Servo Scanning 3D Micro Electro Discharge Machining: Principles and Methods for Machining 3D Microstructures [1st ed. 2023] 9789811931239, 9789811931246, 9811931232

Citation preview

Hao Tong Yong Li

Servo Scanning 3D Micro Electro Discharge Machining Principles and Methods for Machining 3D Microstructures

Servo Scanning 3D Micro Electro Discharge Machining

Hao Tong · Yong Li

Servo Scanning 3D Micro Electro Discharge Machining Principles and Methods for Machining 3D Microstructures

Hao Tong Department of Mechanical Engineering Tsinghua University Beijing, China

Yong Li Department of Mechanical Engineering Tsinghua University Beijing, China

ISBN 978-981-19-3123-9 ISBN 978-981-19-3124-6 (eBook) https://doi.org/10.1007/978-981-19-3124-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

To the families and the students. Hao Tong Yong Li

Preface

Micro machining processes are research and development basic of the frontier fields such as micro mechanics, micro sensors, micro friction, implantable microsystems, etc. Micro electro discharge machining (EDM, also called electrical discharge machining) is capable of machining micro structures on conductive workpieces, removing materials with micro-energy and high-frequency pulsed discharges through narrow gaps filled with dielectric media. Owing to non-contact machining of less force regardless of workpiece strength, stiffness, and hardness, micro EDM has attracted scientific research and industrial attention due to the integrated advantages of cost, efficiency, and accuracy. Micro EDM is early developed and researched in drilling micro holes even to a micro diameter size of ~Φ5 µm, and the drilling technologies and machine tools have achieved successful applications in industrial fields such as micro nuzzles of diesel engines. Novel processes and technologies of micro EDM are being explored and developed considering complex 3D structures, diversified workpiece materials, special applied fields, etc. As a novel process, scanning 3D micro EDM process can machine 3D micro structures/cavities by scanning layer by layer with a simple rod-shaped micro tool electrode. The 3D scanning process utilizes the advanced concept of 2D laminated layers accumulating into 3D complex structures. In this way, scanning 3D micro EDM does not need the preparation process of complex shaped tool electrodes which is generally required by traditional die-sinking EDM. In principle, although the process of die-sinking micro EDM can machine complex 3D micro structures/cavities based on the reverse copying process using the shaped micro tool electrodes, this is not worth process considering that the micro tool electrodes themselves are difficult to be fabricated, especially considering their wear during the machining process. However, compared with micro-EDM processes of drilling and wire-cutting, the process of scanning 3D micro EDM is more complex in terms of processing control and optimization. One of the greatest challenges is serious wear of the micro tool electrode because its cross-sectional area is much smaller than that of the workpiece to be removed. Conventional solutions of the micro tool-electrode wear limit the discharging efficiency and the workpiece-material adaptability.

vii

viii

Preface

Authors proposed a novel process of servo scanning 3D micro electro discharge machining (SS-3D micro EDM) by integrating servo control of micro discharge gaps with 3D scanning process. The highlight is not necessary to measure the specific value of micro tool-electrode wear, while the tool wear can be automatically compensated under the condition of high discharging ratio. With the authors’ research and experience about 15 years, this book provides the systematic knowledge of the SS-3D micro EDM process covering principle, methods, technologies, and optimization for machining 3D micro cavities/structures. In addition, the experimental parameters and results of SS-3D micro EDM are described in details as examples which are easy to understand and practice for readers. In reality, the main contents of this book as the research progress of SS-3D micro EDM have published by ourselves in international journals. This book is beneficial to systematically and comprehensively understand the process and applications of SS-3D micro EDM. Recently, based on the most methods and technologies in this book, a commercial 3D micro-EDM machine tool has been developed for industrial applications or scientific research in universities. The processes and machine tools of SS-3D micro EDM are promising applications in the multi-fields related to micro electromechanical systems (MEMS) for machining micro devices or micro structures made of metal and metal alloy materials. For example, as a key part of an active catheter in bio-MEMS, a thin-walled micro tube with complex 3D micro structures, made from NiTi shape memory alloy (SMA), has been successfully machined by the SS-3D micro EDM process. We believe that this book will have the potential to promote a significant impact on the development of micro EDM process and application. This book consists of four parts divided into 14 chapters. Part I (Chaps. 1–5) introduces the background, proposes the process of SS-3D micro EDM, and illuminates its basic principle, key methods and technologies. Part II (Chaps. 6–9) focuses on the methods and systems for optimizing the process of SS-3D micro EDM considering the processing efficiency and accuracy. Part III (Chaps. 10–12) presents the on-machine hybrid processes mainly considering batch/array machining model and surface integrity of 3D micro cavities. Part IV (Chaps. 13 and 14) illustrates a typical application example and discusses the prospect of SS-3D micro EDM. This book has the main features as follows: • This book emphasizes the systematic knowledge as well as the frontier research progress of SS-3D micro EDM, allowing it to be used as a reference handbook for planning the whole machining process of 3D micro structures/cavities, for designing a machining system or a machine tool, and even for understanding the idea of innovative processes. • The included methods and technologies are verified by testing and machining experiments. Thus, this book presents many machining examples including the experimental parameters, conditions, and systems. These not only help the readers understand the concept, theories, and methods easily, but also provide practical operation guidance for engineering applications in industrial machining processes and design of machine tools.

Preface

ix

• Although the content unfolds around the novel process of SS-3D micro EDM rather than conventional processes, actually a number of methods and technologies including micro-energy pulsed power supply (in Chap. 3), servo control of micro machining gap (in Chap. 4), on-machine precision fabrication and measurement of micro tool electrode (in Chap. 5), vibration-assisted system (in Chap. 7), macro/micro-dual-feed spindle and its control (in Chap. 8), on-machine fabrication of array micro electrodes (in Chap. 11), etc., are valuable to refer and apply to other micro-EDM processes of die-sinking, drilling, wire-cutting, ect. This book is more useful to professional researchers and engineers in the fields of micro EDM and hybrid machining processes based on micro-EDM. In addition, it can provide a significant reference to the educators, undergraduate students, MS and Ph.D. students, and others related to non-traditional micro machining courses/research. Besides, it may be a guide book used by professionals for carrying out micro-EDM related technical training. Beijing, China March 2021

Hao Tong Yong Li

Acknowledgements

The authors express gratitude most sincerely to many members and students in micro and nano manufacturing laboratory (located in Department of Mechanical Engineering, Tsinghua University, China) who contributed directly or indirectly to this book: Jing Cui, Shanjin lv, Manhong Hu, Long Zhang, Jinrong Yang, Hao Zhong, Xin Wu, Ying Xiong, Yan Li, Xueling Liu, Yubin Pu, and Ran Quan. The authors really appreciate the contribution and help from all of them. The related research of this books was funded by the National 973 Plan (grant no. 2003CB716204), National 863 Plan (grant nos. 2007AA04Z346, and 2009AA044205), National Natural Science Foundation of China (grant nos. 50905094 and 51675302), and China Postdoctoral Science Foundation (grant Nos. 20080440378 and 200902097), Independent Research Project of State Key Laboratory of Tribology of China (grant Nos. SKLT11C05 and SKLT2015B08), Open Foundation of State Key Laboratory of Mechanical System & Vibration of China (grant No. MSV-2012-16), and 2016 Annual Cultivation and Development Project for Scientific and Technological Innovation Base (grant No. Z161100005016038). The authors also thank editors and staff from Springer for the publication of this book.

xi

Contents

1

Basic Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Basic Principles of Servo Scanning 3D Micro EDM Process . . . . 1.3 Feasibility Verification of Process Principle . . . . . . . . . . . . . . . . . . 1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 3 4 6 7

2

3D CAD/CAM System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Planning of Path Type and Path Span . . . . . . . . . . . . . . . . 2.2.2 Post Processing of NC Codes . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Implementation Example of CAD/CAM System . . . . . . 2.3 Control Strategy of CAM Process . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 9 10 11 16 17 20 22 24

3

Design and Test of Pulsed Power Supply . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Design and Test of Pulsed Power Supply with Multi-Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Logic Circuit Design for Generating High Frequency Pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 High-Speed Isolated Driving Circuit of MOSFET Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Performance Test of Pulsed Power Supply . . . . . . . . . . . . 3.2.4 Detection Circuit of Discharge Gap State . . . . . . . . . . . . . 3.3 Pulsed Power Supply with Ns-Pulsewidth Based on Triode Avalanche Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Basic Principle of Ns-Pulsewidth Pulsed Power Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 25 27 29 31 33 34 36 36

xiii

xiv

Contents

3.3.2

Design and Performance Tests of Basic Circuit of Ns-Pulsewidth Pulsed Power Supply . . . . . . . . . . . . . . 3.3.3 Design and Performance Tests of Cascaded Circuit with Two Triodes for Improving Ns-Pulsewidth Pulsed Power Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Experimental Verification of Ns-Pulsewidth Pulsed Power Supply with Cascaded Circuit . . . . . . . . . . 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

5

Servo Control of Micro Discharge Gap . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Servo Control Characteristics of Micro Discharge Gap . . . . . . . . . 4.2.1 Experimental System and Method . . . . . . . . . . . . . . . . . . . 4.2.2 Experimental Results and Analysis . . . . . . . . . . . . . . . . . . 4.2.3 Experimental Verification with High Response Frequency Spindle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Threshold Control and Optimization Method . . . . . . . . . . . . . . . . . 4.3.1 Optimization Constraint of Servo Control Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Matching Scanning Speed with Servo Speed of Tool Electrode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Experiments of Optimization Verification in SS-3D Micro EDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Self-Adaptive Fuzzy Control Method with Formulary Rule . . . . . 4.4.1 Control Strategy and Design of Self-Adaptive Fuzzy Controller with a Formulary Rule . . . . . . . . . . . . . 4.4.2 Self-Adaptive Fast Convergence Algorithms . . . . . . . . . . 4.4.3 Experimental Verification of Self-Adaptive Fuzzy Control Method in SS-3D Micro EDM . . . . . . . . . . . . . . . 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Precision Fabrication and Measurement of Micro Tool Electrode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Mechanism of Wire Electro Discharge Grinding (WEDG) . . . . . . 5.3 Tangential-Feed WEDG Method and Hybrid Process . . . . . . . . . . 5.3.1 Principle and Analysis of TF-WEDG . . . . . . . . . . . . . . . . 5.3.2 Hybrid Machining Process of Micro Electrode . . . . . . . . 5.3.3 Experimental Results and Discussion . . . . . . . . . . . . . . . . 5.4 On-Machine Fabrication Process of Flat Micro Tool Electrode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Principle of On-Machine Fabrication for Flat Micro Tool Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

41 45 48 49 51 51 53 53 54 57 59 59 63 65 71 72 74 78 81 82 85 85 87 92 93 95 95 99 99

Contents

xv

5.4.2

Machining Experiments of Flat Electrodes and Array Micro Grooves . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 On-Machine Measurement Method of Intersecting Point Electric Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

102 105 107 108

6

Effect of Process Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Effect of Electric Parameters on Machining Performance . . . . . . . 6.2.1 Effect of Peak Current and Pulse Duration . . . . . . . . . . . . 6.2.2 Effect of Machining Polarity . . . . . . . . . . . . . . . . . . . . . . . 6.3 Effect of Scanning Paths on Machining Performance . . . . . . . . . . 6.3.1 Effect of Path Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Effect of Path Span . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Effect of Scanning Speed on Machining Performance . . . . . . . . . . 6.5 Machining a Typical 3D Micro Structure . . . . . . . . . . . . . . . . . . . . 6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

109 109 111 111 112 114 114 114 117 119 120 121

7

Vibration-Assisted SS-3D Micro EDM . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Method and Experimental System . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Fundamental Machining Experiments . . . . . . . . . . . . . . . . . . . . . . . 7.4 Establishment and Analysis of Machining Process Model . . . . . . 7.5 Machining Experiments for 3D Micro Cavities . . . . . . . . . . . . . . . 7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

123 123 124 125 129 131 133 134

8

SS-3D Micro EDM Based on Macro/Micro-Dual-Feed Spindle . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Method and Experimental System . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Control and Performance Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Control of Macro/Micro Dual-Feed Spindle . . . . . . . . . . 8.3.2 Performance Test of Macro/Micro Dual-Feed Spindle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Application Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Fundamental Machining Experiments . . . . . . . . . . . . . . . . 8.4.2 Machining Experiments of 3D Micro Microstructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

135 135 136 139 139 140 141 141 146 148 148

xvi

9

Contents

Algorithms to Reduce Depth Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Analysis of Machined-Depth Error and Surface Unevenness . . . . 9.3 Illumination of Proposed Algorithms . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 S-Curve Accelerating Algorithm (SCAA) . . . . . . . . . . . . 9.3.2 Layer Depth Constrained Algorithm (LDCA) . . . . . . . . . 9.4 Implementation Process and Control Strategy of Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5 Experimental Verification of Algorithms . . . . . . . . . . . . . . . . . . . . . 9.5.1 Basic Machining Experiments . . . . . . . . . . . . . . . . . . . . . . 9.5.2 Machining Experiments for Typical 3D Micro Cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 On-Machine Process of Rough-And-Finishing SS-3D Micro EDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Rough and Finishing Process of SS-3D Micro EDM . . . . . . . . . . . 10.3 Strategy of 3D-Model Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Machining Experiments of 3D Micro Cavities . . . . . . . . . . . . . . . . 10.4.1 Experimental Method and System . . . . . . . . . . . . . . . . . . . 10.4.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Array SS-3D Micro EDM by Using Array Tool Electrodes . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Processing Method of Array SS-3D Micro EDM . . . . . . . . . . . . . . 11.3 Array SS-3D Micro EDM by Using Off-Line Fabricated Array Micro Tool Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.1 Off-Line Preparation of Array Micro Tool Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.2 Machining Experiments of Array Micro Cavities . . . . . . 11.3.3 Processing Analysis with Off-Line Fabricated Array Micro Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Array SS-3D Micro EDM by Using On-Machine Fabricated Array Micro Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.1 Processing Method with On-Machine Fabrication of Array Tool Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.2 On-Machine Fabrication of Array Tool Electrodes . . . . . 11.4.3 Machining Experiments of Array Micro Cavities . . . . . . 11.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

149 149 150 153 153 155 158 160 161 163 165 166 167 167 168 170 171 171 173 175 177 179 179 180 182 183 183 185 189 189 191 191 195 195

Contents

12 Hybrid Process of SS-3D Micro EDM and Scanning 3D Micro ECM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Hybrid Process of SS-3D Micro EDM and Scanning 3D Micro ECM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3 Experimental System and Processing Strategy . . . . . . . . . . . . . . . . 12.4 Processing Experiments and Results Analysis . . . . . . . . . . . . . . . . 12.4.1 Hybrid Process Experiment for Square Cavity . . . . . . . . 12.4.2 Hybrid Process Experiment for Micro Spherical Crown Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.3 Analysis of Experimental Results for Hybrid Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 SS-3D Micro EDM Applied in Machining Pierced Micro Structures of TiNi Alloy Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 Processing Methods and Experimental System of Four-Axis SS-3D Micro EDM . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.1 Processing Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2.2 Experimental System and Workpiece Clamping Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3 NC Codes Generation and Optimization of Servo Scanning Paths for Complex Pierced Micro Driving Structures . . . . . . . . . . 13.3.1 Machining Experiments of Typical Driving Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xvii

197 197 198 200 202 203 204 205 206 207 209 209 211 211 212 216 218 221 222

14 Discussion and Prospect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

About the Authors

Hao Tong in May 2008, received his Ph.D. degree in the field of 3D micro electro discharge machining from Harbin Institute of Technology, China. From June 2008 to June 2010, he worked at Tsinghua University as a Postdoctoral Fellow. From September 2016 to September 2017, he worked at University of California, Los Angeles (UCLA) as a visiting research scholar. He is currently an associate professor at the Department of Mechanical Engineering at Tsinghua University, China. His research mainly focuses on micro/nano non-traditional machining processes, technologies, and systems including electro discharge machining (EDM), electrochemical machining (ECM), and spark assisted chemical engraving (SACE). He has published more than 80 academic papers and owned more than 40 invention patents. He was also awarded the Beijing Higher Education Young Elite, the Good Youth Award of Intelligent Manufacturing on the 30th Anniversary of China Association for Mechatronics Technology & Application (CAMETA), the Award of China Machinery Industry Science and Technology Invention (first prize), the Outstanding Paper Award on the 40th Anniversary of Chinese Nontraditional Machining Society (1979–2019), the Excellent Paper Award of Chinese Mechanical Engineering Society (CMES), and the Excellent Paper Awards of 14th and 15th Chinese Nontraditional Machining Conference. e-mail: [email protected] Yong Li graduated in mechanical engineering at Harbin Institute of Technology, China, in 1982. He received his Ph.D. in precision engineering at Niigata University, Japan, in 1991. He is currently a tenured professor at the Department of Mechanical Engineering, Tsinghua University, China. His research interest is in micro/nano manufacturing, including micro EDM, micro ECM, ultra-precision machining, and microfluidic devices. He has published more than 200 research papers and received 50 warranted invention patents of China. He has also received a first-class inven-

xix

xx

About the Authors

tion award of science and technology in mechanical industry of China, in 2015, a first-class award for advancement of science and technology from the ministry of education in 2003, a second-class award for advancement of science and technology from Beijing City, in 2000, and a second-class award for advancement of science and technology from the ministry of education in 1999. e-mail: [email protected]. edu.cn

Abbreviations

3D BUE CAD CAM CCD CEA CNC CPP CTC DPP ECM EDM FET FPGA IPC LDCA LDV LIGA MRR NC NiTi PMAC PMMA Pro/E PZT SAFCFR SCAA SCM SEM Si

Three-dimensional Built up edge Computer aided design Computer aided manufacturing Charge coupled device Chemical elements analysis Computer numerical control Contour-parallel path Control target center Direction-parallel path Electrochemical Machining Electro discharge machining, or electrical discharge machining Field effect transistor Field-programmable gate array Industrial personal computer Layer depth constrained algorithm Laser doppler velocimeter German acronym for Lithographie, Galvanoformung, and Abformung, meaning Lithography, Electroplating, and Molding Material removal rate Number control Nickel-titanium Programmable multi-axis controller Polymethyl methacrylate Pro Engineer Piezoelectric Self-adaptive fuzzy controller with a formulary rule S-curve accelerating algorithm Single-chip microcomputer Scanning electron microscopy Silicon xxi

xxii

SMA SS TF UWM WEDG WLI

Abbreviations

Shape memory alloy Servo scanning Tangential feed Uniform wear method Wire electro discharge grinding White light interferometer

Chapter 1

Basic Principle

Abstract The method and process of servo scanning 3D micro EDM (SS-3D Micro EDM) is proposed. Micro tool-electrode wear can be compensated in real time by integrating servo control of discharge gaps with the scanning process. The highlight is not necessary to measure a specific value of micro tool-electrode wear, while the wear can be automatically compensated owing to the servo control of discharge gaps. Basic principle of SS-3D micro EDM is illuminated by analyzing that the machined depth of each scanning layer conforms to consistency-depth principle. Basic configuration of the processing system is introduced. The process feasibility is verified according to the relationship between scanning speeds and layer depths. This chapter provides the theoretical basis for the process and system of SS-3D micro EDM. Keywords Basic principle · Consistency depth · Basic machining system · Process feasibility

1.1 Introduction Electro discharge machining (EDM), also known as electrical discharge machining, is a machining process which can be used to remove conductive materials, via a series of pulsed discharges between a tool electrode and a workpiece. EDM, as a low cost and non-traditional machining technology, possesses a special advantage as non-contact machining of minimal machining force. It is capable of machining a harder workpiece with a softer tool, regardless of the workpiece strength, stiffness, and hardness. It has been applied in machining many types of materials, including metal, alloy, silicon, and even ceramic [1]. Micro EDM can be realized by microenergy electrical discharges, so as to obtain a micro machining unit (removal volume of single discharge). In the late 1960s, one of the earliest experiments of micro EDM was reported by Philips Research Laboratory as a successful result of a Φ30 µm micro hole, with an accuracy of ~0.5 µm [2]. Since this time, multi-faceted research on micro EDM has been carried out. Micro machining technologies are the basis of frontier research such as micro mechanics, micro sensors, micro friction, implantable microsystems, etc. [3–5]. The requirements are being increasingly reflected in the three-dimensional (3D) © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 H. Tong and Y. Li, Servo Scanning 3D Micro Electro Discharge Machining, https://doi.org/10.1007/978-981-19-3124-6_1

1

2

1 Basic Principle

microstructures. In the general macro-size EDM, 3D structures/cavities can be successfully machined by a die-sinking EDM process, which is a copying process performed by using a correspondingly shaped 3D tool electrode. However, it is difficult or uneconomical to realize 3D micro structures/cavities by die-sinking micro EDM, as micro-shaped tool electrodes themselves cannot be easily fabricated and their shapes are difficult to maintained, due to tool-electrode wear during the machining process. In contrast, scanning 3D micro EDM is suitable for machining complex 3D micro structures/cavities which have a high aspect ratio, by scanning one layer at a time using a simple rod-shaped tool electrode, based on the electrical discharges at the tip of the tool electrode. 3D micro cavities/structures can be formed by stacking thin slices layer by layer by removing materials from workpieces. This provides the advantages of design freedom, ease of chip removal, and low setup cost. In 1997, a micro car mould (0.5 × 0.2 × 0.2 mm3 ), as a typical example, was successfully machined using scanning 3D micro EDM [6, 7]. In a scanning 3D micro EDM process, tool-electrode wear is an extrusive issue which affects the processing accuracy and efficiency. The wear is very severe, as the cross-sectional area of the micro tool electrode is much smaller than that of the workpiece that is to be removed. As a result, the machining gap between the tool electrode and workpiece would become larger and larger if the tool wear accumulates during the machining process. When the gap is larger than a discharge gap, then the machining state of continuous electrical discharges cannot be sustained if the tool wear is not timely compensated. Therefore, tool-electrode wear compensation is a key for ensuring an available process of scanning 3D micro EDM [8–10]. A number of methods have been researched with the goal of achieving a lower wear ratio or/and compensating for the wear [11–14]. A basic compensation method has been applied, seeking to feed the tool electrode in the direction of the electrode axis based on the estimation of wear ratio [15]. In order to record the electrode wear in terms of shape and size, an online imaging system has been applied in the wear compensation [16]. In addition, a compensation method was presented with measuring the axial wear by using electric contact between tool electrode and workpiece before each path [8]. A uniform wear method (UWM) with the specially designed tool paths was proposed and experimented with by estimating tool wear value based on the experiments by providing the machining parameters in advance [7]. These compensation methods can be summarized as experimental models [17, 18], discharge statistics [19, 20], and intermittent measurement [21, 22] by estimating or measuring the tool wear value in advance. However, the tool wear in micro EDM is affected by multiple factors, including electric parameters, machining polarity, dielectric fluid, tool shape, and materials used in tool electrodes and workpieces. Among the above methods, the toolelectrode mode of intermittent feed or constant speed feed limits the compensation performances of real-time and adaptability, as the tool-electrode wear varies within a very small period such as 5 µs. In order to compensate micro tool-electrode wear with achieving a high discharging ratio, this book proposes a servo scanning 3D micro EDM (SS-3D micro EDM) method [23–25]. In the SS-3D micro EDM, the micro tool electrode wear is compensated in real time by integrating the servo control of discharge gaps with the

1.2 Basic Principles of Servo Scanning 3D Micro EDM Process

3

3D scanning process. In this manner, the mode of variant speed feed of the micro electrode can adapt to the varying tool-electrode wear. Consequently, the machining efficiency can be expected to reach its maximum. The highlight is not necessarily to measure the specific value of tool-electrode wear, while the tool wear can be automatically compensated due to the servo control of discharge gap. Additionally, SS-3D micro EDM can apply the scanning paths planned by commercial CAM software, such as Pro/Engineer, in machining complex micro cavities. In this book, the systematic methods and technologies of the SS-3D micro EDM process are introduced and illuminated, including the principles, technologies and optimizations for machining 3D micro structures/cavities.

1.2 Basic Principles of Servo Scanning 3D Micro EDM Process Given a tool electrode, a workpiece and electric parameters as the constants, the energy of single spark discharge is a constant W M in a suitable discharge gap of S B . If the S B is kept, then the discharge frequency accords with a statistical constant f e as for a pulsed power supply of micro EDM, so that the discharge energy per unit time is a constant as W T = W M ·f e . Therefore, the material removal rate is a constant as V T = k a ·W T (k a as a coefficient constant). With a scanning speed of vs , a scanning width d s of electrode diameter, and keeping the discharge gap of S B , the machined depth hT each scanning layer in the SS-3D micro-EDM is a constant, as described by Eq. (1.1) hT =

VT ka W M f e = vs ds vs ds

(1.1)

where hT is the machined depth each layer, V T is the material removal rate, vs is the scanning speed, d s is the electrode diameter, k a is a coefficient constant, W M is the discharge energy of a single spark discharge, and f e is the discharge frequency. This is referred to as the consistency-depth principle of SS-3D micro EDM [23]. Figure 1.1 reveals that the axial electrode wear from l 1 to l2 can be automatically compensated by the servo control of discharge gap L B in real time. The machined thickness of each layer exhibits statistical consistency only if the electric parameters, scanning speed and track overlapping are given. By setting the consistency thickness as the laminated thickness, a 3D micro cavity can then be machined by the servo control of discharge gap in conjunction with the XY-worktable motion according to the 3D scanning paths. According to the consistency-depth principle, Fig. 1.2 shows the basic configuration of the processing system of SS-3D micro EDM, which consists of a pulsed power supply, an XY-worktable for moving scanning paths, a spindle for the servo feed of the tool electrode, a sensor for monitoring the discharge state, a CAD/CAM

4

1 Basic Principle

Fig. 1.1 Wear compensation of tool-electrode in SS-3D micro EDM. a Axial wear compensation of tool-electrode; b discharging gap at tool electrode end

Fig. 1.2 Basic configuration of processing system of SS-3D micro EDM

system for generating number control (NC) codes, and a control system for controlling the SS-3D micro EDM process. The feed axis of the tool-electrode and other linkage axes are controlled separately. The tool-electrode is servo controlled to feed or withdraw, so as to keep a discharge gap according to the feedback of interelectrode electric signal. The axial wear of the tool electrode can be compensated in real time. At the same time, the tool electrode rotation, or to-and-fro path, is used for homogenizing the lateral wear of the tool electrode end. In this manner, the 3D micro cavities and structures can be machined by servo scanning of tool electrode layer by layer, according to the 3D NC codes. The highlights of this are that it is not necessary to measure the specific value of tool-electrode wear, and that the wear can be automatically compensated in real time, due to the servo control of the discharge gap. The other axes are moved in the linkage to obtain the designed 3D NC paths. The tool-electrode wear based on the servo control of the discharge gap is then conducive to maximizing the discharging ratio.

1.3 Feasibility Verification of Process Principle In the SS-3D micro EDM, 3D micro cavities/structures are shaped by superimposing the two-dimensional laminations of the scanning layers according to the NC scanning paths. The feasibility of SS-3D micro EDM lies in verifying the consistency

1.3 Feasibility Verification of Process Principle Table 1.1 Experimental parameters

5

Parameter

Value

Open voltage (V)

125

Peak current (A)

1.25

Pulse duration (µs)

0.5

Pulse interval (µs)

10

Material of tool electrode

Tungsten

Size of tool electrode (µm)

Φ100

Dielectric fluid

Oil

Workpiece material

Si (P-doped type)

Path overlap (µm)

40

depth each layer, which is determined via the relationship between the scanning speed and machined layer depth. Machining experiments of micro rectangular cavity (900 µm × 600 µm) are carried out to verify the consistency principle. Table 1.1 presents the experimental parameters. The machined depth is measured using an electric profilometer, and the machined results are envisioned by scanning electron microscopy (SEM). Figure 1.3 shows that the relationship between the machining layer times and the measured depth correlates to the linearity. The nonlinear error stems from the random errors of the machining process. According to the nonlinear error, the dimensional error of the machining depth is less than 4 µm. The experimental process reveals that the discharge state is stable. According to the measured results of the micro-rectangular cavities in Fig. 1.4, the length-and-width dimensions of the micro-rectangular cavities are enlarged by 10– 20 µm more than the designed sizes. By analyzing the discharge process of SS-3D Fig. 1.3 Relationship between machining layer times and machining depth

6

1 Basic Principle

Fig. 1.4 SEM photographs of machined micro cavities by SS-3D micro-EDM. a Multiple micro cavities; b enlarged view of a micro cavity

micro-EDM (Fig. 1.1b), we know that the end discharge of tool electrode inevitably leads to a lateral discharge gap. Consequently, the enlarged sizes of 10–20 µm are mainly caused by the consistent lateral gap. The dimensional accuracy can then be improved by designing a compensation value of the lateral gap during 3D CAD/CAM planning. The high accuracy of shape and dimension is expected to be controllable in the SS-3D micro EDM of 3D micro cavities/structures. As determined from monitoring the discharge state and machined results, the process of SS-3D micro-EDM realizes the real-time compensation of tool-electrode axial wear. Upon completing this process, the stable and continuous machining process of 3D micro structures/cavities is successfully achieved.

1.4 Summary In order to compensate micro tool-electrode wear with the advantages of high discharging ratio and real-time process adaptability, the servo scanning 3D micro EDM (SS-3D Micro EDM) method is proposed. The conclusions can be summarized as follows. (1)

The axial wear of tool-electrode can be automatically compensated by servo control of discharge gaps in real time. The machined thickness of each layer exhibits statistical consistency only if electric parameters, scanning speed, and track overlapping are given, which is referred to the consistency-depth principle. By setting the consistency thickness as the laminated thickness, a 3D micro cavity can then be machined by servo control of discharge gap in conjunction with XY-worktable motion according to 3D scanning paths.

References

(2)

(3)

7

Basic configuration of processing system includes a pulsed power supply, an XY-worktable for moving scanning paths, a spindle for servo feed of tool electrodes, a sensor for monitoring discharge state, a CAD/CAM system for generating number control (NC) codes, and a control system for controlling SS-3D micro EDM process. The key of process control is to separately control feed axis of tool-electrodes and other linkage axes. The feasibility of SS-3D micro EDM is verified by the experimental results of consistency depth of each scanning layer, conforming to the consistency-depth principle.

According to the basic principle and system of SS-3D micro EDM, in order to effectively realize the machining process of complex 3D micro structures/cavities, the key methods and technologies will be proposed and developed in following chapters.

References 1. A. Muttamara, Y. Fukuzawa, N. Mohri, T. Tani, Probability of precision micro-machining of insulating Si3 N4 ceramics by EDM. J. Mater. Process Technol. 140, 243–247 (2003) 2. C. Van Osenbruggen, Micro spark erosion. Philips Technisch Tijdschrift 20, 200–213 (1969) 3. F. Vollertsen, Z. Hu, H.S. Niehoff, C. Theiler, State of the art in micro forming and investigations into micro deep drawing. J. Mater. Process Technol. 151, 70–79 (2004) 4. T. Masuzawa, State of the art of micromachining. CIRP Ann. Manuf. Technol. 49, 473–488 (2000) 5. M. Geiger, M. Kleiner, R. Eckstein, N. Tiesler, U. Engel, Microforming. CIRP Ann. Manuf. Technol. 50, 445–462 (2001) 6. T. Masuzawa, H.K. Tonshoff, Three-dimensional micromachining by machine tools. Ann. CIRP 46(2), 621–628 (1997) 7. Z. Yu, T. Masuzawa, M. Fujino, Micro-EDM for three-dimensional cavities-development of uniform wear method. Ann. CIRP 47(1), 169–172 (1998) 8. D.T. Pham, S.S. Dimov, S. Bigot, A. Ivanov, K. Popov, Micro-EDM recent developments and research issues. J. Mater. Process Technol. 149, 50–57 (2004) 9. P. Bleys, J.P. Kruth, B. Lauwers, A. Zryd, R. Delpretti, C. Tricarico, Real time tool wear compensation in milling EDM. CIRP Ann. Manuf. Technol. 51(1), 157–160 (2002) 10. Z.Y. Yu, J. Kozak, K.P. Rajurkar, Modeling and simulation of micro EDM process. CIRP Ann. Manuf. Technol. 52(1), 143–146 (2003) 11. G. Puthumana, An influence of parameters of micro-electrical discharge machining on wear of tool electrode Arch. Budowy Masz 64(2), 149–163 (2017) 12. U. Maradia, R. Knaak, W.D. Busco, M. Boccadoro, K. Wegener, A strategy for low electrode wear in meso-micro-EDM. Precis. Eng. 42, 302–310 (2015) 13. S. Bigot, A. Ivanov, D.T. Pham, K. Popov, A study of micro-electro discharge machining electrode wear. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 221, 605–612 (2007) 14. D.T. Pham, A. Ivanov, S. Bigot, K. Popov, S. Dimov, An investigation of tube and rod electrode wear in micro EDM drilling. Int. J. Adv. Manuf. Technol. 33, 103–109 (2007) 15. C.L. Kuo, S.T. Chen, Y.Z. Wu, T. Yan, T. Masuzawa, Study on 3D micro EDM, in Proceedings of the Annual Assembly of Japan Society of Electrical Machining Engineers (1997), pp. 111–114 16. T. Kaneko, M. Tsuchiya, A. Kazama, Improvement of 3D NC contouring EDM using cylindrical electrodes-optical measurement of electrode deformation and machining of free-curves, in Proceedings of International Symposium for Electro Machining X (1992), pp. 364–367

8

1 Basic Principle

17. J. Narasimhan, Z.Y. Yu, K.P. Rajurkar, Tool wear compensation and path generation in micro and macro EDM. J. Manuf. Process. 7(1), 75–82 (2005) 18. H.L. Yu, J.J. Luan, J.Z. Li, Y.S. Zhang, Z.Y. Yu, D.M. Guo, A new electrode wear compensation method for improving performance in 3D micro EDM milling. J. Micromech. Microeng. 20(5), 055011 (2010) 19. J.W. Jung, Y.H. Jeong, B.K. Min, S.J. Lee, Model-based pulse frequency control for microEDM milling using real-time discharge pulse monitoring. J. Manuf. Sci. Eng., Trans. ASME 130(3), 03110601–03110611 (2008) 20. G. Bissacco, J. Valentincic, H.N. Hansen, B.D. Wiwe, Towards the effective tool wear control in micro-EDM milling. Int. J. Adv. Manuf. Technol. 47, 3–9 (2010) 21. M.T. Yan, K.Y. Huang, C.Y. Lo, A study on electrode wear sensing and compensation in micro-EDM using machine vision system. Int. J. Adv. Manuf. Technol. 42, 1065–1073 (2009) 22. M.T. Yan, S.S. Lin, Process planning and electrode wear compensation for 3D micro-EDM. Int. J. Adv. Manuf. Technol. 53, 209–219 (2011) 23. Y. Li, H. Tong, J. Cui, Y. Wang, Servo scanning EDM for 3D micro structures, in Proceedings of the International Conference on Integration and Commercialization of Micro and Nanosystems (2007), pp. 1369–1374 24. H. Tong, Y. Li, Y. Wang, D.W. Yu, Servo scanning 3D micro-EDM based on macro/microdual-feed spindle. Int. J. Mach. Tools Manuf. 48, 858–869 (2008) 25. H. Tong, Y. Wang, Y. Li, Vibration-assisted servo scanning 3D micro EDM. J. Micromech. Microeng. 18(2), 501–508 (2008)

Chapter 2

3D CAD/CAM System

Abstract The SS-3D micro EDM of 3D micro structures/cavities is inseparable from a 3D CAD/CAM system for scanning paths and generating NC codes. However, the usual CAD/CAM system applied in CNC milling is not suitable considering the particularity wear compensation of tool-electrode and processing control. A 3D CAD/CAM system is designed and developed by combining Pro/Engineer (Pro/E) software and a post-processing software. The method of double-loop buffers is adopted for orderly reading and transmitting a large number of NC codes. Considering the compensation strategy of tool electrode wear, the tool electrode lifting and electric-contact positioning method is presented for avoiding collision and insufficient machining. The multi-level hierarchical control method is adopted for realizing the processing control of CAM. Keywords 3D CAD · CAM system · Scanning paths · NC codes · Double-loop buffers · Tool electrode lifting

2.1 Introduction 3D micro structures/cavities consist of space curves and curved surfaces. It is difficult to express the scanning paths and machining process by mathematical expressions or manual writing [1]. In the SS-3D micro EDM process for machining complex 3D micro structures/cavities, the number of NC codes is up to tens of thousands of lines, even to hundreds of thousands of lines. The SS-3D micro EDM is inseparable from a 3D CAD/CAM system. However, the usual CAD/CAM system applied in CNC (computer numerical control) milling cannot generate the suitable NC codes including the information of wear compensation of tool-electrode and processing control [2, 3]. Therefore, it is necessary to develop a special 3D CAD/CAM system for generating complex 3D scanning paths and NC codes. For example, the scanning micro EDM with uniform tool-wear compensation method integrated CAD/CAM systems for generating NC codes of complex 3D micro cavities [3]. In order to make full use of commercial software advantages, a 3D CAD/CAM system suitable for SS-3D micro EDM is

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 H. Tong and Y. Li, Servo Scanning 3D Micro Electro Discharge Machining, https://doi.org/10.1007/978-981-19-3124-6_2

9

10

2 3D CAD/CAM System

designed and developed by combining the Pro/Engineer (Pro/E) software with a post-processing software [4]. In this chapter, based on the special analysis of SS-3D micro EDM, the implementation process of the CAD/CAM system is described in detail. The key methods of the CAD/CAM system include the following: (1) The double-loop buffers method for reading and transmitting a large number of NC codes; (2) The tool electrode lifting and positioning method for avoiding collision and insufficient machining; and (3) The multi-level hierarchical control method for controlling the machining process.

2.2 System Design Based on the powerful functions of a commercial CAD/CAM system, the 3D CAD/CAM system of SS-3D micro EDM is developed by combining Pro Engineer (Pro/E) with self-designed post-processing software. The system integrates the functions of 3D model design, planning and simulation of scanning paths, and generation and post-processing of NC codes. It is able to generate suitable NC codes of 3D micro structures/cavities for SS-3D micro EDM. By integrating Pro/E functions, the developed CAD/CAM system can realize parametric design and planning of a variety of paths. The implementation process is shown in Fig. 2.1. The procedure of the Pro/E model design is to build the 3D model of a micro structure/cavity, which is the prototype used in planning and simulating scanning paths. Based on the CNC machining function of Pro/E software, this procedure has the functions of parameter constraint, parameter driving, and parameter correlation among the designed dimensions, machining paths, and CNC codes. In other words, if a designed parameter is modified in any link, the associated links are modified accordingly. It should be noted that in the model design the size unit is the same as that of SS-3D micro EDM system, while the removed minimum geometry size is larger than the tool-electrode diameter. The procedure of planning paths involves setting up the parameters of the machining depth, layer lamination thickness, path type, and path span, according to the electrical parameters and scanning speed. The path type and the path span are more important for the machining accuracy and efficiency of SS-3D micro EDM. The planning and simulation of scanning paths is a testing process of scanning paths, machining origin and end points, retract plane of tool electrode, and machining interference. The procedure of the NC codes’ generation is to generate the NC codes that are suitable for SS-3D micro EDM, by processing a cutter location file of the.ncl file which is automatically generated by Pro/E. The NC codes have the information of the XY axes-linked movement and layering in the Z-axis direction. Finally, the machining simulation seeks to test the correctness and accuracy of the post-processing NC codes.

2.2 System Design

11

Fig. 2.1 Implementation process of 3D CAD/CAM for SS-3D micro EDM

2.2.1 Planning of Path Type and Path Span The scanning path span is the distance between two adjacent paths. During the SS-3D micro EDM process, the end shape of tool electrode can be approximated as a circular arc, as the sharp edge of the tool electrode first wears as a result of electrical discharges. Figure 2.2 shows the effects of scanning-path span on the scanning process under ideal conditions. The size of the path span mainly affects residual height of the workpiece surface and discharge area of each path. The residual height is one of the main factors influencing surface accuracy, while the discharge area is one of the main factors influencing machining efficiency. If the path span was much larger than the tool electrode radius (Fig. 2.2b), then a larger residual height

12

2 3D CAD/CAM System

Fig. 2.2 Effect of path span on SS-3D micro EDM. a Scanning path and path span; b Path span is larger than tool electrode radius; c Path span is equal to tool electrode radius; d Path span is smaller than tool electrode radius

would come into being while the material removal rate (MRR) of each scanning path would be larger with a larger discharge area. If the path span was equal to the tool electrode radius (Fig. 2.2c), then the residual height would be significantly reduced, and the MRR of each scanning path would be moderate. If the path span was much smaller than the tool electrode radius (Fig. 2.2d), then the discharge area would be significantly reduced, although the residual height would be close to zero. As a result, the MRR of each scanning path would be minimized. The small path span causes a larger single-end wear and deformation in the tool electrode, which in turn cases the machining efficiency and accuracy to both be lower. In summary, the path span should be set to be slightly smaller than the tool electrode radius. During the SS-3D micro EDM process, the scanning movement of tool electrode is also subjected to the process of deceleration, stop, and acceleration at every inflection point of the scanning paths. To achieve the higher processing efficiency, it is expected

2.2 System Design

13

Fig. 2.3 Scanning-path comparison between direction-parallel paths and contour-parallel paths. a Direction-parallel paths; b Contour-parallel paths

that the fewer inflection points there are. The shorter the distance of the scanning paths will be, and the time of non-machining paths will be shorter as well. The scanning paths can be planed into either direction-parallel or contour-parallel paths. Figure 2.3 shows a circular cavity with the direction-parallel paths and the contour-parallel paths around a convex island. For the former, the tool electrode must be lifted for the rapid movement to stride across the convex island. The advantage of the direction-parallel paths is that the processing mode remains unchanged, yet the number of inflection points is significantly greater than that of the contour-parallel paths. Therefore, the contour-parallel paths are beneficial to improving the processing efficiency. On the other hand, the contour-parallel paths can also lead to over-cutting issues, due to the superimposed scanning paths at the intersection of the scanning paths. The path-type setting is designed to set scanning paths and patterns when encountering a convex island. The path-type settings can be used to plan different paths via Pro/E. For the direction-parallel paths, the scanning paths mainly include four types, as shown in Fig. 2.4. Type-I: When the island is encountered, lift the tool electrode over the convex island (Fig. 2.4a). Type-II: When the island is encountered, do not lift the tool electrode while scanning around the island (Fig. 2.4b). Type-III: Scan each separate area separated by the island, and after one area is completed, move to the next area to continue the scanning process. Type-I with direction: The scanning paths are all in the same direction. The path direction continues after the tool electrode has been lifted to the other side of the island. During the SS-3D micro EDM process, the electrical discharge machining is generally conducted along all scanning paths of the SS-3D micro EDM. According to the description of the above path types, both Type-I and Type-I with direction increase the number of lifting tool electrodes and the distance of non-machining paths. Type-II increases the scanning-path number around the convex island, as the peripheral path is performed every time when the

14

2 3D CAD/CAM System

Fig. 2.4 Comparison of direction-parallel paths. a Type-I; b Type-II; c Type-III; d Type-I with direction

convex island is encountered, which leads to the over-cutting process. For the contourparallel paths, the scanning paths mainly include two types, as shown in Fig. 2.5. Type-spiral: Scanning uses the wraparound paths. Type-spiral with direction: Scanning uses the wraparound paths, and the surrounding direction remains unchanged. Compared with the other path types, Type-spiral can minimize the number of lifting tool electrodes and improve the processing efficiency. Considering the processing efficiency and accuracy, Type-spiral and Type-III are preferred for planning paths in SS-3D micro EDM. During the SS-3D micro EDM of complex 3D micro structures/cavities, the process of tool-electrode presetting must be managed in the NC codes. The toolelectrode presetting involves withdrawing the tool electrode from one machined district, and then setting the tool electrode position to another machining district. Due to the particularity of the tool-electrode wear, the method of tool-electrode presetting used in CNC mechanical milling cannot be directly applied in the SS-3D micro EDM. An improved method of presetting tool electrodes is presented and applied so as to avoid bumping the tool electrode and insufficient machining. Figure 2.6 shows the respective processes of the different methods for presetting tools.

Fig. 2.5 Comparison of contour-parallel paths. a Type-spiral; b Type-spiral with direction

2.2 System Design

15

Fig. 2.6 Process analysis of different presetting-tool methods. a CNC mechanical milling; b Insufficient machining; c Bumping tool electrode; d Improved method of presetting tool electrode

Figure 2.6a shows the process of tool presetting used in CNC mechanical milling. As it has not the tool wear like that found in the SS-3D micro EDM, the actual machined depth (h1 and h2 ) and the height (h3 ) of the retract plane in NC codes are known as exact values. Thereby, the path of presetting tool is planned in the NC codes as follows. First, the tool is withdrawn as the distance sum (h1 + h3 ) to the retract plane. Second, the tool is moved in the horizontal direction as the idle path to the new position of another machining district. Finally, the tool is fed by the distance sum (h2 + h3 ) to the machining position on the workpiece. In this tool-presetting process, the actual adjusted distance (h1 −h2 ) in the tool-axial direction is known as an exact value. Figure 2.6b and c show the problems that the above-mentioned method of presetting tool is applied directly in the SS-3D micro EDM. Before the tool electrode is withdrawn, although the tool-electrode wear (ΔL) is compensated for by keeping the discharge gap (L B ), the exact value of the tool-electrode wear (ΔL) cannot be precisely obtained. Based on the basic method of SS-3D micro EDM, only the sum (h 1 + L) of the machined depth (h 1 ) and the tool-electrode wear (ΔL) can be obtained as a known value. Moreover, compared with the ideal machining depth (h1 and h2 ) in NC codes, the actual machined depths (h 1 and h 2 ) include machining errors. If the adjusted distance was still an ideal value (h1 −h2 ), then the process of the insufficient machining would occur when the adjusted value (h1 −h2 ) was less than the required value (h 1 − h 2 ), as shown in Fig. 2.6b. If the adjusted distance was

16

2 3D CAD/CAM System

still an ideal value (h1 −h2 ), then the process of bumping tool electrode would occur when the value (h1 −h2 ) was greater than the required value (h 1 − h 2 ), as shown in Fig. 2.6c. The process of insufficient machining or tool-electrode bumping adversely affects the machining accuracy. In particular, the bumping process may cause the tool electrode to bend. Figure 2.6d shows the improved method of presetting tool electrode in SS-3D micro EDM. This improved method adds a retract margin h for the process of electric-touch positioning. The tool electrode can be positioned by feeding to the actual machining position on the workpiece by monitoring the signal of voltage change between the tool electrode and the workpiece. The retract margin h meets the following constraint condition:   h > (h 1 − h 2 ) − (h 1 − h 2 )

(2.1)

This can ensure that the actual adjusted distance (h 1 − h 2 + h) is greater than the required adjusted distance (h 1 − h 2 ), so that a safe height h  can avoid the tool-electrode bumping as follows: h  = (h 1 − h 2 ) − (h 1 − h 2 ) + h

(2.2)

Furthermore, the process of electric-touch positioning can ensure the toolelectrode to feed by the safe distance (h  ) so as to reach the actual machining position and in turn avoid insufficient machining.

2.2.2 Post Processing of NC Codes A commercial CAD/CAM software such as Pro/E can generate a common file of tool paths according to the setting of processing parameters and the planning of scanning paths. As for the requirements of SS-3D micro EDM process and system, the common file of tool paths lacks unique information while containing large amounts of useless information of CNC mechanical milling. A post-processing software program for NC codes has been developed for processing the common file of tool paths into the NC codes suitable to SS-3D micro EDM process. Considering the high versatility of NC codes, the post-processing software can process the common file into two types of NC codes, namely point coordinate codes and G codes. Post processing of point coordinate codes: The straight-line paths described by [GOTO /X, Y, Z] in the common file of tool paths are directly converted into point coordinate values (X, Y, Z) according to the interpolation precision. Next, circular arc paths are approximated by the short linear interpolation method. The interpolation precision is then adjusted according to the radius of the circular arc so as to improve the accuracy of the straight line fitting circular arc. Then, according to the k value in the statement of [CIRCLE / X, Y, Z, 0, 0, K, R] in the common file of the tool paths, the circular arc direction can be determined, while the circular arc is interpolated

2.2 System Design Table 2.1 Description of post-processing G codes

17 G code

Description

M08

Machining begins

G01 X Y Z

Linear interpolation

G02 X Y R

Clockwise circular interpolation

G03 X Y R

Counterclockwise circular interpolation

M05

Lifting tool electrode begins

M06

Lowering tool electrode begins

M30

Code ends

into the coordinate values of n points (X1, Y1, Z1), (X2, Y2, Z2), (X3, Y3, Z3), …, (Xn, Yn, Zn). According to the value change and positive-or-negative of the Z coordinate, the information of the scanning layers and lifting tool-electrode can be obtained to conduct the corresponding process of layering and tool-electrode lifting. The processed NC codes expressed by the point coordinate codes possess strong adaptability. Any motion platform of the three axes with the function of coordinate positioning can realize the scanning motion of NC codes. However, the data of the NC codes with high interpolation accuracy are too large in size, so that the special machining system is required for transmitting the data. Post processing of G codes: G codes are most commonly used as machining codes for CNC machine tools. The line path of [GOTO /X, Y, Z] and the circle arc path of [CIRCLE / X, Y, Z, 0, 0, K, R] in a common file of tool paths are processed by using the standard codes, as shown in Table 2.1. According to the change of the post-processed Z coordinates and M05, the information of layering and lifting tool-electrode can be determined. The CNC system of SS-3D micro EDM can directly perform G codes by applying the function of linear interpolation and circular interpolation. In this manner, the processing control is more convenient, yet requires strong NC performance on behalf of the machining system.

2.2.3 Implementation Example of CAD/CAM System Next the micro-hexaprism cavity is taken as an example to introduce the implementation process of the CAD/CAM system. (1)

(2)

3D model design is intended to build the model of 3D micro structures by using the function of Pro/E, such as stretching according to the designed shape, size and unit (µm). Figure 2.7a shows an example of micro-hexaprism cavity with a side length 800 µm of the outer square cavity, a top side length 150 µm of micro hexaprism, a bottom side length 300 µm of micro hexaprism, and a depth of 200 µm. The planning layers and setting processing parameters introduce the designed 3D model as a reference model into the manufacturing work environment, and

18

2 3D CAD/CAM System

Fig. 2.7 Model design and paths simulation of micro-hexaprism cavity. a 3D model design; b Scanning paths simulation

then the relevant manufacturing parameters are set. These parameters must be set according to the specific conditions to create processing volume, as follows. Coordinate zero point: Create the zero point at the center of the upper surface of the 3D model. Tool electrode setting: Set the tool electrode diameter and length according to the actual situations. For example, tool electrode diameter 100 µm and tool electrode length 1,000 µm. Feed depth: Set the maximum machining depth to 200 µm; Layer depth: Layer thickness 4 µm; Path span: Set as 40 µm; Path-type: Type-spiral; Machining allowance: Set as 5 µm according to the discharge gap; (3)

(4)

(5)

(6)

Retract plane: Coordinate value of 500 µm along the Z direction. The goal of the path simulation is to simulate the processing paths by using Pro/E software, as shown in Fig. 2.7b. The simulation paths are contour-parallel paths. The process of generating a cutter location file of.ncl, if the simulation paths meet the machining requirements, is shown in Fig. 2.8. The NCL file mainly includes the line and circle statements respectively described as GOTO and CIRCLE. The post processing of NC codes seeks to generate point coordinate codes or G codes by processing the NCL file. Figure 2.9 shows an example of the processed file with a portion of the NC codes. The simulation verification of NC codes seeks to verify the correctness and accuracy of the NC codes by means of servo scanning simulation software. Figure 2.10 shows the process and results of such a simulation verification.

2.2 System Design

19

Fig. 2.8 An example of cutter location NCL file

Fig. 2.9 An example of processed file with NC codes. a Point coordinate codes; b G codes

Fig. 2.10 Process and result of machining simulation for 3D NC codes. a Processing simulation verification of NC codes; b Verification result of processing simulation

20

2 3D CAD/CAM System

The above CAD/CAM process is used to design the 3D model, to set the machining parameters, to simulate the machining paths, and to generate and verify the NC codes for 3D microstructures. It is shown that the CAD/CAM process can satisfy the processing requirements of SS-3D micro EDM.

2.3 Control Strategy of CAM Process The CAM process control of SS-3D micro EDM mainly realizes the functions of initialization of processing parameters, transferring and downloading of NC codes, controlling scanning paths with tool-electrode wear compensation, interrupt control of machining process, monitoring machining state, and dealing with abnormal process. The process control of SS-3D micro EDM is described in Fig. 2.11. The main steps of the process control are as follows. According to the processing requirements of the microstructures, the first step is to initialize the machining parameters, and then download a file of NC codes generated by the CAD/CAM system. The second step is to begin the processing cycle. Each cycle first determines whether or not to suspend the process for performing the corresponding double check. If there is no such handling exception, then the first batch of NC codes is read into the double cycle buffer from the file of NC codes. The third step is to enter two parallel procedures: I. Main procedure: In order to read the NC codes one by one, the movement axes are controlled to realize 3D servo scanning machining or rapid positioning according to the NC codes. Then, to compensate tool electrode wear in real time by the SS-3D micro EDM method, the separation control strategy of Z-axis and XY axes is adopted. Namely, the XY axes are controlled via linkage movement for positioning the worktable according to the NC codes, while the Z axis is controlled by servo movement to keep a discharge gap in real time according to the gap detection of electric signal. In this manner, the combined motion can realize the movement function of SS-3D micro EDM. II. Auxiliary procedure: The purposes of this are to monitor the status of the double cycle buffer, and to update the display of feedback parameters. NC codes are read in an orderly way into the double cycle buffer in batches from the file of NC codes. When all of the NC codes have been implemented, the machining process of a 3D microstructure is complete, and this process has ended. After considering a great number of NC codes for a complex 3D microstructures/cavities, the method of double cycle buffer is used to read and write the data so as to transmit the NC codes in real time while using fewer hardware resources. The process of reading and writing NC codes is shown in Fig. 2.12. When the nth batch of NC codes must be compiled and run for the SS-3D micro EDM, the nth batch of NC codes is read from Buffer A one by one. At the same time, the (n + 1)th batch of NC codes is written into Buffer B in batches. This method realizes orderly reading and writing for all NC codes from the file. This method of dynamically transferring data can be carried out by means of read–write lock based on a double cycle buffer.

2.3 Control Strategy of CAM Process

21

Fig. 2.11 Software flow chart of process control for servo scanning 3D micro EDM

It is guaranteed that some of the buffers (e.g. Buffer A) are assigned to reading and others (e.g. Buffer B) to writing. As the writing time is much less than the time of XY axes positioning motion, a large amount of NC codes can be orderly read and transmitted in real time. The process of SS-3D micro EDM is coordinated and organized by a multi-level control method, as shown in Fig. 2.13. This is then divided into the three levels of organization, coordination, and control implementation. By using the organization level with knowledge-based organization, inference logic and experience can easily be applied, so as to better organize the machining process. The coordination level is

22

2 3D CAD/CAM System

Fig. 2.12 Software flow chart of transmission data by double cycle buffer

then used to decompose the complex process into several interrelated sub-processes. At the control implement level, the sub-tasks are carried out using relatively independent function modules. This multi-level control method can simplify complex problems and solve the problem of goal conflicts from several sub-processes.

2.4 Summary The 3D CAD/CAM system is developed for SS-3D micro EDM, integrating the functions of 3D model design, planning and simulation of scanning paths, and generation and post-processing of NC codes. By combining Pro/E with self-designed postprocessing software, the CAD/CAM system can realize parametric design, planning of a variety of paths, generating NC codes with tool-wear compensation algorithm, and testing the correctness and accuracy of the NC codes. The conclusions can be summarized as follows.

2.4 Summary

23

Fig. 2.13 Multi-level control method for SS-3D micro EDM process

(1)

(2)

(3)

In the procedures of dimensional design, path planning, and NC-codes generation, the functions of parameter constraint, parameter driving, and parameter correlation are effective. The dimensional design requires that model unit is suitable for SS-3D micro EDM system and the concave geometry size is larger than tool electrode diameter. Two types of NC codes as point coordinate codes and G codes can be generated by the post-processing software. The path span should be set to be slightly smaller than the tool electrode radius. The contour-parallel paths are beneficial to improving the processing efficiency and accuracy of curved-surface profile. Type-spiral and Type-III are preferred for planning paths. The improved method of presetting tool electrode can avoid the problems of bumping the tool electrode and insufficient machining. The CAM control method can realize the multi-functions of initialization of processing parameters, transferring and downloading of NC codes, controlling scanning paths with tool-electrode wear compensation, interrupt control of machining process, monitoring machining state, and dealing with abnormal process. The double cycle buffer with a read–write lock can orderly download and implement a large number of NC codes, meeting the requirement of realtime transmit during machining process by using fewer hardware resources. The multi-level control method can efficiently and harmoniously organize the machining process.

24

2 3D CAD/CAM System

References 1. W. Zhao, Y. Yang, Z. Wang, Y. Zhang, A CAD/CAM system for micro-ED-milling of small 3D freeform cavity. J. Mater. Process. Technol. 149, 573–578 (2004) 2. D.T. Pham, S.S. Dimov, S. Bigot, A. Ivanov, K. Popov, Micro-EDM recent developments and research Issues. J. Mater. Process. Technol. 149, 50–57 (2004) 3. K.P. Rajurkar, Z.Y. Yu, 3D micro-EDM using CAD/CAM. CIRP Ann. Manuf. Technol. 49, 127–130 (2000) 4. H. Tong, J. Cui, Y. Li, Y. Wang, CAD/CAM integration system of 3D micro EDM, in Proceedings of the International Conference on Integration and Commercialization of Micro and Nanosystems 2007, pp. 1383-1388 (2007)

Chapter 3

Design and Test of Pulsed Power Supply

Abstract A multi-function pulsed power supply with the detection circuit of the discharge state is designed and developed by using transistor switches for deionization, a FPGA (field-programmable gate array) as pulse generator, and a SCM (singlechip microcomputer) for setting pulsed parameters. By matchings the switches and discharge capacitors, the discharge circuit unit can be configured as various pulsecontrol forms including single-switch chopper mode, two-switch chopper mode, Tr-RC mode (controllable RC with single-switch), and controllable RC with two switches. By controlling the switch logic, the work mode of discharge pulse can be exchanged to equal pulse mode or equal energy mode. A snubber circuit is designed for avoiding turn-on and turn-off wear of MOSFET switches at high frequency. Besides, a novel pulsed power supply is designed and developed for realizing the ns-pulsewidth with controllable pulsewidth and peak voltage. The key novelty lies in a cascaded circuit with two triodes working in the state of ultra-fast avalanche conduction, where pF capacitors are applied to adjusting the pulsewidth and pulsed energy precisely. Performance tests verified that a single pulse of 5 ns pulsewidth or continuous pulses up to 9 MHz can be outputted. A single pulsed energy can reach down to 1.75 nJ by outputting a pulsewidth of 10 ns. Keywords Pulsed power supply · Transistor switch · Detection circuit · Nanosecond pulsewidth · Snubber circuit

3.1 Introduction A pulsed power supply plays an important role in the machined surface quality, machining efficiency, tool-electrode wear, and machining stability of micro EDM. It is required to realize a micro discharge energy down to 10–6 –10–8 J, a pulsewidth down to the order of microseconds even to nanoseconds, and high-frequency spark discharges for the discharging dispersion and continuity on a micro area. Wong et al. found that the lower pulsed discharge energy results in the more consistent discharge craters and the higher material removal rate [1]. Narrowing pulsewidth is an effective way to improve the material removal resolution, owing to the ability to emit higherintensity pulses of smaller discharge energy in shorter period of time, allowing the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 H. Tong and Y. Li, Servo Scanning 3D Micro Electro Discharge Machining, https://doi.org/10.1007/978-981-19-3124-6_3

25

26

3 Design and Test of Pulsed Power Supply

more precise removal of the material and the formation of smaller heat affected zones. Son et al. concluded that the narrow pulsewidth can improve machining accuracy and reduce tool electrode wear [2]. Yildiz et al. proved that surface roughness and recast layer thickness increase significantly if increasing discharge pulse time [3]. A pulsed power supply based on RC-relaxation mode is commonly used in micro EDM. This mode has the advantage of a simple structure easy to adjust singlepulse discharge energy. However, its state recovery of deionization depends on the dielectric itself to cut off the power supply. The deionization state is difficult to recover due to lacking of a deionization circuit, which is prone to the adverse discharging arc state [4]. Consequently the controllable RC circuit is proposed. This kind of circuit is a combination of RC relaxation type and transistor type. A switch is added into the RC relaxation-type circuit to cut off the current and to artificially restore insulation between tool and workpiece. When the capacitance is reduced to stray capacitance, the controllable RC circuit can be seen as a transistor-type. In order to achieve micro discharge energy and high discharge frequency in micro EDM, the transistor switches are designed to work at extremely high frequency. The machining efficiency can be 2– 3 times that of the traditional RC-relaxation mode [5]. The detection of discharge-gap state is the basis of feed control of tool electrodes. The detection circuit of dischargegap state is one of the key technologies in micro EDM, as its performance directly affects both the processing stability and quality. Due to the fact that a discharge gap is very narrow in micro EDM, down to a few of microns, and is influenced by random multi-factors, it is difficult to directly measure the gap value. Considering the size of discharge gaps is intrinsically related to the interelectrode voltage or discharge current, the detection circuit of discharge-gap state can be designed according to the voltage, the current, or both signals. In addition, as the single discharge period is very short, even down to U a ). Therefore, the capacitance C 1 of capacitor C1 can influence both peak voltage U peak and pulsewidth t pulse , which means it is difficult to adjust the peak voltage and pulsewidth separately. The single pulse waveform at U 1 = 20 V and C 1 = 20 pF shown in Fig. 3.14b verifies that the circuit can output the single pulse with pulsewidth of 4 ns. Compared with the existing precise and controllable single pulse down to pulsewidth of 240 ns obtained by Wang et al. [17], the pulsewidth of 4 ns realizes the ultra-narrow

40

3 Design and Test of Pulsed Power Supply

Fig. 3.14 Effect of capacitor C1 and DC power supply E1 on output pulses. a Relationship among peak voltage U peak , capacitance C 1 , and voltage U 1 of E1; b relationship among pulsewidth t pulse , capacitance C 1 , and voltage U 1 of E1

pulse, reducing by about two orders of magnitude. However, the peak voltage of the 4 ns pulsewidth is too low as 100 pF). The reason is the slow discharging speed when the capacitor C1 discharges to a certain extent into a low capacitance. Therefore, the basic circuit cannot achieve the required pulse with the higher peak voltage >10 V and ultra-narrow pulsewidth 10 V). In addition, owing to the threshold value of turn-on voltage of TRI2, the tailing part of the pulse

Fig. 3.15 Circuit improvement with two cascaded triodes

42

3 Design and Test of Pulsed Power Supply

Fig. 3.16 Working sequence of improved circuit

on R4 (Fig. 3.16) cannot turn the TRI2 on, avoiding the pulse tailing on R7 (t5–t6 in Fig. 3.16). To quantitatively express the pulse output for the improved circuit in Fig. 3.15, theoretical models of the peak voltage U peak and pulsewidth t pulse are deduced as follows. When the capacitor C1 discharges, the rising time t a for the voltage on the R4 rising up to the turn-on voltage Uon of TRI2 (t3–t4 in Fig. 3.16) is: ta = Uon /k0

(3.3)

where k0 is the slope of pulse rising edge on the R4 (about 2 V/ns) determined by the turn-on speed of triode TRI1. When the capacitor C1 is full, its voltage is the voltage U1 of DC power supply E1. According to Eq. (3.1), the time for the voltage on capacitor C1 dropping to the turn-on voltage Uon of triode TRI2 (t3–t5 in Fig. 3.16) is t b :

3.3 Pulsed Power Supply with Ns-Pulsewidth …

tb = RC1 ln(U1 /Uon )

43

(3.4)

where C1 is the capacitance of capacitor C1, and R is the total resistance of discharging circuit. So the turn-on time t c of TRI2 (t4–t5 in Fig. 3.16) is: tc = tb − ta = RC1 ln(U1 /Uon ) − Uon /k0

(3.5)

When the TRI2 turns on, the C2 discharges on R7 to make the voltage on R7 rising continuously until the TRI2 shuts off. If the rising peak voltage would not reach the voltage U2 of the E2 before TRI2 shuts off, the outputted pulse waveform is shown in Fig. 3.17a, and the peak voltage U peak on R7 could be expressed: Upulse = k1 tc

(3.6)

where k1 is the slope of pulse rising edge on R7 (about 2 V/ns) determined by the turn-on speed of triode TRI2. If the rising voltage on R7 could reach the voltage U2 of the E2, the outputted pulse waveform is shown in Fig. 3.17b, and the peak voltage U peak on R7 is U2 . Thus, considering the two cases, the peak voltage U peak on R7 can be expressed as: Upeak = min{k1 tc , U2 } = min{k1 (RC1 ln(U1 /Uon ) − Uon /k0 ), U2 }

(3.7)

As shown in Fig. 3.17a, when the peak voltage on R7 is k1 tc , considering the speed of turn-on of TRI2 is equal to that of shut-off, the time for rising edge or falling edge Fig. 3.17 Two kinds of pulse waveforms. a Peak voltage of k1 tc ; b peak voltage of U 2

44

3 Design and Test of Pulsed Power Supply

is t c , so the pulsewidth t pulse is: tpulse = tc /2 + tc /2 = tc

(3.8)

As shown in Fig. 3.17b, when peak voltage on R7 is U 2 , the time for rising edge or falling edge is t d , so the pulsewidth t pulse is: tpulse = tc − td /2 + td /2 = tc

(3.9)

Thus, considering the two cases, the pulsewidth t pulse on R7 can be expressed as: tpulse = tc = RC1 ln(U1 /Uon ) − Uon /k0

(3.10)

In order to verify the feasibility and models of the improved circuit, performance tests are conducted by setting C 1 as 20 pF, 40 pF, 60 pF, 100 pF, and 200 pF, setting U 2 as 10 V, 15 V, 20 V, 25 V, and 30 V, respectively. The other conditions are given as U 1 of 30 V, R6 of 30 , and R7 of 100 . The trigger pulse generator V1 is set to output square trigger single pulse and continuous pulses with a voltage of 6 V and a duty cycle of 0.5. Figure 3.18 indicates that the experimental results are basically consistent with theoretical values calculated by the mathematic models of Eqs. (3.7) and (3.10). When the C1 capacitance is greater than 40 pF (Fig. 3.18a), the peak voltage only correlates with the voltage of DC power supply E2. The deviation at C1 = 20 pF results from the relatively small conduction resistance of TRI2 when there is smaller current flowing through TRI2. Figure 3.18b indicates that the pulsewidth increases with the increase of capacitance of capacitor C1. When E2 voltage is too low such as U 2 = 10 V, the experimental value of pulsewidth is higher than the theoretical value. This is because the turn-on speed of triode TRI2 decreases when the E2 voltage is relatively low, resulting in the rising edge is less steep so as to increase the pulsewidth. Compared with the basic circuit (in Figs. 3.12 and 3.14) where the pulsewidth and peak voltage cannot be adjusted separately, the improved circuit (in Figs. 3.15 and 3.18) achieves the separate control of the peak voltage U peak and pulsewidth t pulse , where U peak and t pulse can be adjusted by E2 voltage U 2 and C1 capacitance C 1 respectively. The single pulse waveform at U 2 = 30 V and C 1 = 20 pF shown in Fig. 3.18b indicates that the improved circuit can output the single pulse with 5 ns pulsewidth and 12 V peak voltage which is approximately doubled compared with the basic circuit. The waveform at U 2 = 15 V and C 1 = 100 pF shown in Fig. 3.18b shows that the tailing phenomenon of the basic circuit (Fig. 3.12) is improved, the falling edge is steep and the waveform is closer to the square wave. If the trigger pulse generator V1 outputs continuous trigger pulses, the improved circuit will output continuous pulses on resistor R7 with the same frequency as trigger pulses, and continuous pulses waveform at U 2 = 25 V and C 1 = 60 pF shown as shown in Fig. 3.18b, the frequency can be up to 9 MHz.

3.3 Pulsed Power Supply with Ns-Pulsewidth …

45

Fig. 3.18 Effect of capacitor C1 and DC power supply E2 on output pulses in improved circuit. a Relationship among peak voltage U peak , capacitance C 1 , and voltage U 2 of E2; b relationship among pulsewidth t pulse , capacitance C 1 , and voltage U 2 of E2

3.3.4 Experimental Verification of Ns-Pulsewidth Pulsed Power Supply with Cascaded Circuit Nano EDM experiments were conducted to verify that the ns-pulsewidth pulsed power supply can realize a nanometer removal resolution. Figure 3.19 shows an AFM-tip-based nano EDM system, where the AFM tip serving as a tool electrode is connected to the negative port of the pulsed power supply, and a silicon wafer with a gold layer (surface roughness U ref2 , the open-circuit state is determined to feed the tool electrode downward; when U gap < U ref1 , the short-circuit state is determined to withdraw the tool electrode upward; and when U gap is within the threshold interval [U ref1 , U ref2 ], then the normal discharge state is determined to maintain the tool-electrode position. The micro-feed spindle adopts a stepping motor to drive a friction wheel, so as to feed the micro tool electrode with the advantage of not having transmission gaps of feeding and withdrawing. The spindle has a movement resolution of 0.16 µm and a response frequency of 22 Hz. The guider ensures the linear-feed accuracy of micro tool electrode. The micro tool electrode can be automatically fed to compensate for its accumulated wear by the inchworm feed based on the two clamps as a normally close clamp and a normally open clamp. The pulsed power supply is a controllable (Tr) RC mode, which is advantageous for deionization and high discharge ratio. The purpose of the basic experiments is to drill micro holes based on the threshold control method. The servo control effect of micro discharge gaps is analyzed and studied. An oscilloscope is used in monitoring the discharge waveform, while a displacement sensor of eddy current is used in monitoring the spindle movement. The displacement sensor can convert a micro displacement into a voltage signal as the output sensitivity of 21 mV/µm, with a measurement range of 1 mm and a response frequency of 5 kHz.

4.2.2 Experimental Results and Analysis Figure 4.2 shows the discharge waveforms monitored in the basic experiments, while Fig. 4.3 shows the displacement curve of the spindle movement monitored by the displacement sensor. The discharge waveforms reveal that the normal discharge ratio is as low as 10–20%, and that the discharges mainly occur in the alternate moment of open-circuit and short-circuit state. The trend of the displacement curve in Fig. 4.3a

4.2 Servo Control Characteristics of Micro Discharge Gap

55

Fig. 4.2 Discharge waveforms monitored in basic experiments. a State from short ciruit to open circuit; b State from open circuit to short circuit

Fig. 4.3 Displacement curve of spindle movement under normal depth. a Displacement curve in longer time; b Displacement curv in shorter time

illustrates the fact that the tool electrode continuously feeds with the increase of the micro-hole depth. During the feeding process, the displacement vibrates within a range of 9.5–19.0 µm, according to the value range of 200–400 mV (Fig. 4.3b) from the feedback signal of the eddy current sensor. This indicates that the tool electrode is servo controlled to feed and withdraw quickly between short circuit state and open circuit state. Figure 4.4 presents a comparison of the processing time under the conditions of different machining depths. The experimental results show that the processing state and efficiency is stable when the depth ranges from 0.5 to 1.0 mm, through a steelsheet workpiece with a tool electrode of F100 µm. In other words, the processing time and depth basically follows a linear relationship. When the depth is increased to 1.2–1.5 mm by using a steel sheet with a thickness of 1.7 mm, the processing state changes to an unstable state, as a result of the depth effect. At this time, the displacement curve of the spindle movement is that shown in Fig. 4.5. The curve slope significantly decreases because it is difficult for the machined debris to be

56

4 Servo Control of Micro Discharge Gap

Fig. 4.4 Comparison of processing time under different machining depths

Fig. 4.5 Displacement curve of spindle movement with depth effect. a Machining depth of 1.2– 1.4 mm; b Machining depth of 1.4–1.5 mm

removed from the narrow discharge gaps. It can be seen from Fig. 4.5b that the tool electrode displacement vibrates up to a larger range of 47.6–95.2 µm, according to the value range of 1,000–2,000 mV from the feedback signal of the eddy current sensor when the depth is increased to 1.4–1.5 mm. At this point it is almost impossible to continue the machining process. Compared with Fig. 4.3 in the experiments, it can be concluded that a depth should be lower than a normal depth such as 0.5–1.0 mm if the processing efficient is expected to be excessively great. By analyzing the above experimental results, the servo motion characteristics of the tool electrode can be determined, as follows: (1)

Normal discharges occur more easily at a certain position during the alternating process of open circuit and short circuit between the tool electrode and

4.2 Servo Control Characteristics of Micro Discharge Gap

(2)

(3)

(4)

(5)

57

workpiece. As a result, the position is within a relative gap range between the tool electrode and workpiece. By increasing the response frequency and movement speed of a tool-electrode spindle, the alternating frequency of open circuit and short circuit can be increased, so that the ratio of normal discharges can increase. However, an excessively high movement speed would cause the amplitude of movement vibration to increase, and in turn the increased amplitude would decrease the machining efficiency and accuracy. Within a certain statistical period, the closer the open circuit ratio and short circuit ratio are together, the more frequently the normal discharge ratio occurs, due to the greater number of alternating times between open circuit and short circuit. In addition, the movement speed of tool electrode decelerates near the normal discharge gap, which can in turn improve the normal discharge ratio. According to the depth effect, there must be a certain depth as a starting point for the processing state to be destroyed. Although the tool electrode can feed at a low speed after the certain depth, this is mainly the wear of the tool electrode caused by abnormal discharges between the tool electrode and the machined debris. The processing efficiency has a direct relationship with the frequency and amplitude of the tool electrode movement. The higher the frequency is and the smaller the amplitude is, the higher the processing efficiency will be.

According to the results of the experimental results and the above analysis, the optimized control scheme of tool-electrode spindle is as follows: (1) (2)

(3)

The normal discharge ratio can be increased by using a spindle of high response frequency to drive the tool electrode. The normal discharge ratio can be increased by using the variable speed movement of the tool electrode spindle. This slows down the movement speed near normal discharge gap, and increases the movement speed during open circuit state and short circuit state. As for the issue of the depth effect, an effective method to remove debris out of micro discharge gap should be adopted so as to achieve a deeper micro hole with processing stability.

4.2.3 Experimental Verification with High Response Frequency Spindle Next, in order to verify the improvement effect of a high response frequency spindle on the servo control of micro discharge gap, a spindle driven by a linear motor is applied for machining experiments of micro holes. Table 4.2 presents the main performance parameters of the linear motor, while Fig. 4.6 shows the spindle photo and the step response curve of the spindle control. Given a step signal of 20 µm amplitude, it is observed that the spindle can reach a response frequency of 200 Hz,

58

4 Servo Control of Micro Discharge Gap

Table 4.2 Performance parameters of linear motor

Processing parameter

Value

Peak force (N)

289

Continuous force (N)

51

Maximum speed (m/s)

14

Maximum acceleration (m/s2 )

268

Position feedback resolution (µm)

0.1

Fig. 4.6 Spindle photo and its step response curve. a Photo of linear motor spindle; b Step response curve of linear motor

although the influence of static inertia and friction of the guide rail. This response frequency is significantly larger than that of the spindle driven by a stepper motor. In order to compare the processing effect of the spindles with different response frequencies, machining experiments of micro holes are carried out by using the threshold control method. Fig. 4.7 shows the displacement curve monitored in an experiment, using the linear-motor spindle. Compared with Fig. 4.3, the curve slope in Fig. 4.7a is clearly larger. In other words, the feed speed in the direction of the machining depth is faster, and the processing efficiency is improved by 40–60%. In addition, the vibration amplitude is significantly decreased to 4.8–14.3 µm, according to the curve of Fig. 4.7b. These results indicate that the servo control accuracy and stability of the micro discharge gap is improved by using the high response frequency spindle. The results of this experiment verify the optimized control scheme of the spindle with high response frequency. According to the experimental results and analysis, the following conclusions can be drawn: (1)

It is beneficial to increase the normal discharge ratio by increasing the alternating frequency of the short circuit and open circuit, and by decreasing the amplitude of the spindle feed forward-and-backward.

4.3 Threshold Control and Optimization Method

59

Fig. 4.7 Displacement curve of linear-motor spindle. a Displacement curve in longer time; b Displacement curve in short time

(2)

(3)

(4)

Within a certain statistical period, the normal discharge ratio tends to reach its maximum if the open-circuit ratio and the short-circuit ratio tend to be equal and minimum. The normal discharge ratio can be increased by using the control method with variable-speed feed to decrease the spindle feed speed near the point position of the normal discharge. Due to difficulty in removing the machined debris, a specific depth results in the depth effect as a result of the fact that the normal machining state is broken.

4.3 Threshold Control and Optimization Method In this section, the threshold control method is studied and discussed for the application in SS-3D micro EDM. Theoretical models are proposed to obtain optimization constraints, and SS-3D micro-EDM experiments are performed to verify the proposed method and theory.

4.3.1 Optimization Constraint of Servo Control Parameters Figure 4.8 shows the geometric meaning of the threshold control method of machining gap. Under the given conditions of the electrode material, workpiece material, dielectric, and discharge power supply, the maximum discharge gap max and the minimum discharge gap min remain unchanged. When the actual interelectrode gap gap >max , the tool electrode is controlled to feed downward at the speed of vf . When gap >min , the tool electrode is controlled to withdraw upward at the speed of vb . When gap is within the ideal gap span, the tool electrode is controlled to maintain its position. The feed speeds of vf and vb can be set artificially.

60

4 Servo Control of Micro Discharge Gap

Fig. 4.8 Geometric meaning of threshold control method of machining gap

The speeds of vf and vb are important servo control parameters for retaining a machining gap. Theoretically, the higher the speeds are, the faster they will return to the discharge-gap range. However, the speeds are limited by the response time of servo control spindle as for an actual machine. Fig. 4.9 shows the response delay of tool-electrode movement during the servo control of the discharge gap. Given an initial speed of v0 , if a control command of target speed vg was sent at the time of t 0 , then the speed of v0 would be still kept for a period of (t d −t 0 ), due to the response delay of t w (t w = t d −t 0 ). After the time span of t w , the speed would quickly change into the speed vg with the acceleration time (t g −t d ), due to the (t g −t d ) Δmax −Δmin ), the tool electrode will stop at the short-circuit position, or collide onto the workpiece. At this moment, the control system sends the command “withdraw upward with the speed of vb ” (Proc-6). Similarly, after the t w , the tool electrode withdraws upward at the speed of vb (Proc-7). When it moves into the ideal gap span, the command “stop motion” is sent (Proc-8), then the tool electrode withdraws upward by the overshot length of vf *t w . According to the length size, the short-circuit withdrawal is analyzed as follows. (2-a)

Case II of tool-electrode movement: When the overshoot length is less than the discharge gap span (vb *t w < Δmax −Δmin ), the tool electrode stops within the ideal gap span (Proc-9), just like the state of Proc-1. The machining process is repeated as Proc-1-2-3-4-6-7-8-9 over and over again. In this case, the movement trajectory and the

62

4 Servo Control of Micro Discharge Gap

Fig. 4.11 Tool-electrode movement for servo control of machining gap with response delay t w ; a Case-I of tool electrode movement (Tool-electrode end close to Δmin considering larger value of vf ); b Case-II of tool electrode movement; c Case-III of tool electrode movement

electrode-end position are shown in Fig. 4.11b. During the procedures, the tool-electrode end is in the short-circuit state for a period of time, or collides onto the workpiece. (2-b)

Case III of tool-electrode movement: When the overshoot length is greater than the discharge gap span (vb *t w > Δmax −Δmin ), the tool electrode stops at the open-circuit position (Proc-10), just like the state of Proc-2. The machining process is repeated as Proc-2-3-4-6-7-8-10 over and over again. In this case, the movement trajectory and the electrode-end position are shown in Fig. 4.11c. During the procedures, the electrode end oscillates back and forth through the ideal gap span as the cyclic process of short circuit state (or electrode collision), normal discharge, and open circuit state. Therefore, the time in the ideal gap span is shorter than in the above two cases.

The three cases are summarized as follows. Case I results show the longest time in the ideal gap span, and the disadvantageous state of short circuit or electrode collision can be avoided. Cases II and III may result in a greater time ratio of the disadvantageous states of short circuit (electrode collision) and open circuit. In addition, the larger the servo speed of tool electrode is, the longer the disadvantageous time will

4.3 Threshold Control and Optimization Method

63

be. Therefore, Case I is the preferred case and its constraints of the servo speed and response delay are as follows: 

v f • tw < max − min vb • tw < max − min

(4.1)

Equation (4.1) gives the constraints of the upper limits of vf and vb . Considering the basic control strategy as short-circuit state as soon as possible to withdraw upward and open-circuit state to immediately feed downward, vf and vb should be as large as possible under the constraints of Eq. (4.1). The above analysis has not considered the influence of tool-electrode wear or workpiece material removal on the servo speed of tool electrode. For SS-3D micro EDM, the influence of workpiece material removal can be ignored, as the surface to be machined is new at the scanning points. The effect of the relative speed ve of tool-electrode wear on the servo speed is as follows. The instantaneous wear leads to an increase in the discharge gap, which is equivalent to the speed reduction by ve for the open-circuit feed and the speed increase by ve for the short-circuit withdraw. Therefore, Eq. (4.1) can be amended as follows: 

(vf − ve ) • tw < max − min (vb + ve ) • tw < max − min

(4.2)

4.3.2 Matching Scanning Speed with Servo Speed of Tool Electrode In SS-3D micro EDM, the servo control effect of machining gaps is determined by the combined tool-electrode movement of axial servo and lateral scanning. The axial servo speed and the lateral scanning speed must be matched properly. According to the principle of SS-3D micro EDM (Sect. 1.2), with the discharge energy per unit time being a constant as W T = W M ·f e , the machined depth hT each scanning layer is consistent, as shown below: hT =

ka WT vs ds

(4.3)

where k a is a coefficient constant, W T is the discharge energy per unit time as a constant, vs is the scanning speed, and d s is the tool-electrode diameter. Based on the preferred Case I (vf *t w > Δmax ; b hT ≤ Δmax

depth hT was much greater than the maximum of the discharge gap (hT >>Δmax ), the tool-electrode end would be too deep into the workpiece surface during machining (Fig. 4.12a). This would result in a longer length of lateral discharges, and severe lateral wear on the tool electrode. If the lateral material removal speed was less than the scanning speed vs , a short-circuit state would occur between the tool electrode and the sidewall of the workpiece, which can cause unnecessary tool-electrode withdraw, or even lateral collision. If the scanning speed vs was increased, the depth hT in each layer could be decreased. In other words, the scanning speed is the faster, the tool-electrode end goes into the shallower workpiece surface. It is clear that the scanning speed should not be too fast, for two reasons. The first is that the faster speed results in a longer unprocessed scanning path. According to Fig. 4.10 (Proc-2 and Proc-3) and Fig. 4.11, the unprocessed path in the distance of vs* t w occurs within the delay time of ~t w due to the open-circuit state. The second reason is that the machined depth hT would be too thin if the scanning speed was too fast. In fact, it is difficult to accurately control a very thin layer for an actual machining system, due to the limitations of movement resolution, systematic error, and random error from the micro-EDM process. Therefore, in this research the preferred value of scanning speed is taken as the case, as shown in Fig. 4.12b. The scanning speed ensures that the machined depth of each layer is not greater than the maximum discharge gap Δmax (hT ≤Δmax ). Under the servo speed condition of Case I, we then take k s = k a W T /d s according to Eq. (4.3) to obtain hT = k s /vs , thus the constraint for the theoretical boundary value of scanning speed is as follows: vs ≥

ks max

(4.4)

where k s is the scanning coefficient for a given processing condition and can be measured by experiments. Due to the fact that the scanning speed should not be too fast, its actual optimization value is taken as (1.0–1.1) times the theoretical boundary value.

4.3 Threshold Control and Optimization Method

65

4.3.3 Experiments of Optimization Verification in SS-3D Micro EDM In order to verify the theoretical analysis, machining experiments are carried out by means of the micro-EDM system as shown in Fig. 4.13. The experimental system mainly consists of a XY-axis worktable, a Z-axis spindle, a pulsed power supply, a wire electric discharge grinding (WEDG) mechanism, and a CNC system. The displacements of the X-axis, Y-axis and Z-axis are 140 mm, 100 mm, and 60 mm, and their positioning accuracy is ±2 µm, ±2 µm, and ±0.2 µm, respectively. The Z-axis spindle has the servo response frequency of 63 Hz, rotational speed range of 20–1800 r/min, and radial run out of max −min

vf > 0.145 vb < 0.145

vf > 0.145 vb > 0.145

Fig. 4.16 Tool-electrode movement of case-I, case-II, and case-III

for covering the fluctuation range from the measurement errors of t w , Δmax , and Δmin . The method of drilling EDM is used in the experiments with positive polarity machining (workpiece linked to positive polarity of pulsed power supply). The feed depth is set to a small value of 0.1 mm, so as to avoid the disadvantageous influence of the machined debris and lateral wear of tool-electrode end on the discharge process. The servo-control results are evaluated by recording the tool-electrode displacement of the feed or withdraw and the tool-electrode retraction ratio Rr (total retraction time divided by total processing time).

4.3 Threshold Control and Optimization Method

69

The experimental results in Fig. 4.16 show that the tool-electrode movement of Cases I, II, and III conforms to Fig. 4.11, which verifies the theoretical analysis regarding the effect of the servo speed on the servo control of discharge gap considering the response delay. Case I has the best discharge effect, the most stable process, and the lowest retraction ratio (Rr >Δmax (Δmax = 4.4 µm). When the scanning speed is excessively high (vs >1.2 mm/s), clear multi-segments of unprocessed scanning paths occur. This verifies the theoretical analysis. Compared with the non-rotation of the tool electrodes with unilateral wear, the rotation of tool electrodes can equalize the end wear, so as to make the grooves’ width and depth more uniform. A white light interferometer (WLI) is used to measure the depth hT (Fig. 4.18 as an example), and the results are shown in Fig. 4.19. Considering the depth stability and flatness of the tool-electrode end, the scanning speed in the range of 0.5–0.9 mm/s is used to calculate the k s more accurately. According to Eq. (4.4), the lower limits of the optimized scanning speed are 0.57 mm/s without tool rotation and 0.925 mm/s with tool rotation. As a result, the optimized value with rotation may be higher than that without rotation. As seen from Fig. 4.17, the machined results with the speeds around the theoretical limit are better by observing the end wear of tool electrodes and the width uniformity of the grooves. Due to the fact that the scanning speed should not be too high, the actual optimization values as 0.6 mm/s without tool rotation and 1.0 mm/s with tool rotation are taken to be slightly larger than the calculated lower limits. With the optimization values, the typical S-shaped micro grooves are

70

4 Servo Control of Micro Discharge Gap

Fig. 4.17 Machined results with scanning speed of 0.1–1.8 mm/s; a Machined results without tool rotation; b Machined results with tool rotation

4.4 Self-Adaptive Fuzzy Control Method with Formulary Rule

71

Fig. 4.18 An example of depth measurement by WLI

Fig. 4.19 Machined depth hT and scanning coefficient k s

achieved with high dimensional accuracy, as shown in Fig. 4.20, by means of the SS-3D micro EDM of 20 layers. In addition, the evenness of the machined surface with tool rotation is better than that without.

4.4 Self-Adaptive Fuzzy Control Method with Formulary Rule In micro EDM, it is difficult for servo control of a narrow discharge gap with the characters of non-linear and quick change. Essentially, the difficult task lies in that the control target center (CTC, non-error target reference) of an optimal discharge gap is

72

4 Servo Control of Micro Discharge Gap

Fig. 4.20 Machined results of S-shaped micro grooves by using optimized parameters. a Rotation vs = 0.6 mm/s; b Non-rotation vs = 1.0 mm/s

nondeterministic. Moreover, CTC shifts with the changes of machining process, electric parameters, electrode or workpiece materials, etc. Conventional control methods need a certain CTC, resulting in the low discharging efficiency during the controlling process of discharge gap. It is a great challenge for researchers to evaluate the non-deterministic CTC although they tried to use fuzzy-control methods to control a discharge gap. The control rules of traditional fuzzy-control methods are heuristics, lacking of the theoretical basis of optimal control target. In this section, a self-adaptive fuzzy controller with a formulary rule (SAFCFR) is proposed in order to solve the servo-control problem of narrow discharge gap in micro EDM. For the sake of the features of both self-optimizing and real-time, the formulary rule is designed with a tuning factor. With the feedback of electrical discharge statistic and the fast convergence algorithms, both the CTC and the tool-feed velocity are corrected simultaneously for trending to the optimal values. The comparative experiments are performed to verify the control effect.

4.4.1 Control Strategy and Design of Self-Adaptive Fuzzy Controller with a Formulary Rule The servo-control objective of narrow discharge gap is to achieve the highest normal discharge ratio. However, the measurement of normal discharge ratio is difficult due to the complex process of micro EDM. During a given period, the sum of open-circuit ratio, short-circuit ratio, and normal discharge ratio is nearly a constant. Hence, the normal discharge ratio could be the highest value if both open-circuit ratio and short-circuit ratio would tend to a least. The apportionment between open-circuit ratio and short-circuit ratio depends on the deflection of a given control target center (CTC). If CTC leaned to the sampling value of short-circuit, short-circuit ratio would be higher than open-circuit ratio. If CTC leaned to the sampling value of open-circuit, open-circuit ratio would be higher

4.4 Self-Adaptive Fuzzy Control Method with Formulary Rule

73

Fig. 4.21 Control strategy of SAFCFR method

than short-circuit ratio. In addition, the output scale factor of spindle-velocity is directly related to both open-circuit ratio and short-circuit ratio. Figure 4.21 shows the control strategy of SAFCFR with a structure of two-input and single-output. The e and the ec are respectively the error and the error change between the sampling value of interelectrode-voltage and the CTC. The u is the output velocity of spindle feed. The E, the EC and the U are respectively the quantized variables of the error, error change, and output. The K u is the output scale factor of spindle velocity. The control strategy is described as follows: (1)

(2)

(3)

The e and the ec are calculated by comparing the sampling value of interelectrode voltage signal with the CTC reference value. According to the formulary fuzzy rule, the servo-control signal of spindle velocity is outputted. Based on the feedback channel of parameter modification, the CTC and the output scale factor can be adaptively adjusted. In this way, both open-circuit ratio and short-circuit ratio can tend to the least and equal value. To enhance the control characteristics of self-optimization and real time, the formulary fuzzy rule is designed with a turning factor being dynamically adjusted with the changing of the quantized error E. The fuzzy rule helps the optimal CTC be reached quickly and then be kept steadily.

The interelectrode voltage can sense a narrow discharge gap, so the input variable uses the error between the interelectrode voltage and the CTC. In respect that the discharge process is dynamic instead of static, the output variable uses the velocity vector of spindle feed. Given a threshold interval [a, b], the corresponding fuzzification interval [c, d] can be converted by a linear mapping Eq. (4.5): F=

(d − c)[ f − (a + b)/2] b−a

(4.5)

74

4 Servo Control of Micro Discharge Gap

where F is the converted fuzzy variable and f is the exact variable within [a, b]. Control resolution can be improved by increasing the elements in the fuzzyvariable subsets. Owing to the high computing efficiency using a formulary fuzzy rule, the range of [−6, 6] is taken to be the fuzzification interval for the input variables (E,EC) and the output variable (U), and then Eq. (4.5) is transformed into Eq. (4.6): F=

12 • [ f − (a + b)/2] b−a

(4.6)

A formulary fuzzy rule is easy to be written into a real-time software program. The designed formulary fuzzy rule with a turning factor is described as Eq. (4.7): ⎧ ⎪ ⎨ VU = −(αU E + (1 − α)U EC ) 1 α = • (αs − α0 )|U E | + α0 ⎪ 3 ⎩ 0 ≤ α0 ≤ αs ≤ 1, α ∈ [α0 , αs ]

(4.7)

where U E and U EC respectively are the quantized-error input and the quantized-errorchange input, V U is the quantized output of spindle velocity, and α is the self-turning factor. Taking α 0 = 0.3 and α s = 0.9, then Eq. (4.7) is converted into Eq. (4.8): 

Vu = −(αU E + (1 − α)U EC ) α = 0.2 • |U E | + 0.3

(4.8)

V U is weighted by α according to U E . When U E is large, the weight of U E is increased to rapidly eliminate the error. When U E is small, the control stability needs to be achieved as soon as possible, so the weight of U EC is increased to reduce overshoot. In this way, α is linearly adjusted by the absolute value of U E .

4.4.2 Self-Adaptive Fast Convergence Algorithms During a micro EDM process, the times of open-circuit or short-circuit can be counted by a sampling electric circuit in a statistical period. If Ugap is a real-time sampling value of interelectrode voltage, given the values of open-circuit upper limit (U o −) and short-circuit lower limit (U s +), the opencircuit times is added by one when U gap > (U o −) and the short-circuit times is added by one when U gap < (U s +) at each sampling cycle. The following Eq. (4.9) gives the calculation of open-circuit ratio and short-circuit ratio in a statistical period:

4.4 Self-Adaptive Fuzzy Control Method with Formulary Rule

⎧ N ⎨ ϕo = No × 100% Ns ϕ = N × 100% ⎩ s ϕ = ϕo − ϕs

75

(4.9)

where N , No and Ns are separately the statistical total times, open-circuit times, and short-circuit times; ϕo , ϕs and ϕ are separately open-circuit ratio, short-circuit ratio, and their difference.  after adjustment, the optiGiven the CTC as U M before adjustment and U M mized accuracy δϕ for reaching the equal between open-circuit ratio and short-circuit ratio, and the adjustment coefficient kϕ of CTC, the adaptive adjustment algorithm is illuminated as follows: (1)

(2)

(3)

When |ϕ| > δϕ and ϕ > 0, CTC is leaning to open-circuit (ϕo > ϕs ), indicating that the discharge gap is larger than an expected value, so CTC is  = U M − kϕ • |ϕ|. adjusted to U M When |ϕ| > δϕ and ϕ < 0, CTC is leaning to short-circuit (ϕo < ϕs ), indicating that the discharge gap is less than an expected value, so CTC should  = U M + kϕ • |ϕ|. be adjusted to U M Repeating the above steps until |ϕ| < δϕ , the equal between open-circuit ratio and short-circuit ratio is realized in this algorithm.

Based on the linear relationship between the CTC adjustment and the ϕ, the  could tend to stability if convergence could be more rapid if ϕ was larger and U M ϕo was close to ϕs . The open-circuit ratio and the short-circuit ratio can tend to equal by using the adaptive adjustment algorithm of CTC. As long as one of the open-circuit ratio and the short-circuit ratio is adjusted to minimum by optimizing output scale factor, the optimal control objective could be achieved. Figure 4.22 describes the relationship between output scale factor and short-circuit ratio. Curve 1 expresses the relationship in a normal state. Curve 2 or curve 3 shows the shifted relationship with the introduction of some random disturbances. Seen from Fig. 4.22, the optimal value of output scale factor lies in the lowest point of the curves. The basic idea of convergence algorithm of output scale factor is as follows: (1)

(2)

The convergence direction of the output scale factor is predicted by the symbol of short-circuit ratio change ϕs (plus or minus of the first derivative ϕs ). The decrease of short-circuit ratio indicates that the convergence direction is right, and otherwise the direction will be changed. Thus, the output scale factor can be self-adjusted to an optimal value with the lowest short-circuit ratio even if an arbitrary output scale factor is given as an initial value. The adjusted amount of output scale factor is proportional to the change ϕs of short-circuit ratio. Thereby, the optimized speed of short-circuit ratio could be more rapid if ϕs was larger and output scale factor could tend to stability if ϕs was less.

76

4 Servo Control of Micro Discharge Gap

Fig. 4.22 Relational curves between output scale factor and short-circuit ratio

The adaptive adjustment algorithm of output scale factor is expressed by   ⎧ ⎨ K u(n+1) = K u(n) + λn+1 k ϕs(n)  ϕs(n) = ϕs(n) − ϕs(n−1) ⎩ |λn+1 | = 1 and k > 0

(4.10)

where K u(n) and K u(n+1) are output scale factors adjusted by n times and (n + 1) times; ϕs(n) is the short-circuit ratio change adjusted by n times; ϕs(n−1) and ϕs(n) are short-circuit ratio adjusted by (n−1) times and n times; k is a coefficient constant; λn+1 is the convergence direction coefficient for (n + 1) times adjustment. Figure 4.22 and Eq. 4.10 must satisfy the following convergence-direction conditions: If ϕs(n) > 0, then λn+1 = −λn ; if ϕs(n) < 0, then λn+1 = λn . Figure 4.23 shows the flow chart of the self-adaptive fuzzy control software. At first, initialization parameters are set up according to the sampling range of interelectrode voltage signal and the maximum of output spindle velocity. After entering every servo-control circulation, an interelectrode-voltage signal is sampled. The next step is to judge whether the statistical times N has been reached. If N was reached, CTC and output scale factor could be optimized by using the fast convergence algorithms. If N was not been reached, the current CTC and output scale factor would be utilized. After this, the input error and the error change are calculated by comparing the sampling value of interelectrode voltage and the reference value of CTC, and then the spindle velocity is output by used of the formulary fuzzy rule and the output scale factor.

4.4 Self-Adaptive Fuzzy Control Method with Formulary Rule Fig. 4.23 Software flow chart of SAFCFR method

77

78

4 Servo Control of Micro Discharge Gap

4.4.3 Experimental Verification of Self-Adaptive Fuzzy Control Method in SS-3D Micro EDM In the verification experiments of SAFCFR based on the micro-EDM system with a spindle of high-frequency response up to 100 Hz [2], micro-rectangular cavities (2 mm in length and 1 mm in width) are machined by the method of SS-3D micro EDM. An oscilloscope is used to monitor discharge waveforms for evaluating the discharging effect of servo control. A surface topography measuring instrument is used for measuring machining depth of micro-rectangular cavities, and then machining efficiency can be calculated. Based on the real-time feedback of interelectrode voltage, the decision of tool-electrode feed velocity is made by the ser-vo controller of SAFCFR. Considering the basic principle of SS-3D micro EDM, the wear compensation of tool electrode is realized by realtime servo control of micro discharge gap. In this way, the statistical consistency of machined depth each layer is ensured during scanning process. The designed 3D micro cavities can be machined by the superposition of the consistent thickness each layer. If the real-time optimization algorithm of SAFCFR was carried out during SS-3D micro EDM of a special 3D cavity, the removal amount each scanning point in a scanning layer would be unequal to destroy the consistency of machined depth each layer, although the discharge ratio could continue to be optimized. Therefore, the application method of SAFCFR is adopted as the adaptive optimization of control parameters is carried out before the practical application. The CTC and output scale factor are optimized by basic machining experiments, and then the optimized parameters are applied to SS-3D micro EDM. Experimental parameters are presented in Table 4.5. In the basic machining experiments of SAFCFR, the statistical times of discharge ratio is set as 100, the adjustment coefficient k Φ of CTC is set as 0.005 considering Table 4.5 Experimental parameters for verification experiments of SAFCFR

Processing parameter

Value

Open circuit voltage (V)

110

Peak current (A)

2.4

Pulse duration (µs)

5

Pulse interval (µs)

15

Capacitance (pF)

2 × 104

Tool electrode material

Tungsten

Tool electrode diameter (µm)

F254

Workpiece material

Nickel alloy

Workpiece thickness (mm)

0.5 or 1.0 or 1.7

Dielectric

Deionized water

Scanning speed (mm/s)

0.2

Path span (µm)

100

4.4 Self-Adaptive Fuzzy Control Method with Formulary Rule

79

the detection signals of interelectrode short circuit and open circuit of 0 V and 5 V respectively, and the coefficient constant k of output scale factor of spindle speed was set as 0.02 considering the size of a discharge gap. During a basic experiment of SS-3D micro EDM, the optimal convergence curve of CTC is obtained as shown in Fig. 4.24, and the optimal convergence curve of the speed proportional factor K u is obtained as shown in Fig. 4.25. It can be seen from Fig. 4.24 that the control target center (CTC) obtains the characteristic of fast optimization convergence. As a result, it can quickly converge to the target value of 1.96 V where the open-circuit ratio and the short-circuit ratio tend to be equal, regardless of whether the initial value of CTC is inclined to shortcircuit (1.5 V) or open-circuit (3.5 V). Namely, steady-state accuracy of the optimal CTC is good. Figure 4.25 indicates that the optimization convergence characteristic of the speed proportional factor K u is not good even to oscillate in a large range. If the speed scaling factor was small, it takes long time to approach the optimal value. The reason is mainly due to the limitation of spindle output speed and discharge gap size. In order to avoid the state of short-circuit or interelectrode collision, the single adjustment

Fig. 4.24 Optimal convergence curve of CTC. a CTC initial value of 1.5 V; b CTC initial value of 3.5 V

Fig. 4.25 Optimal convergence curve of speed proportional factor. a Initial value of 5; b Initial value of 30

80

4 Servo Control of Micro Discharge Gap

amount of K u has to be set as a small value. The oscillation of K u in Fig. 4.25 is mainly affected by the random interference factors in the scanning process. According to the results of Figs. 4.24 and 4.25, the optimal values of CTC 1.96 V and K u 33 are applied in SAFCFR for verifying the effectiveness in SS3D micro EDM. Using the same electrical parameters in Table 4.5, the comparative machining experiments are conducted for comparing the control effect between the SAFCFR method and the threshold control method (in Sect. 4.3). Figure 4.26 shows the comparison of micro-rectangular cavities machined by SS-3D micro EDM. Figure 4.27 shows the comparison of typical discharge waveforms during the process of SS-3D micro EDM. Figure 4.28 shows the comparison of machining efficiency. The experimental results indicate that the two control methods can achieve almost the same shape and dimension accuracy of micro-rectangular cavities. Compared with the threshold control method, the SAFCFR method improves the effective discharge ratio and machining stability, resulting in the machining efficiency increased by 14%. The advantage of the SAFCFR method is to provide a theoretical basis for improving the optimization efficiency of servo control parameters.

Fig. 4.26 Micro-rectangular cavities machined 8 layers. a Threshold control method; b SAFCFR method

Fig. 4.27 Typical discharge waveforms. a Threshold control method; b SAFCFR method

4.5 Summary

81

Fig. 4.28 Relationship between machining depth and scanning layers

4.5 Summary The relationship between micro discharge gap and servo motion characteristics of a tool-electrode spindle is obtained, and then the optimal control strategy of tool electrode motion is discussed. Two control methods of threshold control and selfadaptive fuzzy control are studied and applied to SS-3D micro EDM. Based on the threshold control method, the servo-control process of machining gap is analyzed by considering the actual influence of delay response time as for a machining system. The optimization procedures with the theoretical models are proposed and verified for the reasonable matching of servo control and scanning parameters. Furthermore, the self-adaptive fuzzy controller with a formulary rule (SAFCFR) is proposed for the sake of the features of both self-optimizing and real-time. In the SAFCFR method, the highest discharge ratio can be obtained by the self-adaptive approach as the opencircuit ratio and the short-circuit ratio automatically trend to equal and minimum. The comparative experiments between threshold control and SAFCFR are performed. The conclusions can be summarized as follows. (1)

Normal discharges occur more easily at a certain position during the alternating process of open circuit and short circuit between tool electrode and workpiece. If open circuit ratio and short circuit ratio could trend to be equal and minimum, normal discharge ratio would tend to reach its maximum. Variable speed movement of tool electrode spindle requires as slowing down the movement speed near normal discharge gap and increasing the movement speed during opencircuit and short-circuit states. The high response frequency of tool-electrode spindle is beneficial to improving the servo control accuracy and stability.

82

(2)

(3)

(4)

4 Servo Control of Micro Discharge Gap

During drilling a hole, the processing efficiency has a direct relationship with the frequency and amplitude of the tool electrode movement. If the frequency could be higher and the amplitude could be smaller, the processing efficiency would be higher. As for the depth effect, an effective method to remove debris out of micro discharge gap should be adopted so as to achieve a deep micro hole. For avoiding the disadvantageous states of short circuit and electrode collision, the preferred condition is that the feed overshoot length is smaller than the discharge gap. The preferred constraints of open-circuit feed speed, shortcircuit withdraw speed, and scanning speed are obtained based on the process analysis of SS-3D micro EDM using the threshold control method. The optimized scanning speed with tool rotation can be larger than that without tool rotation. In addition, the machined surface with tool rotation is more flat and even. In the method of SAFCFR, the servo-control performances of rapidity and stability are enhanced by adjusting dynamically the turning factor in the formulary fuzzy rule. The fuzzy rule is easy to write into a computer program ensures the real-time capability. Compared with the method of threshold control, the SAFCFR method can improve by 14% in SS-3D micro EDM. SAFCFR provides a theoretical basis for automatic optimization of servo control parameters.

References 1. K. Kumar Saxena, A. Suman Srivastava, S. Agarwal, Experimental investigation into the microEDM characteristics of conductive SiC. Ceram. Int. 42, 1597–1610 (2016) 2. H. Tong, Y. Li, Y. Wang, D.W. Yu, Servo scanning 3D micro-EDM based on macro/microdual-feed spindle. Int. J. Mach. Tools Manuf. 48, 858–869 (2008) 3. M.P. Jahan, P. Kakavand, E.L.M. Kwang, M. Rahman, Y.S. Wong, An experimental investigation into the micro-electro-discharge machining behaviour of aluminium alloy (AA 2024). Int. J. Adv. Manuf. Technol. 78(5), 1127–1139 (2015) 4. M. Boccadoro, D.F. Dauw, About the application of fuzzy controllers in high-performance die-sinking EDM machines. CIRP Ann. Manuf. Technol. 44(1), 147–150 (1995) 5. J.H. Zhang, H. Zhang, D.S. Su, Y. Qin, M.Y. Huo, Q.H. Zhang, L. Wang, Adaptive fuzzy control system of a servomechanism for electro-discharge machining combined with ultrasonic vibration. J. Mater. Process. Technol. 129(1–3), 45–49 (2002) 6. T. Kaneko, T. Onodera, Improvement in machining performance of die-sinking EDM by using self-adjusting fuzzy control. J. Mater. Process. Technol. 149(1–3), 204–211 (2004) 7. Y. Zhang, The study on a new-type self-adaptive fuzzy logic control system in EDM process, in Proceeding of the International Conference on Machine Learning and Cybernetics, pp. 726– 730 (2005) 8. O. Yilmaz, O. Eyercioglu, N.N.Z. Gindy, A user-friendly fuzzy-based system for the selection of electro discharge machining process parameters. J. Mater. Process Technol. 172(3), 363–371 (2006) 9. C.C. Kao, A.J. Shih, Design and tuning of a fuzzy logic controller for micro-hole electrical discharge machining. J. Manuf. Processes. 10(2), 61–73 (2008)

References

83

10. C.C. Kao, A.J. Shih, S.F. Miller, Fuzzy logic control of microhole electrical discharge machining. J. Manuf. Sci. Eng. 130(6), 0645021–0645026 (2008) 11. H. Tong, X. Liu, Y. Pu, Y. Li, W. Liang, J. Li, Servo control optimization of micro discharge gap and its reasonable matching with scanning speed in servo scanning 3D micro EDM based on threshold control method. Int. J. Adv. Manuf. Technol. 105(7–8), 3057–3066 (2019) 12. H. Tong, Y. Li, Self-adaptive fuzzy controller with formulary rule for servo control of discharge gap in Micro EDM. High Technol. Lett. 18(3), 223–229 (2012) 13. M.H. Hu, Y. Li, H. Tong. Design and experimental study of a multi-mode controllable RC pulse generator for micro-EDM, in Proceeding of the International Conference on Advanced Technology of Design and Manufacture, pp. 297–300 (2010) 14. H. Tong, Y. Li, L. Zhang, B.Q. Li, Mechanism design and process control of micro EDM for drilling spray holes of diesel injector nozzles. Precis. Eng. 37(1), 213–221 (2013) 15. H. Tong, Y. Wang, Y. Li, Vibration-assisted servo scanning 3D micro EDM. J. Micromech. Microeng. 18(2), 501–508 (2008)

Chapter 5

Precision Fabrication and Measurement of Micro Tool Electrode

Abstract On-machine fabrication and measurement of micro tool electrodes is the premise of SS-3D micro EDM, in particular for machining micro structures with the feature size 1,000 µm, and depth > 1,000 µm, a flat micro tool electrode with a thickness of 60 µm is fabricated from a tungsten rod blank of F500 µm. A copper plate with a thickness of 500 µm is used as a reverse-copying plate to remove the material from a rod-shaped blank. Table 5.3 presents the processing parameters for machining a slot through the reverse-coping plate as the first procedure. Figure 5.22 shows the machined slot with an inlet width of 560 µm (left) and outlet width of 540 µm (right) by SS-3D micro EDM. The side wall has a slope error of 20 µm between the inlet and outlet, which

Fig. 5.22 A reverse-copying slot machined by tungsten rod blank of F500 µm

5.4 On-Machine Fabrication Process of Flat Micro Tool Electrode

103

stems from the inevitable secondary discharges between the machined debris and the side wall. In order to overcome the adverse effect of the slop error on the fabrication accuracy of the flat electrode, the processing strategies of large discharge gap, high discharge energy, and multiple reverse copy are adopted to fabricate a uniform flat electrode with a target thickness of 60 µm. Based on the processing parameters listed in Table 5.3, the specific parameters of each step are presented in Table 5.4 for fabricating the flat micro tool electrode with a length of 2,400 µm (Fig. 5.23). Its thickness accuracy can be controlled within ±1 µm in the experiments. By applying the fabricated flat electrodes, machining experiments of micro grooves are then performed on three types of workpiece materials, namely stainless steel, copper, and brass. Table 5.5 presents the processing parameters, and Fig. 5.24 shows the experimental results. Stainless steel is the most difficult to machine, as the results include a groove depth of only 64 µm and groove width of 66 µm. The volume wear ratio between the tool electrode and the stainless steel workpiece is Table 5.4 Processing data of each fabrication step for flat micro electrodes Reverse-copying times First step Second step Third step

Fig. 5.23 An example of flat micro tool electrode

Offset distance (µm)

Capacitance (pF)

Processing time (s)

210

33,000

91.4

−210

33,000

102.6

220

10,000

40.9

−220

10,000

51.3

225

10,000

21.8

−225

10,000

24.0

104 Table 5.5 Processing parameters for machining micro grooves

5 Precision Fabrication and Measurement of Micro Tool Electrode Parameters

Value

Open voltage (V)

120

Pulse duration (µs)

1

Pulse interval (µs)

5

Capacitance (pF)

2,200

Dielectric fluid

Oil

Length of micro groove (µm)

1,000

Processing time (min)

7

Fig. 5.24 Effect of workpiece materials on experimental results

close to 40%. Brass is the easiest to machine as the results include a groove depth of 844 µm and groove width of 79.9 µm, while the volume wear ratio is only ~10%. The processing difficulty of copper is moderate, as the results include a groove depth of 440 µm and groove width of 74.4 µm, and the volume wear ratio is close to 23%. If a micro slot of 1,000 µm in depth and 1,000 µm in length is machined, a rod micro tool electrode of F60 µm requires an axial length of 7.8 mm for a stainless steel workpiece, 4.8 mm for a copper workpiece, and 2.7 mm for a brass workpiece, while a flat micro tool electrode with a thickness of 60 µm and width of 500 µm only requires an axial length of 1.8 mm for the stainless steel workpiece, 1.46 mm for the copper workpiece, and 1.2 mm for the brass workpiece. By using the flat tool electrodes, the processing time for fabricating tool electrodes can be shortened greatly, and the processing efficiency can be improved due to the larger electrical discharge area compared with the rod tool electrode. Typical experiments of array micro grooves with high aspect ratio are carried out on brass by using flat micro tool electrodes. Figure 5.25 shows the machined

5.5 On-Machine Measurement Method …

105

Fig. 5.25 Machining examples of micro grooves by using flat micro electrodes. a Array micro grooves; b enlarged top view of array grooves

results as ~710 µm in depth, ~1,500 µm in length, and 16 ± 2 µm in width. The array grooves achieve high accuracy of dimensional consistency and high parallel accuracy between array grooves.

5.5 On-Machine Measurement Method of Intersecting Point Electric Contact Figure 5.26 shows the measurement method of the intersecting-point electric contact. The two axial directions of micro-electrode and standard thin-rod are arranged as mutually perpendicular (Fig. 5.26a). The standard rod is fixed on an XY-worktable, and then the electrode is moved to electric contact (low voltage 24 V) with the

Fig. 5.26 Measurement process by intersecting-point electric contact. a YZ coordinate plane; b XZ coordinate plane; c XY coordinate plane

106

5 Precision Fabrication and Measurement of Micro Tool Electrode

Fig. 5.27 Measurement error analysis in YZ-plane. a Error of YZ coordinate plane; b XZ coordinate plane

outer diameter of the rod (Fig. 5.26b). At the moment that electric-signal senses the point contact, the position coordinate of the electrode is recorded by means of a computer numerical control (CNC) system. Given the standard-rod diameter, the micro-electrode diameter can be calculated as |X 2 − X 1 | − D by the electric contact of both sides (Fig. 5.26b–c). With the mode of the vertical alignment, the measuring process is easy to operate as every point of the rod can be used as a measuring point. Due to the high accuracy of standard rod itself, the measurement errors mainly originate from the standard rod positioning and electric-contact feedback. Using the high-speed transmission of the electric signal to record the exact position of momentary contact, the measurement accuracy is not affected by movement speed or contact deformation. Furthermore, the effect of the rod positioning on the measuring error is analyzed as follows. The spatial positioning error of standard rod can be divided into the errors in the planes of YZ, XZ, and XY (Figs. 5.27 and 5.28). As known from Fig. 5.27, the error of the YZ-plane has no effect on the measurement accuracy (Fig. 5.27b), even if the misalignment error exists (Fig. 5.27a). According to the error analysis of the XZ-andXY planes (Fig. 5.28), and given the error angle θ (Fig. 5.28a, b), the measurement error d can be derived as     1 d =  X 2 − X 1  − D − d = (D + d) · (5.3) −1 cos θ where X 1 and X 2 are the position coordinates of the electric contact recorded by the CNC system, D is the standard-rod diameter, and d is the micro-electrode diameter. According to Eq. (5.3), the measurement error is determined by error angle θ and standard-rod diameter D, so that the use of a thin rod can reduce the error. For example, by using a standard rod of 10 mm in length and Φ0.5 mm in diameter, with an easily adjustable value of θ = 0.7° (namely δ = 0.122 mm in Fig. 5.28c), the introduced error is only 0.042 µm as calculated by Eq. (5.3), when the micro-electrode diameter is Φ60 µm. Due to the advantages of axial intersection, point electric contact by low-voltage of 24 V, and standard thin-rod, in theory the measurement error can be reduced to