Table Of ContentRobotic Nondestructive Testing
Technology
Robotic Nondestructive Testing
Technology
Chunguang Xu
MATLAB is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the
accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB software or related products
does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular
use of the MATLAB software.
First edition published 2022
by CRC Press
6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742
and by CRC Press
2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
CRC Press is an imprint of Taylor & Francis Group, LLC
© 2022 Chunguang Xu
Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot
assume responsibility for the validity of all materials or the consequences of their use. The authors and p ublishers
have attempted to trace the copyright holders of all material reproduced in this publication and apologize to
copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been
acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or
utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including
photocopying, microfilming, and recording, or in any information storage or retrieval system, without written
permission from the publishers.
For permission to photocopy or use material electronically from this work, access www.copyright.com or contact the
Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. For works that are
not available on CCC please contact [email protected]
Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for
identification and explanation without intent to infringe.
Library of Congress Cataloging‑in‑Publication Data
Names: Xu, Chunguang, 1964- author.
Title: Robotic nondestructive testing technology / Chunguang Xu.
Description: First edition. | Boca Raton, FL : CRC Press, 2022. |
Includes bibliographical references. | Summary: “This book introduces a variety
of non-destructive testing (NDT) methods, including testing and application cases.
New ultrasonic testing technology for complex workpieces is p roposed”— Provided by publisher.
Identifiers: LCCN 2021031691 (print) | LCCN 2021031692 (ebook) |
ISBN 9781032079547 (hbk) | ISBN 9781032079561 (pbk) |
ISBN 9781003212232 (ebk)
Subjects: LCSH: Nondestructive testing. | Automatic test equipment. |
Robotics—Industrial applications.
Classification: LCC TA417.2 .X83 2022 (print) | LCC TA417.2 (ebook) |
DDC 620.1/127—dc23
LC record available at https://lccn.loc.gov/2021031691
LC ebook record available at https://lccn.loc.gov/2021031692
ISBN: 978-1-032-07954-7 (hbk)
ISBN: 978-1-032-07956-1 (pbk)
ISBN: 978-1-003-21223-2 (ebk)
DOI: 10.1201/9781003212232
Typeset in Minion
by codeMantra
Contents
Preface, xv
Author, xix
Chapter 1 ◾ Introduction 1
1.1 BACKGROUND 3
1.1.1 Automatic NDT Methods of Complex Components 4
1.1.2 Development Trend of Robotic NDT Technique 5
1.2 BASIS OF MANIPULATOR 7
1.2.1 Type and Structure of Manipulators 8
1.2.2 Working Mode of Manipulators 8
1.3 MATHEMATICAL RELATIONSHIP BETWEEN THE COORDINATE
SYSTEM AND EULER ANGLE 11
1.3.1 Definition of a Manipulator Coordinate System 11
1.3.2 Relationship between Position & Attitude and Coordinate System 14
1.3.2.1 Position Description 14
1.3.2.2 Attitude Description 15
1.3.2.3 Spatial Homogeneous Coordinate Transformation 15
1.3.3 Quaternion and Coordinate Transformation 17
REFERENCES 21
Chapter 2 ◾ Method of Acoustic Waveguide UT 23
2.1 WAVE EQUATION AND PLANE WAVE SOLUTION 23
2.1.1 Acoustic Wave Equation for an Ideal Fluid Medium 23
2.1.2 Plane Wave and Solutions of Wave Equations 31
2.2 ULTRASONIC REFLECTION AND TRANSMISSION
AT THE INTERFACE 33
2.3 ANALYSIS OF SOUND FIELD IN AN ACOUSTIC WAVEGUIDE TUBE 38
v
vi ◾ Contents
2.4 MEASUREMENT OF SOUND FIELD IN AN ACOUSTIC
WAVEGUIDE TUBE 51
REFERENCES 53
Chapter 3 ◾ Planning Method of Scanning Trajectory on
Free-Form Surface 55
3.1 MAPPING RELATIONS BETWEEN MULTIPLE COORDINATE SYSTEMS 55
3.1.1 Translation, Rotation and Transformation Operators 55
3.1.1.1 Translation Operator 55
3.1.1.2 Rotation Operator 56
3.1.1.3 Transformation Operator 57
3.1.2 Equivalent Rotation and Quaternion Equation 57
3.1.2.1 Representation in an Angular Coordinate System 58
3.1.2.2 Representation in an Equivalent Axial Angular
Coordinate System 59
3.2 SURFACE SPLIT AND RECONSTRUCTION BASED ON NUBRS 59
3.2.1 Parametric Spline Curve and Surface Split Method 59
3.2.2 Scanning of Non-uniform Rational B-Splines (NURBS) 60
3.2.3 Surface Construction Based on Differential Equation and
Interpolation Algorithm 61
3.3 SURFACE SCANNING TRAJECTORY ALGORITHM BASED ON
CAD/CAM 65
3.3.1 Generation of Discrete Point Data of Free-Form Surface 67
3.3.2 Coordinate Transformation under the Constraint of Ultrasonic
Testing (UT) Principle 71
3.4 SCANNING TRAJECTORY SMOOTHNESS JUDGMENT AND DATA
DISCRETIZATION PROCESSING 73
3.4.1 Wavelet Processing Method of Surface Data 73
3.4.2 Handling and Judgment of Surface Smoothness 75
REFERENCES 80
Chapter 4 ◾ Single-Manipulator Testing Technique 83
4.1 COMPOSITION OF A SINGLE-MANIPULATOR TESTING SYSTEM 84
4.1.1 Workflow of a Testing System 84
4.1.2 Principle of Equipment Composition 85
4.2 PLANNING OF SCANNING TRAJECTORY 93
4.2.1 Ultrasonic/Electromagnetic Testing Parameters 93
4.2.2 Trajectory Planning Parameters 102
Contents ◾ vii
4.3 CALIBRATION AND ALIGNMENT OF ASSEMBLY ERROR 104
4.3.1 Method of Coordinate System Alignment 104
4.3.2 Alignment Method Based on Ultrasonic A-Scan Signal 107
4.3.3 Error Compensation Strategy and Gauss-Seidel Iteration 110
4.3.4 Positioning Error Compensation 112
4.4 MANIPULATOR POSITION/ATTITUDE CONTROL AND
COMPENSATION 114
4.4.1 Kinematics Analysis 114
4.4.2 End-Effector Position Error and Compensation Strategy 122
4.4.3 Method of Joint Position/Attitude Feedback 126
4.5 METHOD OF SYNCHRONIZATION BETWEEN POSITION AND
ULTRASONIC SIGNAL 128
REFERENCES 132
Chapter 5 ◾ Dual-Manipulator Testing Technique 133
5.1 BASIC PRINCIPLE OF ULTRASONIC TRANSMISSION DETECTION 134
5.1.1 Basic Principles of Ultrasonic Reflection and Ultrasonic
Transmission 134
5.1.1.1 Basic Principle of Ultrasonic Reflection Detection 134
5.1.1.2 Basic Principle of Ultrasonic Transmission Detection 134
5.1.1.3 Comparison between the Elements of an Ultrasonic
Reflection Method and Those of an Ultrasonic
Transmission Method 135
5.1.2 Ultrasonic Transmission Testing of Curved Workpieces 135
5.1.2.1 Principle of Reflection and Transmission of Ultrasonic
Wave Incident on Curved Workpieces 135
5.1.2.2 Principle of Refraction of Ultrasonic Wave Incident on a
Curved Surface 136
5.2 COMPOSITION OF A DUAL-MANIPULATOR TESTING SYSTEM 136
5.2.1 Hardware Structures in a Dual-Manipulator Testing System 137
5.2.1.1 Six-DOF Articulated Manipulator 138
5.2.1.2 Manipulator Controller 141
5.2.1.3 Data Acquisition Card 142
5.2.1.4 Ultrasonic Signal Transceiver System 142
5.2.1.5 Water-Coupled Circulation System 143
5.2.2 Upper Computer Software of a Dual-Manipulator Testing System 144
5.2.2.1 Overall Design of Upper Computer Software 144
viii ◾ Contents
5.2.2.2 Data Acquisition 145
5.2.2.3 Synchronous Control of Dual Manipulator 145
5.2.2.4 Automatic Scanning Imaging Module 148
5.2.3 Lower Computer Software of a Dual-Manipulator Testing System 149
5.3 MAPPING RELATION BETWEEN DUAL-MANIPULATOR BASE
COORDINATE SYSTEMS 150
5.3.1 Transformation Relationship between Base Coordinate Systems 151
5.3.1.1 Definition of Parameters of a Manipulator
Coordinate System 151
5.3.1.2 Solution of an Unified Variable Method 152
5.3.1.3 Solving with a Homogeneous Matrix Method 155
5.3.2 Orthogonal Normalization of Rotation Matrix 157
5.3.2.1 Basis of Lie Group and Lie Algebra 157
5.3.2.2 Orthogonalization of Rotation Matrix Identity 160
5.3.3 Experiment of Dual-Manipulator Base Coordinate
Transformation Relationship 162
5.3.4 Analysis of Transformation Relation Error 166
5.4 DUAL-MANIPULATOR MOTION CONSTRAINTS DURING TESTING 170
5.4.1 Constraints on the Position and Attitude of Dual-Manipulator
End-Effectors in the Testing of Equi-Thickness Workpiece 171
5.4.2 Constraints on the Position and Attitude of Dual-Manipulator
End-Effectors in the Testing of Variable-Thickness Workpiece 175
REFERENCES 179
Chapter 6 ◾ Error Analysis in Robotic NDT 181
6.1 KINEMATICS ANALYSIS FOR ROBOTIC TESTING PROCESS 181
6.1.1 Establishment of the Coordinate System in a Moving Device 181
6.1.2 Matrix Representation of the Position/Attitude Relationship
between Coordinate Systems 182
6.1.3 Coordinated Motion Relation between Manipulator and Turntable 184
6.1.4 Matrix Representation of Coordinated Motion Relation 186
6.2 PLANNING OF MOTION PATH IN THE TESTING PROCESS 187
6.2.1 Algorithm of Detection Path Generation 187
6.2.2 Resolving of Manipulator Motion Path 189
6.3 ERROR SOURCES IN ROBOTIC UT PROCESS 193
6.3.1 Geometric Error in Path Copying 194
6.3.2 Localization Error in Manipulator Motion 195
Contents ◾ ix
6.3.3 Clamping Error of Tested Component 196
REFERENCES 198
Chapter 7 ◾ Error and Correction in Robotic Ultrasonic Testing 199
7.1 ULTRASONIC PROPAGATION MODEL 199
7.1.1 Fluctuation of Sound Pressure in an Ideal Fluid Medium 200
7.1.2 Expression of Sound Pressure Amplitude 203
7.1.3 Superposition of Multiple Gaussian Beams 204
7.1.4 Influence of the Curved Surface on Ultrasonic Propagation 205
7.2 3D POINT CLOUD MATCHING ALGORITHM BASED ON NORMAL
VECTOR ANGLE 208
7.2.1 Matching Features of 3D Point Clouds 209
7.2.2 Calculation of the Normal Vector on a Curved Surface 209
7.2.3 Identification and Elimination of Surface Boundary Points 210
7.2.4 Calculation of Spatial Position/Attitude Deviation of
3D Point Cloud 211
7.3 CORRECTION EXPERIMENT FOR 3D POINT CLOUD
COLLECTION AND INSTALLATION DEVIATION 213
7.3.1 Steps of 3D Point Cloud Matching 213
7.3.2 Simulation Verification of Position/Attitude Deviation
Correction Algorithm 215
7.3.3 Experiment and Detection Verification of Curved-Component
Deviation Correction 217
REFERENCES 219
Chapter 8 ◾ Kinematic Error and Compensation in Robotic
Ultrasonic Testing 221
8.1 THREE-DIMENSIONAL SPATIAL DISTRIBUTION MODEL OF
ROBOTIC UT ERROR 221
8.1.1 Model of Manipulator Localization Error 221
8.1.2 Relationship between Distance Error and Kinematic
Parameter Error 225
8.1.3 Three-Dimensional Spatial Distribution of Errors 227
8.2 FEEDBACK COMPENSATION MODEL OF ROBOTIC UT ERROR 228
8.2.1 Principle of Error Feedback Compensation 229
8.2.2 Calculation of Kinematic Parameter Errors 230
8.2.3 Step of Feedback Compensation of Kinematic Parameter Error 232
