.DChannel2DataValue(channel); message = daqIO.DigitalOut(value); isError = ulStatMsg.ULStatMsgAna(message); } } }

1.3.7 Advanced analog IO control

Codes listed in this section are used for analogue data transmission between the PC and the DAQ

device.

using System.Linq; using System.Threading; namespace ELE_Application.Class.USB1208FS { public class AnalogAdv {

371

DAQIO daqIO = new DAQIO(); ULStatMsg ulStatMsg = new ULStatMsg(); public double GetLaserReading(int sampleSize, int waitTimer) { string msg = ""; double[] voltage = new double[sampleSize]; double distance = 0; string time = ""; bool isError = false; for (int i = 0; i < sampleSize; i++) { daqIO.AnalogIn(out msg, out voltage[i], out time); isError = isError & ulStatMsg.ULStatMsgAna(msg); if(waitTimer>0) Thread.Sleep(waitTimer); } double mode = voltage.GroupBy(i => i) //Grouping same items .OrderByDescending(g => g.Count()) //now getting frequency of a value .First() .Key; if (!isError) distance = daqIO.AVoltageToDistance(mode); return distance; } public double GetLaserReading() { double distance = GetLaserReading(1, 0); return distance; } public double GetLaserReading(int sampleSize) { double distance = GetLaserReading(sampleSize, 5); return distance; } public void LogData(string path, double data) { daqIO.LogData(path, data); } } }

372

1.4 Stepper motor control

1.4.1 Connect to the stepper motor

Codes listed in this section are used for connecting to, disconnecting from and initialising the stepper

motor.

using System; using System.IO.Ports; using System.Windows.Forms; namespace ELE_Application.Class.STPMotor { public class ConnectSTPMotor { public static SerialPort STPMotorComport = new SerialPort(); public bool Connect(string port, bool doInitialization) { // When data is recieved through the port, call this method //STPMotorComport.DataReceived += new SerialDataReceivedEventHandler(ReceiveData); STPMotorComport.BaudRate = RS232Constants.stpMotorBaud; STPMotorComport.DataBits = RS232Constants.stpMotorBits; STPMotorComport.StopBits = (StopBits)Enum.Parse(typeof(StopBits), RS232Constants.stpMotorStopBits); STPMotorComport.Parity = (Parity)Enum.Parse(typeof(Parity), RS232Constants.stpMotorParity); try { STPMotorComport.PortName = port; STPMotorComport.Open(); } catch { MessageBox.Show("An error occurs. Cannot open COM port. Most likely this port has already been in use, or is not avaiable.", "COM Port Unavalible", MessageBoxButtons.OK, MessageBoxIcon.Stop); return false; } if (doInitialization) { STPMotorInstruction motorIns = new STPMotorInstruction(); motorIns.SetACR(RS232Constants.defaultACR); motorIns.SetDirection(RS232Constants.defaultDir); motorIns.SetCurrent(RS232Constants.defaultCur); } return true; } public bool Connect(string port) { return Connect(port, false);

373

} public void Disconnect() { STPMotorComport.Close(); } public string[] COMList() { string[] ports = SerialPort.GetPortNames(); return ports; } } }

1.4.2 Stepper motor instructions

Codes listed in this section are used for sending stepper motor instructions.

using System.Windows.Forms; namespace ELE_Application.Class.STPMotor { public class STPMotorInstruction { #region base method public void SendData(string instruction) { if (ConnectSTPMotor.STPMotorComport.IsOpen == true) { try { ConnectSTPMotor.STPMotorComport.Write(instruction); } catch { MessageBox.Show("An error has occured. Please check the connection between the PC and the device.", "Communication error", MessageBoxButtons.OK, MessageBoxIcon.Stop); return; } } else { MessageBox.Show("An error has occured. COM port is closed; Please check the connection between the PC and the device.", "Communication error", MessageBoxButtons.OK, MessageBoxIcon.Stop); return; } } #endregion /// <summary>

374

/// Discard buffer already received from the device. /// </summary> public void DiscardInBuffer() { try { ConnectSTPMotor.STPMotorComport.DiscardInBuffer(); } catch { } } /// <summary> /// Discard buffer waiting to be sent to the device. /// </summary> public void DiscardOutBuffer() { try { ConnectSTPMotor.STPMotorComport.DiscardOutBuffer(); } catch { } } /// <summary> /// Read all existing buffer received from the device. /// </summary> public byte[] ReadBuffer() { int bytes= ConnectSTPMotor.STPMotorComport.BytesToRead; byte[] buffer = new byte[bytes]; try { ConnectSTPMotor.STPMotorComport.Read(buffer, 0, bytes); } catch { buffer = null; } return buffer; } #region configration public void HandShaking() { SendData("ABC;"); } public void SetBaudRate(int bdr) { if(bdr<=57600 & bdr>=9600) SendData(string.Format("BDR{0};", bdr)); } #endregion #region basic control public void SetEnable() { SendData("ENA;"); }

375

public void SetOffline() { SendData("OFF;"); } public void SetCurrent(int cur) { SendData(string.Format("CUR{0};", cur)); } public void SetACR(bool active) { if (active) SendData("ACR1;"); else SendData("ACR0;"); } public void SetMicroStepping(int mcs) { SendData(string.Format("MCS{0};", mcs)); } public void SetSpeed(int spd) { SendData(string.Format("SPD{0};",spd)); } public void SetStep(int stp) { SendData(string.Format("STP{0};", stp)); } public void SetDirection(int dir) { SendData(string.Format("DIR{0};", dir)); } public void SetOrigin() { SendData("ORG;"); } public void GetFeedback() { SendData("FBK;"); } public void GetPosition() { SendData("POS;"); } #endregion } }

376


Codes listed in this section are used for defining variables related to the stepper motor and the RS232

ports. These variables are constantly used in the software and can be configured by user.

namespace ELE_Application.Class.STPMotor { public class RS232Constants { public const int stpMotorBaud = 9600; public const int stpMotorBits = 8; public const string stpMotorParity = "None"; public const string stpMotorStopBits = "1"; public const double anglePerFullStep = 1.8; public const int pulleyTeethMotor = 12; public const int pulleyTeethShaft = 60; public const double gearboxRatio = 1.0 / 6.0; public const double eeOutRatio = gearboxRatio * pulleyTeethMotor / pulleyTeethShaft; public const int defaultSpeed = 100; public const int criticalSpeed = 250; public const int minimumMCS = 16; public static int[] availableMCSList = { 1, 2, 4, 16 }; public const int defaultCur = 20; public const int defaultDir = 1; public const bool defaultACR = true; } }

1.4.4 Advanced stepper motor control

Codes listed in this section are used for controlling the stepper motor and translating messages

received from the RS232 port.

using System; using System.Linq; using System.Collections.Generic; using ELE_Application.Class.General; namespace ELE_Application.Class.STPMotor { public class STPMotorAdv { STPMotorInstruction motorIns = new STPMotorInstruction(); private const double eeOutRatio = RS232Constants.eeOutRatio; #region calculations //Motor output public double CalculateRPM(int spd, int mcs) { double rpm = 1.8 * spd / mcs;

377

return rpm; } //End effect public double CalculateRPMEE(int spd, int mcs) { double _rpm = CalculateRPM(spd, mcs); double rpm = _rpm * eeOutRatio; return rpm; } //Motor output public double CalculateDegree(int stp, int mcs) { double degree = 1.8 * stp / mcs; return degree; } //End effect public double CalculateDegreeEE(int stp, int mcs) { double _degree = CalculateDegree(stp, mcs); double degree = _degree * eeOutRatio; return degree; } public int CalculateStep(double degree, int mcs) { int stp = (int)(degree / eeOutRatio / 1.8 * mcs); return stp; } /// <summary> /// Calculate the number of steps required for a certain angle, but instead of rounding it to the nearest integer, this method rounds it down. /// </summary> /// <param name="degree"></param> /// <param name="mcs"></param> /// <returns></returns> public int CalculateStepRoundD(double degree, int mcs) { int stp = (int)Math.Floor(degree / eeOutRatio / 1.8 * mcs); ExecutedAngleofRotation += CalculateDegreeEE(stp, mcs); return stp; } private List<int[]> AutoStepping(double degree) { List<int[]> stpList = new List<int[]>(); int stp, mcs; double remainingAngle, accuracyCheck, sign; double degree_=Math.Abs(degree); int[] listItem = new int[2]; sign = degree / Math.Abs(degree); mcs = RS232Constants.availableMCSList[0]; stp = CalculateStepRoundD(degree_, mcs); listItem[0] = stp * (int)sign; listItem[1] = mcs; stpList.Add(listItem);

378

for (int i = 1; i < RS232Constants.availableMCSList.Length; i++) { listItem = new int[2]; mcs = RS232Constants.availableMCSList[i]; remainingAngle = degree_ - ExecutedAngleofRotation; accuracyCheck = CalculateDegreeEE(1, mcs); if (remainingAngle >= accuracyCheck) { stp = CalculateStepRoundD(remainingAngle, mcs); listItem[0] = stp * (int)sign; listItem[1] = mcs; stpList.Add(listItem); } } return stpList; } double _executedAngleofRotation = 0; private double ExecutedAngleofRotation { get { return _executedAngleofRotation; } set { _executedAngleofRotation = value; } } public double CalculateTimeCost(int spd, int stp, int mcs) { double rpm = CalculateRPM(spd, mcs); double degree = CalculateDegree(stp, mcs); double time = degree / (rpm * 6); return time; } #endregion #region motor instructions public void RotateD(double degree, int mcs, int spd = RS232Constants.defaultSpeed) { spd *= mcs; int stp = CalculateStep(degree, mcs); motorIns.SendData(string.Format("STP{0};SPD{1};MCS{2};ENA;",stp,spd,mcs)); } public double RotateDAutoMCS(double degree, int baseSpeed = RS232Constants.defaultSpeed) { //Reset rotated angle check; ExecutedAngleofRotation = 0; List<int[]> stpList = AutoStepping(degree); int stp, spd, mcs; for (int i = 0; i < stpList.Count; i++) { stp = stpList[i][0]; mcs = stpList[i][1]; spd = mcs * baseSpeed; if (stp == 0) return ExecutedAngleofRotation; if (Math.Abs(mcs) != 1)

379

spd = 1; motorIns.SendData(string.Format("STP{0};SPD{1};MCS{2};ENA;", stp, spd, mcs)); while (isRunning()) System.Threading.Thread.Sleep(50); } return ExecutedAngleofRotation; } #endregion #region motor feedback message public bool isRunning() { motorIns.DiscardInBuffer(); motorIns.SendData("POS;"); System.Threading.Thread.Sleep(50); byte[] pos1 = motorIns.ReadBuffer(); System.Threading.Thread.Sleep(100); motorIns.DiscardInBuffer(); motorIns.SendData("POS;"); System.Threading.Thread.Sleep(50); byte[] pos2 = motorIns.ReadBuffer(); if (!pos1.SequenceEqual((pos2))) { return true; } return false; } //message returned with FBK, starts with CC, ends with FF //Examples: CC 00 7F 14 00 0C 40 00 00 01 38 45 FF public bool FbkAnalyser(string message, out int acrFBK, out int enaFBK, out int dirFBK, out int mcsFBK, out int curFBK, out int spdFBK, out int stpFBK) { acrFBK = 0; enaFBK = 0; dirFBK = 0; mcsFBK = 0; curFBK = 0; spdFBK = 0; stpFBK = 0; //Return if message does not start with CC or is incomplete (less than 38 chars) if (!message.StartsWith("CC") | message.Length < 38) { return false; } //trim message to 38 chars message = message.Substring(0, 38); //return if message does not end with FF. if (!message.EndsWith("FF")) { return false; } //take ASM part

380

string asm = message.Substring(6, 2); //take cur part string cur = message.Substring(9, 2); //take spd part string spd2 = message.Substring(12, 2); string spd1 = message.Substring(15, 2); string spd0 = message.Substring(18, 2); //take stp part string stp4 = message.Substring(21, 2); string stp3 = message.Substring(24, 2); string stp2 = message.Substring(27, 2); string stp1 = message.Substring(30, 2); string stp0 = message.Substring(33, 2); //Translate ASM asm = ConvertExt.Hex2Binary(asm); acrFBK = Convert.ToInt32(asm.Substring(0, 1)); enaFBK = Convert.ToInt32(asm.Substring(1, 1)); dirFBK = Convert.ToInt32(asm.Substring(2, 1)); mcsFBK = Convert.ToInt32(ConvertExt.ReverseString(asm.Substring(3, 4)), 2) + 1; //Translate current cur = ConvertExt.Hex2Binary(cur); curFBK = Convert.ToInt32(cur, 2); //Translate speed string spd = ConvertExt.Hex2Binary(spd2).PadLeft(2, '0') + ConvertExt.Hex2Binary(spd1).PadLeft(7, '0') + ConvertExt.Hex2Binary(spd0).PadLeft(7, '0'); spdFBK = Convert.ToInt32(spd, 2); //Translate stp string stp = ConvertExt.Hex2Binary(stp4).PadLeft(4, '0') + ConvertExt.Hex2Binary(stp3).PadLeft(7, '0') + ConvertExt.Hex2Binary(stp2).PadLeft(7, '0') + ConvertExt.Hex2Binary(stp1).PadLeft(7, '0') + ConvertExt.Hex2Binary(stp0).PadLeft(7, '0'); stpFBK = Convert.ToInt32(stp, 2); return true; } #endregion } }

381

1.5 Matlab interaction

Codes listed in this section are used to interact with Matlab using the control software.

using System.Diagnostics; namespace ELE_Application.Class.Matlab { public class Matlab { public MLApp.MLApp matlab; private Stopwatch stopwatch; /// <summary> /// Initialize Matlab instance without setting tool path or showing cmd window. /// </summary> public void Initialize() { matlab = new MLApp.MLApp(); matlab.Visible = 0; stopwatch = new Stopwatch(); } /// <summary> /// Prepare Matlab instance. /// </summary> /// <param name="matlabPath">path of *.m files</param> /// <param name="isVisible">set true to show matlab cmd window, vice versa. </param> public void Initialize(string matlabPath, bool isVisible) { matlab = new MLApp.MLApp(); if (!isVisible) matlab.Visible = 0; else matlab.Visible = 1; SetPath(matlabPath); SendCmd("clc;clear all;"); System.Threading.Thread.Sleep(2000); stopwatch = new Stopwatch(); } /// <summary> /// Send command to matlab /// </summary> /// <param name="cmd">cmd line</param> public void SendCmd(string cmd) { matlab.Execute(cmd); } /// <summary> /// Set Matlab cmd window invisibility. /// </summary> /// <param name="isVisible">set true to show Matlab cmd window, vice versa. </param> public void StVisible(bool isVisible) {

382

if (isVisible) matlab.Visible = 1; else matlab.Visible = 0; } /// <summary> /// Quite Matlab instance /// </summary> /// <param name="doCloseAll">set true to close all active Matlab windows including figures.</param> public void Quit(bool doCloseAll) { if (doCloseAll) SendCmd("close all"); matlab.Quit(); } /// <summary> /// Add Matlab current path. /// </summary> /// <param name="path"></param> public void SetPath(string path) { //example of cmd: "cd 'X:\\Dropbox\\Ultrasonic KTP\\ELE-Laptop Documents'" string cmd = "cd '" + path + "'"; matlab.Execute(@cmd); } /// <summary> /// Run Matlab function script /// </summary> /// <param name="scriptName"></param> public void RunScript(string scriptName) { matlab.Execute(string.Format("run('{0}')", scriptName)); } /// <summary> /// Send Matlab cmd advanced /// </summary> /// <param name="cmd">Matlab command</param> /// <param name="ans">results of the command</param> /// <param name="time">time of execution</param> public void SendCmd(string cmd, out string ans, out string time) { stopwatch.Start(); //Execute command ans = matlab.Execute(cmd); stopwatch.Stop(); stopwatch.Reset(); //Get time time = stopwatch.ElapsedMilliseconds.ToString(); } } }

383

1.6 Miscellaneous classes

1.6.1 Extended type conversions

The following codes are extensions to the built-in C# type conversions.

using System; using System.Text; namespace ELE_Application.Class.General { public static class ConvertExt { public static double[] ToDoubleArray(float[] array) { int l = array.Length; double[] a = new double[l]; for (int i = 0; i < l; i++) a[i] = (double)array[i]; return a; } public static float[] ToFloatArray(double[] array) { int l = array.Length; float[] a = new float[l]; for (int i = 0; i < l; i++) a[i] = (float)array[i]; return a; } public static char[] ToCharArray(byte[] array) { int l = array.Length; char[] a = new char[l]; for (int i = 0; i < l; i++) a[i] = Convert.ToChar(array[i]); return a; } public static string Hex2Binary(string hexValue) { string binaryVal = ""; binaryVal = Convert.ToString(Convert.ToInt32(hexValue, 16), 2); return binaryVal; } public static string ByteArrayToHexString(byte[] data) { StringBuilder sb = new StringBuilder(data.Length * 3); foreach (byte b in data) { sb.Append(Convert.ToString(b, 16).PadLeft(2, '0').PadRight(3, ' ')); } return sb.ToString().ToUpper(); }

384

public static string ReverseString(string s) { char[] charArray = s.ToCharArray(); Array.Reverse(charArray); return new string(charArray);

385

1.7 Demo software

1.7.1 Initilisation

The codes presented here are used for defining variables and initialize user interface.

using System; using System.Collections.Generic; using System.ComponentModel; using System.Drawing; using System.Windows.Forms; using System.Threading; using System.IO; using ELE_Application.Class.FANUC.Programs; using ELE_Application.Class.FANUC; using ELE_Application.Class.USB1208FS; using ELE_Application.Class.STPMotor; using ELE_Application.Class.Ultrasonics; using System.Text.RegularExpressions; using System.Globalization; namespace ELE_Application.Test.Demo { public partial class Sep2015 : Form { #region starting up //Communication public static ConnectRobot connectRobot = new ConnectRobot(); public static ConnectUSB1208FS connectDAQ = new ConnectUSB1208FS(); public static ConnectSTPMotor stpMotor = new ConnectSTPMotor(); //Robot public static SetRobotProgram fanucProg = new SetRobotProgram(); public static MoveToPos fanucMove = new MoveToPos(); public static RobotPosition fanucPos = new RobotPosition(); public static AnalogAdv daqAna = new AnalogAdv(); public static DigitalAdv daqDigi = new DigitalAdv(); //DAQ private int lowerFloatSWChannel = USB1208FSConstants.lowerFloatSWChannel; private int upperFloatSWChannel = USB1208FSConstants.upperFloatSWChannel; private int pumpChannel = USB1208FSConstants.pumpChannel; private int valveChannel = USB1208FSConstants.valveChannel; private ConnectUSB1208FS.DPortATypeEnum DPortAtype = ConnectUSB1208FS.DPortATypeEnum.DIn; private CurrentTool tool; //Ultrasonic private static DLink ultra = new DLink(); //Stepper motor private static STPMotorAdv stpMotorAdv = new STPMotorAdv(); //Logs

386

private enum LogMsgType { Incoming, Outgoing, Normal, Warning, Error }; private enum CurrentTool { Laser, Ultrasonic }; private Color[] LogMsgTypeColor = { Color.Blue, Color.Green, Color.Black, Color.Orange, Color.Red }; //Variables public static string mainDirectory = @"C:\Users\MACE-USER\OneDrive\Ultrasonic KTP\ELE-Laptop Documents\01. Experiments\18. Gain and water path\"; public static string matlabDire = mainDirectory + @"Matlab\"; public static string resultsFileDire = matlabDire;// + @"Results\"; private string laserPath = ""; private string ultrasonicToolPath = ""; private string ultrasonicPath = ""; private int ultrasonicBufferSize = 2000; public static bool isBGWorkerRunning = false; private bool overwriteUSToolPathFile = true; private string overwriteUSToolPathFileLoc = mainDirectory + @"Toolpath_19022016_1446.txt"; public Sep2015() { InitializeComponent(); grpb_ctrl.Enabled = false; grpb_inspection.Enabled = false; } #endregion

1.7.2 Connect to equipment

In this section, the PC is trying to establish communication with different devices including the robot

controller, the DAQ device and the stepper motor. It is noted that there is no need to connect to the

ultrasonic PCI card because it has been inserted on the PC motherboard and can be used directly by

creating an DLL instance.

#region Connect bool isRobConn = false; bool isDAQConn = false; private void btn_connectRob_Click(object sender, EventArgs e) { Cursor.Current = Cursors.WaitCursor; if (!isRobConn) { try { isRobConn = connectRobot.Connect(FanucConstants.ipAddress); } catch { } } else if (isRobConn) { try { isRobConn = connectRobot.Disconnect(); }

387

catch { } } updateConnectionStatus(); } private void btn_connectDAQ_Click(object sender, EventArgs e) { Cursor.Current = Cursors.WaitCursor; if (!isDAQConn) { try { //DAQ connectDAQ.Connect(); connectDAQ.SetDigitalPortType(DPortAtype); //Stepper motor isDAQConn = stpMotor.Connect("COM10"); } catch { } } else if (isDAQConn) { try { stpMotor.Disconnect(); } catch { } } updateConnectionStatus(); } private void updateConnectionStatus() { if (isRobConn) { btn_connectRob.Text = "Disconnect Robot"; lbl_robotStats.Text = "Robot Connected"; lbl_robotStats.ForeColor = Color.ForestGreen; } else { btn_connectRob.Text = "Connect Robot"; lbl_robotStats.Text = "Robot Disconnected"; lbl_robotStats.ForeColor = Color.Crimson; } if (isDAQConn) { btn_connectDAQ.Text = "Disconnect DAQ"; lbl_daqStats.Text = "DAQ Connected"; lbl_daqStats.ForeColor = Color.ForestGreen; } else { btn_connectDAQ.Text = "Connect DAQ"; lbl_daqStats.Text = "DAQ Disconnected"; lbl_daqStats.ForeColor = Color.Crimson; } if (isDAQConn && isRobConn)

388

{ grpb_ctrl.Enabled = true; grpb_inspection.Enabled = true; } else { grpb_ctrl.Enabled = false; grpb_inspection.Enabled = false; } } #endregion

1.7.3 Private Methods

This section of codes presents methods that are used multiple times during the inspection processes.

This includes:

1. instructing the robot to park at Home position (RobHomePos),

2. checking water level (CheckWaterLevel),

3. update event status in the UI (Log) and

4. save acquired data in text file (LogToFile).

#region Robot Routine private void RobHomePos(short UF, short UT, float elevation = 0, int spd = 300) { elevation = 0; if (elevation != 0) { float[] pos = { 0, 0, elevation, 0, 0, 0 }; fanucMove.LMoveRel(pos, spd, 0, FanucConstants.Tool.Laser, true, UF, UT); } fanucProg.RunProg("TOOLDOWN", true); } //Self-looping method for checking water level according float switch status private bool isFixingWaterLevel = false; //set true for pumping/draining water in progress; false for fixed water level. private string CheckWaterLevel() { Thread.Sleep(500); DigitalAdv daqAdvanced = new DigitalAdv(); string time; int[] channel; int floatSWChn = 9; //channel in DAQ for the lower/upper float switches; lowerFloatSWChannel - lower float switch; upperFloatSWChannel - upper float switch; 9 - reset int desiredValue = 9; //1 - channel open; 0 - channel closed; 9 - reset string msg = "";

389

int[] bothOff = { 0, 0, 0, 0, 0, 0, 0, 0 }; //bit info to be sent to DAQ for turning off both the pump and the valve int[] valveOn = { 0, 0, 0, 0, 0, 0, 0, 0 }; //bit info to be sent to DAQ for turning on the valve int[] pumpOn = { 0, 0, 0, 0, 0, 0, 0, 0 }; //bit info to be sent to DAQ for turning on the pump valveOn[valveChannel] = 1; //set bit info for turning valve on by setting the corresponding channel bit to 1 pumpOn[pumpChannel] = 1; //set bit info for turning pump on by setting the corresponding channel bit to 1 //Read bit info of all channels from DAQ channel = daqAdvanced.GetChannelInfo(); time = HrMinS(); //set rule for water level checking according to the current tool type if (tool == CurrentTool.Laser) //safety water level for laser: lower float switch - open { floatSWChn = lowerFloatSWChannel; //Open desiredValue = 1; } else if (tool == CurrentTool.Ultrasonic) //safety water level for ultrasonic: upper float switch - close { floatSWChn = upperFloatSWChannel; //Close desiredValue = 0; } else //if current tool is none { Log(LogMsgType.Error, time, "Error! Tool [" + tool + "] not recognised!"); return msg = "Error! Tool not recognised"; } //In case channel info returned from DAQ is invalid if (channel[1] == 9) { Log(LogMsgType.Error, time, "Error occurred when checking water level."); isFixingWaterLevel = false; } else if (channel[floatSWChn] == desiredValue) //if float switch is at desired status { daqAdvanced.SendChannelInfo(bothOff); //turn off the pump or/and the valve Log(LogMsgType.Outgoing, time, "Water level is safe for the next operation."); isFixingWaterLevel = false; } else //if float switch is at incorrect status { if (tool == CurrentTool.Laser) //for laser { if (!isFixingWaterLevel) { Log(LogMsgType.Error, time, "Current water level is above safety level for laser scanning."); Log(LogMsgType.Outgoing, time, "Draining water."); daqAdvanced.SendChannelInfo(valveOn); //drain water out of the tank isFixingWaterLevel = true;

390

} CheckWaterLevel(); } if (tool == CurrentTool.Ultrasonic) //for ultrasonic { if (!isFixingWaterLevel) { Log(LogMsgType.Error, time, "Current water level is below required level for ultrasonic scanning."); Log(LogMsgType.Outgoing, time, "Pumping water."); daqAdvanced.SendChannelInfo(pumpOn); //pump water into the tank isFixingWaterLevel = true; } CheckWaterLevel(); } } return msg = "current water level is safe for the next operation"; } //Return current Hour:Minute:Second. private string HrMinS() { return DateTime.Now.ToLongTimeString(); } //Log message with time into log window private void Log(LogMsgType msgtype, string time, string msg) { rtb_log.Invoke(new EventHandler(delegate { rtb_log.AppendText(time + ", ", LogMsgTypeColor[(int)msgtype]); rtb_log.AppendText(msg + "\n", LogMsgTypeColor[(int)msgtype]); rtb_log.ScrollToCaret(); })); } //Log message without time into log window private void Log(LogMsgType msgtype, string msg) { rtb_log.Invoke(new EventHandler(delegate { rtb_log.AppendText(msg, LogMsgTypeColor[(int)msgtype]); rtb_log.ScrollToCaret(); })); } //Log data to file public static void logToFile(string path, float[] curPos, double laser) { string str = ""; float[] pos = new float[6]; pos[0] = curPos[0]; pos[1] = curPos[1]; pos[2] = curPos[2]; pos[3] = curPos[3]; pos[4] = curPos[4]; pos[5] = curPos[5]; foreach (float i in pos)

391

{ str += string.Format("{0}\t", i); } str += string.Format("{0}", laser.ToString()); using (StreamWriter write = File.AppendText(@path)) { write.WriteLine(str); } } private void logToFile(string path, string str) { using (StreamWriter write = File.AppendText(@path)) { write.WriteLine(str); } } #endregion

1.7.4 Laser digitization

In this section, the laser probe is used for digitizing the turbine blade which has been fixed on the

rotary axis.

private bool _isLaserAttached = false; private bool IsLaserAttached { set { _isLaserAttached = value; if (_isLaserAttached) btn_attachLaser.Text = "Dettach laser"; else btn_attachLaser.Text = "Attach laser"; } get { return _isLaserAttached; } } private int rot = 0; private void btn_laserScan_Click(object sender, EventArgs e) { SetRobotPosReg.intConfig.SetValue((short)0, 0); SetRobotPosReg.intConfig.SetValue((short)1, 2); SetRobotPosReg.intConfig.SetValue((short)1, 3); SetRobotPosReg.intConfig.SetValue((short)0, 4); SetRobotPosReg.intConfig.SetValue((short)0, 5); SetRobotPosReg.intConfig.SetValue((short)0, 6); #region variables rot++; string saveFileName = "laserData";

392

DateTime now = DateTime.Now; laserPath = resultsFileDire + saveFileName + "_" + now.ToString("dd-MM-yy-hhmmss") + ".txt"; short UF = 3; short UT = 7; int descendingSpd = 30; int slowSpd = 100; int fastSpd = 300; float maxX, minX, maxY, minY, z, safeZ; float ix;//increment in x float iy;//increment in y int nx, ny; //number of points in x and y respectively double laserReading; int waitTimer = 500; //time to wait before taking laser reading float[] safeMove = { 0, 0, 300, 0, 0, 0 }; bool startPointIsNextPoint = false; bool startMinX = true; bool startMinY = true; #endregion Log(LogMsgType.Outgoing, HrMinS(), "System: Initiating laser scan."); #region initiallization Log(LogMsgType.Outgoing, HrMinS(), "Robot: Moving to home position."); RobHomePos(0, 0); tool = CurrentTool.Laser; Log(LogMsgType.Outgoing, HrMinS(), "Tank: Checking water level."); CheckWaterLevel(); Log(LogMsgType.Outgoing, HrMinS(), "Tank: Water level is safe for laser scanning."); //confirm tool DialogResult ans = MessageBox.Show("Is it safe to attach laser sensor?", "Confirmation required", MessageBoxButtons.YesNo); if (ans == DialogResult.No) return; Log(LogMsgType.Outgoing, HrMinS(), "Robot: Grabbing laser sensor."); if (!IsLaserAttached) { fanucProg.RunProg(FanucConstants.progAttachLaser, true); IsLaserAttached = true; } #endregion #region start laser scanning //PSM104 - R1 maxX = 442.975f; minX = 396.895f; maxY = -120.997f; minY = -161.317f; z = -372f; nx = 15; ny = 6; ix = (maxX - 0.01f - minX) / nx; iy = (maxY - 0.01f - minY) / ny; rot = 1; startMinY = true;

393

//PSM104 - R2 maxX = 452.736f; minX = 434.889f; maxY = -120.997f; minY = -161.317f; z = -347f; nx = 11; ny = 6; ix = (maxX - 0.01f - minX) / nx; iy = (maxY - 0.01f - minY) / ny; rot = 2; startMinY = true; bool istesting = true; float safeHeightRise = 10; switch (rot) { case 1: safeZ = -388f; break; case 2: safeZ = -360f; break; default: safeZ = 0; break; } Log(LogMsgType.Outgoing, HrMinS(), "System: Initiation completed. Start laser scan."); float xEnd, yEnd, xStart, yStart; int ixSign, iySign; if (startMinY) { yStart = minY; yEnd = maxY; iySign = 1; } else { yStart = maxY; yEnd = minY; iySign = -1; } if (startMinX) { xStart = minX; xEnd = maxX; ixSign = 1; } else { xStart = maxX; xEnd = minX; ixSign = -1; } float[] nextPos = { xStart, yStart, z, 180, 0, 180 };

394

//Move to start position, minimum x, maximum y and the actual starting z+200. float[] startPos = { xStart, yStart, z + 200, 180, 0, 180 }; fanucMove.LMove(startPos, fastSpd, 0, FanucConstants.Tool.Laser, true, UF, UT); //Make sure it won't collide after adjusting the z. if (startPos[2] - 200 <= safeZ) startPos[2] = safeZ; else startPos[2] -= 200; do { fanucMove.LMove(startPos, fastSpd, 0, FanucConstants.Tool.Laser, true, UF, UT); laserReading = daqAna.GetLaserReading(10); //Re-adjust the height to allow laser measuring. while (Math.Abs(laserReading) > 10) { if (startPos[2] == safeZ) { if (Math.Abs(laserReading) > 12) break; startPointIsNextPoint = true; break; } if (startPos[2] - 3 <= safeZ) { startPos[2] = safeZ; } else { startPos[2] -= 3; } fanucMove.LMove(startPos, slowSpd, 0, FanucConstants.Tool.Laser, true, UF, UT); laserReading = daqAna.GetLaserReading(10); } startPos.CopyTo(nextPos, 0); do { fanucMove.LMove(nextPos, slowSpd, 0, FanucConstants.Tool.Laser, true, UF, UT); laserReading = daqAna.GetLaserReading(10); //If the reading is around 21(in +/-5V analog range), it reflects that either the position being measured is outside //the blade or the surface of the blade blocks the laser capture camera //It is noted that instead of using 21 as the critical reading, use 12 in case something wierd may happen. //The actual measuring range of the laser sensor is +/-10mm anyway, so 12 should be safe. if (Math.Abs(laserReading) > 12) { if (!startPointIsNextPoint) break; } startPointIsNextPoint = false; //The accurate measuring range of the laser is +/-5mm, so if the distance exceeds 4mm (just to be safe),

395

//readjust the height. if (Math.Abs(laserReading) > 4) { if (nextPos[2] + (float)laserReading >= safeZ) nextPos[2] += (float)laserReading; else nextPos[2] = safeZ; } fanucMove.LMove(nextPos, descendingSpd, 0, FanucConstants.Tool.Laser, true, UF, UT); Thread.Sleep(waitTimer); laserReading = daqAna.GetLaserReading(10); if (laserReading < 10) logToFile(laserPath, nextPos, laserReading); nextPos[1] += iySign * iy; } while (iySign * nextPos[1] < iySign * yEnd); startPos[0] += ixSign * ix; //Go to somewhere safe: [safeHeightReset] above the starting point. startPos[2] = nextPos[2] + safeHeightRise; } while (ixSign * startPos[0] <= ixSign * xEnd); #endregion //Return laser sensor if (!istesting) { RobHomePos(UF, UT, 0, 300); fanucProg.RunProg(FanucConstants.progDettachLaser, true); } IsLaserAttached = false; Log(LogMsgType.Outgoing, HrMinS(), "System: Laser scan has completed."); }

1.7.5 Probe path localisation

In this section, a Matlab instance is created and the pre-determined probe path is selected and

localised in the coordinate system of the inspection machine. The path is then grouped and saved in

a text file which is then opened in the C# software and the path information is parsed and stored in

a list type variable. The Matlab script for localisation is presented in Chapter 2.3.

List<object> toolPathList = new List<object>(); private void btn_toolPath_Click(object sender, EventArgs e) { toolPathList = new List<object>(); MLApp.MLApp mLab = new MLApp.MLApp(); Log(LogMsgType.Outgoing, HrMinS(), "Matlab: A Matlab instance has been initialized."); //Create save file path DateTime now = DateTime.Now; ultrasonicToolPath = resultsFileDire + "toolPath" + "_" + now.ToString("dd-MM-yy-hhmmss") + ".txt"; //Set Matlab path

396

string cmd = "cd '" + matlabDire + "'"; mLab.Execute(@cmd); if (matlabDire != resultsFileDire) { cmd = "addpath('" + resultsFileDire + "')"; mLab.Execute(@cmd); } //Set Matlab window invisible. mLab.Visible = 1; //Send the command for calculating toolpath. laserPath = resultsFileDire + @"laserData_09-12-15-054947.txt"; cmd = string.Format("CalculateUSToolPath('{0}','{1}')", laserPath, ultrasonicToolPath); try { //mLab.Execute(@cmd); } catch { Log(LogMsgType.Error, HrMinS(), "Error: tool path for ultrasonic probe not generated."); return; } if (overwriteUSToolPathFile) ultrasonicToolPath = overwriteUSToolPathFileLoc; string[] coordS; float[] coords; int lineCount = -1; int rotationCount = -1; int coordsCount = -1; int paraPerLine = 11; DialogResult dialogResult = DialogResult.Cancel; if (File.Exists(ultrasonicToolPath)) { do { try { using (StreamReader sr = new StreamReader(ultrasonicToolPath)) { string line; while ((line = sr.ReadLine()) != null) { lineCount++; if (line.StartsWith("R")) { rotationCount++; Regex regex = new Regex(@"-*\d+.\d+"); Match match = regex.Match(line); if (match.Success) { double a = double.Parse(match.Value, CultureInfo.InvariantCulture); toolPathList.Add(a); } } else { coordsCount++; coordS = line.Split('\t');

397

coords = new float[paraPerLine]; for (int i = 0; i < paraPerLine; i++) { if (i == 6) continue; coords[i] = float.Parse(coordS[i]); } coords[6] = float.Parse(Regex.Match(coordS[6], @"\d+").Value); toolPathList.Add(coords); } } } Log(LogMsgType.Outgoing, HrMinS(), "Matlab: Tool path has been successfully loaded."); Log(LogMsgType.Outgoing, HrMinS(), String.Format("Matlab: Number of spindle rotation requied:{0}.", rotationCount)); Log(LogMsgType.Outgoing, HrMinS(), String.Format("Matlab: Number of points to be inspected:{0}.", coordsCount + 1)); dialogResult = DialogResult.Cancel; } catch { dialogResult = MessageBox.Show(String.Format("Invalid data format at line {0}!", lineCount + 1), "Error", MessageBoxButtons.RetryCancel, MessageBoxIcon.Error); if (dialogResult == DialogResult.Cancel) Log(LogMsgType.Error, HrMinS(), String.Format("Error: An error occured during reading tool path file. Invalid data format at line {0}!", lineCount + 1)); } } while (dialogResult == DialogResult.Retry); } else Log(LogMsgType.Error, HrMinS(), "Error: tool path for ultrasonic probe not generated."); mLab.Execute("clear all;"); mLab.Quit(); Log(LogMsgType.Warning, HrMinS(), "Matlab: The Matlab instance has been closed."); }

1.7.6 Ultrasonic data acquisition

This section of code is divided into two parts. The first part is initialisation, where ultrasonic PCI card

is configured and the robot is instructed to prepare for ultrasonic inspection. In the second part, the

robot is instructed to move the ultrasonic probe according to the calculated probe path and the

ultrasonic PCI card is instructed to excite ultrasonic pulses and collect ultrasonic data when needed.

The execution of the robot task and the ultrasonic task are separated in two threads. Although multi-

threading may not be required at this stage, it is ultimately needed for more an intelligent process.

398

Initialisation

public static double usGainHigh = 70; public static double usGainLow = 50; private static double _curGain = 0; public static double CurGain { get { return _curGain; } set { ultra.SetGain(value); _curGain = value; } } private void btn_ultrasonicScan_Click(object sender, EventArgs e) { #region variables string saveFileName = "ultrasonicData"; DateTime now = DateTime.Now; ultrasonicPath = resultsFileDire + saveFileName + "_" + now.ToString("dd-MM-yy-hhmmss") + ".txt"; short UF = 3; short UT = 5; int slowSpd = 50; int fastSpd = 100; float[] safeMove = { 0, 0, 150, 0, 0, 0 }; #endregion Log(LogMsgType.Outgoing, HrMinS(), "System: Initiating ultrasonic scan."); #region initiallization Log(LogMsgType.Outgoing, HrMinS(), "System: Communicating with ultrasonic components."); UltrasonicScan us = new UltrasonicScan(); UltraScanRobot rm = new UltraScanRobot(); int check = ultra.SetTransducerMode(0); if (check != 1) { MessageBox.Show("Error: An error occured during establishing communication!"); return; } check += ultra.SetPulseVoltage(300); check += ultra.SetPulseWidth(18); check += ultra.SetDamping(0); check += ultra.SetRectifier(3); check += ultra.SetGain(usGainHigh); check += ultra.SetDCOffset(0.02); check += ultra.SetLowPassFilter(7); check += ultra.SetHighPassFilter(0);

399

check += ultra.SetSamplingRate(0); check += ultra.SetADTriggerSource(1); check += ultra.SetTriggerDelay(2000); check += ultra.SetBufferLength(1000); check += ultra.SetLogAMP(0); if (check != 14) { Log(LogMsgType.Error, HrMinS(), "Error: Please check the settings for ultrasonic probes!"); return; } tool = CurrentTool.Ultrasonic; Log(LogMsgType.Outgoing, HrMinS(), "Tank: Checking water level."); CheckWaterLevel(); Log(LogMsgType.Outgoing, HrMinS(), "Tank: Water level is suitable for ultrasonic scanning."); Log(LogMsgType.Outgoing, HrMinS(), "Robot: Grabbing ultrasonic sensor."); fanucProg.RunProg(FanucConstants.progAttachUltra, true); //Set FUP SetRobotPosReg.intConfig.SetValue((short)1, 0); SetRobotPosReg.intConfig.SetValue((short)1, 2); SetRobotPosReg.intConfig.SetValue((short)1, 3); SetRobotPosReg.intConfig.SetValue((short)0, 4); SetRobotPosReg.intConfig.SetValue((short)0, 5); SetRobotPosReg.intConfig.SetValue((short)0, 6); //Move to a FUP position float[] fupPos = new float[6] { -11.7f, 1.4f, -50.2f, 0, 10, 0 }; fanucMove.JMove(fupPos, 10, 0, FanucConstants.Tool.Ultrasonic, true, UF, UT); //Add arguments to background worker which handles robot movements. List<object> arguments = new List<object>(); arguments.Add(rm); arguments.Add(slowSpd); arguments.Add(fastSpd); arguments.Add(FanucConstants.Tool.Ultrasonic); arguments.Add(true); //checkPos arguments.Add(safeMove); arguments.Add(toolPathList); arguments.Add(UF); arguments.Add(UT); arguments.Add(false); //laserVerifyProbePath //Start ultrasonic data logging. bgworker_ultraDataAcq.RunWorkerAsync(us); //Start robot. bgworker_ultraScanRobot.RunWorkerAsync(arguments); #endregion }

Multi-threading

#region background workers public static bool triggerUltrasonics = true; public static bool isNewHole = false; public static bool ultrasonicDataCollected = true;

400

The ultrasonic thread

#region ultrasonic data acquisition private void bgworker_ultraDataAcq_DoWork(object sender, DoWorkEventArgs e) { BackgroundWorker worker; worker = (BackgroundWorker)sender; UltrasonicScan us = (UltrasonicScan)e.Argument; us.scan(worker, e, ultra.BufferLength, ultrasonicPath, 50); } private void bgworker_ultraDataAcq_RunWorkerCompleted(object sender, RunWorkerCompletedEventArgs e) { bgworker_ultraDataAcq.CancelAsync(); Thread.Sleep(100); Application.DoEvents(); } public static bool usSelfStop = false; public static int curHoleNum = 0; public static int curSecNum = 0; private class UltrasonicScan { /// <summary> /// /// </summary> /// <param name="worker"></param> /// <param name="e"></param> /// <param name="bufferSize"></param> /// <param name="filePath">file name and path for saving result. MUST use double forword slash!</param> public void scan(BackgroundWorker worker, DoWorkEventArgs e, int bufferSize, string filePath, int triggerFrequency) { List<byte[]> dataList = new List<byte[]>(); List<string> dataInfo = new List<string>(); DateTime d = new DateTime(); byte[] data = new byte[bufferSize]; byte[] emptydata = new byte[1]; #region gain stepping double gainMin = 30; double gainMax = 80; double gainCache = gainMin; double gainStep = 5; bool gainStepping = true; if (gainStepping) CurGain = gainCache; #endregion #region general settings int noOfBackwall = 100; int noOfInterface = 0; bool scanningInterface = false; int count = 0; #endregion double[][] dataCollection = new double[noOfBackwall][];

401

double[] averagedUSData = new double[noOfBackwall]; while (!worker.CancellationPending & !usSelfStop) { ultra.ResetMemory(); ultra.ResetCounter(); // send a pulse out int isSent = 0; while (isSent != 1) { isSent = ultra.SetSoftwareTrigger(); } // read data from memory when ready int isReady = 0; while (isReady != 1) { isReady = ultra.IsDataReady(); } d = DateTime.UtcNow; ultra.GetData(out data, bufferSize); if (triggerUltrasonics) { dataCollection[count] = Array.ConvertAll(data, Convert.ToDouble); count++; } else { count = 0; } if (count == noOfBackwall) { averagedUSData = Average(dataCollection); bool fileLogged = LogUSData(filePath, averagedUSData); if (gainStepping) { dataCollection = new double[noOfBackwall][]; gainCache += gainStep; if (gainCache <= gainMax) { CurGain = gainCache; } else { gainCache = gainMin; CurGain = gainCache; triggerUltrasonics = false; ultrasonicDataCollected = true; } } else { if (noOfInterface != 0) { dataCollection = new double[noOfInterface][];

402

CurGain = usGainLow; Thread.Sleep(50); } scanningInterface = true; } count = 0; } else if ((scanningInterface & count == noOfInterface) || (scanningInterface & noOfInterface == 0)) { scanningInterface = false; triggerUltrasonics = false; ultrasonicDataCollected = true; count = 0; if (noOfInterface != 0) { CurGain = usGainHigh; averagedUSData = Average(dataCollection); LogUSData(filePath, averagedUSData); } dataCollection = new double[noOfBackwall][]; } } e.Cancel = true; } private bool LogUSData(string filePath, double[] usdata) { try { using (StreamWriter sw = File.AppendText(@filePath)) { string s = string.Format("{0} {1} {2} {3} {4} ", CurGain, curSecNum, curHoleNum, ultra.SamplingRate, ultra.BufferLength); sw.Write(s); for (int row = 0; row < usdata.Length; row++) sw.Write(usdata[row].ToString() + " "); sw.WriteLine(); } } catch (Exception e) { Console.WriteLine("{0} Exception caught.", e); return false; } return true; } private double[] Average(double[][] m) { double[] d = new double[m[1].Length]; for (int col = 0; col < m[1].Length; col++) { for (int row = 0; row < m.Length; row++) { d[col] += m[row][col]; } d[col] /= m.Length;

403

} return d; } } #endregion

The robot thread

#region ultraScanRobot public static int ultraScanL = 0; private void bgworker_ultraScanRobot_DoWork(object sender, DoWorkEventArgs e) { BackgroundWorker worker; worker = (BackgroundWorker)sender; List<object> genericlist = e.Argument as List<object>; UltraScanRobot robot = (UltraScanRobot)genericlist[0]; int slowSpd = (int)genericlist[1]; int fastSpd = (int)genericlist[2]; FanucConstants.Tool tool = (FanucConstants.Tool)genericlist[3]; bool checkPos = (bool)genericlist[4]; float[] safeMove = (float[])genericlist[5]; List<object> toolpath = (List<object>)genericlist[6]; short UF = (short)genericlist[7]; short UT = (short)genericlist[8]; bool laserVerifyProbePath = (bool)genericlist[9]; int cnt = 0; robot.move(worker, e, safeMove, toolpath, slowSpd, fastSpd, cnt, tool, checkPos, UF, UT, laserVerifyProbePath); } private void bgworker_ultraScanRobot_RunWorkerCompleted(object sender, RunWorkerCompletedEventArgs e) { Log(LogMsgType.Outgoing, HrMinS(), "Ultrasonic Scanning has been finished"); bgworker_ultraScanRobot.CancelAsync(); bgworker_ultraDataAcq.CancelAsync(); Thread.Sleep(100); Application.DoEvents(); } private class UltraScanRobot { public void move(BackgroundWorker worker, DoWorkEventArgs e, float[] safeMove, List<object> toolpath, int slowSpd, int fastSpd, int cnt, FanucConstants.Tool tool, bool checkPos, short UF, short UT, bool laserVerifyProbePath) { double oldAngle = 0; double angle; float[] coords; int spdbit; int spd = slowSpd; int curHole; int curSec; string check = ""; DateTime now = DateTime.Now; string laserPath = resultsFileDire + "PathVerification" + "_" + now.ToString("dd-MM-yy-hhmmss") + ".txt";

404

for (int i = 0; i < toolpath.Count; i++) { //Current line is an integer => spindle rotation if (toolpath[i] is double) { //stop recording ultrasonic data triggerUltrasonics = false; //safe move if not the first rotation if (i != 0) { if (!laserVerifyProbePath) { usSelfStop = true; fanucMove.LMoveRel(safeMove, fastSpd, 0, tool, true, UF, UT); ReturnUSProbe(UF, UT); } } angle = (double)toolpath[i] - oldAngle; oldAngle = (double)toolpath[i]; if (angle != 0) { if (!laserVerifyProbePath) { double executedAngleOfRotation; executedAngleOfRotation = stpMotorAdv.RotateDAutoMCS(angle); } } usSelfStop = false; } //Current line is not an interger => xyzwprSpd else { coords = new float[6]; for (int n = 0; n < 6; n++) coords[n] = ((float[])toolpath[i])[n]; spdbit = (int)((float[])toolpath[i])[6]; curSec = (int)((float[])toolpath[i])[7]; curHole = (int)((float[])toolpath[i])[8]; if (spdbit == 1) spd = slowSpd; else spd = fastSpd; if (curSec != 0) { // Move to the next point when data is collected while (!ultrasonicDataCollected) { Thread.Sleep(50); } fanucMove.LMove(coords, spd, cnt, tool, true, UF, UT); // Use laser to verify probe path or collect ultrasonic data if (laserVerifyProbePath & tool == FanucConstants.Tool.Laser) { double laserReading = daqAna.GetLaserReading(10); if (laserReading < 10) logToFile(laserPath, coords, laserReading); }

405

else { Thread.Sleep(500); triggerUltrasonics = true; ultrasonicDataCollected = false; } check = string.Format("{0} {1}", curSec, curHole); } } } return; } private void ReturnUSProbe(short UF, short UT) { float[] curJoint; float[] jointPos = new float[6]; string posTime; fanucPos.GetJointPosition(out curJoint, out posTime, 5); jointPos[0] = curJoint[0]; jointPos[1] = 0; jointPos[2] = curJoint[2]; jointPos[3] = curJoint[3]; jointPos[4] = curJoint[4]; jointPos[5] = 0; fanucMove.JMove(jointPos, 10, 0, FanucConstants.Tool.Ultrasonic, true, UF, UT); if (jointPos[3] < 0) jointPos[3] = -90; else jointPos[3] = 90; fanucMove.JMove(jointPos, 10, 0, FanucConstants.Tool.Ultrasonic, true, UF, UT); jointPos[4] = 0; fanucMove.JMove(jointPos, 10, 0, FanucConstants.Tool.Ultrasonic, true, UF, UT); jointPos[3] = 0; fanucMove.JMove(jointPos, 10, 0, FanucConstants.Tool.Ultrasonic, true, UF, UT); fanucProg.RunProg("TOOLDOWN", true); fanucProg.RunProg(FanucConstants.progDettachUltra, true); } } #endregion #endregion

1.7.7 Wall thickness evaluation

Finally, after all required ultrasonic data are collected, the wall thickness evaluation script is called.

The Matlab script for thickness evaluation is presented in Chapter 2.5.

private void btn_results_Click(object sender, EventArgs e) { MLApp.MLApp mLab = new MLApp.MLApp(); Log(LogMsgType.Outgoing, HrMinS(), "Matlab: A Matlab instance is initialized."); //Set Matlab path

406

string dir = @"C:\Users\MACE-USER\OneDrive\Ultrasonic KTP\ELE-Laptop Documents\04. Matlab Coding\MATLAB\LAST EXPERIMET FOR BLOCK WITH HOLES FROM FLAT"; string cmd = "cd '" + dir + "'"; mLab.Execute(@cmd); //Set Matlab window invisible. mLab.Visible = 1; mLab.Execute("UI_Develop_Integ_v2"); }

407

Chapter 2

Matlab Codes

Matlab is a convenient tool for solving complex mathematical equations and matrix evaluations.

Therefore, all calculations including ultrasonic data processing are completed in Matlab.

These calculations include B-spline curve, 2D Delaunay triangulation, shape-preserving

parameterisation, B-spline surface, probe path calculation, localisation, probe path grouping and wall

thickness evaluation. In this chapter, codes of the Matlab scripts for realising these calculations are

presented.

408

2.1 Reverse engineering

2.1.1 The main Matlab function

This section presents the main Matlab function that collects user input, executes calculation in sub-

functions and generates output. It is noted that 2D Delaunay triangulation is calculated in this

function.

function [ P_surf, ctrlPCell, uCell, knotV] = FuncBspline_Main( nos,nc_u,nc_w,ku,kw,nnu,nnw,sectionData) % SectionData, a cell wherein each set is one complete section % nos, number of sections for measured blade data % nc_u, number of control points for fitted Bspline curves in u direction % nc_w, number of control points for fitted Bspline curves in w direction % ku, number of control points for each segment in u dorection ,ku-1 is the degree of each segment % kw, number of control points for each segment in w dorection ,kw-1 is the degree of each segment % nnu, number of generated points in each section in u directoin % nnw, number of generated points in each section in w directoin %% Sort out input data and 2D parameterization % For each section, generate equal number of points that are uniformly % spaced. This is done by fitting a B-spline curve to each section. % figure; k=1;c=1; for i=1:nos pread=sectionData{1,i}; [ps,nop,us,C_sec,knotV]= FuncBspline_curve(pread,nc_u,ku,nnu); p(k:k+nop-1,:)=ps; uCell{c}=us; ctrlPCell{c}=C_sec; %Calculate the u value x=ps(:,1); y=ps(:,2); z=ps(:,3); l_sumxy=0; l_uweight=0; for j= 1:nop-1 l_pxy=((x(j+1)-x(j)).^2+(y(j+1)-y(j)).^2+(z(j+1)-z(j)).^2).^1/2; l_sumxy=l_sumxy+l_pxy; l_uweight(j+1,:)=l_sumxy; end u(k:k+nop-1,:)=l_uweight/l_sumxy; k=k+nop; c=c+1; end %% Define boundary points, reorder data points and apply Delaunay triangulation % construct w w = 0:1/(nos-1):1;

409

w = repmat(w,nnu,1); w =w(:); % combine u and w uw = [u, w]; uw_inside = uw; p_inside = p; % find boundary bu1i = find(uw_inside(:,2)==0); bu1_ = uw_inside(bu1i,:); uw_inside(bu1i,:) = []; pu1_ = p_inside(bu1i,:); p_inside(bu1i,:) = []; bu2i = find(uw_inside(:,2)==1); bu2_ = uw_inside(bu2i,:); uw_inside(bu2i,:) = []; pu2_ = p_inside(bu2i,:); p_inside(bu2i,:) = []; bw1i = find(uw_inside(:,1)==0); bw1_ = uw_inside(bw1i,:); uw_inside(bw1i,:) = []; pw1_ = p_inside(bw1i,:); p_inside(bw1i,:) = []; bw2i = find(uw_inside(:,1)==1); bw2_ = uw_inside(bw2i,:); uw_inside(bw2i,:) = []; pw2_ = p_inside(bw2i,:); p_inside(bw2i,:) = []; boundary=[bu1_;bw1_;bu2_;bw2_]; uw_c = [uw_inside;boundary]; t=delaunay(uw_c); p_c = [p_inside;pu1_;pw1_;pu2_;pw2_]; x = p_c(:,1); y = p_c(:,2); z = p_c(:,3); %% Shape-preserving paramerization n=size(boundary,1); [tp,td]=FuncBspline_SPP_edge(t,x,y,z,n); % compute barycentric coordinates of data points pu=tp\(td*boundary(:,1)); % compute the u and w value for each point pw=tp\(td*boundary(:,2)); puw=[pu,pw boundary(:,1),boundary(:,2)]; uu=puw(:,1); ww=puw(:,2);

410

%% B-spline surface Fitting [P_surf]=FuncBspline_surface(x,y,z,uu,ww,nc_u,nc_w,ku,kw,nnu,nnw); end

2.1.2 B-spline curve

The following code calculates the B-spline curve.

function [fitP,nop,uvalue,ctrlP,knotV]=FuncBspline_curve(inputPoints,noOfCtrlPoints,degreeOfSeg,noOfFittedPoints) npoints= length(inputPoints); totalulength=zeros(npoints,1); QX=inputPoints(:,1); QY=inputPoints(:,2); QZ=inputPoints(:,3); %% Calculate u values k=degreeOfSeg+1; n=noOfCtrlPoints-1; knotV=[]; no_of_segments=n-k+2; uvalue(2:npoints) = sqrt((QX(2:npoints)-QX(1:npoints-1)).^2 +(QY(2:npoints)-QY(1:npoints-1)).^2+(QZ(2:npoints)-QZ(1:npoints-1)).^2); for i=2:npoints totalulength(i)=totalulength(i-1)+uvalue(i); %Adding small curve lengths together end uvalue(1:npoints)=totalulength(1:npoints)/totalulength(npoints)*no_of_segments; u(1:npoints)=uvalue(1:npoints); for i=1:1:(n+k+1) if i<k+1 knotV(i)=0; else if i>=k+1 if i<=n+1 knotV(i)=i-k; else knotV(i)=n-k+2; end else end end end NA=[];N=[]; for j=1:npoints for i=1:n+2 if i<k NA(i,1)=0; else if u(j)>=knotV(i) && u(j)<knotV(i+1) NA(i,1)=1; else if u(j)==knotV(i) && u(j)==knotV(i+1) NA(i-1,1)=1;NA(i,1)=0;

411

else NA(i,1)=0; end end end end N(1:n+1,1)=NA(1:n+1,1); for m=2:k for i=1:n+1 if knotV(i+m-1)-knotV(i)==0 p1=0; else p1=(u(j)-knotV(i))/[knotV(i+m-1)-knotV(i)]*N(i,m-1); end if knotV(i+m)-knotV(i+1)==0 p2=0; else p2=[knotV(i+m)-u(j)]/[knotV(i+m)-knotV(i+1)]*N(i+1,m-1); end N(i,m)=p1+p2; end end U(j,1:n+1)=N(1:n+1,k); end CX=U\QX; CY=U\QY; CZ=U\QZ; ctrlP=[CX,CY,CZ];%%C are control points %% Redivide the curve and fit a B-spline curve to it span=no_of_segments/(noOfFittedPoints-1); u1=0:span:no_of_segments; npoints=length(u1); for j=1:npoints for i=1:n+2 if i<k NA(i,1)=0; else if u1(j)>=knotV(i) && u1(j)<knotV(i+1) NA(i,1)=1; else if u1(j)==knotV(i) && u1(j)==knotV(i+1) NA(i-1,1)=1;NA(i,1)=0; else NA(i,1)=0; end end end end

412

N(1:n+1,1)=NA(1:n+1,1); for m=2:k for i=1:n+1 if knotV(i+m-1)-knotV(i)==0 p1=0; else p1=(u1(j)-knotV(i))/[knotV(i+m-1)-knotV(i)]*N(i,m-1); end if knotV(i+m)-knotV(i+1)==0 p2=0; else p2=[knotV(i+m)-u1(j)]/[knotV(i+m)-knotV(i+1)]*N(i+1,m-1); end N(i,m)=p1+p2; end end U1(j,1:n+1)=N(1:n+1,k); end fitP=U1*ctrlP; nop=length(fitP); for i=1:length(u1) uvalue(i,1)=u1(1,i); end

2.1.3 Shape-preserving parameterisation

The following codes calculate shape-preserving parameterisation.

function[tp,td]=FuncBspline_SPP_edge(t,x,y,z,np1) % compute the barycentric coordinate of data points %% Sorting the edges of each polygon np=size(x,1); N=np-np1; v=ones(1,N); tp=diag(v); td=zeros(N,np1); %% Initialize the variables n=1; for id=1:N % Check every point in sequence clear e e2 e3 checkt tri edge ve angle angleplane lin newve x1 y1 z1 ppx ppy % b=size(bound_points_order); % if ~isempty(find(id==bound_points_order(1:b))) % continue; % end %% STEP 1. Define the polygon

413

ppx(1)=0; ppy(1)=0; angleplane(1)=0; % Initialize variables at start of each loop checkt=any(t==id,2); %% extracting the polygon of which the center is "id" tri=t(checkt,:); nt=size(tri,1); if isempty(tri)%% In case of any noisy points, skip the noisy points continue end % figure(8) % trimesh(tri,x,y,z) checkt=true(nt,1); for j=1:nt %% position the center point of the polygon in the first column if tri(j,2)==id; tri(j,2)=tri(j,1); elseif tri(j,3)==id; tri(j,3)=tri(j,1); end tri(j,1)=id; end l=1:nt; %% extracting all edges from a polygon e=[tri(:,[1,2]); tri(:,[1,3])]; [e,j,j] = unique(sort(e,2),'rows'); %% Remove duplicated edges e2 = [j(l), j(l+nt)]; % e2 stores the relationship between the triangle and its edges ne=size(e,1); e3 = zeros(ne,2); count= ones(ne,1); % e3 defines the two triangles owned by one edge for l=1:nt for j=1:2 ce = e2(l,j); e3(ce,count(ce))=l; count(ce)=count(ce)+1; end end % position center point in the first column for j=1:ne if e(j,2)==id e(j,2)=e(j,1); end e(j,1)=id; end k=1; m=1; % m is the ID of the triangle that will be extracted n=1; edge(k,:)=e(e2(m,1),:); % define the first edge that is selected idp(k)=edge(k,2); % take all boundary points of the polygon

414

k=k+1; while any(checkt==1) tri1=e3(e2(m,n),1); % Select two adjacent triangles which share a common edge tri2=e3(e2(m,n),2); tri2=e3(e2(m,n),2); checkt(m)=false; if tri1==m % If tri1 is the last triangle ed1=e(e2(tri2,1),:); ed2=e(e2(tri2,2),:); % one edge of tri2 is the next edge in sequence if ed1(2)==edge(k-1,2) edge(k,:)=ed2; idp(k)=ed2(2); k=k+1; m=tri2; n=2; elseif ed2(2)==edge(k-1,2) edge(k,:)=ed1; idp(k)=ed1(2); k=k+1; m=tri2; n=1; end else % If tri2 is the last triangle ed1=e(e2(tri1,1),:); ed2=e(e2(tri1,2),:); % one edge of tri2 is the next edge in sequence if ed1(2)==edge(k-1,2) edge(k,:)=ed2; idp(k)=ed2(2); k=k+1; m=tri1; n=2; elseif ed2(2)==edge(k-1,2) edge(k,:)=ed1; idp(k)=ed1(2); k=k+1; m=tri1; n=1; end end end k=k-1; %% STEP 2. Mapping the space polygon into plane % Extract the coordinates of the end points of each edge for j=1:k x1(j,:)=x(edge(j,:)); y1(j,:)=y(edge(j,:)); z1(j,:)=z(edge(j,:)); end % Calculate the length of each edge for j=1:k ve(j,:)=[x1(j,2)-x1(j,1),y1(j,2)-y1(j,1),z1(j,2)-z1(j,1)];

415

lin(j)=norm(ve(j,:)); end % Calculate the sum of the solid angles of two adjacent edges sumangle=0; for j=1:k-1 result = dot(ve(j+1,:),ve(j,:))/(norm(ve(j+1,:))*norm(ve(j,:))); if result>1 result = 1; end angle(j)=acos(result); sumangle=angle(j)+sumangle; end % Solve Eq.1 of shape-preserving parameterization for j=1:k-1 angleplane(j+1)=angle(j)/sumangle*2*pi; end newve(1,:)=[1,0]; % reference vector nor=1; % Calculate the transformation matrix for j=1:k cs=cos(angleplane(j)); si=sin(angleplane(j)); ro=[cs,si;-si, cs]; newve(j+1,:)= newve(j,:)/nor*ro.*lin(j); % map the polygon onto plane nor=lin(j); end % Store the coordinate of vertices of polygon for j=2:k ppx(j,:)=newve(j,1)+ppx(1); ppy(j,:)=newve(j,2)+ppy(1); pp=[ppx,ppy]; end %% STEP 3. Get final stuff done % Calculate the Barycentric Coordinates [tarea]=FuncBspline_SPP_area(ppx,ppy); for l=1:k-1 % save λ in tp and td if idp(l)<=N tp(id,idp(l))=tp(id,idp(l))-tarea(l+1); else idp(l)=idp(l)-N; td(id,idp(l))=tarea(l+1); end end end

2.1.4 B-spline surface

Matlab codes for calculation of a B-spline surface are presented below.

416

function [P_surf]=FuncBspline_surface(PX,PY,PZ,u,w,ncp,ncpw,k,kw,npoints2,npoints3) %% STEP 1. Generate control points using given u and w coordinates %% U direction - parameters n=ncp-1; % number of control points -1 t=[];% the knot vector no_of_segments=n-k+2; % number of segments QX=PX;QY=PY;QZ=PZ; u=no_of_segments*u; npoints=size(QX,1); % Calculate Knot value t(i) for u direction % see page 150 mortenson for i=1:1:(n+k+1) if i<k+1 t(i)=0; else if i>=k+1 if i<=n+1 t(i)=i-k; else t(i)=n-k+2; end else end end end %% Calculate basis function for each u NA=[];N=[]; for j=1:npoints %u(j):from u(1) to u(npoints) % Calculate basis function N(i,1), for i=1:n+2 if i<k NA(i,1)=0; else if u(j)>=t(i) && u(j)<t(i+1) NA(i,1)=1; else if u(j)==t(i) && u(j)==t(i+1) NA(i-1,1)=1;NA(i,1)=0; else NA(i,1)=0; end end end end N(1:n+1,1)=NA(1:n+1,1); % Calculate basis function N(i,m) m=2:k for m=2:k for i=1:n+1 if t(i+m-1)-t(i)==0

417

p1=0; else p1=(u(j)-t(i))/[t(i+m-1)-t(i)]*N(i,m-1); end if t(i+m)-t(i+1)==0 p2=0; else p2=[t(i+m)-u(j)]/[t(i+m)-t(i+1)]*N(i+1,m-1); end N(i,m)=p1+p2; end end

U(j,1:n+1)=N(1:n+1,k); % relocate the computed basis functions N(i,k) in U end %% W direction - parameters npoints_w=length(QX); % number of data points. nw=ncpw-1; % n=number of control points -1; tw=[]; no_of_segments_w=nw-kw+2; % number of segments % w coordinates w=no_of_segments_w*w; %%%%%%% Calculate Knot value t(i) in w direction for i=1:1:(nw+kw+1) if i<kw+1 tw(i)=0; else if i>=kw+1 if i<=nw+1 tw(i)=i-kw; else tw(i)=nw-kw+2; end else end end end NAw=[];Nw=[];UW=[]; %% Calculate basis functions for each w for e=1:npoints_w %w(e) from w(1) to w(npoints) % Calculate basis function Nw(i,1) for i=1:nw+2 if i<kw NAw(i,1)=0; else if w(e)>=tw(i) && w(e)<tw(i+1) NAw(i,1)=1; else if w(e)==tw(i) && w(e)==tw(i+1) NAw(i-1,1)=1;NAw(i,1)=0; else NAw(i,1)=0; end

418

end end end Nw(1:nw+1,1)=NAw(1:nw+1,1); % Calculate basis functions Nw(i,m),m=2:k; for m=2:kw for i=1:nw+1 if tw(i+m-1)-tw(i)==0 p1w=0; else p1w=(w(e)-tw(i))/[tw(i+m-1)-tw(i)]*Nw(i,m-1); end if tw(i+m)-tw(i+1)==0 p2w=0; else p2w=[tw(i+m)-w(e)]/[tw(i+m)-tw(i+1)]*Nw(i+1,m-1); end Nw(i,m)=p1w+p2w; end end

W(1:nw+1,e)=Nw(1:nw+1,kw); % relocate the computed basis functions in W end % Calculate U*W matrix UW = zeros(npoints, ncp); for i=1:npoints % npoints: number of data points for j=1:ncp % ncp: number of control points UW(i,1+(j-1)*ncpw:ncpw+(j-1)*ncpw)=U(i,j)*W(1:ncpw,i); % U*W end end % Calculate the control points CX=UW\QX; CY=UW\QY; CZ=UW\QZ; % Rearrange the control points into matrix form for i=1:ncp CXX(i,1:ncpw)=CX(1+(i-1)*ncpw:ncpw+(i-1)*ncpw,1); CYY(i,1:ncpw)=CY(1+(i-1)*ncpw:ncpw+(i-1)*ncpw,1); CZZ(i,1:ncpw)=CZ(1+(i-1)*ncpw:ncpw+(i-1)*ncpw,1); end %% STEP 2. Generate surface points %% U matrix for j=1:npoints2; u_generated(j)=(j-1)/(npoints2-1)*no_of_segments; end

419

u2=u_generated; % Creat new w coordinates for j=1:npoints3; w_generated(j)=(j-1)/(npoints3-1)*no_of_segments_w; end w2=w_generated; % Reset matrices NA2_matrix=[];N2_matrix=[];NAw2_matrix=[];Nw2_matrix=[];UW2_matrix=[]; U2_matrix=[];W2_matrix=[]; for j=1:npoints2 % new u(j) from u(i) to u(npoints2) % Calculate basis fucntion N(i,1) for each u for i=1:n+2 if i<k NA2_matrix(i,1)=0; else if u2(j)>=t(i) && u2(j)<t(i+1) NA2_matrix(i,1)=1; else if u2(j)==t(i) && u2(j)==t(i+1) NA2_matrix(i-1,1)=1;NA2_matrix(i,1)=0; else NA2_matrix(i,1)=0; end end end end N2_matrix(1:n+1,1)=NA2_matrix(1:n+1,1); % Calculate basis fucntion N(i,k) for each u; i is from 2 to k; for m=2:k for i=1:n+1 if t(i+m-1)-t(i)==0 p1=0; else p1=(u2(j)-t(i))/[t(i+m-1)-t(i)]*N2_matrix(i,m-1); end if t(i+m)-t(i+1)==0 p2=0; else p2=[t(i+m)-u2(j)]/[t(i+m)-t(i+1)]*N2_matrix(i+1,m-1); end N2_matrix(i,m)=p1+p2; end end U2_matrix(j,1:n+1)=N2_matrix(1:n+1,k); end %% W matrix % Calculate basis functions for each w. w(1) to w(npoints3) for e=1:npoints3 %w(e) % Calculate basis functions N(i,1) for each w for i=1:nw+2

420

if i<kw NAw2_matrix(i,1)=0; else if w2(e)>=tw(i) && w2(e)<tw(i+1) NAw2_matrix(i,1)=1; else if w2(e)==tw(i) && w2(e)==tw(i+1) NAw2_matrix(i-1,1)=1;NAw2_matrix(i,1)=0; else NAw2_matrix(i,1)=0; end end end end Nw2_matrix(1:nw+1,1)=NAw2_matrix(1:nw+1,1); % Calcutlate N(i,k) for each w;

for m=2:kw % k is from 2 to k;

% Calcutlate N(i,k) for each w with k fixed;i is from 1 to n+1; for i=1:nw+1 if tw(i+m-1)-tw(i)==0 p1w=0; else p1w=(w2(e)-tw(i))/[tw(i+m-1)-tw(i)]*Nw2_matrix(i,m-1); end if tw(i+m)-tw(i+1)==0 p2w=0; else p2w=[tw(i+m)-w2(e)]/[tw(i+m)-tw(i+1)]*Nw2_matrix(i+1,m-1); end Nw2_matrix(i,m)=p1w+p2w; end end W2_matrix(1:nw+1,e)=Nw2_matrix(1:nw+1,kw); end %% Surface points k_1=0; P_surf=zeros(npoints3*npoints2,3); for j=1:npoints3 for i=1:npoints2 k_1=k_1+1; FX=U2_matrix(i,:)*CXX*W2_matrix(:,j); FY=U2_matrix(i,:)*CYY*W2_matrix(:,j); FZ=U2_matrix(i,:)*CZZ*W2_matrix(:,j); P_surf(k_1,:)=[FX FY FZ]; end end

421

2.2 Probe path calculation

2.2.1 Data preparation

The main Matlab function gathers user inputs and prepares data for calculation in the sub-function.

function CalculateUSToolPath_generalToolPath2(sectionInfo,holeInfo,laserInfo,toolPathSaveFile) % Load section data deltaZ = 2; axisNo = 3; if ischar(sectionInfo) sectionCell = cell(1,nos); [~,~,ext] = fileparts(sectFile); if strcmp(ext, '.mat') load(sectFile); else sectionCell=xlsread(sectFile,1); sectionCell = FuncUSToolPath_matrix2Cell(sectionCell, axisNo, deltaZ); end else sectionCell = sectionInfo; end % read hole center position if ischar(holeInfo) [~,~,ext] = fileparts(holePosFile); if strcmp(ext,'.mat') load(holePosFile); holePosCell = holeCentre; else holePosCell = xlsread(holePosFile); end else holePosCell = holeInfo; end if ~iscell(holePosCell) holePosCell = FuncUSToolPath_matrix2Cell(holePosCell, axisNo, deltaZ); end % read laser scan result if ischar(laserInfo) [~,~,ext] = fileparts(laserInfo); if strcmp(ext, '.mat') load(laserInfo); else [a,b,c,d] = FuncUSToolPath_readLaserScan(laserInfo); P_scan=[a,b,c+d]; end else P_scan = laserInfo; end % read toolPathSaveFile [~,fName,ext] = fileparts(toolPathSaveFile);

422

if ~strcmp(ext, '.mat') toolPathSaveFile = fName+'.mat'; end doCalculation(sectionCell,holePosCell,P_scan,toolPathSaveFile);

2.2.2 The main path calculation function

This Matlab function gathers data and uses sub-functions for specific calculations. Results from the

sub-functions are collected and progressively generates an ordered probe path for the entire cross

section.

function doCalculation(sectionCell,holeCell,P_scan,toolPathSaveFile) %Inputs % sectionCell is an excel file with the section data. % holeCell is an excel file with the hole positions % P_scan is a txt file with the laser scans from the robot %% Customer setting – predefined transformation matrix trans_predefined = [-0.164255972665765,0.00250922612179932,0.986414557489855,582.408679234385;0.985830874054514,0.0349074325108971,0.164069981765176,-588.319614736541;-0.0340215109092956,0.999387399830407,-0.00820742686119589,49.5114250365749;0,0,0,1]; % Bspline parameters nc_u=25; % number of control points for fitted Bspline curves in u direction nc_w=10; ku=4; % degree of each segment in Bspine curves in u direction % Toolpath d_w=3; % degree of each segment in Bezier curves in w direction ac=0.2; % pitch used to find the blade point which has shortest distance with hole gb=10; % number of point go back when setting the inspection region gf=10; % number of point go foward when setting the inspection region wRange = 20; % extract points that are within wRange surrounding a path point. % Localisation kw=3; % Degree of B-spline surface in the w direction nnu=500; % Number of genorated points in the u direction nnw=500; % Number of genorated points in the w direction % ICP parameters tou=0.000001; d_min=0.005; k_max=100; n_o_app=1; % Evaluate data sizes nos = size(sectionCell,2); % number of sections noh = size(holeCell{1},1); % number of cooling channels nosM = size(holeCell, 2); % number of sections to be measured %% Fit a B-spline surface to measured points

423

[ P_surf, ~, ~, ~ ] = FuncBspline_Main(nos,nc_u,nc_w,ku,kw,nnu,nnw,sectionCell); for i = 1:nnw P_surfCell{i} = P_surf((i-1)*nnu+1:i*nnu,:); listOfZ(i) = mean(P_surfCell{i}(:,3)); end %% Define inspection region for each cooling hole centre % Find the closest points on Bspline curve in u direction for each hole centre % and take its foward and back points, the number of points could be set by % changing gb and gf in customer setting n=1; po=zeros(nosM,noh); for isec=1:nosM hole = holeCell{isec}; s = size(hole); if s(2) == 4 radius{isec} = hole(:,4); hole(:,4) = []; end curZ = mean(hole(:,3)); zM(isec) = curZ; diffZ = abs(listOfZ - curZ*ones(1, nnw)); secList(isec) = find(min(diffZ)==diffZ,1); curP = P_surfCell{secList(isec)}; curNop = size(curP,1); x=curP(:,1); y=curP(:,2); z=curP(:,3); % Fit a B-spline curve to these curP, so that this curve can be % differentiated to find tangent vectors [fitP,~,u,ctrlP,knotV]=FuncBspline_curve(curP,nc_u,ku,nnu); uCell{isec} = u; ctrlPCell{isec} = ctrlP; knotVCell{isec} = knotV; pMCell{isec} = fitP; x=fitP(:,1); y=fitP(:,2); z=fitP(:,3); for ihole=1:noh d = zeros(curNop,1); for k=1:curNop % Find the distance between the hole position and all points % in this section d(k,:)=sqrt((hole(ihole,1)-x(k))^2+(hole(ihole,2)-y(k))^2 +(hole(ihole,3)-z(k))^2); end % Find the point po on the Bspline curve which is closest to the % hole centre if isec==1 [d_min(n),po(isec,ihole)]=min(d); %po(isec,ihole)=po(isec,ihole)+(isec-1)*nop; else d_dummy=d;

424

[d_min(n),po(isec,ihole)]=min(d_dummy); %po(isec,ihole)=po(isec,ihole)+(isec-1)*nop; while po(isec,ihole)<(po(isec-1,ihole)-8+curNop) || po(isec,ihole)>(po(isec-1,ihole)+8+curNop) [d_min(n),po(isec,ihole)]=min(d_dummy); d_dummy=[d_dummy(1:(po(isec,ihole)-1),:); d_dummy((po(isec,ihole)+1):end,:)]; po(isec,ihole)=find(d==d_min(n)); po(isec,ihole)=po(isec,ihole)+(isec-1)*curNop; end end po1=po(isec,ihole)-gb; % po1 is the foward point po2=po(isec,ihole)+gf; % pow is the back point if po1 < 1 po1 = 1; end if po2 > nnu po2 = nnu; end pc(n,:)=[po1,po2]; % the curve between po1 and po2 is the inspection region n=n+1; end end %% Re-divide the inspection region for each hole according to required pitch and calculate tangent vectors % Change the order of pc from section-by-section to channel-by-channel n=1; for ihole=1:noh for isec=1:nosM rpc{isec}(n,:)=pc(ihole,:); d_dist{isec}(n)=d_min(ihole); n=n+1; end end if (s(2)==4) for isec = 1:nosM d_dist{isec} = d_dist{isec} - radius{isec}; end end g=1; l_s=1; ihole_independant=1; % Acquire the differential equation of Bspline regarding u in Matlab Symbolic form [D]=FuncBspline_curveDiff(ku,knotV,nc_u); for ihole=1:noh pg_hole =[]; ug_hole =[]; u_vector =[]; w_vector =[];

425

dis = zeros(nos,1); % Calculate the size of the inspection region for one wall thickness in each section for isec=1:nosM p1=pMCell{isec}(rpc{isec}(ihole,1),:); p2=pMCell{isec}(rpc{isec}(ihole,2),:); dis(isec,:)=norm(p1-p2); end % Select the longest inspection region and generate new points inbetween the two points for each hole n_np=ceil(max(dis)/ac); % Calculate tangent vectors in u direction for isec=1:nosM u1=uCell{isec}(rpc{isec}(ihole,1)); u2=uCell{isec}(rpc{isec}(ihole,2)); % Reorder u1 and u2, so that u1 is smaller than u2 if u1>u2 a=u1; u1=u2; u2=a; end span=(u2-u1)/n_np; [pn,un,u_n,ln]=FuncUSToolPath_redivide(ku,ctrlPCell{isec},knotVCell{isec},span,u1,u2); % Substitute u values to evaluate the differential equation acquired eariler. [u_v]=FuncBspline_curveDiffPart2(ku,knotVCell{isec},u_n,ctrlPCell{isec},D); pg_hole((isec-1)*ln+1:isec*ln,:)=pn; ug_hole((isec-1)*ln+1:isec*ln,:)=un; u_vector((isec-1)*ln+1:isec*ln,:)=u_v/norm(u_v); end % Calculate tangent vectors in w direction [w_vector, Q] = FuncUSToolPath_tangentVw(P_surf, pg_hole, wRange, u_vector); QCell{ihole_independant} = Q{ceil(size(Q,2)/2)}; pg(g:ln*nosM+g-1,:)=pg_hole; ug(g:ln*nosM+g-1,:)=ug_hole; ug_vector(g:ln*nosM+g-1,:)=u_vector; wg_vector(g:ln*nosM+g-1,:)=w_vector; span_rec{l_s}=g:(ln*nosM+g-1); g=g+ln*nosM; l_s=l_s+1; ihole_independant=ihole_independant+1; end %% Calculate the normal vectors and probe path for j=1:length(pg); v_normol=cross(ug_vector(j,:),wg_vector(j,:)); % Calculate the verticle vecter in both of u and w directon unit_v(j,:)=v_normol/norm(v_normol); % Unit is the verticle vecter with unit length Prob_path(j,1)=pg(j,1);

426

Prob_path(j,2)=pg(j,2); Prob_path(j,3)=pg(j,3); end %% Sort tool paths n=0; for ihole=1:noh for isec=1:nosM n=n+1; span=span_rec{1,ihole}; [~,b]=size(span); b_p_h=b/nosM; span_sec=span(((isec-1)*b_p_h+1):(isec*b_p_h)); id_m=[ones(b_p_h,1)*isec ones(b_p_h,1)*ihole]; holes_tool_path{:,:,ihole,isec}=[Prob_path(span_sec,:) id_m unit_v(span_sec,:) ones(b_p_h,1)*d_dist{isec}(ihole)]; end end k=0; for isec=1:nosM for ihole=1:noh k=k+1; tool_path_ord{k}=holes_tool_path{:,:,ihole,isec}; end end % Reverse vectors if necessary i=1;j=1; for ihole = 1:k xyz = tool_path_ord{ihole}(:,1:3); normalV = tool_path_ord{ihole}(:,6:8); try hole = holeCell{i}(j,:); j=j+1; catch i=i+1;j=1; hole = holeCell{i}(j,:); end v1 = xyz + normalV; dist1 = sqrt((hole(1)-v1(:,1)).^2+(hole(2)-v1(:,2)).^2+(hole(3)-v1(:,3)).^2); dist2 = sqrt((hole(1)-xyz(:,1)).^2+(hole(2)-xyz(:,2)).^2+(hole(3)-xyz(:,3)).^2); check = dist2 - dist1; % check = check./abs(check); % if check was negative, now -1, otherwise 1. normalV = normalV.*[check check check]; tool_path_ord{ihole}(:,6:8)=normalV; end %% Plot toolpath % figure(3) figure; hold on; for i=1:nosM

427

plot3(pMCell{i}(:,1),pMCell{i}(:,2),pMCell{i}(:,3)) plot3(holeCell{i}(:,1),holeCell{i}(:,2),holeCell{i}(:,3),'or') curSec = secList(i); colorcode = '-y'; inc = 2; X = zeros(length(P_surfCell{curSec}(:,1)),1); Y = zeros(length(P_surfCell{curSec}(:,1)),1); Z = zeros(length(P_surfCell{curSec}(:,1)),1); if curSec + inc*2 < length(P_surfCell) X(:,end+1) = P_surfCell{curSec+inc*2}(:,1); Y(:,end+1) = P_surfCell{curSec+inc*2}(:,2); Z(:,end+1) = P_surfCell{curSec+inc*2}(:,3); end if curSec + inc*1 < length(P_surfCell) X(:,end+1) = P_surfCell{curSec+inc*1}(:,1); Y(:,end+1) = P_surfCell{curSec+inc*1}(:,2); Z(:,end+1) = P_surfCell{curSec+inc*1}(:,3); end X(:,end+1) = P_surfCell{curSec}(:,1); Y(:,end+1) = P_surfCell{curSec}(:,2); Z(:,end+1) = P_surfCell{curSec}(:,3); if curSec - inc*1 > 0 X(:,end+1) = P_surfCell{curSec-inc}(:,1); Y(:,end+1) = P_surfCell{curSec-inc}(:,2); Z(:,end+1) = P_surfCell{curSec-inc}(:,3); end if curSec - inc*2 > 0 X(:,end+1) = P_surfCell{curSec-inc*2}(:,1); Y(:,end+1) = P_surfCell{curSec-inc*2}(:,2); Z(:,end+1) = P_surfCell{curSec-inc*2}(:,3); end X(:,1) = [];Y(:,1) = [];Z(:,1) = []; surf(X,Y,Z,'EdgeColor','none'); end my_colour = [71 188 17] ./ 255; for i=1:size(tool_path_ord,2) curMat = tool_path_ord{i}; %plot3(curMat(:,1),curMat(:,2),curMat(:,3),'*','Color',my_colour) pv1 = curMat(:,1:3)'; nv = curMat(:,6:8)'; pv2 = pv1 - wRange/4*nv; xv = [pv1(1,:); pv2(1,:); nan([1, size(pv1,2)])]; yv = [pv1(2,:); pv2(2,:); nan([1, size(pv1,2)])]; zv = [pv1(3,:); pv2(3,:); nan([1, size(pv1,2)])]; plot3(xv(:),yv(:),zv(:),'Color', my_colour); end axis equal;axis tight;grid on;box on; view(0,90); save('thesis_toolpathPlotter.mat', 'nosM', 'pMCell', 'holeCell', 'curSec', 'secList', 'P_surfCell', 'tool_path_ord', 'wRange') %% Load laser measurments for localisation % ICP to find the transformation matrix if P_scan~=0 trans_init=0; [ trans,~] = FuncICP_Main(P_scan',P_surf',tou,d_min,k_max,n_o_app,trans_init); else trans = trans_predefined;

428

end % Save calculated data for next use save(toolPathSaveFile,'tool_path_ord','P_surf','trans','x','y','z')

2.2.3 Tangent vectors in u direction

Instead of differentiating a B-spline surface, it was found it is sufficiently accurate to generate

tangent vectors by differentiating a B-spline curve in the u direction and a Bezier curve in the w

direction. The differentiation of a B-spline curve is divided into three parts. The first part calculates

a differential equation in form of Symbolics. In the second part, u coordinates with equal spacing

are generated within an inspection region. In the third part, u values are substituted into the Symbolic

equation to calculate tangent vectors.

Part 1 FuncBspline_curveDiff

function [D]=FuncBspline_curveDiff(d,t,nc) k=d+1; n=nc-1; for i=1:1:n-k+2 ut(i)=i-1+0.5; end [utr, utc]=size(ut); NA=sym(zeros());N=sym(zeros());U=sym(); for j=1:utc for i=1:n+2 if i<k NA(i,1)=0; else if ut(j)>=t(i) && ut(j)<t(i+1) NA(i,1)=1; else if ut(j)==t(i) && ut(j)==t(i+1) NA(i-1,1)=1;NA(i,1)=0; else NA(i,1)=0; end end end end N(1:n+1,1)=NA(1:n+1,1); for m=2:k syms u for i=1:n+1 if t(i+m-1)-t(i)==0 p1=0; else p1=(u-t(i))/[t(i+m-1)-t(i)]*N(i,m-1); end if t(i+m)-t(i+1)==0

429

p2=0; else p2=(t(i+m)-u)/(t(i+m)-t(i+1))*N(i+1,m-1); end N(i,m)=p1+p2; end end U(j,1:n+1)=N(1:n+1,k);

D=diff(U); End

Part 2 FuncUSToolPath_redivide

function

[Fit,u_new,un,l]=FuncUSToolPath_redivide(degreeOfCurve,ControlPoints,knotV,spacing,u1,u2) k=degreeOfCurve+1; nc=length(ControlPoints); n=nc-1; un=u1:spacing:u2; npoints=length(un); for j=1:npoints for i=1:n+2 if i<k NA(i,1)=0; else if un(j)>=knotV(i) && un(j)<knotV(i+1) NA(i,1)=1; else if un(j)==knotV(i) && un(j)==knotV(i+1) NA(i-1,1)=1;NA(i,1)=0; else NA(i,1)=0; end end end end N(1:n+1,1)=NA(1:n+1,1); for m=2:k for i=1:n+1 if knotV(i+m-1)-knotV(i)==0 p1=0; else p1=(un(j)-knotV(i))/(knotV(i+m-1)-knotV(i))*N(i,m-1); end if knotV(i+m)-knotV(i+1)==0 p2=0; else p2=(knotV(i+m)-un(j))/(knotV(i+m)-knotV(i+1))*N(i+1,m-1); end N(i,m)=p1+p2;

430

end end U1(j,1:n+1)=N(1:n+1,k); end Fit=U1*ControlPoints; l=length(Fit); for i=1:length(un) u_new(i,1)=un(1,i); end

Part 3 FuncBspline_curveDiffPart2

function u_vector = FuncBspline_curveDiffPart2(d,t,u2,C, D) npoints2=length(u2); nc=length(C); n=nc-1; k=d+1; D2=sym(); D3=[]; du=[]; u1=u2; syms u for j=1:npoints2 %%%% new u(j) from u(i) to u(npoints2) a=u1(j); for i=k:n+2 %%%[0,1,2,3]; if u1(j)>=t(i) && u1(j)<t(i+1) D2=D(i-k+1,1:nc); else if u1(j)==t(i) && u1(j)==t(i+1)%% D2=D((i-1)-k+1,1:nc); else end end end D3=[D3;D2]; E=subs(D2,u,a); du=[du;E]; D2=sym(); end u_vector=du*C; u_vector = eval(u_vector);

2.2.4 Tangent vectors in w direction

Part 1 The main function - FuncUSToolPath_tangentVw

function [wvector, QCell] = FuncUSToolPath_tangentVw(psurf, pathP, r, uvector) % Inputs % psurf, surface points % pathP, path points % r, radius of the sphere % uvector, the tangent vector in u direction at pathP

431

% Output % QCell, extracted points for i = 1:size(pathP,1) clear angle qmA p = pathP(i,:); uv = uvector(i,:); % Extract all points inside a spherical area of radius 1 surrounding p dist = sqrt((p(1)-psurf(:,1)).^2 + (p(2)-psurf(:,2)).^2 + (p(3)-psurf(:,3)).^2); Q = [psurf(dist<=r,:) dist(dist<=r)]; qbound = Q(Q(:,4)>=0.8*r,1:3); % Search for a point, qs, in psurr which makes an angle of 90 degree or % closest to 90 degree with the u vector, and this point has to be at % least 0.8r away from pathP. % psurr = sortrows(psurr',2)'; angle = zeros(1,size(qbound,1)); for j = 1:size(qbound,1) pp0 = qbound(j,:) - p; angle(j) = atan2(norm(cross(pp0,uv)), dot(pp0,uv)); end qs = qbound(min(abs(angle-pi/2))==abs(angle-pi/2),:); % Extend the segment in both directions, so that the length of the % segment is 2r and p is the mid-point and generate lots of points on % this segment. vs = (qs-p)/norm(qs - p); qs1 = p-r*vs; qs2 = p+r*vs; spacing = norm(psurf(1,:)-psurf(2,:)); % check the spacing between each surface point nopOnSeg = ceil(norm(qs1-qs2)/spacing) * 2; % apply half of the spacing to generate points on the segment. spacing = norm(qs1-qs2)/nopOnSeg; qsA = repmat(qs1, nopOnSeg, 1) + spacing*[1:nopOnSeg]'*vs; % Find the point, qm, in Q makes the minimum distance to each point in qsA. for j = 1:size(qsA,1) dist = sqrt((qsA(j,1)-Q(:,1)).^2 + (qsA(j,2)-Q(:,2)).^2 + (qsA(j,3)-Q(:,3)).^2); qmA(j,:) = Q(min(dist)==dist,1:3); end % Delete repeated points qmA = unique(qmA,'rows'); % Check whether the path point is in the extracted point set qmA if ~ismember(p, qmA,'rows') [rowqmA,~] = size(qmA); p_ = ones(rowqmA,1)*p; dp_ = qmA - p_; dist = sqrt(dp_(:,1).^2 + dp_(:,2).^2 + dp_(:,3).^2); pathPoint = qmA(min(dist)==dist,1:3); else pathPoint = p; end

432

% Fit a Bezier curve to qmA and extract w value at pathP k = 2; [~,CtrlP,wP]=FuncUSToolPath_bezierCurve(qmA,k,pathPoint); [w_v]=FuncBezier_curveDiff(wP,CtrlP); w_v = eval(w_v); wvector(i,:) = w_v/norm(w_v); QCell{i} = Q; end

Part 2 FuncUSToolPath_bezierCurve

function [fitP,CtrlP,wPathP]=FuncUSToolPath_bezierCurve(dataPoints,k,pathP) x=dataPoints(:,1); y=dataPoints(:,2); z=dataPoints(:,3); nc=k+1; lp=length(dataPoints); %%calculate value of u l_sum=0; l_wweight(1)=0; wPathP = 0; s=size(pathP,1); s2 = 0; for j= 1:lp-1 l_p=((x(j+1)-x(j)).^2+(y(j+1)-y(j)).^2+(z(j+1)-z(j)).^2).^1/2; l_sum=l_sum+l_p; l_wweight(j+1,:)=l_sum; if s~=s2 for i = 1:s if isequal([x(j+1),y(j+1),z(j+1)], pathP(i,:)) wPathP(i) = l_wweight(j); s2 = size(wPathP(i)); continue end end end end w(1:lp,:)=l_wweight/l_sum; wPathP = wPathP./l_sum; B=zeros(lp,nc); for i=1:lp for j=0:k CC=nchoosek(k,j); B(i,j+1)=CC*w(i)^j*(1-w(i))^(k-j); end end CX=B\x; CY=B\y; CZ=B\z; CtrlP=[CX,CY,CZ]; fitP = B*CtrlP;

Part 3 FuncBezier_curveDiff

function [w_v]=FuncBezier_curveDiff(wvalue,CtrlP) nc=length(CtrlP); n=nc-1; lw=length(wvalue);

433

syms w D=sym(zeros(1,n)); for j=0:n cc=nchoosek(n,j); D(j+1)=cc*j*w^(j-1)*(1-w)^(n-j) - cc*w^j*(n-j)*(1-w)^(n-j-1); end for j=1:lw a=wvalue(j); Dw(j,:)=subs(D,w,a); end w_v=Dw*CtrlP;

434

2.3 Localisation

2.3.1 Initialisation

In the initialisation section, user data are loaded and arguments are parsed.

function [ trans,d_avg, icp ] = FuncICP_Main_2(P_mp,P_surf,varargin) % P_mp smaller set of points inp = inputParser; inp.addRequired('P_mp', @(x)isreal(x) && size(x,1) == 3); inp.addRequired('P_surf', @(x)isreal(x) && size(x,1) == 3); inp.addOptional('k_max', 100, @(x)x > 0); inp.addParameter('InitialTrans', eye(4), @(x)isreal(x) && size(x) == [4,4]); inp.addParameter('ConvergeCrit', 0.000001, @(x)x >= 0); inp.addParameter('MinE', 0.005, @(x)x >= 0); inp.addParameter('NoApproach', 1, @(x)x > 0); validMinimize = {'SVD','Quaternion'}; inp.addParameter('Minimize', 'Quaternion', @(x)any(strcmpi(x,validMinimize))); inp.parse(P_mp,P_surf,varargin{:}); arg = inp.Results; clear('inp'); %% terminationInfo = {'Minimum error reached!','Convergence reached!',... 'Maximum number of iteration...' }; rot_map = [180,0,0; 0,180,0; 0,0,180;]; if arg.NoApproach > size(rot_map,1) arg.NoApproach = size(rot_map,1)+1; end %% The ICP startes here, where some initial parameters are defined [~,N]=size(P_mp); if arg.InitialTrans==0 arg.InitialTrans=eye(4); end % Center of gravity of both the surface and the measured points are % calculated and the vector between them mu_p_mp=sum(P_mp,2)/size(P_mp,2); mu_p_surf= sum(P_ surf,2)/size(P_ surf,2; % The length scale is found l_scale=zeros(1,3); for i=1:3 l_scale(i)=max(P_surf(i,:))-min(P_surf(i,:)); end L_scale=max(l_scale); e=1/0;

435

k_count=1; k_to_t=1; converge=0; k_next=-1; k=0; d=1/0;

2.3.2 Multi-approach algorithm

In this section, the multi-approach ICP algorithm is implemented.

while d(end)>=arg.MinE && k_count<=arg.NoApproach clear qr qt timeCost = 0; terminateCondi_ = 0; nextProgressReport = 0; d=1/0; % d is reset for every approach Rot_init(:,:,1,k_count)=eye(3); % Initial rotation matrix created Rot_init(:,:,2,k_count)=eye(3); % Initial rotation matrix created Rot_init(:,:,3,k_count)=eye(3); % Initial rotation matrix created P=P_mp; % Measured points are reset for every approach if k_count==1 % Initial alignment error is not changed if this is the first approach T_rand(:,k_count)=[0;0;0]; P=arg.InitialTrans*[P;ones(1,N)]; P=P(1:3,:); else curRot = rot_map(k_count-1,:); theta_x=curRot(1); R_x=FuncICP_rotMat(theta_x,'x','d'); theta_y=curRot(2); R_y=FuncICP_rotMat(theta_y,'y','d'); theta_z=curRot(3); R_z=FuncICP_rotMat(theta_z,'z','d'); T_rand(:,k_count)=[(rand-0.5)*L_scale;(rand-0.5)*L_scale;(rand-0.5)*L_scale]; P=P-[mu_p_mp(1)*ones(1,N);mu_p_mp(2)*ones(1,N);mu_p_mp(3)*ones(1,N)]; Rot_init(:,:,1,k_count)=Rot_init(:,:,1,k_count)*R_x; Rot_init(:,:,2,k_count)=Rot_init(:,:,2,k_count)*R_y; Rot_init(:,:,3,k_count)=Rot_init(:,:,3,k_count)*R_z; P=R_x*P; P=R_y*P; P=R_z*P;

P=P+repmat([T_rand(1,k_count)+mu_p_surf(1);T_rand(2,k_count)+mu_p_surf(2);T_rand(3,k_count)+mu_p_surf(3)],1,N);

436

end while converge<2 && d(end)>arg.MinE && k<arg.k_max tic; k=k+1; % Calculate the corresponding closest points [ X,~,~] = FuncICP_closestPoint_m(P,P_surf); % Calculate centres of gravity for both sets of points mu_p=sum(P,2)/size(P,2); mu_x=sum(X,2)/size(X,2); % Calculate the cross-covariance matrix M = size(P,2); P_ = P - repmat(mu_p, 1, M); X_ = X - repmat(mu_x, 1, M); Sigma = P_*transpose(X_); switch arg.Minimize case 'SVD' [U,~,V]=svd(sigma); % Calculate SVD of the cross-covariance matrix qr_ = V*diag([1 1 det(U*V')])*U'; % Compute the optimal rotation matrix case 'Quaternion' [qr_] = Quat(sigma); end qr(:,:,k)=qr_; % Compute the optimal translation vector qt(:,k)=mu_x-qr(:,:,k)*mu_p; % Transform the measured point set P=qr(:,:,k)*P + repmat(qt(:,k),1,size(P,2)); % Calculate the mean error d(k)=sum(sum((P-X).^2).^0.5)/N; % Convergence check if k==1 e=d(k); else e=abs(d(k)-d(k-1)) ; end k_conv=k; if e<arg.ConvergeCrit converge=converge+1 ; if k_conv==(k_next+1) && converge==2 terminateCondi_ = 2; % Iteration Termination condition: convergence reached. elseif converge==2 converge=0; k_next=k_conv; else k_next=k_conv; end

437

end timeCost(k) = toc; if k/arg.k_max>nextProgressReport; disp(['k count: ',num2str(k),'/',num2str(arg.k_max),... '; Approach: ',num2str(k_count),'/',num2str(arg.NoApproach),... '; deviation = ',num2str(round(d(k),6))]); timeEst = mean(timeCost)*(arg.k_max-k+(arg.NoApproach-k_count)*arg.k_max)/60; disp(['Estimated time remaining: ',num2str(round(timeEst,2)),'min']); nextProgressReport = nextProgressReport+0.33; end end % Iteration Termination condition: minimum error reached if d(end)<= arg.MinE terminateCondi_ = 1; disp(['Minimum error reached!',num2str(d(end))]); elseif terminateCondi_~= 2 % Iteration Termination condition: if not converged terminateCondi_ = 3; % Iteration Termination condition: maximum iteration reached else disp(['Convergence reached!',num2str(d(end))]); end k_col(k_count)=k; % Number of iterations of the approach collected % Transolation matrix of the approach collected Trans_collect{k_count}=qt(:,:); % Rotational array of the approach collected Rotation_collect{k_count}=qr(:,:,:); % The final mean error of the apporach collected d_col(k_count)=d(end); icp.d{k_count}=d; icp.terminateCondi{k_count} = terminationInfo{terminateCondi_}; icp.timeCost_col{k_count}=timeCost; % Parameters for the next approach set k_count=k_count+1; k=0; e=1/0; converge=0; end %% The following section calcualtes the best transformation matrix found % The best aproach is found by selecting the set corresponding to the % minimum mean error [d_avg, I]=min(d_col); % Optimal transforamtion matrix initiated trans(:,:)=eye(4); num_of_iter=k_col(I); Trans=cell2mat(Trans_collect(I)); Rotation=cell2mat(Rotation_collect(I)); for i=0:(num_of_iter-1) trans(:,:)=trans(:,:)*[eye(3) Trans(:,(num_of_iter-i));0 0 0 1];

438

trans(:,:)=trans(:,:)*[Rotation(:,:,(num_of_iter-i)) zeros(3,1);0 0 0 1]; end if I==1 trans(:,:)=trans(:,:)*arg.InitialTrans; else trans(:,:)=trans(:,:)*[eye(3) (T_rand(:,I)+mu_p_surf);0 0 0 1]; trans(:,:)=trans(:,:)*[Rot_init(:,:,1,I) zeros(3,1);0 0 0 1]; trans(:,:)=trans(:,:)*[Rot_init(:,:,2,I) zeros(3,1);0 0 0 1]; trans(:,:)=trans(:,:)*[Rot_init(:,:,3,I) zeros(3,1);0 0 0 1]; trans(:,:)=trans(:,:)*[eye(3) mu_p_mp*(-1);0 0 0 1]; end icp.Trans=Trans_collect; icp.Rot=Rotation_collect; end

2.3.3 Quaternion method

Subfunction for solving rotational matrix using the quaternion method.

function [R] = Quat(Sigma) % The anti-symmetric part of the cross covariance matrix is found Delta=Sigma-Sigma'; % The cyclic components are found from the anti-symmetric matrix Delta=[Delta(2,3) Delta(3,1) Delta(1,2)]'; % The Q matrix is constructed B=Sigma+Sigma'-trace(Sigma)*eye(3); Q=[trace(Sigma) Delta';Delta B]; % Eigen vectors and eigenvalues are found [eig_Vec,eig_Val]=eig(Q); % The maximum eigenvalue is found C_1=max(eig_Val); [~,C_2]=max(C_1); % The unit quaternion vector is defined as the eigenvector % correspoinding to the maximum eigenvalue q=eig_Vec(:,C_2); % The optimum rotational matrix is found R=[q(1)^2+q(2)^2-q(3)^2-q(4)^2 2*(q(2)*q(3)-q(1)*q(4)) 2*(q(2)*q(4)+q(1)*q(3)); 2*(q(2)*q(3)+q(1)*q(4)) q(1)^2-q(2)^2+q(3)^2-q(4)^2 2*(q(3)*q(4)-q(1)*q(2)); 2*(q(2)*q(4)-q(1)*q(3)) 2*(q(3)*q(4)+q(1)*q(2)) q(1)^2-q(2)^2-q(3)^2+q(4)^2]; end

2.3.4 Closest point

A simple function uses Matlab built-in k-d tree algorithm to find the closest points.

function [ closest_points,mindist,match] = FuncICP_closestPoint_m(meas_points,surf_points) % find the closest point in p for each point in pt.

439

% i.e. pt covers a smaller area. kdOBJ = KDTreeSearcher(transpose(surf_points)); [match, mindist] = match_kDtree(meas_points,kdOBJ); closest_points = surf_points(:,match); function [match, mindist] = match_kDtree(p, kdOBJ)

[match, mindist] = knnsearch(kdOBJ,transpose(p));

440

2.4 Path grouping

2.4.1 The main function

After user data are read and arguments are parsed, the main function as presented below starts to

localise the specified probe path to the coordinate system of the inspection machine using the

localisation method introduced in the previous section. After the localisation, path grouping is started

in sub-functions. The results are collected at the end of the main function and saved in a text file.

function CalculateUSToolPath(toolPathLibInfo, laserInfo, usToolPath,rot_r,varargin) inp = inputParser; inp.addRequired('toolPathLibInfo'); inp.addRequired('laserInfo'); inp.addRequired('usToolPath'); inp.addRequired('rot_r'); inp.addParameter('ProofPlot', true, @(x)isbool(x)); inp.addParameter('SaveRotationFile', false, @(x)isbool(x)); inp.addParameter('ReadRotationFile', false, @(x)isbool(x)); inp.addParameter('DeleteRotationFile', false, @(x)isbool(x)); inp.addParameter('Minimize', 'Quaternion', @(x)any(strcmpi(x,validMinimize))); inp.parse(toolPathLibInfo,laserInfo,usToolPath, rot_r, varargin{:}); arg = inp.Results; clear('inp'); % Load toolPathFile [~,name,ext] = fileparts(toolPathLibInfo); if ~strcmp(ext, '.mat') toolPathLibInfo = name+'.mat'; end load(toolPathLibInfo); if trans == 0 ICP_n_o_app=10; doProffPlot = true; else ICP_n_o_app=1; end % Read laser scan result if ischar(laserInfo) [~,~,ext] = fileparts(laserInfo); if strcmp(ext, '.mat') load(laserScanFile); else [a,b,c,d] = FuncUSToolPath_readLaserScan(laserInfo); P_scan=[a,b,c+d]; end else P_scan = laserInfo; end % Deal with rotation file operation

441

rotationFile='MLData_RotDataFile_1.mat'; if arg.DeleteRotationFile if exist(rotationFile,'file') delete(rotationFile) end end [~,name,ext] = fileparts(laserInfo); if ~strcmp(ext, '.txt') toolPathLibInfo = name+'.txt'; end argpassed.save = arg.SaveRotationFile; argpassed.read = arg.ReadRotationFile; doCalculation(toolPathLibInfo, usToolPath, P_scan, argpassed, ICP_n_o_app, arg.ProofPlot ,rot_r, rotationFile); function doCalculation(toolPathLibInfo, usToolPath, P_scan, argpassed, ICP_n_o_app, doProofPlot,rot_r, rotationFile) %% Customer setting %%Input data structure and Bspline parameters sec=5;% sec is the number of sections for measured blade data nh=13; % Number of cooling channels load(toolPathLibInfo); %% Check for previouse rotations first_rot = 1; delta_theta = 0; if argpassed.read if ~exist(rotationFile,'file') first_rot = 1; delta_theta = 0; else load(rotationFile) if length(order_scan) < 2 msgbox('End of current scan session'); error('Terminated'); end order_scan = order_scan(2:end); delta_theta = theta_group(order_scan(1)); first_rot = 0; end end trans_theta = FuncUSToolPath_transRotInit( delta_theta ); %% Load laser measurments for localisation % ICP to find the transformation matrix tou=0.000001; d_min=0.005; k_max=100; trans_init=trans*trans_theta^-1; [ trans,d_avg ] = FuncICP_Main(P_scan',P_surf',tou,d_min,k_max,ICP_n_o_app, trans_init); [ P_surf ] = FuncUSToolPath_toHomoCord(P_surf,2); P_surf=(trans^-1*P_surf')';

442

P_surf=P_surf(:,1:3); xyz=[x y z]; [ xyz ] = FuncUSToolPath_toHomoCord(xyz,2); xyz=(trans^-1*xyz')'; xyz=xyz(:,1:3); x=xyz(:,1); y=xyz(:,2); z=xyz(:,3); %% Transform tool path [ tool_path_ord_1 ] = FuncUSToolPath_transProbePath( tool_path_ord,trans ); % set a color map notp = 0; for i = 1:size(tool_path_ord_1,2) notp = notp + size(tool_path_ord_1{i},1); end colorm = colormap(winter(notp)); icolor = 1; if doProofPlot figure;hold on;set(gcf,'Color',[1,1,1]); if length(P_surf)/500 == 500 pxx = reshape(P_surf(:,1),500,500); pyy = reshape(P_surf(:,2),500,500); pzz = reshape(P_surf(:,3),500,500); surf(pxx,pyy,pzz,'EdgeColor', 'none') plot3(P_scan(:,1),P_scan(:,2),P_scan(:,3),'+','MarkerSize',3,'Color',[0.2,0.2,0.2]); else plot3(P_surf(1:43:end,1),P_surf(1:43:end,2),P_surf(1:43:end,3),'.-r'); plot3(P_scan(:,1),P_scan(:,2),P_scan(:,3),'*b'); end for i=1:size(tool_path_ord_1,2) curMat = tool_path_ord_1{i}; %plot3(curMat(:,1),curMat(:,2),curMat(:,3),'*g') pv = curMat(:,1:3) - 4*curMat(:,7:9); for m=1:size(curMat,1) plot3([curMat(m,1) pv(m,1)],[curMat(m,2) pv(m,2)],[curMat(m,3) pv(m,3)],'Color',colorm(icolor,:)'); icolor = icolor+1; end end title(['Average deviation of ICP result = ', num2str(d_avg)]); grid on;axis equal;hold off;axis tight;view(180,0);xlabel('x');ylabel('y');zlabel('z');legend('B-spline surface','Laser points','Probe path') msgbox('Program paused. When inspection of the plot is done, press any key to continue...'); pause h = questdlg('Do you want to continue or terminate the program?','title','Continue','Terminate','Terminate') ; if strcmp(h, 'Terminate') error('Breaking out'); end end %% Group tool paths theta_robo_lim=63;

443

%load('temp_groupToolPath.mat'); if ~exist('order_scan','var') order_scan = 0; pathGrouping = 0; [ final_path_collect,order_scan,no_init_rot,theta_group,B, pathGrouping ] = FuncUSToolPath_groupToolPath( tool_path_ord_1,theta_robo_lim, pathGrouping); else [ final_path_collect,~,no_init_rot,~,B ] = FuncUSToolPath_groupToolPath( tool_path_ord_1,theta_robo_lim, pathGrouping); end %% Rotate tool paths [ final_path_collect_new,P_surf_rot,xyz,theta_rot ] = FuncUSToolPath_rotateToolPath(x,y,z,B,P_surf,final_path_collect,order_scan,no_init_rot,theta_group); %% Sort and assemble the tool paths [ path_output ] = FuncUSToolPath_sortAssemble( final_path_collect_new,sec,nh,order_scan,B,rot_r ); if first_rot==1 && theta_rot(order_scan(1))~=0 msg = ['Rotate ' num2str(-theta_rot(order_scan(1))) ' degrees and scan again. If this should not be the case, please review your settings or input files.']; h = questdlg([msg ' Do you want to continue or terminate the program?'],'title','Continue','Terminate','Terminate') ; if strcmp(h, 'Terminate') error('Breaking out'); end fileID = fopen(outputFile,'w+'); fprintf(fileID,'%s %.3f\n','R',-theta_rot(order_scan(1))); fclose(fileID); else %% Offset x_offset = 0; y_offset = -0; z_offset = 0; if abs(x_offset)+abs(y_offset)+abs(z_offset) ~= 0 for i=1:size(path_output,2) path_output_temp=path_output{i}; path_output_temp(:,end+1) = zeros(length(path_output_temp),1); [N,~]=size(path_output_temp); for j=1:N path_output_temp(j,1)=path_output_temp(j,1)+x_offset; path_output_temp(j,2)=path_output_temp(j,2)+y_offset; path_output_temp(j,3)=path_output_temp(j,3)+z_offset; end path_output{i} = path_output_temp; end end if doProofPlot for i=1:size(path_output,2) figure;hold on;set(gcf,'Color',[1,1,1]); if length(P_surf)/500 == 500 pxx1 = reshape(P_surf_rot(:,1,order_scan(i)),500,500); pyy1 = reshape(P_surf_rot(:,2,order_scan(i)),500,500); pzz1 = reshape(P_surf_rot(:,3,order_scan(i)),500,500); surf(pxx1,pyy1,pzz1,'EdgeColor', 'none') else

444

scatter3(P_surf_rot(1:43:end,1,order_scan(i)),P_surf_rot(1:43:end,2,order_scan(i)),P_surf_rot(1:43:end,3,order_scan(i)),'.') end plot3(xyz(:,1,order_scan(i)),xyz(:,2,order_scan(i)),xyz(:,3,order_scan(i)),'.r') path_output_temp=path_output{i}; path_output_temp(:,end+1) = zeros(length(path_output_temp),1); [N,~]=size(path_output_temp); colorm = colormap(winter(N)); icolor = 1; for j=1:N n_new = FuncUSToolPath_wprTransformation(path_output_temp(j,4), path_output_temp(j,5), path_output_temp(j,6), 0); pv = path_output_temp(j,1:3) - 4*n_new; plot3([path_output_temp(j,1) pv(1)],[path_output_temp(j,2) pv(2)],[path_output_temp(j,3) pv(3)],'Color',colorm(icolor,:)'); icolor = icolor+1; end axis equal; axis tight;xlabel('x');ylabel('y');zlabel('z');legend('B-spline surface','Section curve','Probe path');grid on; view(-30,28) end end %% File writer fileID = fopen(usToolPath,'w+'); for i=1:1 path_output_temp=path_output{i}; [N,~]=size(path_output_temp); fprintf(fileID,'%s %.3f\n','R',-theta_rot(order_scan(i))); for j=1:N spdstr = 'SPD1'; if j==1 spdstr = 'SPD2'; hole_num=path_output_temp(9); elseif path_output_temp(1,9)~= hole_num spdstr = 'SPD2'; hole_num=path_output_temp(1,9); else end fprintf(fileID,'%.3f %.3f %.3f %.3f %.3f %.3f %s %.3f %.3f %.3f \n',path_output_temp(j,1:6),spdstr,path_output_temp(j,7:9)); end if size(order_scan,2)==1 else fprintf(fileID,'%s %.3f\n','R',-theta_group(order_scan(1)+1)); end end fclose(fileID); end %% Update the rotational file or create/delete it if it is the first/last rotation

445

if argpassed.save save('MLData_RotDataFile.mat', 'order_scan', 'theta_group', 'trans','pathGrouping'); end

2.4.2 Path grouping sub-function

In this sub-function, path points and path orientations are analysed and grouped.

function [ final_path_collect,order_scan,no_init_rot,theta_group,B, pathGrouping ] = FuncUSToolPath_groupToolPath( tool_path_ord_1,theta_robo_lim, pathGrouping) if pathGrouping ~= 0 group = 0; for i = 1:size(tool_path_ord_1,2) if pathGrouping(i)~=group group = pathGrouping(i); final_path_collect{group} = tool_path_ord_1{i}; else final_path_collect{group}(end+1:end+size(tool_path_ord_1{i},1),:) = tool_path_ord_1{i}; end end no_init_rot = 1; theta_group = 0; order_scan = 0; B = size(final_path_collect,2); else [ final_path_collect,order_scan,no_init_rot,theta_group,B,pathGrouping] = doCal( tool_path_ord_1,theta_robo_lim ); end function [ final_path_collect,order_scan,no_init_rot,theta_group,B, pathGrouping ] = doCal( tool_path_ord_1,theta_robo_lim) tp_ori=tool_path_ord_1; [~,B]=size(tp_ori); %clear tp_temp angleList % Assume: the sequence of the holes is correctly defined in tool_path_ord and % cell components in tool_path_ord is ordered in the sequence of the holes. % STEP. 1, determine whether we start from the first hole or the last hole % or any where else on the surface. % This is dependant on two factors: % 1. the angles that the tool path vectors at the first hole and the last % hole make with [0 0 -1]; % 2. the direction of scanning, i.e. the sequence the tool path vectors are % ordered e.g. either from left to right or right to left. % The angles that the tool path vectors made with [0 0 -1] % Extract max and min angles that normal vectors of each scanning region for i = 1:B angleList(i,:) = [max(tp_ori{i}(:,6)), min(tp_ori{i}(:,6))]; % angle with z end

446

% Check whether we will scan the first hole or the last hole. if angleList(1,1)<angleList(end,1) starthole = 1; else starthole = B; end % Check the direction of scanning % First get the direction of the hole arrangement try vhole = tp_ori{starthole}(1,1:3) - tp_ori{starthole+1}(1,1:3); catch vhole = tp_ori{starthole}(1,1:3) - tp_ori{starthole-1}(1,1:3); end % Second get the direction of tool path arrangement and compare it with % vhole vpath = tp_ori{starthole}(1,1:3) - tp_ori{starthole}(end,1:3); if atan2(norm(cross(vhole,vpath)),dot(vhole,vpath))*180/pi <90 isdiraligned = true; else isdiraligned = false; end % STEP. 2 Grouping. % We can now determine the end of scan for the first path group and the % rotation needed for the next path group, consequently the end of the next % scan. If isdiraligned == false, i.e. directions of tool path and vhole % are different, we reverse the tool path. groupNo = 1; pathNo = 1;rot = 0; for i = 1:B if angleList(i,1) - sum(rot) > theta_robo_lim/2 groupNo = groupNo + 1; pathNo = 1; rot(groupNo) = theta_robo_lim/2 + angleList(i,2) - sum(rot); end if isdiraligned tp_temp{groupNo}{pathNo} = tp_ori{i}(1:end,:); else tp_temp{groupNo}{pathNo} = tp_ori{i}(end:-1:1,:); end tp_temp{groupNo}{pathNo}(:,6) = tp_temp{groupNo}{pathNo}(:,6) - sum(rot); pathNo = pathNo + 1; pathGrouping(i) = groupNo; end for i = 1:size(rot,2) final_path_collect{i} = tp_temp{i}{1}; for j = 2:size(tp_temp{i},2) final_path_collect{i}(end+1:end+size(tp_temp{i}{j},1),:) = tp_temp{i}{j}; end end B=size(rot,2); order_scan = 1:1:B; no_init_rot = rot(1) == 0; theta_group = rot;

447

2.4.3 Probe path transformation sub-function

In this sub-function, rotation matrices are constructed to transform the grouped probe paths.

function [ final_path_collect_new,P_surf_rot,xyz,theta_rot ] = FuncUSToolPath_rotateToolPath(x,y,z,B,P_surf,final_path_collect,order_scan,no_init_rot,theta_group) n_x=0.0084; n_y=0.999950003749688; n_z=0.0018; P_0=[432.547, -406.404, -359.440]; [N,~]=size(x); P_0_xyz=[ones(N,1)*P_0(1) ones(N,1)*P_0(2) ones(N,1)*P_0(3)]'; [N,~]=size(P_surf); P_0_surf=[ones(N,1)*P_0(1) ones(N,1)*P_0(2) ones(N,1)*P_0(3)]'; for i=1:B final_path_temp=final_path_collect{1,i}; [N,~]=size(final_path_temp); if no_init_rot==1 && order_scan(1)==i; theta_rot(i)=0; final_path_collect_new{1,i}=final_path_temp; xyz(:,:,i)=[x y z]; P_surf_rot(:,:,i)=P_surf; else theta_rot(i) = sum(theta_group(1:i)); v_th=1-cosd(-theta_rot(i)); c_th=cosd(-theta_rot(i)); s_th=sind(-theta_rot(i)); R=[ n_x^2*v_th+c_th , n_x*n_y*v_th-n_z*s_th , n_x*n_z*v_th+n_y*s_th ; n_x*n_y*v_th+n_z*s_th , n_y^2*v_th+c_th , n_y*n_z*v_th-n_x*s_th; n_x*n_z*v_th-n_y*s_th , n_y*n_z*v_th+n_x*s_th , n_z^2*v_th+c_th]; xyz(:,:,i)=(R*([x y z]'-P_0_xyz)+P_0_xyz)'; P_surf_rot(:,:,i)=(R*(P_surf'-P_0_surf)+P_0_surf)'; P_0_temp=[ones(N,1)*P_0(1) ones(N,1)*P_0(2) ones(N,1)*P_0(3)]'; final_path_temp(:,1:3)= (R*(final_path_temp(:,1:3)'-P_0_temp)+P_0_temp)'; final_path_temp(:,7:9)= (R*(final_path_temp(:,7:9)'))'; final_path_collect_new{1,i}=final_path_temp; end end

448

2.4.4 Path ordering sub-function

In this sub-function, path points are re-ordered so the inspection sequence is optimal. Then the

robot rotation parameters w, p and r are calculated based on the normal vectors.

function [ path_output ] = FuncUSToolPath_sortAssemble( final_path_collect_new,sec,nh,order_scan,B,rot_r ) %% Sort so each section get scanned at a time and from hole 1 to end for i=1:B final_path_temp=final_path_collect_new{1,i}; [N,~]=size(final_path_temp); k=0; final_path_temp_ord=[]; for l=1:sec for q=1:nh for j=1:N if final_path_temp(j,5) == q && final_path_temp(j,4) == l k=k+1; final_path_temp_ord(k,:)= final_path_temp(j,:); end end end end final_path_collect_new{1,i}=final_path_temp_ord; end %% Calculate the robot angles and assemble an output file B = size(order_scan,2); for i=1:B final_path_temp=final_path_collect_new{1,order_scan(i)}; [N,~]=size(final_path_temp); path_output_temp=[]; for j=1:N unit_v_temp=final_path_temp(j,7:9); wpr = FuncUSToolPath_vectorToWpr_RM(unit_v_temp, rot_r); Ang_x = wpr(1,1); Ang_y = wpr(1,2); Ang_z = wpr(1,3); path_output_temp(j,:)=[final_path_temp(j,1:3) Ang_x Ang_y Ang_z final_path_temp(j,4:5) final_path_temp(j,10)]; end path_output{i}=path_output_temp; end end

449

2.4.5 Robot rotation parameter calculation

This function calculates robot rotation parameters w, p and r based on a vector in Cartesian

coordinates specified by the user.

function wpr = FuncUSToolPath_vectorToWpr_RM(vector, r) % Warning: With this solution, r is not calculated. The output of r is % zero or is identical to the user specified r. % This method converts a vector into W,P,R with a method involving rotation % matrix. % Assume we have an arbitrary unit vector, A, and a unit vector N=[0 0 1]. % N needs to be rotated at most three times about x, y and z axis in % sequence to be aligned with A. % The angles of rotations are defined as w, p and r respectively and we % need to calculate them. This can be done by solving rotation matrices. % Rotation about x is defined by: % Rx = [ 1 0 0; 0 cos sin; 0 -sin cos ]; % Rotation about y is defined by: % Ry = [ cos 0 -sin; 0 1 0; sin 0 cos ]; % Rotation about z is defined by: % Rz = [ cos sin 0; -sin cos 0; 0 0 1 ]; % Therefore, we have A = N * Rx(w) * Ry(p) * Rz(r). % Let r = 0, we only need to simplify A = N * Rx(w) * Ry(p). % So we have A = [ cos(w)*sin(p), -sin(w), cos(p)*cos(w) ]. % Finally: A(1) = cos(w)*sin(p) ... Eq.1 % A(2) = -sin(w) ......... Eq.2 % A(3) = cos(p)*cos(w) ... Eq.3 % Either for w or p, we have two solutions taking quadrant into % consideration. Eventually, we end up with four different pairs of % solution and we only pick one from them. This will be decided by % converting each pair of solution back to the vector. % If an r value is specified, for a specific end effect orientation, we % can always have A/Rz(r) = N * Rx(w) * Ry(p); isTesting = 0; %% Find all four solutions % Normalize vector A_ori = vector; if size(A_ori,1) == 3 A_ori = A_ori'; end A_ori = A_ori/norm(A_ori); % A/Rz(r) Rz = [ cosd(r) sind(r) 0; -sind(r) cosd(r) 0; 0 0 1 ]; A = A_ori/Rz; % Get two solutions for w by solving Eq.2 w1 = asind(-A(2)); % When sin > 0, the second solution w2 in [-pi, pi] is 180 - w1. % When sin < 0, the second solution w2 in [-pi, pi] is -180 - w1. if -A(2) > 0

450

w2 = 180 - w1; else w2 = -180 - w1; end % Get two solutions for p by solving Eq.1/Eq.3 p1 = atand(A(1)/A(3)); % When tan > 0, the second solution p2 in [-pi, pi] is -180 + p1; % When tan < 0, the second solution p2 in [-pi, pi] is 180 + p1; if A(1)/A(3) > 0 p2 = -180 + p1; else p2 = 180 + p1; end w = [w1 w2]; p = [p1 p2];

451

2.5 Thickness evaluation

2.5.1 The main function

In the main function, the user can specify search windows = [lower thickness limit, upper thickness

limit]; thereby, in the backwall echo detection algorithm, the script is focused in the specified

thickness ranges. This would increase the chance that the wall thicknesses are evaluated at the

correct backwall echoes, especially when signal-to-noise ratio is low. However, this search window

should be reasonably wide; otherwise the calculated thicknesses may be invalid. The user is also

required to select the text file that contains ultrasonic data. The ultrasonic data are then loaded and

parsed. Interface echoes and backwall echoes are determined in sub-functions. Finally, wall

thicknesses results are plotted and saved.

clearvars -except tc ac dc;%close all; % Specify search windows for backwall echoes if available searchwindow = 0; noOfDataReadAhead = 3; % the number of data/parameters to be read ahead of ultrasonic data, i.e. timestamp, buffersize etc. [filename, pathname, filterindex] = uigetfile({'*.mat';'*.txt'}, 'Choose a ultrasonic data file required to be processed'); %% Read the original data and separate them into subsets according to hole number path(path,pathname); [~,Fname,Fext] = fileparts(filename); if strcmp(Fext,'.txt') usdata = load([Fname,Fext]); % extract info columns info_gain = usdata(:,1); info_step = usdata(:,2); info_wp = usdata(:,3); info_samplingrate = usdata(:,4); info_buffer = usdata(:,5); % delete info columns usdata(:,1:5) = []; % Seperate data regarding step number and water path % find index where discontiuities are found in info_step s_ = diff(info_step); s_ = find(s_~=0); s_ = [0;s_;size(usdata,1)]; for i = 1:length(s_)-1 % extract data for the same step data_ = usdata(s_(i)+1:s_(i+1),:); % get buffer length b_ = info_buffer(s_(i)+1:s_(i+1),:); % find index where discontiuities are found in info_wp

452

w_ = info_wp(s_(i)+1:s_(i+1),:); w_ = diff(w_); w_ = find(w_~=0); w_ = [0;w_;size(data_,1)]; % seperate data based on water path for j = 1:length(w_)-1 data_2{j} = data_(w_(j)+1:w_(j+1),1:b_(w_(j)+1)-3); end datac{i} = data_2; clear data_2 end save([Fname,'.mat'], 'usdata', 'info_gain', 'info_step','info_wp','info_samplingrate','info_buffer', 'datac'); else load(filename); end %% Seperate backwall echo and interface echo % Not implemented in the first data set xcoords = data_ori(1:2:end,2); interfaceData = data_ori(2:2:end,4:end); usdata = data_ori(1:2:end,4:end); noiseT = [130, 140]; noiseT = 0; [interfaceLoc, waterpath, ~] = USInterface_v5 (interfaceData, 3000, noiseT); [backwall, backwallAmp, thickness, noiseThreshold, backwallTreshold] = USBackwall_v2(usdata, xcoords, interfaceLoc, waterPath, searchwindow); h1 = figure;hold on; [hAx, hT, hB] = plotyy(1:length(thickness),thickness,1: length(backwallAmp),backwallAmp); plot(desiredT(:,1),desiredT(:,2),'ob'); ylabel(hAx(1), 'Thickness') ylabel(hAx(2), 'Amplitude') hAx(1).YTick=[0,2,4,6,8,10,12,14]; hAx(2).YLim = [135,260]; hAx(2).YTick=[135,150,175,190,215,230,245,260]; hdt = datacursormode; title(filename) save([filename, '_wallthickness.txt'], 'thickness')

2.5.2 Interface echo detection

The locations of interface echoes are determined in this function.

function [interfaceIndex, waterpath, amp, noiseThreshold] = USInterface_v5 (data,firstinterfacerange, noiseT) % noiseT = [low limit of noise filtre, up limit of noise filtre]; peakAmplitudeConfidentDiff = 50; % max amplitude difference between the 2nd and the 1st peak in an interface echo lowDT = 4; %low distance treshold - the distance between the 2nd and the 1st peak in an interface echo

453

highDT = 15; %high distance treshold - the distance between the 2nd and the 1st peak in an interface echo data = data'; data_ori = data; buffersize = size(data,1); ndata = size(data,2); lowunits = 5; % Waterpath treshold waterPath = 10; vwater= 0.00142342; %speed of sound in water [m/ns] waterPathTresh= waterPath/(10*vwater); %number of data points between the probe and the top surface of the workpiece. waterPathTresh= 2*(round(waterPathTresh)); %number of data points for return journey in water for i = 1:ndata %% Remove noise % if noiseT is defined if ~isempty(noiseT) if any(noiseT) noise(i) = mean(noiseT); noiseThreshold(:,i) = noiseT; data((data(:,i)>=noiseT(1) & data(:,i)<=noiseT(2)),i) = noise(i); else % 1. Take average amplitude % 2. Specify high and low threshold by scaling the average amplitude % with multipliers % 3. The high threshold must be smaller than the maximum amplitude so % the peak won't be filtered vice versa for the low threshold. % 4. However, it the peak/valley is only 5 units higher than the % average amplitude, the peak/valley is ignored, i.e. no interface echo. noise(i) = mean(data(:,i)); data(1:600,:) = noise(i); peakAmp = max(data(:,i)); valleyAmp = min(data(:,i)); if peakAmp - noise(i) < lowunits interfaceIndex(i) = 0; amp(i) = 0; waterpath(i) = 0; noiseThreshold(:,i) = [0,0]; continue; end noiseHT = noise(i) * 1.04; noiseLT = noise(i) * 0.96; noiseHT = 141; noiseLT = 135;

454

if noiseHT > peakAmp noiseHT = peakAmp - 1; end noiseThreshold(:,i) = [noiseHT,noiseLT]; data((data(:,i)>noiseLT & data(:,i)<noiseHT),i) = noise(i); end end %% Search for the first interface echo data_diff=diff(data(:,i)); %find changes in amplitude if ~any(data_diff) %if no peak, skip this row. interfaceIndex(i) = 0; amp(i) = 0; waterpath(i) = 0; continue end ampChangedIndex=find(data_diff~=0); %Indexate the places where there is a change in amplitude ampChangedIndex_diff=diff(ampChangedIndex); flatPeakIndex=find(ampChangedIndex_diff~=1 & ampChangedIndex_diff<10); %Indexate the last data point in a flat peak ampChangedIndex(flatPeakIndex+1)=ampChangedIndex(flatPeakIndex+1) - ceil((ampChangedIndex_diff(flatPeakIndex)-1)/2); %locate the middle of the flat peak and replace the loca_flat in loca_change % * ampChangedIndex(flatPeakIndex+1) returns the last point in the flat % peak(s). % * use floor() instead of ceil() to take the point to the right of the % midpoint for flat peaks consisting of even number of points. % * or use neither for a unrounded number. dataFiltered=[data(ampChangedIndex,i);data(buffersize,i)]; %get rid of all noise and reduce the flat peak to a sharp peak logiPosNeg=diff(dataFiltered)>0; %logic_positive_or_negative: +tive slope = 1, -tive slope = 0 logiMaxMin=diff(logiPosNeg); %logic_maxima_or_minima: -1 = maxima, +1 = minima peakIndex=ampChangedIndex(find(logiMaxMin==-1)+1); %Indexate the maxima valleyIndex=ampChangedIndex(find(logiMaxMin==1)+1); peakAmp=data(peakIndex,i); %find data points of the maxima valleyAmp=data(valleyIndex,i); %Take out fake maxima which are start point of a valley fakeIndex = find(peakAmp == noise(i)); peakIndex(fakeIndex) = []; peakAmp(fakeIndex) = []; fakeIndex = find(valleyAmp == noise(i)); valleyIndex(fakeIndex) = []; valleyAmp(fakeIndex) = []; if ~any(peakIndex) interfaceIndex(i) = 0; amp(i) = 0; waterpath(i) = 0; continue

455

end if length(peakIndex) == 1 interfaceIndex(i) = peakIndex; amp(i) = peakAmp; waterpath(i) = 999; continue end % find 2nd interface echo secndPeakIndex = peakIndex(peakIndex>firstinterfacerange); secndPeakAmp = peakAmp(peakIndex>firstinterfacerange); secndValleyIndex = valleyIndex(valleyIndex>firstinterfacerange); secndValleyAmp = valleyAmp(valleyIndex>firstinterfacerange); % and 1st interface echo firstPeakIndex = peakIndex(peakIndex<=firstinterfacerange); firstPeakAmp = peakAmp(peakIndex<=firstinterfacerange); firstValleyIndex = valleyIndex(valleyIndex<=firstinterfacerange); firstValleyAmp = valleyAmp(valleyIndex<=firstinterfacerange); % for a fix pulse frequency of 17MHz, the distance between two biggest % peaks in the first interface echo is usually within 150ns. % therefore, locating the first peak in the first interface echo the % peak of maximum amplide should be picked as the first try, looking % for a second peak 150ns after it. % if not find, pick the 2nd biggest peak and so on. % be aware of the exisitance of surface bubble, which may result in a % small echo. % this echo is usually very weak at low gain, therefore, can be easily % detected by comparing the amplitude of each peak with the maximum % amplitude. % also be aware of strong backwall echo. A strong backwall echo is % usually followed by a strong valley, while the second peak in the % first interface echo is typically not followed by a noticeable valley if ~any(firstPeakAmp) interfaceIndex(i) = 0; amp(i) = 0; waterpath(i) = 0; continue end if length(firstPeakAmp) == 1 interfaceIndex(i) = firstPeakIndex; amp(i) = firstPeakAmp; else % Further work: % 1. Interferance from backwall echo % 2. What if the valley between the two peaks are distorted and there % is a small peak on it? isDone = false; firstPeakAmp_ = firstPeakAmp; while ~isDone

456

if ~any(firstPeakAmp_) break; end % look for the maximum amplitude peakAmpMax = max(firstPeakAmp_); peakAmpPeakIndex = find(peakAmpMax == firstPeakAmp, 1); % check whether there is another strong peak within 150ns right after it. indexCache = firstPeakIndex(peakAmpPeakIndex:end); ampCache = firstPeakAmp(peakAmpPeakIndex:end); if any(indexCache) possible2ndPeakAmp = (firstPeakIndex(peakAmpPeakIndex) + lowDT<indexCache & indexCache<firstPeakIndex(peakAmpPeakIndex) + highDT); if any(possible2ndPeakAmp) possible2ndPeakAmp = max(ampCache(possible2ndPeakAmp)); isDone = abs(peakAmpMax - max(possible2ndPeakAmp)) < peakAmplitudeConfidentDiff; end end if ~isDone peakAmpPeakIndex = find(peakAmpMax == firstPeakAmp_, 1); firstPeakAmp_(peakAmpPeakIndex)=[]; end end if ~isDone interfaceIndex(i) = 0; amp(i) = 0; waterpath(i) = 0; continue; end interfaceIndex(i) = firstPeakIndex(peakAmpPeakIndex); amp(i) = firstPeakAmp(peakAmpPeakIndex); end % locate the 2nd interface eacho, this does not need to be very % accuracy for the time being, so simply take the maximum peak. if any(secndPeakAmp) peakAmpMax = max(secndPeakAmp); secondInterfaceIndex = secndPeakIndex(peakAmpMax == secndPeakAmp); waterpath(i) = (secondInterfaceIndex(1) - interfaceIndex(i)) / 0.2 * vwater; else waterpath(i) = 0; end end

2.5.3 Backwall echo detection and thickness calculation

The locations of the backwall echoes are determined in this function. At the end of this function,

thickness values are calculated.

function [backwall, amplitude, thickness, noiseThreshold, backwallTreshold] = USBackwall_v4(data, interface, waterPath, searchwindow) % data - U.S. data % searchwindow structure:

457

% col 1 col 2 % lowbound highbound data = data'; data_ori = data; buffersize = size(data,1); ndata = size(data,2); minbackwallamp = 16; % Waterpath treshold vwater= 0.00142342; %speed of sound in water [m/ns] waterPathTresh= (waterPath-2)/(10*vwater); %number of data points between the probe and the top surface of the workpiece. waterPathTresh= 2*(round(waterPathTresh)); %number of data points for return journey in water noise = mean(data,1); for i = 1:ndata %% Treshold

if searchwindow == 0 searchwindow = [0, ndata] end

lt_ = searchwindow(1); ut_ = searchwindow(2); lt = lt_ + interface; ut = ut_ + interface; if lt>buffersize backwall(i) = 0; thickness(i) = 0; amplitude(i) = 0; backwallTreshold(:,i) = [0,0]; noiseThreshold(:,i) = [0,0]; continue end if ut>buffersize ut=buffersize; end backwallTreshold(:,i) = [lt, ut]; %% Remove noise % 1. Take average amplitude % 2. Specify high and low threshold by scaling the average amplitude % with multipliers % 3. The high threshold must be smaller than the maximum amplitude so % the peak won't be filtered vice versa for the low threshold. % 4. However, if the peak/valley is only 5 units higher than the % average amplitude, the peak/valley is ignored, i.e. no interface echo. edata = [(1:buffersize)',data(:,i)]; try edata_ = edata(lt:ut,:); catch

458

aaa=1; end % flat peak shouldn't be the end ut_ = ut; while ~any(edata_(end,2) - edata_(end-1,2)) && edata_(end,2)> noise(i) ut_ = ut_+1; if ut>buffersize || ut_ - ut > 5 edata_(end,2) = edata_(end,2)-0.01; break; end edata_ = edata(lt:ut,:); end edata = edata_; maxamp = max(edata(:,2)); minamp = min(edata(:,2)); if maxamp < minbackwallamp backwall(i) = 0; thickness(i) = 0; amplitude(i) = 0; noiseThreshold(:,i) = [0,0]; continue; end noiseHT = noise(i) * 1.02; noiseLT = noise(i) * 0; if noiseHT > maxamp noiseHT = maxamp - 1; end noiseThreshold(:,i) = [noiseHT,noiseLT]; edata((edata(:,2)>noiseLT & edata(:,2)<=noiseHT),2) = noise(i); %% Search for the first backwall echo data_diff=diff(edata(:,2)); %find changes in amplitude if ~any(data_diff) %if no peak, skip this row. backwall(i) = 0; thickness(i) = 0; amplitude(i) = 0; continue end locChange=find(data_diff~=0); %locate the places where there is a change in amplitude locChange_diff=diff(locChange); locFlatPeak=find(locChange_diff~=1 & locChange_diff<10); %locate the last data point in a flat peak locChange(locFlatPeak+1)=locChange(locFlatPeak+1) - ceil((locChange_diff(locFlatPeak)-1)/2); %locate the middle of the flat peak and replace the loca_flat in loca_change % * locChange(locFlatPeak+1) returns the last point in the flat peak(s). % * use floor() instead of ceil() to take the point to the right of the % midpoint for flat peaks consisting of even number of points. % * or use neither for a unrounded number.

459

dataFiltered=[edata(locChange,2);edata(end,2)]; %get rid of all noise and reduce the flat peak to a sharp peak % Problem unsolved here: % if the data points are ascending or decending all the way from the % begining till the end, i.e. no valley or peak, it should give a % warning and take the start or end as the max. logiPosNeg=diff(dataFiltered)>0; %logic_positive_or_negative: +tive slope = 1, -tive slope = 0 logiMaxMin=diff(logiPosNeg); %logic_maxima_or_minima: +1 = maxima, -1 = minima locMax=locChange(find(logiMaxMin==-1)+1); %locate the maxima locMax = edata(locMax,1); if ~any(locMax) backwall(i) = 0; thickness(i) = 0; amplitude(i) = 0; continue end try dataMax=data(locMax,i); %find data points of the maxima catch aaa=1; end if length(locMax) == 1 backwall(i) = locMax; amplitude(i) = dataMax; thickness(i) = CalT(interface(i),locMax, mwp, cwp); continue end %Find the max backwall echo dataMax_ = dataMax; dataBcw = max(dataMax); locBcw = find(dataMax == dataBcw,1); dataMax_(locBcw) = 0; dataBcw2 = max(dataMax_); locBcw2 = find(dataMax == dataBcw2,1); locBcw = locMax(locBcw); locBcw2 = locMax(locBcw2); if locBcw > locBcw2 && locBcw2 - locBcw < 15 && dataBcw - dataBcw2 < 5 locBcw = locBcw2; dataBcw = dataBcw2; end amplitude(i) = dataBcw; backwall(i) = locBcw; thickness(i) = CalT(interface(i),locBcw); end function t = CalT(interface, backwall) tof = backwall-interface; [mwp,cwp] = Calibrate(tof, false); t = (tof) * mwp + cwp;

460

function [m,c] = Calibrate(value, useThickness) mc_data=[0.65 0.95 23.3 35.8 0.02403 0.08891 0.95 1.99 35.8 67.4 0.03285 -0.2244 1.99 2.98 67.4 100.9 0.02889 0.06614 2.98 3.98 100.9 128.1 0.03544 -0.5598 3.98 5.87 128.1 197.6 0.02685 0.5634 5.97 8.01 197.6 260.8 0.03412 -0.8885 8.01 10 260.8 334.9 0.02665 1.075 0 9999 0 9999 0.03043 -0.06453 ]; if useThickness i = find(value>=mc_data(:,1) & value<mc_data(:,2)); if ~any(i) i=size(mc_data,1); end else i = find(value>=mc_data(:,3) & value<mc_data(:,4)); if ~any(i) i=size(mc_data,1); end end m = mc_data(i(1),5); c = mc_data(i(1),6);