Metal Micro-Droplet Based 3D Printing Technology 9819909643, 9789819909643

Table of contents :
Foreword
Preface
Contents
1 Introduction
1.1 Classification and Characteristics of Uniform Metal Droplet Ejection Technology
1.1.1 Continuous-Ink-Jet Jetting Technology
1.1.2 Drop-On-Demand Jetting Technology
1.2 State-of-the-Art and Trends of the Uniform Metal Droplet Ejection Technology
1.2.1 State-of-the-Art of the Uniform Metal Droplet Ejection Technology
1.2.2 Trends in Uniform Metal Droplet Ejection 3D Printing Technology
References
2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition
2.1 Introduction
2.2 Theory of Continuous Uniform Metal Droplet Ejection and Mechanism of Droplet Charging and Deflection
2.2.1 Theory of Continuous Uniform Metal Droplet Ejection (Theory of Rayleigh Jet Instability)
2.2.2 Mechanism of Charging and Deflection of Uniform Droplets
2.3 Drop-On-Demand Ejection of Metal Droplets
2.3.1 Theory of Pneumatic Pulse-Driven Drop-On-Demand Ejection
2.3.2 Theory of Piezoelectric Pulse-Driven Drop-On-Demand Ejection
2.3.3 Model of Stress Wave-Driven Drop-On-Demand Ejection
2.4 Dynamics and Thermodynamic Theory of Uniform Metal Droplet Flight Process
2.4.1 Flight Dynamics of Metal Droplets
2.4.2 Temperature History of Metal Droplets During Flight
2.5 Fundamental Theory for Uniform Metal Droplet Deposition
2.5.1 Non-Dimensional Analysis of Metal Droplet Impact Behavior
2.5.2 Non-Isothermal Impact and Spreading Behaviors of Metal Droplets
References
3 Devices and Equipment for Uniform Droplet Ejection
3.1 Introduction
3.2 Brief Introduction of Equipment for Uniform Metal Droplet Ejection
3.3 Device for Continuous Uniform Droplet Streams Ejection, Charging, and Deflection
3.3.1 Device for Ejecting Continuous Uniform Droplet Streams
3.3.2 Charging and Deflection Device for the Continuous Uniform Droplet Stream
3.4 Design and Implementation of the Pneumatic Pulse-Driven Drop-On-Demand (DOD) Droplet Ejection System
3.4.1 Pneumatic Pulse-Driven DOD Droplet Generator for Tin Solder
3.4.2 Pneumatic Pulse-Driven DOD Droplet Generator for Aluminum Alloy
3.5 Piezoelectric Pulse-Driven DOD Droplet Generator
3.6 Stress Wave-Driven DOD Droplet Generator
3.7 Parameter Acquisition and Control System of the Metal Droplet Ejection and Deposition
3.7.1 Control System for Uniform Metal Droplet Ejection and Deposition
3.7.2 Key Parameters Acquisition System of the Droplet Ejection and Deposition
References
4 Uniform Metal Droplet Continuous Ejection and Printing Process Control Technology
4.1 Introduction
4.2 Research on Uniform Droplet Continuous Ejection Behavior and Its Influencing Factors
4.2.1 Numerical Simulation of Continuous Uniform Droplet Ejection Process and Research on Influencing Factors
4.2.2 The Influence of the Experimental Parameters on the Metal Jet Breakup Process
4.3 Charging and Deflection Control of Uniform Metal Micro Droplet Stream
4.3.1 Control of Droplet Charge of Uniform Metal Micro Droplets
4.3.2 Study on the Dispersion Behavior of Charged Uniform Droplet Stream
4.3.3 Implementation and Control of Deflected Flight of Charged Uniform Micro Droplets
4.3.4 Temperature History of Uniform Metal Droplets During the Deflection Flight
4.4 Free Forming by Continuous Ejection of Uniform Metal Droplets and Its Controlling Method
4.4.1 Influencing Factors and Research Methods for Free Forming by Continuous Droplet Ejection
4.4.2 Parameter Control of Free Forming by Continuous Ejection of Uniform Metal Droplets
References
5 On-Demand Ejection and Control of Uniform Metal Droplets
5.1 Introduction
5.2 On-Demand Ejection Behavior of Metal Droplets Driven by Pneumatic Pulse and the Influence of Parameters
5.2.1 Research on On-Demand Ejection of Uniform Tin–Lead Alloy Droplets
5.2.2 Research on Ejection of Uniform Aluminum Droplets On-Demand Driven by Pneumatic Pressure Pulse
5.3 Ejection Behaviors of Metal Droplets On-Demand Driven by a Stress-Wave Pulse and the Influence of Parameters on Droplet Ejection
5.3.1 Influence of Parameters of Experiment Device on Metal Droplet Ejection
5.3.2 Effect of Stress Wave Pulse Parameters on Metal Droplet Ejection
5.4 Comparison of Various Metal Drop-On-Demand Technologies
References
6 Uniform Solder Droplet Deposition and Its 3D Printing Technology
6.1 Introduction
6.2 Deposition Behaviors of Uniform Solder Droplet Deposition and Effect Factors of the Morphology of Deposited Droplets
6.2.1 Deposition and Spreading Behaviors of Uniform Solder Droplets
6.2.2 Effect of Experimental Parameters on Final Shapes of Solidified Micro Droplets
6.2.3 The Method to Reduce the Height Deviation of Solder Bumps and the Analysis of the Height Accuracy
6.3 Printing Path Planning of the Metal Droplet and the Effect Factor
6.3.1 Effect of Sequential Printing Parameters on the Morphology of Printed Traces
6.3.2 Line Formation Experiment by Using the Alternate Printing
6.3.3 Controlling of the Deposition Path of Micro Metal Parts by Using Uniform Metal Droplet-Based Printing
6.4 Fabrication of Micro Metal Parts by Drop-On-Demand Printing
6.4.1 Fabrication of Micro-Finned Heat Sinks
6.4.2 Fabrication of Micro-Honeycomb Parts
6.4.3 Fabrication of Micro-Squared Parts
6.4.4 Fabrication of Micro Gears
6.4.5 Fabrication of Micro Racks
6.5 Electronic Packaging via Uniform Micro Lead–Tin Alloy Droplet 3D Printing Technology
6.5.1 Rapid Printing of Ball Grid Array and Solder Column Array
6.5.2 Rapid Printing and Soldering of Electronic Circuits
References
7 Uniform Aluminum Droplet Deposition Manufacturing and Its Controlling Technique
7.1 Introduction
7.2 Deposition Behaviors of Uniform Aluminum Droplets
7.2.1 Impact Behaviors of Aluminum Droplets
7.2.2 Effect of Process Parameters on the Profile of Deposited Aluminum Droplets
7.3 Deposition of Aluminum Lines by Uniform Droplets
7.3.1 Effect of Platform Velocity on Printed Lines
7.3.2 Effect of Substrate Temperature on Printed Lines
7.4 Drop-On-Demand Printing of Aluminum Pillars by Uniform Droplets
7.4.1 Temperature Change During the Deposition of Aluminum Droplets
7.4.2 Morphology Features of Deposited Pillars
7.4.3 Pillar Forming by Drop-On-Demand Printing of Aluminum Droplets
7.4.4 Forming of Thin-Walled Aluminum Parts
7.5 Forming of Aluminum Solid Parts
References
8 Microstructure Evolution and Interface Bonding of Uniform Aluminum Droplet Deposition Manufacturing
8.1 Introduction
8.2 Microstructure Evolution of Uniform Aluminum Droplet Deposition
8.2.1 Microstructure Evolution of Uniform Aluminum Droplets During the Vertical Pileup
8.2.2 Microstructure Evolution of Lines Deposited by Uniform Aluminum Droplets
8.3 Influence of Interface Bonding Between Metal Droplets on Printed Aluminum Parts
8.3.1 Effect of Interface Bonding on the Microstructure of Aluminum Parts
8.3.2 Effect of Interface Bonding on the Mechanical Properties of Aluminum Parts
8.4 Internal Defects and Their Influencing Factors of As-Deposited Aluminum Components
8.4.1 Hole Defects Inside Printed Aluminum Parts
8.4.2 Internal Cracks of Printed Aluminum Parts
References
9 Application Prospect of Uniform Metal Droplet-Based 3D Printing
9.1 Introduction
9.2 Preparation of Mono-Sized Spherical Metal Particles
9.3 Printing and Packaging of Microcircuits
9.4 Micron Scaled Metal Parts Printing
9.5 Micro Thin-Wall Parts Printing
9.6 3D Printing for Functional Parts
References

Citation preview

Lehua Qi Jun Luo He Shen Hongcheng Lian

Metal Micro-Droplet Based 3D Printing Technology

Metal Micro-Droplet Based 3D Printing Technology

Lehua Qi · Jun Luo · He Shen · Hongcheng Lian

Metal Micro-Droplet Based 3D Printing Technology

Lehua Qi School of Mechanical Engineering Northwestern Polytechnical University Xi An, Shaanxi, China

Jun Luo School of Mechanical Engineering Northwestern Polytechnical University Xi An, Shaanxi, China

He Shen School of Marine Science and Technology Northwestern Polytechnical University Xi An, Shaanxi, China

Hongcheng Lian School of Mechanical Engineering Northwestern Polytechnical University Xi An, Shaanxi, China

ISBN 978-981-99-0964-3 ISBN 978-981-99-0965-0 (eBook) https://doi.org/10.1007/978-981-99-0965-0 Jointly published with National Defense Industry Press The print edition is not for sale in China (Mainland). Customers from China (Mainland) please order the print book from: National Defense Industry Press. © National Defense Industry Press 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 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 publishers, 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 publishers 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 publishers remain 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

Foreword

Micro-metal droplet-based additive manufacturing (3D printing) technology is an emerging printing technology that originated from digital inkjet printing. It uses uniform metal droplets as basic building blocks to construct three-dimensional structures with drop-by-drop layer-by-layer deposition. Due to the advantages of no need for special raw materials or expensive equipment and low-cost, micro-metal droplet-based additive manufacturing is a promising 3D printing technology for rapid manufacturing of micro-metal parts, heterogeneous parts, and micro-functional parts in the fields of aviation, aerospace, weapons, and microelectronic packaging. The metal droplet ejection, deposition, and solidification processes of micro-metal droplet-based additive manufacturing concern multiple scientific fields, including fluid dynamics, metallurgical solidification, material science, and control science, and raise many theoretical and technical challenges, such as multi-field coupling behaviors and process control of metal droplet ejection, heat transfer, and accurate positioning during droplet deposition and spreading, rapid solidification, and three-dimensional formation control. This book provides a systematic summary of the theories, techniques, and applications of micro-metal droplet-based additive manufacturing. Studies regarding uniform metal droplet-based 3D printing technology started early in the 1990s. Since then, the Massachusetts Institute of Technology, the University of California, Irvine, and Northeastern University in the USA, Osaka University in Japan, the University of Toronto in Canada, and the University of Twente in the Netherlands have successively carried out theoretical and experimental investigation on uniform metal droplet ejection and 3D printing. Research about metal droplet ejection, deposition, and manufacturing in China began in the early twenty-first century, when the Northwestern Polytechnical University and Harbin Institute of Technology commenced exploring metal droplet-based near-net forming. Recently, researchers at Xi’an Jiaotong University, Dalian University of Technology, Beijing University of Technology, and Huazhong University of Science and Technology continuously probed uniform metal droplet ejection and manufacturing technology.

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However, reports on uniform metal droplet-based 3D printing technology sporadically appeared in journals and partial chapters of monographs. No books have been published to discuss droplet ejection and 3D printing theory and applications systematically. Therefore, an academic monograph is needed to comprehensively reveal inherent laws in metal droplet ejection, deposition, and manufacturing and guide practical applications of this technology. This monograph would push the development of uniform metal droplet-based 3D printing, which might lay the foundation for reducing the production cost of metal 3D printing and expanding the application area of this technology. For more than ten years, Prof. Lehua Qi’s team has devoted themselves to the theory and application of uniform metal droplet ejection and 3D printing technology. A novel method for multi-scale droplet ejection under pulsed waves has been proposed. Breakthroughs have been made in key technologies such as on-demand multi-material uniform droplet ejection and uniform droplet deposition forming and controlling. Several proprietary experimental setups have been developed for metal droplet ejection and deposition manufacturing in different application fields. Many doctoral and master students under supervision have conducted in-depth and systematic research on the general law of uniform metal droplet ejection and deposition. Remarkable achievements have been made in this area, including more than 30 high-quality papers published in high-impact journals and more than ten patents granted. This book summarizes the results from long-term, in-depth, and systematic research on the theory and technology of uniform metal droplet-based 3D printing supported by multiple grants from the National 863 program, Basic Scientific Research for National Defense, National Natural Science Foundation of China, and some provincial and ministerial funds. This book systematically and comprehensively explains the related theories and applications of uniform metal droplet-based 3D printing technology, including fundamentals of micro-metal droplet ejection, flight, deposition, and spreading process, the influence of printing parameters on the shape of deposited droplets, forming trajectory, internal microstructure, and mechanical properties of formed parts. At present, this book is the first academic monograph that systematically describes the 3D printing technology based on uniform metal droplet ejection, which has significant academic value.

Foreword

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By integrating theory with practice, this book has strong pertinence and rich and novel content, which is instructive for scientific researchers, engineering technicians, and teachers and students in the related field.

August 2018

Huaming Wang Member of the Chinese Academy of Engineering Professor at Beihang University Beijing, China

Preface

3D printing technology is a major symbol of the Third Industrial Revolution and has shown broad application prospects in national defense, civil, and other fields. 3D printing based on uniform metal droplet ejection is a new additive manufacturing technology proposed in recent years. It uses inkjet printing and the “dispersingstacking” principle to deposit uniform metal droplets at specified locations and gradually form parts to realize the goal of low energy consumption and low-cost manufacturing. It can be used for the rapid manufacturing of micro-metal parts, heterogeneous parts, and small functional devices, as well as the packaging of microelectronics. Due to the advantages of no need for expensive equipment, low-cost, flexibility, and broad choices for raw materials and other characteristics, this technology has extensive development prospects in many areas. Uniform metal droplet-based 3D printing concerns the formation, ejection, deposition, and solidification of uniform metal droplets and the three-dimensional forming process. In addition, many scientific and technical problems, such as nonlinear fluid– solid coupling, nonlinear dynamics, heat transfer and solidification of liquid metal, multi-field coupling, and process control, are involved, which are challenging to resolve. Despite numerous literature about related technologies and theories, as a new technology in its infancy, no academic monograph has been published to systematically discuss the principle and technology of uniform metal droplet manufacturing, reveal inherent laws, and guide practical applications yet. This book systematically and comprehensively probes the scientific problems and key technologies involved in the ejection, flight, and deposition manufacturing of metal micro-droplets under high-temperature conditions. Theoretical models of metal droplet ejection, flight, and deposition forming processes have been established. Influence mechanisms of various experimental parameters on the metal droplet ejection process and parts properties have been revealed. Several uniform metal droplet 3D printing setups have been developed. Breakthroughs have been made in key technologies such as controllable droplet ejection, deposition forming, metal droplet fusion, and coordination control. Several new processes for printing micro-metal parts and heterogeneous parts based on uniform metal droplets have been invented. The basic theory and technology problems described in this book ix

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may provide valuable guidance on the 3D printing of microstructures, complex metal parts, multi-material parts, and intelligent devices. This book also demonstrates a wide range of potential applications. The work presented in this book is partially funded by multiple projects such as the National 863 key projects, the National Natural Science Foundation of China, and the National Foundation for Outstanding Doctoral Thesis Authors. The book summarizes the theoretical and experimental research results on uniform metal droplet printing, uniform metal droplet ejection, and manufacturing complex micro-metal parts. The main content of this book comes from the research results of the authors and their students, and the latest research progress in uniform metal droplet 3D printing from other scholars is also included. Doctoral students Xiaoshan Jiang, Hua Huang, Yuan Xiao, Yanpu Chao, and master student Linfeng Xu under the authors’ supervision have made significant contributions to the development of uniform droplet deposition equipment and its controlling system. The completion of this monograph is inseparable from the contributions of these graduate students. The School of Mechanical Engineering and Key Laboratory of Modern Design and Integrated Manufacturing Technology of Northwestern Polytechnical University provided research facilities. We would like to express our heartfelt thanks to all the above-mentioned funding agencies, contributors, and institutions. The book consists of nine chapters, including Introduction; Fundamental theories in uniform metal droplet ejection and deposition; Equipment for uniform metal droplet printing; Control of droplet ejection and printing process; Uniform metal drop-on-demand ejection and control; 3D printing of uniform solder droplets; 3D printing of uniform aluminum droplets; Evolution of microstructure of uniform aluminum droplets in deposition; The application prospect of uniform droplet-based 3D printing. Limited by the knowledge we have, there might be errors or points of confusion in this book; any comments and feedback from the readers are welcome and highly appreciated. Xi An, China December 2013

Lehua Qi Jun Luo He Shen Hongcheng Lian

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Classification and Characteristics of Uniform Metal Droplet Ejection Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Continuous-Ink-Jet Jetting Technology . . . . . . . . . . . . . . . . . . 1.1.2 Drop-On-Demand Jetting Technology . . . . . . . . . . . . . . . . . . . 1.2 State-of-the-Art and Trends of the Uniform Metal Droplet Ejection Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 State-of-the-Art of the Uniform Metal Droplet Ejection Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Trends in Uniform Metal Droplet Ejection 3D Printing Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Theory of Continuous Uniform Metal Droplet Ejection and Mechanism of Droplet Charging and Deflection . . . . . . . . . . . . . 2.2.1 Theory of Continuous Uniform Metal Droplet Ejection (Theory of Rayleigh Jet Instability) . . . . . . . . . . . . . 2.2.2 Mechanism of Charging and Deflection of Uniform Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Drop-On-Demand Ejection of Metal Droplets . . . . . . . . . . . . . . . . . . 2.3.1 Theory of Pneumatic Pulse-Driven Drop-On-Demand Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Theory of Piezoelectric Pulse-Driven Drop-On-Demand Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Model of Stress Wave-Driven Drop-On-Demand Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Dynamics and Thermodynamic Theory of Uniform Metal Droplet Flight Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2 2 3 7 7 15 18 21 21 21 21 27 34 34 38 40 41

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2.4.1 Flight Dynamics of Metal Droplets . . . . . . . . . . . . . . . . . . . . . 2.4.2 Temperature History of Metal Droplets During Flight . . . . . 2.5 Fundamental Theory for Uniform Metal Droplet Deposition . . . . . . 2.5.1 Non-Dimensional Analysis of Metal Droplet Impact Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Non-Isothermal Impact and Spreading Behaviors of Metal Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Devices and Equipment for Uniform Droplet Ejection . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Brief Introduction of Equipment for Uniform Metal Droplet Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Device for Continuous Uniform Droplet Streams Ejection, Charging, and Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Device for Ejecting Continuous Uniform Droplet Streams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Charging and Deflection Device for the Continuous Uniform Droplet Stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Design and Implementation of the Pneumatic Pulse-Driven Drop-On-Demand (DOD) Droplet Ejection System . . . . . . . . . . . . . . 3.4.1 Pneumatic Pulse-Driven DOD Droplet Generator for Tin Solder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Pneumatic Pulse-Driven DOD Droplet Generator for Aluminum Alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Piezoelectric Pulse-Driven DOD Droplet Generator . . . . . . . . . . . . . 3.6 Stress Wave-Driven DOD Droplet Generator . . . . . . . . . . . . . . . . . . . 3.7 Parameter Acquisition and Control System of the Metal Droplet Ejection and Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.1 Control System for Uniform Metal Droplet Ejection and Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.2 Key Parameters Acquisition System of the Droplet Ejection and Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Uniform Metal Droplet Continuous Ejection and Printing Process Control Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.2 Research on Uniform Droplet Continuous Ejection Behavior and Its Influencing Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.2.1 Numerical Simulation of Continuous Uniform Droplet Ejection Process and Research on Influencing Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.2.2 The Influence of the Experimental Parameters on the Metal Jet Breakup Process . . . . . . . . . . . . . . . . . . . . . . . 107

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4.3 Charging and Deflection Control of Uniform Metal Micro Droplet Stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Control of Droplet Charge of Uniform Metal Micro Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Study on the Dispersion Behavior of Charged Uniform Droplet Stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Implementation and Control of Deflected Flight of Charged Uniform Micro Droplets . . . . . . . . . . . . . . . . . . . . 4.3.4 Temperature History of Uniform Metal Droplets During the Deflection Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Free Forming by Continuous Ejection of Uniform Metal Droplets and Its Controlling Method . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Influencing Factors and Research Methods for Free Forming by Continuous Droplet Ejection . . . . . . . . . . . . . . . . 4.4.2 Parameter Control of Free Forming by Continuous Ejection of Uniform Metal Droplets . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 On-Demand Ejection and Control of Uniform Metal Droplets . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 On-Demand Ejection Behavior of Metal Droplets Driven by Pneumatic Pulse and the Influence of Parameters . . . . . . . . . . . . . 5.2.1 Research on On-Demand Ejection of Uniform Tin–Lead Alloy Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Research on Ejection of Uniform Aluminum Droplets On-Demand Driven by Pneumatic Pressure Pulse . . . . . . . . . 5.3 Ejection Behaviors of Metal Droplets On-Demand Driven by a Stress-Wave Pulse and the Influence of Parameters on Droplet Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Influence of Parameters of Experiment Device on Metal Droplet Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Effect of Stress Wave Pulse Parameters on Metal Droplet Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Comparison of Various Metal Drop-On-Demand Technologies . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Uniform Solder Droplet Deposition and Its 3D Printing Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Deposition Behaviors of Uniform Solder Droplet Deposition and Effect Factors of the Morphology of Deposited Droplets . . . . . . 6.2.1 Deposition and Spreading Behaviors of Uniform Solder Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Effect of Experimental Parameters on Final Shapes of Solidified Micro Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6.2.3 The Method to Reduce the Height Deviation of Solder Bumps and the Analysis of the Height Accuracy . . . . . . . . . . 6.3 Printing Path Planning of the Metal Droplet and the Effect Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Effect of Sequential Printing Parameters on the Morphology of Printed Traces . . . . . . . . . . . . . . . . . . . 6.3.2 Line Formation Experiment by Using the Alternate Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 Controlling of the Deposition Path of Micro Metal Parts by Using Uniform Metal Droplet-Based Printing . . . . . 6.4 Fabrication of Micro Metal Parts by Drop-On-Demand Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Fabrication of Micro-Finned Heat Sinks . . . . . . . . . . . . . . . . . 6.4.2 Fabrication of Micro-Honeycomb Parts . . . . . . . . . . . . . . . . . 6.4.3 Fabrication of Micro-Squared Parts . . . . . . . . . . . . . . . . . . . . . 6.4.4 Fabrication of Micro Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.5 Fabrication of Micro Racks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Electronic Packaging via Uniform Micro Lead–Tin Alloy Droplet 3D Printing Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Rapid Printing of Ball Grid Array and Solder Column Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.2 Rapid Printing and Soldering of Electronic Circuits . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Uniform Aluminum Droplet Deposition Manufacturing and Its Controlling Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Deposition Behaviors of Uniform Aluminum Droplets . . . . . . . . . . . 7.2.1 Impact Behaviors of Aluminum Droplets . . . . . . . . . . . . . . . . 7.2.2 Effect of Process Parameters on the Profile of Deposited Aluminum Droplets . . . . . . . . . . . . . . . . . . . . . . 7.3 Deposition of Aluminum Lines by Uniform Droplets . . . . . . . . . . . . 7.3.1 Effect of Platform Velocity on Printed Lines . . . . . . . . . . . . . 7.3.2 Effect of Substrate Temperature on Printed Lines . . . . . . . . . 7.4 Drop-On-Demand Printing of Aluminum Pillars by Uniform Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Temperature Change During the Deposition of Aluminum Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.2 Morphology Features of Deposited Pillars . . . . . . . . . . . . . . . 7.4.3 Pillar Forming by Drop-On-Demand Printing of Aluminum Droplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.4 Forming of Thin-Walled Aluminum Parts . . . . . . . . . . . . . . . . 7.5 Forming of Aluminum Solid Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contents

8 Microstructure Evolution and Interface Bonding of Uniform Aluminum Droplet Deposition Manufacturing . . . . . . . . . . . . . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Microstructure Evolution of Uniform Aluminum Droplet Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Microstructure Evolution of Uniform Aluminum Droplets During the Vertical Pileup . . . . . . . . . . . . . . . . . . . . . 8.2.2 Microstructure Evolution of Lines Deposited by Uniform Aluminum Droplets . . . . . . . . . . . . . . . . . . . . . . . 8.3 Influence of Interface Bonding Between Metal Droplets on Printed Aluminum Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Effect of Interface Bonding on the Microstructure of Aluminum Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Effect of Interface Bonding on the Mechanical Properties of Aluminum Parts . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Internal Defects and Their Influencing Factors of As-Deposited Aluminum Components . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Hole Defects Inside Printed Aluminum Parts . . . . . . . . . . . . . 8.4.2 Internal Cracks of Printed Aluminum Parts . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Application Prospect of Uniform Metal Droplet-Based 3D Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Preparation of Mono-Sized Spherical Metal Particles . . . . . . . . . . . . 9.3 Printing and Packaging of Microcircuits . . . . . . . . . . . . . . . . . . . . . . . 9.4 Micron Scaled Metal Parts Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5 Micro Thin-Wall Parts Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 3D Printing for Functional Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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271 271 271 275 282 285 285 288 294 294 298 303 305 305 305 306 308 309 310 311

Chapter 1

Introduction

3D printing, also known as additive manufacturing, is a method of creating complex parts layer-by-layer from a CAD model. This method has been widely applied in military, civil, and high-tech fields in recent years. Materials used in 3D printing technology include plastics, ceramic pastes, metals, etc. 3D printing of metals can directly form complex metal parts with mechanical properties meeting engineering requirements, showing a great application value. Currently, for metal 3D printing, scientific researchers and engineering technicians focus on reducing the cost of printing equipment, raw materials, and manufacturing process, improving fabrication precision, and enhancing the mechanical properties of printed parts. Uniform metal droplet-based 3D printing is a novel 3D printing technology that is developed in recent years. In the droplet printing process, complex 3D metal structures can be formed by drop-wise depositing uniform molten metal droplets layer by layer. Compared to other 3D printing technologies, uniform metal droplet-based 3D printing technology has many advantages as follows: (1) Low equipment cost. A uniform metal droplet ejection equipment mainly consists of an induction heater, a metal droplet generator, a 3D motion platform, and an inert gas environment. Since it does not need high-power and expensive power sources, such as the high-power laser or electron beams, droplet-based 3D printing can be achieved with a very low equipment and operation cost. (2) Wide choices of raw materials with no requirement of special processing. Metal blocks or casting ingots, available from markets, can be directly melted in the crucible to print structures. Since it does not require fine metal powders and special wires are not required, the printing materials are widely available and inexpensive. (3) Homogeneous microstructure. The deposited droplets have similar inner microstructures due to the uniform size of metal droplets, which experience a similar cooling and solidification process. Therefore, it is easy to print parts with the homogeneous inner structure by using uniform droplet-based 3D printing. © National Defense Industry Press 2023 L. Qi et al., Metal Micro-Droplet Based 3D Printing Technology, https://doi.org/10.1007/978-981-99-0965-0_1

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1 Introduction

(4) Ability to fabricate heterogeneous parts made of multiple materials. Heterogeneous parts can be printed by droplets deposition of various materials according to the requirement of parts. (5) Easily formation of miniature parts or thin-walled parts. The diameter of metal droplets can be at the microns level. By printing micrometer droplets on-demand, small parts or thin-walled structures with a dimension in the order of subcentimeter can be made. In addition, the droplet deposition process is conducted in a low oxygen environment (≤ 10 PPM), which is beneficial for printed parts to develop improved quality and mechanical properties.

1.1 Classification and Characteristics of Uniform Metal Droplet Ejection Technology According to the difference in the working principle of droplet generation, uniform microdroplet jetting can be mainly divided into two categories: Continuous-ink-jet (CIJ) jetting and Drop-on-demand (DOD) jetting [1]. CIJ refers to the technology that generates the capillary jet from a small orifice and breaks the liquid stream into uniform droplets by inducing small perturbations, while DOD jetting ejects liquid via a small orifice to form mono-sized droplets based on the demand by using pressure pulses.

1.1.1 Continuous-Ink-Jet Jetting Technology Continuous-ink-jet (CIJ) jetting technology is developed based on the RayleighPlateau instability theory. According to this theory, the laminar jet can break into a droplet stream with uniform size and spacing when disturbed by utilizing a weak perturbation with a specific frequency. The working principle of CIJ jetting is schematically illustrated in Fig. 1.1 [2, 3]. After the metal is melted inside the crucible, the molten metal will be ejected through a small orifice to form a laminar jet under constant pressure. Meanwhile, the piezo ceramic actuator generates a small mechanical vibration and transfers the vibration into the metal liquid and the jet surface via the solid bar waveguide. The waveguide has one end attached to the piezo actuator and the other end inserted in the metal liquid. In this way, small perturbations are generated on the jet surface. This perturbation gradually intensifies along the axis of the laminar jet, forcing the metal liquid jet to break into uniformly sized and spaced micro metal droplets. Droplet charge and deflection electrodes are used to control the printing process. The charge electrodes are placed under the nozzle and close to the jet break point. The droplets are charged via the skin effect of electric charge by the electrostatic induction. Droplets with different quantities of charges can be continuously deposited into different locations.

1.1 Classification and Characteristics of Uniform Metal Droplet Ejection …

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Fig. 1.1 Schematic diagram of continuous inkjet (CIJ) jetting technology [5]

The main advantage of CIJ jetting is its rapid droplet generation rate, which can be as high as ten thousand droplets per second. When used for direct part formation, the droplet stream can form a large melt pool on the substrate, resulting in rough printing traces. Therefore, the droplet charge and deflection technology are typically used to produce mono-sized metal particulate products or near-net shapes and simple prototypes [4].

1.1.2 Drop-On-Demand Jetting Technology The working principle of the drop-on-demand (DOD) jetting technology is schematically illustrated in Fig. 1.2. The metal material is first melted inside the crucible. Then, metal droplets are ejected from the small orifice by applying mechanical vibration or pneumatic pulses. When the ejection parameters (i.e., pulse frequency, amplitude, and orifice size) are set, single droplets with the same size, temperature, and initial velocity can be generated repeatedly. DOD droplet ejection has the characteristic of good controllability. The drop-on-demand generation and deposition can be achieved by controlling the motion of the platform and the start/stop of the pressure pulse. That means the droplet ejection can be triggered at desired printing places, which is beneficial for controlling the printing resolution and forming accuracy. It is advantageous in printing thin-wall parts and miniatured parts. Additionally, since the DOD

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1 Introduction

Fig. 1.2 Schematic diagram of the pneumatic pulse-driven DOD droplet ejection technology [6]

droplet ejection process is controllable, heterogeneous function parts can be easily embedded into printed parts during the metal droplet printing process. Mechanical properties and special functions are integrated in this way. However, the droplet generation frequency, ranging from 1 to 2000 Hz, is lower than that of CIJ jetting, leading to a low production rate. According to different methods of generating pressure pulses, DOD droplet ejection can be divided into several categories, such as pneumatic pulse-driven, piezoelectric vibration-driven, and stress wave-driven ejections. Introductions of these methods are provided as follows. 1. Pneumatic pulse-driven DOD droplet ejection technology The working principle of pneumatic pulse-driven DOD ejection technology is illustrated in Fig. 1.2. The top of the crucible installs a T-shaped joint with an inlet connected to the air source through a high-speed solenoid valve, one outlet connected to the crucible (marked as air inlet in Fig. 1.2), and the other outlet opens to the environment (vent valve in Fig. 1.2). After the metal is melted in the crucible, a single droplet is ejected on-demand by rapidly opening and closing the high-speed solenoid valve. The solenoid valve opens and closes quickly to generate a pressure impulse inside the crucible. When the solenoid valve shuts off the gas entering the crucible, the crucible pressure releases quickly through the pressure release valve. With these sudden pressure pulses created inside the crucible, molten metal droplets are ejected from the orifice at the crucible bottom. The characteristic of pneumatic pulse-driven DOD droplet ejection lies in the device’s simplicity; since no complex mechanism is required inside the crucible, it can work with metals with a high-melting point or high chemical activation temperature.

1.1 Classification and Characteristics of Uniform Metal Droplet Ejection …

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However, since the fluctuation of the pneumatic pressure pulse is relatively slow, the ejected droplet size is larger, and the initial droplet velocity is slower than those generated by other droplet ejection technologies. Therefore, pneumatic pulse-driven DOD droplet printing has slow printing efficiency and low printing accuracy, which should be beneficial to produce particulates of metal mentioned above, and be utilized to analyze dynamic and thermal droplet behaviors during impact. 2. Piezo pulses driving droplet ejection on-demand Piezoelectric pulse-driven on-demand droplet ejection technology ejects metal droplets via a small orifice using a pulse generated by the piezoceramic actuator and transferred by a solid waveguide. According to the location and the vibration method of the piezo ceramic actuator, the piezoelectric DOD droplet ejection technology is categorized into two forms: the radial vibration DOD ejection (as shown in Fig. 1.3) [7] and the axial vibration DOD ejection [8]. The principle of the radial piezoelectric vibration drop-on-demand droplet ejection technology is described as follows. After metal materials are melted inside the crucible, the metal liquid fills the capillary nozzle under the gas pressure. A piezoelectric sleeve, located around the capillary tube, vibrates radially to compress the capillary tube and force the metal liquid out of the nozzle to form a single metal droplet [7, 9, 15]. The characteristic of the radial vibration DOD method is that it is easy to achieve high-frequency droplet ejection (or highly efficient printing) because of the small volume of the piezoelectric ceramic. However, since the piezoceramic is heated to an elevated temperature for metal droplet ejection, high-temperature piezoceramics should be adopted for this application, and the printing temperature should also be strictly limited to protect the temperature-sensitive piezoceramic actuator. Fig. 1.3 Schematic diagram of radial piezoelectric vibration pulse on demand ejection technology

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1 Introduction

The working temperature of such a droplet generator is approximately 300–400 °C. This generator is mainly utilized to print solder droplets for preparing BGA balls, 3D packaging of microelectronics, and direct printing uniform solder bump array. The working principle of axial vibration DOD droplet ejection is that the axially deformed piezoelectric ceramic actuator is placed in a cooling case atop the crucible. Then, the piezoelectric ceramic vibration pulse is transferred into metal liquid close to the nozzle at the crucible bottom through a solid bar waveguide, forcing the metal liquid to jet out from the small nozzle to form a single metal droplet. In axial vibration DOD ejection, the solid rod insulates the piezoelectric ceramic from the high-temperature metal liquid. Therefore, this droplet generator can work at the crucible temperature above 1200 °C, and print metal droplets of copper, gold, silver, and other high melting point materials for printing circuits, metal parts, etc. 3. Stress wave pulse-driven DOD droplet ejection technology The working principle of the stress wave pulse-driven DOD droplet ejection technology is schematically illustrated in Fig. 1.4 [10]. When the power of the solenoid is on, the impact rod moves downwards under the electromagnetic force to impact the solid bar waveguide and generate a stress wave pulse inside the waveguide. The stress wave pulse is transferred along the waveguide to the liquid metal and ejects metal liquid out of the small orifice to form a single metal droplet. With stress wave pulses, droplets smaller than the nozzle size can be produced. However, since the stress pulses are generated by the impact of two metal rods, the impact area deforms over time. The deformation leads to changes in the stress wave pulses, in consequence, changes in droplet ejection. Hence, this technology is mainly

Fig. 1.4 Schematic diagram of the stress wave pulse driven DOD droplet ejection technology [12]

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Table 1.1 Main characteristics of CIJ technology and DOD droplet ejection technology [1, 11, 12] Classification

Driven model

Ejection rate (particles per second)

Droplet Efficiency Working Applications ejection temperature velocity (m/s)

Continuous Piezoelectric 5000 ~ 44,000 10 ~ 20 high inkjet jetting perturbation (CIJ) technology dispersion laminar jet

~1000 °C

Uniform droplets preparation Parts manufacturing

Drop-on-demand Pneumatic (DOD) droplet pulse driven ejection technology

~1200 °C

Electronic packaging Parts manufacturing

Radial 0 ~ 2000 piezoelectric vibration pulse driven

~340 °C

Electronic packaging

Axial 0 ~ 50 piezoelectric vibration pulse driven

~1200 °C

Molding parts

Stress wave pulse driven

~1200 °C

Microparticle preparation

0 ~ 50

0 ~ 50

0.1 ~ 1

low

used to generate micro metal droplets with sizes smaller than that of the orifice. Since the droplet size is not limited by the orifice size, stress wave pulse-driven droplet ejection is suitable for DOD printing of microstructures. In summary, CIJ jetting technology has the advantages of high droplet ejection rate, high ejection speed, and high cooling rate. This technology is suitable for forming large and simple near-net shapes. DOD ejection technology has the advantage of easy control, high repeatability, etc. It is suitable for printing complex structures. The main characteristics of the two above technologies are listed in Table 1.1.

1.2 State-of-the-Art and Trends of the Uniform Metal Droplet Ejection Technology 1.2.1 State-of-the-Art of the Uniform Metal Droplet Ejection Technology IBM first proposed uniform metal DOD droplet ejection technology in 1972 [13]. In 1989, Philips of North America granted the first patent for liquid metal jet ejection technology (A method of applying small drop-shaped quantities of molten solder from a nozzle to surfaces to be wetted and a device for carrying out the method)

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1 Introduction

[14]. Subsequently, in the 1980s and 1990s, MicroFab company developed and successfully commercialized uniform solder DOD droplet ejection equipment [16]. The solder droplet deposition equipment and printing products from this company are shown in Fig. 1.5. The equipment is mainly utilized for printing solder bumps in microelectronic circuits, manufacturing rapid types of microcircuits [16], and packaging of micro-optics [18], etc. During the same period, the Droplet-Based Manufacture Laboratory of MIT also proposed a Uniform Droplet Spray (UDS) technology. It developed a metal Droplet ejecting device (shown in Fig. 1.6) as well as the control method of solder droplet ejection [17]. Furthermore, researches on the ejection of tiny and uniform metal droplets (such as tin and aluminum droplets.) and the basic theory of the droplet deposition collision process [18, 19] are also carried out.

Fig. 1.5 printing equipment and printing products of MicroFab company in U.S [16]. a Printing equipment jetLab, b Solder bump arrays, and c 3D packaging of MEMS devices

Fig. 1.6 a Picture of equipment for the micro droplet ejection in MIT [17], b Schematic diagram of the droplet generator, and c Solder laminar disc formed by deposited solder droplets

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In the 1990s, the University of California, Irvine UCI, Northeastern University, Oak Ridge National Laboratory of the United States conducted systematic studies on fundamental theoretical problems of the UDS technology and discussed its industrial applications and commercial value [18], including the ejection behavior of uniform metal droplets, thermodynamic behavior of microdroplets during the droplet flight process, microstructures and mechanical properties of printed structures, including tin, copper, aluminum, and their alloys. Prof. Melissa Orme’s team at the Drop Dynamic and Net Forming Laboratory at the University of California, Irvine, studied the generation and manipulation of uniform droplets, metal droplet charge and deflection, production of uniform metal particles, aluminum net shaping formation, etc. The equipment for uniform metal droplet production and printing by Prof. Melissa Orme’s team [20] is illustrated in Fig. 1.7a. The uniform metal droplet generator is located in the low-oxygen environment, crucible and the nozzle assembly are made from Titanium alloy with TiC coating. By using this equipment, printed thin-wall aluminum tubes with a length of 11 cm are shown in Fig. 1.7b. Ball Grid Array (BGA) and letter symbols printed by using solder droplets are obtained by using droplet charging and deflection technology, as shown in Fig. 1.7c. The research on the mechanical properties of the printed

Fig. 1.7 Schematic diagram of the UDS process and printed parts and a principle of the UDS process, b printed aluminum tubes, c printed solder bumps array [20]

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1 Introduction

Fig. 1.8 Experimental results of UDS device developed by Northeastern University [21, 22]: a Experimental device, b metal jet, c microstructure morphology of metal droplet

aluminum parts demonstrates the significant enhancement of the mechanical properties of the printed parts compared to the raw material. The tensile strength increases by 30%, and the yield strength increase by 31%. Professor Teiichi Andob and his team at Advanced Materials Processing Laboratory at Northeastern University developed a microdroplet ejection system for producing high melting-point metal streams such as ferroalloy [21] and magnesium alloy [22]. They proposed the heterogeneous nucleation model to describe droplet solidification during the flight process and studied the eject behavior, heteronucleation mechanism, and rapid solidification behaviors (Fig. 1.8). Since the droplet ejection rate and deposition rate are very fast, it is hard to precisely control the metal droplet deposition in the UDS process, even if the droplet charge and deflection are adopted. Pressure pulses, generated by using a pneumatic actuator or a piezoelectric actuator, are employed to eject and deposit droplets on demand. Devices and technologies for ejecting mono-sized metal droplets on demand have been developed at Osaka University, the University of Toronto, the Korea Institute of Machinery and Materials, the University of Twente, etc. The Joining and Welding Research Institute at Osaka University in Japan [23] developed a pneumatic droplet on-demand ejection equipment (Fig. 1.9a). This equipment ejects aluminum droplets of diameter close to one millimeter and manufactures simple aluminum alloy parts (Fig. 1.9b). Furthermore, using self-propagating combustion, aluminum micro aluminum droplets are deposited on the Ti powder bed to form Al–Ti intermetallic compounds (Fig. 1.9c). The pneumatic pulse-driven metal droplet on-demand ejection equipment developed by the University of Toronto [24] is shown in Fig. 1.10a. Small tin or tin solder droplets with a diameter ranging from 100 to 300 µm are ejected under an incident pulse. Small metal parts are printed by depositing metal droplets layer by layer (as shown in Fig. 1.10b) [25]. Researchers at the University of North Carolina [25] proposed a 3D printing technology for printing liquid metals at room temperature. The principle of this technology is that low-melting-point metal droplets are ejected at room temperature

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Fig. 1.9 Aluminum droplet on-demand manufacturing technology [23]. a Schematic diagram of the aluminum droplet ejection and deposition equipment. b Aluminum parts printed by aluminum droplets. c Al–Ti intermetallic compounds formed by depositing aluminum droplet on the Ti powder bed

Fig. 1.10 The equipment developed by the University of Toronto [24] for metal droplet ejection and deposition on-demand. a The picture of the developed equipment. b Printed parts

in the atmosphere. The metal droplets are formed and combined to form complex stereo shapes by the oxygen skin on metal droplets (Fig. 1.11b). The Korea Institute of Machinery and Materials proposed piezoelectric pulsedriven droplets on-demand ejection technology [26]. The principle of this technology is that vibration pulses, generated by the piezoelectric actuator and transferred into

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1 Introduction

Fig. 1.11 Droplet printing technology developed in the University of North Carolina [25], a the low-melting-point droplets generation process. b Stereo metal parts printed by using liquid metal droplets at room temperature

the metal liquid near to nozzle, forcing metal droplets out of the nozzle to form metal droplets (Fig. 1.12a). Lead–tin pillars printed by using this technology are shown in Fig. 1.12b. Tohoku University in Japan proposed the Pulsed Orifice ejection Method (POEM) [27, 28]. This technology uses a vibration-transferring rod to transfer the axial vibration pulse generated by the piezoelectric actuator into the metal liquid near the orifice. In this way, mono-sized metal droplets can be ejected by forcing the liquid metal through the small orifice. Metal droplets, such as ferrous alloy droplets and

Fig. 1.12 Solder droplets printing on-demand technology developed by the Korea Institute of Machinery and Materials [26]: a Solder droplet printing equipment. b Small solder pillars formed by printing metal droplets

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Fig. 1.13 Pulsed Orifice Ejection Method developed by Tohoku University, Japan [27, 28]. a Schematic diagram of the droplet ejection principle, and b Fe-based metallic glass particles prepared by this method

copper droplets, have been ejected controllably by using this method. The monosized Fe-based metallic glass alloy particles generated by this method are shown in Fig. 1.13. The TNO Science and Industry, Eindhoven, Netherlands, has developed the piezoelectric pulse-driven metal droplet ejection technology [29]. The mechanical pulse generated by a piezoelectric transducer is transferred into the nozzle through a waveguide rod in the form of a compression wave. Then the liquid metal is ejected out of the nozzle to form mono-sized metal droplets. Gold particles of a diameter of 100 µm are generated by using this technology (Fig. 1.14). In China, systematic research on metal droplet-based 3D printing technology began in 2002. The first patent, titled “Heterogeneous functional parts rapid forming micro-manufacturing method”, is proposed by the Droplet-based Manufacturing group at Northwestern Polytechnical University. Other research institutes also conducted research in this area, such as Harbin Institute of Technology, General Research Institute for Nonferrous Metals, Tianjin University, Huazhong University of Science and Technology, Dalian University of Technology, and Xi’an Jiaotong University. The current technologies for metal droplet generation are uniform droplet spray, piezoelectric pulse-driven droplet on-demand ejection, pneumatic pulse-driven droplet on-demand ejection, etc. Researchers at the Harbin University of Technology have developed a continuous uniform metal droplet ejection device [30], which can continuously eject uniform metal droplet streams. Simple lead–tin alloy rings have been formed by selectively charging and deflecting the mono-sized metal droplets.

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Fig. 1.14 Piezoelectric pulse driven on-demand ejection equipment developed in the TNO Science and Industry, Eindhoven, Netherlands [29]. a Droplet ejection on-demand equipment. b Mono-sized gold particles

Uniform tin solder droplet stream generation technologies have been researched at General Research Institute for Nonferrous Metals [31] and Tianjin University [32]. The experimental parameters’ influence on the uniformity and the microstructures of the solder particles have been investigated. Uniform solder particles have been prepared by using this technology. Researchers at Huazhong University of Science and Technology [33] developed a pneumatic diaphragm driven solder microdroplet ejection technology. They deformed a metal diaphragm by applying an air pressure pulse to force metal liquid out of the small nozzle and form micro metal droplets. By using this technology, droplets of lead–tin alloy and high-viscosity polymer have been ejected, and micro solder bump and micro polymer lens arrays have been printed. Researchers at Dalian University of Technology [34] developed a pulsed orifice ejection equipment, of which the principle is similar to the method proposed by researchers at Osaka University Japan. Solder droplets were ejected from a small orifice using a waveguide rod, which transfers incident vibration pulses into liquid metal near the small orifice. Simple lead–tin tubes have been printed by using this equipment. Researchers at Xi’an Jiaotong University have developed a pneumatic pulsedriven micro metal droplet on-demand ejection equipment [35]. Lead–tin alloy droplets and aluminum alloy droplets have been ejected on demand. Complex tin–lead alloy parts used in electric power equipment have been printed [36]. Since 2002, the authors’ group (the Droplet-based Manufacturing group) at Northwestern Polytechnical University has been studying the technology and related fundamental theories about the uniform metal droplet ejection, with the support of the National 863 Key Projects, the National Natural Science Foundation of China, the

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Foundation of National Excellent Doctoral Dissertation Authors, etc. The research details will be introduced in subsequent chapters. To sum up, great progress has been made in uniform metal droplet ejection technology in recent years. The classification, characteristics, and application areas of this technology are listed in Table 1.2.

1.2.2 Trends in Uniform Metal Droplet Ejection 3D Printing Technology Metal droplet-based 3D printing technology is a very promising additive manufacturing technology since it has advantages such as wide materials choice, free forming, and free of expensive special equipment. At present, this technology has been applied in various areas like the manufacturing of electronic circuits, heterogeneous materials and parts, and structural–functional integration parts. However, the metal dropletbased manufacturing technology for high melting-point metals, such as aluminum and copper alloy, is still in the laboratory research stage. For applying the technology in the industry, profound studies should be taken in the following areas: 1. Development of high precise metal droplet generators and printing equipment for various applications In various applications, the ejection and deposition of different metal droplets are required. Since the physical properties of different metal liquids are unique, the specific droplet generator and the corresponding controlling method should be developed. The customized equipment should be developed according to the special requirement of the applications. 2. Uniform metal droplet-based 3D printing technology for microgravity environment An urgent need for on-orbit metal additive manufacturing exists in space exploration activities. With the advantages of being free of specially prepared raw materials and expensive equipment, metal droplet-based 3D printing technology is very promising for manufacturing metal parts in a microgravity environment. For developing the in-space 3D printing equipment and technology, the physical simulation equipment should be developed to investigate the scientific problems involving droplet ejection and deposition behaviors and the evolution of microstructures. Key technologies such as the low-power high-temperature droplet ejection, the printing trajectories and temperature field controlling in space environment should be broken through. 3. Heterogeneous/gradient functional materials and parts manufacturing technology By controlling the precise deposition of multi-materials droplets, the distribution of the part materials can be customized. This is a promising way to rapidly manufacture heterogeneous/gradient functional materials and parts. User

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1 Introduction

Table 1.2 The state-of-art of uniform metal droplet-based printing technology [12] Country

Research institution

Classification

Drive models Materials

Application areas

China

Northwestern Polytechnical University

CIJ (Continuous InkJet)

Constant pneumatic pressure and mechanic perturbation generated by piezoelectric vibration

Lead–tin alloy

Metal parts forming, uniform droplet preparation

DOD (Drop-on-Demand)

Pneumatic pulse

Lead–tin alloy, aluminum alloy

Metal parts forming

Axial piezoelectric vibration pulse

Lead–tin alloy, aluminum alloy

Electronics packaging, circuit prints

Stress wave pulse

Lead–tin alloy

Metal droplet ejection

Huazhong University of Science and Technology

DOD

Pneumatic pressure pulse

Lead–tin alloy

Tin solder bump array printing

Harbin Institute of Technology

CIJ

Pneumatic pressure electric vibration

Lead–tin alloy

Uniform metal particles preparation, metal parts forming

General Research Institute for Nonferrous Metals

CIJ

Pneumatic pressure electric vibration

Lead–tin alloy

Uniform tin solder droplet preparation

Tianjin University

CIJ

Pneumatic pressure electric vibration

Lead–tin alloy

Uniform tin solder droplet preparation

National Cheng Kung University

CIJ

Pneumatic pressure electric vibration

Lead–tin alloy, aluminum alloy

Uniform Metal particles preparation (continued)

1.2 State-of-the-Art and Trends of the Uniform Metal Droplet Ejection …

17

Table 1.2 (continued) Country

Research institution

Classification

Drive models Materials

Application areas

USA

University of California, Irvine

CIJ

Pneumatic pressure electric vibration

Lead–tin alloy, aluminum alloy

Metal parts printing, uniform bump array preparation

Massachusetts Institute of Technology

CIJ

Pneumatic pressure electric vibration

Lead–tin alloy, zinc alloy, copper alloy, aluminum alloy

Ejection mechanism Charge deflection mechanism solder joint preparation

DOD

Radial piezoelectric vibration pulse

Lead–tin alloy

Circuit printing, Solder joint preparation

Northeastern University

CIJ

Pneumatic pressure electric vibration

Magnesium alloy, copper alloy, fe-based metallic glass

Fundamental research of solidification behavior of microdroplet

Microfab Co

DOD

Radial piezoelectric vibration pulse

Lead–tin alloy

Circuit printing, Electronics packaging

Canada

University of Toronto

DOD

Pneumatic pulse

Tin alloy, aluminum alloy

Metal parts forming, droplet ejection and deposition collision behavior

Japan

Osaka University

DOD

Axial piezoelectric vibration pulse

Copper alloy, Uniform Fe-based metal metallic glass particles preparation

Pneumatic pulse

aluminum alloy

Metal parts and intermetallic compounds printing

Axial piezoelectric vibration pulse

Lead–tin alloy

Electronics packaging

Korea

Korea Institute DOD of Machinery and Materials

18

1 Introduction

demand-driven material and performance design manufacturing integrated additive manufacturing can be established by building the multi generators printing system, developing multi material/part model processing software and printing trajectory planning algorithm, and breaking multi materials droplets’ precise deposition controlling technology. 4. Structure function integration manufacturing by combining other manufacturing technologies Integrated manufacturing of structure and function of parts can be achieved by combining uniform metal droplet printing, design and optimization of metamaterial or topological structures, and microscopic thermal exchange technologies. For instants, functional parts with negative Poisson’s ratio or zero thermal expansion coefficient can be printed by combining the uniform metal droplet printing technology with the design of lightweight lattice metamaterials. Furthermore, the integration of structural load-bearing capacity with heat transfer and heat dissipation can be obtained by embedding the thermal management units inside the printed parts.

References 1. Hutchings IM. Ink-jet printing in micro-manufacturing: opportunities and limitations. In: International conferences on multi-material micro manufacture, 4M/International conferences on micro manufacturing, ICOMM, September 23, 2009–September 25, 2009. pp. 47–57. 2. Orme M, Liu Q, Fischer J. Mono-disperse aluminum droplet generation and deposition for net-form manufacturing of structural components. In: Eighth international conference on liquid atomization and eject systems, Pasadena, CA, USA, July 2000. pp. 200–207. 3. Orme M, Willis K, Nguyen TV. Droplet patterns from capillary stream breakup. Phys Fluids A Fluid Dyn. 1993;5(1):80–90. 4. Orme M, Courter J, Liu Q, et al. Electrostatic charging and deflection of nonconventional droplet streams formed from capillary stream breakup. Phys Fluids. 2000;12(9):2224–35. 5. Luo J, Qi LH, Zhou JM, et al. Study on stable delivery of charged uniform droplets for freeform fabrication of metal parts. Sci China Technol Sci. 2011;54(7):1833–40. 6. Luo J, Qi LH, Zhou JM, et al. Modeling and characterization of metal droplets generation by using a pneumatic drop-on-demand generator[J]. J Mater Process Technol. 2012;212(3):718– 26. 7. Hayes DJ, Wallace DB, Cox WR. MicroJet printing of solder and polymers for multi-chip modules and chip-scale packages; 1999. pp. 242–247. 8. Takagi K, Masuda S, Suzuki H, et al. Preparation of monosized copper micro particles by pulsated orifice ejection method. Mater Trans. 2006;47(5):1380–5. 9. Shah VG. Fabrication of passive elements using ink-jet technology by. Imaps Atw. 2002(June):1–6. 10. Luo J, Qi L, Tao Y, et al. Impact-driven ejection of micro metal droplets on-demand. Int J Mach Tools Manuf. 2016;106:67–74. 11. Liu Q, Orme M. High precision solder droplet printing technology and the state-of-the-art. J Mater Process Technol. 2001;115(3):271–83. 12. Qi LH, Zhong SY, Luo J. Uniform metal droplet-based 3D printing. Sci China (Inf Sci). 2015;2:5. 13. Northrup WF, Sonsini AJ. Pulse jet solder deposition. IBM Tech Discl Bull. 1972;14(8):2354–5.

References

19

14. Hieber H. Method of applying small drop-shaped quantities of melted solder from a nozzle to surfaces to be wetted and device for carrying out the method: U.S. Patent 4,828,886, 1989.5.9. 15. Wallace DB, Hayes DJ. Solder jet technology update, 1997. Spie International Society For Optical, 1997. 16. Nallani AK, Chen T, Hayes DJ, et al. A method for improved VCSEL packaging using MEMS and ink-jet technologies. J Lightwave Technol. 2006;24(3):1504–12. 17. Passow CH. A study of eject forming using uniform droplet ejects. Massachusetts Institute of Technology, 1992. 18. Ridge O. Uniform droplets benefit advanced particulates. Met Powder Rep. 1999;54(3):30–4. 19. Shin JH. Feasibility study of rapid prototyping using the uniform droplet spray process. Massachusetts: Massachusetts Institute of Technology, 1998. p. 44. 20. Orme M, Liu Q, Smith R. Molten aluminum micro-droplet formation and deposition for advanced manufacturing applications. Alum Trans J. 2000;3(1):95–103. 21. Bialiauskaya V, Ando T. Nucleation kinetics of continuously cooling Fe-17 at.%B droplets produced by controlled capillary jet breakup. J Mater Process Technol. 2010;210(3):487–496. 22. Fukuda H. Droplet-based processing of magnesium alloys for the production of highperformance bulk materials. 2009. 23. Matsuura K, Kudoh M, Oh JH, et al. Development of freeform fabrication of intermetallic compounds. Scripta Mater. 2001;44(3):539–44. 24. Fang M, Chandra S, Park CB. Experiments on remelting and solidification of molten metal droplets deposited in vertical columns. J Manuf Sci Eng. 2007;129(2):311. 25. Ladd C, So JH, Muth J, et al. 3D printing of free standing liquid metal microstructures. Adv Mater. 2013;25(36):5081–5. 26. Lee T, Kang TG, Yang JS, et al. Gap adjustable molten metal DoD inkjet system with coneshaped piston head. J Manuf Sci Eng. 2008;130(3):31113. 27. Miura A, Dong W, Fukue M, et al. Preparation of Fe-based monodisperse spherical particles with fully glassy phase. J Alloy Compd. 2011;509(18):5581–6. 28. Takagi K, Seno K, Kawasaki A. Fabrication of a three-dimensional terahertz photonic crystal using monosized spherical particles. Appl Phys Lett. 2004;85(17):3681–3. 29. Houben R. Equipment for printing of high viscosity liquids and molten metals; 2012. pp. 10–34. 30. Yao Y, Gao S, Cui C. Rapid prototyping based on uniform droplet ejecting. J Mater Process Technol. 2004;146(3):389–95. 31. He LJ, Zhang SM. Research on breakup of metal jet. Chin J Rare Metals. 2004;28(1):117–21. 32. Wu Ping, Teiichi A, Hiroki F, Chuck T. Microstructure of Sn-Pb droplets prepared by uniform droplet spray. Chin J Mater Res. 2003;(01):92–96. 33. Xie D, Zhang H, Shu X, et al. Multi-materials drop-on-demand inkjet technology based on pneumatic diaphragm actuator. Sci China Technol Sci. 2010;53(6):1605–11. 34. Fu YF. Preparation of uniform spherical micron particles by micro pulsed orifice ejection and its influencing factors Master Dissertation. Dalian University of Technology; 2013. pp. 1–20. 35. Du J, Wei Z. Numerical analysis of pileup process in metal microdroplet deposition manufacture. Int J Therm Sci. 2015;96:35–44. 36. Li SL, Wei ZY, Du J, Zhao GX, Wang X, Liu W, Lu BH. Research of 3D printing technology based on metal double nozzle to form the hanging parts, 2016;24(6):1–7

Chapter 2

Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

2.1 Introduction Uniform metal droplets will go through a series of physical processes during ejection and deposition, including liquid metal jet breakups, droplet formation, droplet flight, droplet impact on a substrate or pre-deposited droplets, cooling, and solidification, etc. It involves complex metal liquid flow and heat transfer behaviors. Therefore, understanding the underlying theories is essential for controlling the size of metal droplets and printing accuracy. This chapter focuses on a series of fundamental theories concerning metal droplet ejection, flight, and deposition, providing theoretical guidance for metal droplet 3D printing. These theories consist of the theory of continuous uniform droplet ejection and the mechanism of droplet charging and deflection, theories of pneumatic pulse, piezoelectric pulse, and stress wave-driven drop-ondemand metal droplet ejection, the dynamics and thermodynamics coupling behavior of metal droplet flight process, and the fluid-thermal coupling behavior during metal droplet deposition and impact.

2.2 Theory of Continuous Uniform Metal Droplet Ejection and Mechanism of Droplet Charging and Deflection 2.2.1 Theory of Continuous Uniform Metal Droplet Ejection (Theory of Rayleigh Jet Instability) It is well known that when a faucet is opened to a certain position, a jet of water flowing down at a certain velocity breaks into droplets. This phenomenon was first described experimentally by the Belgian physicist Joseph Plateau [1] in 1873. In the mid-late nineteenth century, the British physicist Lord Rayleigh [2] mathematically analyzed the phenomenon and established the theory of Rayleigh jet instability. Subsequently, © National Defense Industry Press 2023 L. Qi et al., Metal Micro-Droplet Based 3D Printing Technology, https://doi.org/10.1007/978-981-99-0965-0_2

21

22

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

Weber et al. [3] established the instability theory for viscous jets by considering the effects of jet viscosity and ambient medium. Metal jets have similar hydrodynamic behavior to nonmetallic jets such as water; thus, the theory of Rayleigh jet instability is also applicable to metal jets. In this section, the classical Rayleigh instability theory is introduced to explore the relationship between ejection parameters (e.g., ejection pressure, nozzle aperture, and disturbance frequency) and jet material properties during the jetting process. This relationship guides the parameter matching for uniform metal droplet ejection and the calculation for initial parameter settings for uniform metal droplets. The liquid ejected from a nozzle under a certain pressure can form a laminar liquid jet, whose internal particles move smoothly along the streamline direction parallel to the jet. This jet can break into droplets under external disturbances (Fig. 2.1). Assuming the jet is an incompressible liquid with density ρ l , surface tension σ, and nozzle radius Rn , a cylindrical coordinate system is established with the jet axis as the symmetry axis. The origin is set at the nozzle center, and the jet direction is along the z direction. When a sinusoidal perturbation is applied to the jet, the jet can remain axisymmetric, but pressure fluctuations might occur inside the jet. Under the combined effect of pressure fluctuations and jet surface tension, the jet radius will change, producing the varicose pattern as shown in Fig. 2.1, whose radius is r j = r0 + ηeβt+ikz

(2.1)

where r 0 is the initial jet radius, η is a weak disturbance, β is the disturbance growth rate, t is the jet runtime, and wave number k = 2π/λ. According to Weber’s viscous jet instability theory, the growth rate equation of jet surface disturbance can be obtained by

Fig. 2.1 Breakup model of a laminar liquid jet

2.2 Theory of Continuous Uniform Metal Droplet Ejection and Mechanism …

⎞2

⎛ ⎜ β ⎜/ ⎝ ( σ

ρl d 3j

23

⎞

⎛

⎟ ⎜ ⎟ + 12Oh · k 2 · ⎜ / β ⎠ ⎝ ( σ )

ρl d 3j

⎟ ( ) ⎟ − 4 1 − k 2 k 2 = 2k 3 K 0 (k) W e2 (2.2) g ⎠ K 1 (k) )

where Oh is a dimensionless number that measures / the relationship among viscous force, inertial force, and surface tension, Oh = μl / ρl d j σ ; Weg is the Weber number of the ambient medium, Weg = ρ g d j uj 2 /σ; K 0 and K 1 are the first kind of zero-order and first-order modified Bessel functions, respectively; d j is the jet diameter. The ambient medium in this study is nitrogen. When the jet velocity is less than 4 m/s, Weg is less than 0.1. In this case, the wave number change that produces the maximum disturbance growth rate β max is less than 5%, and the influence of ambient gas on the jet flow can be ignored. Therefore, neglecting the right-hand side of Eq. (2.2) results in )| (/ | σ ( ) 2 ) 36Oh 2 − 4 k 4 + 4k 2 − 6Oh · k | β= |( ρl d 3j

(2.3)

According to Eq. (2.3), the disturbance growth rate β is related to Oh (jet properties, including surface tension, viscosity, diameter, etc.) and wave number k. It can thus be deduced by nondimensionalizing the disturbance growth rate β β∗ = /

β ( σ ) ρl d 3j

(2.4)

The variation of β * is shown in Fig. 2.2. From Fig. 2.2, we can see that for a certain Oh, β * increases gradually at first with the rise of k, and then decreases after reaching the local maximum value β * max . As Oh goes down, β * max gradually ascends. When the jet breaks into uniform droplets, the disturbance growth rate reaches its maximum. The optimal wave number and the maximum disturbance growth rate are obtained by calculating the maximum value of Eq. (2.3). 1 kopt = √ 2(1 + 3Oh) / βmax =

(2.5)

( σ ) ρl d 3j

1 + 3Oh

(2.6)

In the uniform metal droplet ejection process, the jet velocity is a key parameter for predicting the optimal frequency and a necessary prerequisite for calculating many important initial parameters, such as droplet breakup length and droplet diameter. Therefore, the jet velocity should be modeled and calculated.

24

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

Fig. 2.2 Variation of dimensionless disturbance growth rate β *

There are two kinds of methods for jet velocity prediction, namely, the analytical method based on fluid mechanics and the numerical calculation method based on finite element analyses. Tseng et al. [4] of Arizona State University developed an analytical model for jet velocity prediction using the Bernoulli equation. In this model, the internal structure of the crucible and nozzle was simplified into a shrinking tubular model with several stepped surfaces [5] (Fig. 2.3). The Bernoulli equation for the fluid during jet ejection can be expressed as α2 u 22 α0 u 2n P2 P0 + + h0 + h1 + h2 = + + h f + hm ρl g 2g ρl g 2g Fig. 2.3 Crucible and nozzle model with shrinking stepped surface

(2.7)

2.2 Theory of Continuous Uniform Metal Droplet Ejection and Mechanism …

25

where u2 is the liquid surface flow velocity in the crucible; α 0 and α 2 are the kinetic energy correction coefficients; h0 , h1 , and h2 are the nozzle thickness, step thickness, and the distance from the step surface to the liquid surface, respectively; hm is the local loss caused by the sudden narrowing of the orifice, hf is the flow loss from the liquid surface to the nozzle outlet, which can be calculated according to the relevant theoretical knowledge in fluid mechanics; P2 and P0 are the absolute ejection pressure and atmospheric pressure, respectively; un is the fluid velocity in the nozzle. By solving Eq. (2.7), we can obtain

un =

−A2 +

/

A22 + 4 A1 A3

2 A1

(2.8)

In Eq. (2.8), ) ( d4 ρl α0 + ξ2 + ξ1 04 2 d1 ) ( h0 h1 h2 A2 = 32μl dn2 4 + 4 + 4 dn d1 d2 A1 =

A3 = ΔP + ρl g(h 0 + h 1 + h 2 ) ( ) )) ( ( d2 d2 ξ1 = 0.5 1 − 12 , ξ2 = 0.5 1 − n2 d2 d1

(2.9)

where α 0 is 1.05; the values of ξ 1 and ξ 2 can be determined according to the actual condition of the crucible, usually 0.48–0.5; d n , d 1 , and d 2 are the nozzle diameter, step diameter, and crucible diameter, respectively; ΔP is the internal and external pressure difference. The nozzle diameter is slightly larger than the jet diameter. According to the law of conservation of mass, the jet velocity is slightly faster than the internal fluid velocity of the nozzle. Usually, the fluid velocity inside the nozzle is modified somewhat to approximate the jet velocity, namely uj = un /0.95. Then the Rayleigh instability theory can be used to predict the initial parameters of uniform droplets, including jet breakup length, breakup time, and droplet diameter. When the jet breaks into droplets, Eq. (2.1) is zero, and the jet breakup time is ( ) t=

ln

r0 η

βmax

( = ln

) r0 1 + 3Oh / η ( σ ) ρl d 3j

Under the optimal disturbance frequency, the jet breakup length is

(2.10)

26

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

L j−opt = u j t

(2.11)

After substituting Eq. (2.10) into Eq. (2.11) and simplifying, the length can be obtained as ( ) r0 √ W e(1 + 3Oh) (2.12) L j−opt = d j ln η where We is the jet Weber number, We = ρ j d j uj 2 /σ. According to the law of conservation of mass, the mass of the jet column M j is equal to that of the droplet M d , namely M j = ρl V j = ρl

π d 2j λ 4

= ρd

π Dd3 = Md 6

(2.13)

where V j is the jet volume, Dd is the droplet diameter, ρ d is the droplet density after solidification. The relationship between wavelength λ and excitation frequency f is λ=

uj f

(2.14)

Solving Eqs. (2.13) and (2.14) yields the droplet diameter as / Dd = d j

3

3ρl u j 2ρd f d j

(2.15)

According to Eqs. (2.5), (2.14), and (2.15), the optimal excitation frequency is calculated as f opt =

uj √ π d j 2(1 + 3Oh)

(2.16)

Equations (2.15) and (2.16) can be used to calculate the breakup time, breakup length, uniform droplet diameter, and optimal excitation frequency of the jet under certain nozzle and pressure conditions. However, the jet instability theory cannot reflect the changes of the flow field and pressure field during the process of a jet breaking into droplets. The above analytical method can only roughly estimate the above parameters, and the results have some errors with the real values, which need to be supplemented by experimental and numerical simulation methods for detailed analysis.

2.2 Theory of Continuous Uniform Metal Droplet Ejection and Mechanism …

27

2.2.2 Mechanism of Charging and Deflection of Uniform Droplets Due to random perturbations and air damping, continuously generated metal droplets might coalesce with each other during the ejection process. The droplet coalescence can be prevented by using the principle of “like charges repel” via charging uniform droplets with the same charge. In addition, by passing charged uniform droplets through an electrostatic field perpendicular to their trajectory, the droplets can be deflected by Lorentz force by a certain distance, which is an effective method to control the deposition position of uniform droplets flying at high speed. 1. Principle of uniform droplet charging and prediction model of charging quantity The charging principle of uniform droplets works as follows. The unbroken jet carries a certain electrostatic charge through electrostatic induction. As the jet breaks into droplets, the charge carried by the broken part remains on its surface, realizing the charging of droplets. To realize this charging principle, an induced electrostatic field should be constructed at the breaking point of the metal jet. Typically, a hollow circular or parallel plate electrode is used as the positive electrode of the electric field with the jet as the negative electrode, breaking the jet between the electrodes to carry a charge. Due to the complex morphology in the form of a varicose vein pattern as the jet breaks up, it is difficult to establish an accurate analytical model to predict the quantity of charge in the droplets. Here, a method combining transient microscopic images and electrostatic field finite element analysis is introduced to precisely predict the charged amount of droplets [6]. The method uses a high-speed camera to capture the instantaneous morphology of the jet surface, based on which a physical model of droplet charging is established. Numerical methods are used to calculate the droplet charging quantity during the jet breakup process to obtain accurate prediction results. Figure 2.4a shows the water jet breakup morphology obtained by stroboscopic photography with a nozzle diameter of 150 μm, an ejection pressure of 26 kPa, and the optimal disturbance frequency of 5.8 kHz calculated based on Rayleigh instability theory for the jet to break up. Figure 2.4b illustrates the simplified jet surface profile. The jet part (length L jet ) forming the droplet can be reduced to a geometry (charging part) consisting of a cone with height a and base radius b and a large spherical crown with radius R' . According to Rayleigh instability theory, after the formation of a uniform droplet stream, droplets with radius R are equidistant from each other with a disturbance wavelength λ. Here, Se is the electrode parameter, which denotes the charging electrode radius for circular charging electrodes and half of the electrode spacing for parallel plate charging electrodes. After establishing the physical model of the jet, the electrostatic field distribution among the jet, droplets, and electrodes can be solved by the finite element method, namely solving the electrostatic potential Poisson equation in this space: ∇2φ = 0

(2.17)

28

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

Fig. 2.4 Water jet morphology and physical model of droplet charging. a Picture of an unbroken jet and uniform droplets. b Physical model of uniform droplet charging obtained by simplifying the surface profile of the jet and droplets

where ϕ is the electric potential inside the charging electrode. Boundary conditions include the potential of the jet, droplets, and electrodes: ϕ|si = Ui

(2.18)

where S i is the surface geometry equation describing the surface morphology of the i-th droplet or the inner surface morphology of the electrode, U i represents the voltage of the surface S i . The potential distribution function ϕ can be obtained from Eq. (2.17). Accordingly, the electrostatic field strength can be obtained by taking the gradient of ϕ as E = − ∇ϕ, and then the electrostatic field energy of the multi-conductor system can be calculated by 1 WE = 2

{

1 ε E dv = 2

{ ε2 ϕdv

2

V

(2.19)

V

where ε is the dielectric constant. The relationship among the electric field energy, capacitance, and voltage is WE =

1 T U CU 2

(2.20)

where the element C ij in matrix C represents the partial capacitance matrix between the i-th and the j-th droplet (or electrode), U is the droplet surface potential matrix. The partial capacitance matrix C between conductors in the multi-conductor system can be derived by combining Eqs. (2.19) and (2.20). By establishing the charging model of n droplets, the matrix describing the charging capacitance of each droplet can be obtained. Under the initial charging condition, the capacitance matrix of the conductive system can be acquired from Eqs. (2.19) and (2.20). Then the charged amount of the droplet can be calculated according to the applied voltage by

2.2 Theory of Continuous Uniform Metal Droplet Ejection and Mechanism …

29

Fig. 2.5 Equivalent circuit model when the first droplet is generated

Q = CU

(2.21)

where Q is the droplet charge matrix, U is the relative potential matrix. The initial charging conditions include the electrode potential boundary condition and the droplet charge boundary condition. When the first droplet is generated, the electrode potential condition U 1 is the only actual boundary condition. The model is shown in Fig. 2.5 with its electric field energy expressed as WE =

1 g 2 C U 2 11 1

(2.22)

where W E is the energy of the electrostatic field, U 1 is the relative potential of the droplet or electrode. The charge Q1 carried by the droplet can be calculated by the finite element method according to Eq. (2.21). While the second droplet is produced, the model is shown in Fig. 2.6. The actual boundary conditions include the electrode potential U 2 and the charged quantity of the first droplet Q1 , resulting in the electric field energy as WE =

1 g 2 1 g 2 1 g C U + C22 U2 + C12 U2 U1 2 11 1 2 2

(2.23)

By solving Eqs. (2.19) and (2.23), the lumped and working capacitances of the conductive system are obtained as C 11 , C 22 , and C 12 , respectively. At this time, the relationship between the uncreated droplet and the generated droplet and potential can be calculated by Eq. (2.21), i.e., Q 1 = C11 U1 + C12 (U1 − U2 ) Q 2 = C12 (U2 − U1 ) + C22 U2

(2.24)

Since the charging voltage U 2 is known, Q2 can thus be obtained by using Eq. (2.22).

30

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

Fig. 2.6 Equivalent circuit model when the second droplet is generated

Repeating the above derivation process, when the i-th droplet is generated, the actual boundary conditions include the potential boundary condition U i and the charge boundary conditions of charging droplets Q1 , Q2 , … Qi-1 . As the charging droplet moves away from the jet breakpoint, its electrostatic field effect on the forming droplet gradually weakens and eventually becomes negligible. In calculation, the charging quantity of the droplet when this influence quantity is less than 1% of the final charging quantity is taken as the average charged amount Qave of a continuous droplet stream. The calculation process is shown in Fig. 2.7 [7]. 2. Lateral instability behavior of charged droplet stream During uniform droplet formation, there is a tiny random position disturbance of the droplet relative to the jet axis. This random position perturbation causes a transverse component force between the charged droplets that drives them off their axis, leading to the electrostatic repulsive force on them no longer along the axis direction. With the increase of droplet deposition distance, the displacement of the charged droplet away from the axis continues to increase [8], which ultimately affects the printing accuracy of the metal droplet. Figure 2.8a exhibits an instantaneous photograph of continuous uniform water droplets, showing that uniform droplets with relative velocities tend to coalesce (the coalescence of two droplets forms a large droplet at the top of the figure). When the droplet stream is charged, the electrostatic repelling force between the charged droplets inhibits the tendency of droplet coalescence. This makes the droplets that tend to coalesce disperse from each other and form a uniformly distributed droplet stream (Fig. 2.8b). With a longer droplet deposition distance, the dispersion behavior of the jet becomes obvious, leading to droplets arranged in a zigzag pattern, as shown in Fig. 2.8c. It can be inferred that droplets are arranged in a spiral pattern in space. The initial random position disturbance of the droplet stream is mainly caused by the roughness of the nozzle outlet, impurities, jet evaporation or oxidation, and other factors. The initial position of the droplet is assumed to be superimposed by a sinusoidal distribution and a random distribution. Thereinto, the sinusoidal distribution represents the component of periodic variation in the initial disturbance with the assumption that its variation period is the same as the period of the jet

2.2 Theory of Continuous Uniform Metal Droplet Ejection and Mechanism …

31

Fig. 2.7 Algorithm flow chart for droplet charging quantity prediction

disturbance, while the random distribution characterizes the randomness of the initial position. According to the theory of Rayleigh jet instability, the spacing of uniform droplets during formation is an optimal disturbance wavelength λopt . Therefore, the charged droplets can be calculated with λopt as the interval, and the initial position of each droplet entering the calculation can be described as ( ) } ⎨ xint_n = ζ ( Dd sin(2π f opt t ) + Dd N1 ) = ζ Dd sin(2π f opt t + Dd N1 ) y ⎩ int_n z int_n = L br eak

(2.25)

where x int_n and yint_n are the coordinates of the initial position of the n-th droplet, ζ is the test parameter taken as 10–6 , t is the calculated droplet flying time, N 1 , N 2 are two random numbers between 0 and 1, L break is the jet breakup length which can be calculated by Eq. (2.11). Charged droplets during ejection experience the following three kinds of forces. (1). Electrostatic repelling force between droplets: F ele =

1 Q 2d r 4π ε0 |r| |r|

(2.26)

32

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

Fig. 2.8 Dispersion behavior of charged uniform droplet stream. a Uncharged uniform droplet stream. b Charged uniform droplet stream. c Dispersive charged droplet stream. d Schematic diagram of random position deviation and electrostatic repulsive force during uniform droplet generation. The nozzle diameter is 150 μm, the perturbation frequency is 3.89 kHz, and the ejection pressure is 45.6 kPa

where r is the distance vector between two droplets, |r| is the magnitude of the vector. They can be expressed as ) ( ) ( ) ( r = xi − x j i + yi − y j j + z i − z j k, |r| =

/

(xi − x j )2 + (yi − y j )2 + (z i − z j )2 ,

(2.27) (2.28)

(2). Aerodynamic drag force of flying droplets: F drag =

ρg Cd π(Dd /2)2 |u d |u d , 2

(2.29)

where ud is the droplet velocity vector, |ud | is its magnitude. They are denoted by u d = u x i + u y j + u z k,

(2.30)

/ u 2x + u 2y + u 2z ,

(2.31)

|u d | =

2.2 Theory of Continuous Uniform Metal Droplet Ejection and Mechanism …

33

(3). Droplet gravity: F grav =

π 3 D ρl g 6 d

(2.32)

Based on the above analysis, the flying kinetic equations for a droplet under the electrostatic force of 2n neighboring droplets can be established as ( md

) j=i+n E ∂u yi ∂u xi ∂u zi i+ j+ k = F ele + F drag + F grav ∂t ∂t ∂t j=i−n

(2.33)

dx dy dz = ux , = uy, = uz dt dt dt

(2.34)

j/=i

3.

By combining Eqs. (2.33) and (2.34) and using the improved Euler formula, the whole region of the above first-order differential equations is integrated with a fixed-step method. The flight trajectory of the droplet under electrostatic repulsive force can be calculated, which can be used to predict the dispersion range. Deflection flight model for charged droplets in an electrostatic field A charged metal droplet flying in an electrostatic field can be deflected by the Lorentz force. This physical phenomenon can be used to separate charged droplets and control their flight trajectory. This section focuses on the computational model of the deflection trajectory for charged droplets under electrostatic force.

During the charging and deflection of metal droplets with a certain density and size, the influence of gravity, electrostatic repulsion, aerodynamic drag force, and electrostatic deflection force on the deflection distance of metal droplets should all be considered. The force analysis of a metal droplet flying through the deflection electric field is shown in Fig. 2.9. Since the electrostatic force between metal droplets decreases with the increase of droplet distance, only the influence of the electrostatic force of the six charged droplets near the calculated droplet is considered here. When the droplet flies out of the deflection electric field, it is no longer affected by the electric field deflection force. In a deflection electric field, the direction of the electric field deflection force is the same as the direction of the electrostatic electric field. The electrostatic deflection force applied to the charged droplet is F E = E Q 'd

(2.35)

where Qd ' is the modified droplet charging quantity considering the effect of deflection electric field on droplet charging amount, generally as 1.1Qd to 1.2Qd . The force equations for a droplet under the electrostatic force of the 2n neighboring droplets are

34

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

Fig. 2.9 Force diagram of a droplet in an electrostatic field

( md

) j=i+n E ∂u yi ∂u zi ∂u xi i+ j+ k = F ele + F drag + F grav + F E ∂t ∂t ∂t j=i−n

(2.36)

dx dy dz = ux , = uy, = uz dt dt dt

(2.37)

j/=i

The flight trajectory of droplet deflection can be obtained by combining Eqs. (2.36) and (2.37) and performing the full interval integration with a fixed-step method. When the droplet flies away from the deflection electric field, the flight trajectory outside the electric field can be calculated by removing the electrostatic deflection force term.

2.3 Drop-On-Demand Ejection of Metal Droplets 2.3.1 Theory of Pneumatic Pulse-Driven Drop-On-Demand Ejection The working principle of pneumatic drop-on-demand ejection was initially described in Sect. 1.1.2. Here, the schematic diagram of the ejection device is shown in Fig. 2.10a. The internal cavity of the crucible and T-joint constitute a closed cavity with an opening at the top. A pressure pulse is fed into the closed chamber through the rapid opening and closing of a solenoid valve installed on the inlet pipe. Thus, the

2.3 Drop-On-Demand Ejection of Metal Droplets

35

pressure oscillation, called the Helmholtz resonance phenomenon [9], is formed in the cavity of the ejection device to facilitate the droplet ejection. For ease of analysis, the crucible and T-joint can be simplified to a Helmholtz resonator model with an opening on the top (Fig. 2.10b). In this model, it is assumed that the volume of the crucible inner cavity is V p and a top vent tube with the cross-section of Ap , diameter of 2r p , and length of L p is connected to the atmosphere. When the compressed gas enters the vent tube, it forces the air inside the tube to move inward with a displacement x. At this time, the air cavity volume decreases by ΔV p = xπr p 2 , and the pressure variation in the cavity is ΔP. From the adiabatic equation V p ΔP + γ PΔV p = 0,

(2.38)

Then

Fig. 2.10 Equivalent physical model of pneumatic pulse-driven drop-on-demand ejection. a Schematic diagram of the ejection device structure. b Equivalent physical model

36

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

ΔP = −γ P

πr 2p ΔV p = −γ P x Vp Vp

(2.39)

where the constant γ can be expressed as γ = c2 ρg /P,

(2.40)

The force on the gas in the tube is F = ΔP A p P = Pγ A2p x/V p ,

(2.41)

The elastic coefficient of the system is S p = ρg c2 A2p /V p ,

(2.42)

According to the acoustic principle, the sound wave damping of a circular tube with a cross-sectional area Ap is Rr = ρg ck 2 A2p /(2π )

(2.43)

The gas mass in the vent pipe is M p = ρg Al ' ,

(2.44)

where l' is the corrected vent tube length considering the sudden change of the air √ inlet, which can be expressed as l ' = L P + 0.8 AP . The differential equation for the pressure change of the air in the vent tube under pulse pressure F can be approximated by a second-order mass-spring-damping system as Mp

d2x dx + Rr + Sx = F dt dt

(2.45)

When the solenoid valve is turned on and off once, it causes air pressure oscillation inside the crucible, resulting in liquid ejection from the nozzle at the cavity bottom. The pressure oscillation frequency in the cavity at this time is 1 ωn = fp = 2π 2π

/

/ Sp 1 = Mp 2π

ρg c2 A2p /V p ρg A p

l'

c = 2π

/

Ap l ' Vp

(2.46)

The pulse width and action time of the pressure fluctuation inside the crucible can be approximately predicted according to the frequency. To deeply analyze the ejection process of metal droplets under pressure fluctuations, the pressure pulse waveform can be measured first. Then the ejection process

2.3 Drop-On-Demand Ejection of Metal Droplets

37

can be modeled and analyzed based on this waveform, as illustrated in the following example. The pressure change curve in the crucible collected by the dynamic pressure sensor is shown in Fig. 2.11, where Ps is the lowest pressure at time t s for the jet to overcome the surface tension at the nozzle orifice. The pressure amplitude rises linearly until it reaches the peak Pp at time t p , after which it decays to negative pressure and gradually becomes zero again. The nozzle is simplified as a cylindrical model with radius d n and length L n (Fig. 2.12). The fluid flow in the nozzle under pulse pressure can be approximated as incompressible isothermal Newtonian fluid flow, namely the fluid flow with constant density, viscosity, and temperature. The assumptions of the ejection process are as follows. (1) The radial flow of fluid can be ignored due to the small pressure gradient changes and weak influence of gravity in the radial direction. (2) There is no circulation in the nozzle, i.e., no flow in the θ direction. (3) The metal fluid viscosity is small enough to ignore the influence of viscosity on its motion. The velocity field is u = (ur , uθ , uz ). Fig. 2.11 Typical pressure variation curve. Notes Air pressure is 65 kPa, pulse width is 0.66 ms, and nozzle diameter is 200 μm

Fig. 2.12 Schematic diagram of nozzle cross-section

38

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

The fluid mass conservation equation (namely continuity equation) can be simplified as ∂u z =0 ∂z

(2.47)

where uz is the z-direction velocity of the fluid. The momentum equation in z-direction is 1 ∂P ∂u z =− ∂t ρl ∂z

(2.48)

During metal droplet ejection, the pulse pressure rises from Ps to Pp (peak pressure) as t changes from t s to t p , producing one droplet accordingly. By approximating the pressure rise in the crucible as a linearly increasing function (as shown in Fig. 2.12 inlet pressure conditions), the length of fluid ejected from the nozzle at time t can be calculated as ( ) { ts2 t2 1 Pp t 3 − ts + t + c3 L j (t) = u(t)dt ⇒ s(t) = (2.49) ρl L n t p 6 2 2 where L n is the nozzle thickness. At the moment of t s , the jet starts to eject with its length L j (t s ) as zero. While at time t p , the jet reaches its maximum length as ( ) L jmax = L j t p =

)3 1 Pp ( t p − ts 6ρl L n t p

(2.50)

Assuming that the jet breaks at this moment and the broken liquid forms a droplet under surface tension, the droplet diameter can be calculated by (

dj π 2

)2 L jmax

( )3 Dd 4 = π 3 2

(2.51)

The above equations can be used to predict the diameter of metal droplets, the maximum length of jet breakup, and the maximum velocity of jet movement.

2.3.2 Theory of Piezoelectric Pulse-Driven Drop-On-Demand Ejection The radial contraction of a piezoelectric tube causes the glass tube inside it to vibrate, creating a pulse pressure to eject the internal fluid from the nozzle to form droplets, as shown in Figs. 2.13a and 1.3. Bogy [10] studied the propagation and reflection of

2.3 Drop-On-Demand Ejection of Metal Droplets

39

Fig. 2.13 Schematic diagram of pressure wave propagation in the cavity of a radial piezoelectric pulse-driven drop-on-demand ejection device [10]

the pressure wave in the liquid inside the glass tube. His research pointed out that the propagating pressure wave is reflected in an opposite phase when it meets the free surface in liquid, that is, it changes from a compression wave to a tensile wave (and vice versa). While the pressure wave is directly reflected when it meets the closed wall; namely, it returns directly without changes in pressure wave amplitude and properties. According to the above theory, the glass tube tail in a radial piezoelectric print-head is a free liquid surface, while the nozzle end of that can be regarded as a closed wall. The pressure wave propagation process in the glass tube is shown in Fig. 2.13b–g. At the moment of Fig. 2.13b, the piezoelectric tube in a state of compression expands and generates a tensile wave in the fluid. The tensile wave is transmitted to both sides of the glass tube (Fig. 2.13c). As shown in Fig. 2.13d, the tensile wave turns to a compression wave and returns at the glass tube tail (free liquid surface), while it returns originally at the nozzle end (closed wall surface). For Fig. 2.13e, the pulse signal is reloaded to contract the piezoelectric tube and form a compression wave inside the glass tube. This compression wave is superimposed with that returning from the tail end to form a local high pressure (Fig. 2.13f). Then it is transferred to the nozzle end to promote the liquid metal ejection from the nozzle to form molten metal microdroplets (Fig. 2.13g). To achieve the compression stress wave superposition in Fig. 2.13e, the piezoelectric tube should be located in the middle part of the glass tube. At the same time, the response of tubular piezoelectric ceramics must be at the nanosecond level to achieve fast pressure loading. When the above conditions are satisfied, the relationship between the pressure pulse width τ loaded on the piezoelectric tube, the speed

40

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

of pressure wave propagation c in the molten metal, and the length of the glass tube l glass is τ = l glass /c

(2.52)

2.3.3 Model of Stress Wave-Driven Drop-On-Demand Ejection The collision of impacting rod and vibration transferring rod produces a stress wave, which can drive the fluid out of the micro-nozzle to generate microdroplets. The principle is shown in Fig. 1.4. This process can be divided into two steps. Firstly, the impact rod and vibration transferring rod collide with each other to form a solid internal stress wave. Secondly, the stress wave is transferred to the fluid at the bottom end of the vibration transferring rod, which pushes the fluid out to form microdroplets (Fig. 2.14). The detailed processes are as follows. (1) The impacting rod is the same as the vibration transferring rod in diameter, but shorter in length. The two rods collide with each other (Fig. 2.14a), which generates compressive stress in the finite thin layer at the collision end (Fig. 2.14b). (2) The compressive stress in the two rods propagates along the rod at the sound speed, forming a compressive stress wave after a certain time (Fig. 2.14c). (3) When the compressive stress wave reaches the other free end of the impacting rod or vibration transferring rod, it is reflected as a tensile wave. Since the

Fig. 2.14 Schematic diagram of stress wave formation process [11]

2.4 Dynamics and Thermodynamic Theory of Uniform Metal Droplet …

41

impacting rod is shorter, its internal compression wave is reflected as a tensile wave first and quickly transfers back to the collision area. At this time, the impacting rod is separated from the vibration transferring rod, and the impact process finishes (Fig. 2.14d). (4) The compression wave inside the vibration transferring rod is transmitted to and reflected on the lower free end. At the same time, the stress wave is transferred to the fluid, which forces the liquid metal out of the nozzle to form metal droplets. According to the above analysis, the stress wave amplitude driving the droplet ejection is determined by the magnitude of collision energy of the two rods, while the stress wave width τ is determined by the time of the stress wave back and forth in the impacting rod, namely τ = 2limpact /c.

(2.53)

where l impact is the length of the impinging rod. The stress wave applied to the nozzle can be described by a damped sinusoidal vibration (Fig. 2.14f) as ( Z (t) = Uimpact sin

) πt . τ

(2.54)

where U impact is the impact velocity amplitude of the impacting rod.

2.4 Dynamics and Thermodynamic Theory of Uniform Metal Droplet Flight Process As a metal microdroplet falls, its speed changes due to a combination of gravity and air drag. At the same time, convection and radiation heat transfer occurs between the high-temperature metal droplet and the protective gas, resulting in a dramatic reduction of its thermal energy. This process is influenced by the size, initial velocity, and initial temperature of the metal droplet, and the physical properties of the environmental protective gas. Therefore, clarifying the physical process of uniform metal droplet flight can predict the final morphology of droplet printing, providing an important basis for the parameter selection of metal droplet-based 3D printing, which is discussed in this section.

2.4.1 Flight Dynamics of Metal Droplets To analyze the kinematic process of metal droplets during flight and falling, the following assumptions are made. (1) Droplets are always spherical, that is, the surface

42

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

fluctuation behavior is ignored. (2) The initial droplet velocity is vertically downward. (3) The ambient gas is stationary. (4) The droplet spin motion is ignored. (5) Considering that the ambient gas density is quite small compared with the metal density, the droplet’s additional mass force and Basset force are ignored [12–14]. Based on the above assumptions, droplets are subject to the combined action of gravity and air drag force during flight, which satisfies the following simplified Newton equation of motion 3Cdrag (u d )ρg u 2d du d = g− dt 4Dd ρl

(2.55)

where C drag is the drag coefficient, ud is the droplet velocity. The drag coefficient is only dependent on the dimensionless Reynolds number Reg (Reg = ρ g ud Dd /μg ) under the condition of metal droplet deposition. The standard drag coefficient function is [15]

Cdrag (u) =

} | | | | | | ⎨

24 , Reg 24 , Re0.646 g

0 < Reg < 1 0 < Reg < 400

0.5, 400 < Reg < 3 × 105 | | 0.428 −4 | | 3.66 × 10 Reg , 3 × 105 < Reg < 2 × 106 | | ⎩ 0.18, 2 × 106 < Reg

(2.56)

Starting from the moment of droplet ejection from the nozzle, the relationship between the droplet flight distance and flight time is {t Ld =

u d dt

(2.57)

0

2.4.2 Temperature History of Metal Droplets During Flight During their flight, the uniform metal droplets experience cooling in the liquid state, solidification, and cooling in the solid state. When the metal droplet diameter is less than 300 μm, the temperature gradient inside the droplet is much smaller than the temperature difference between the droplet and the ambient gas, which can thus be ignored. The lumped-parameter analysis method [16] is used to analyze the temperature change of the droplet during cooling. In this method, the metal droplet is regarded as a particle, inside which the temperature distribution is uniform and changes with time. The temperature change of the droplet during deposition is Td = f (t)

(2.58)

2.4 Dynamics and Thermodynamic Theory of Uniform Metal Droplet …

43

Fig. 2.15 Schematic of solidification of different liquid metals. a Solidification of pure metal. b Solidification of a binary alloy

Generally, the cooling process of pure metal droplets includes four thermodynamic stages [17]: (I) cooling in the liquid state, (II) recalescence, (III) heat transfercontrolled solidification, and (IV) cooling in the solid state, as shown in Fig. 2.15a. In contrast, the solidification process of alloys is relatively complex, including (I) cooling in the liquid state, (II) recalescence, (III) first-stage segregated solidification, (IV) peritectic transformation, (V) second-stage segregated solidification, and (VI) cooling in the solid state (Fig. 2.15b). Similar to the pure metal cooling process, the heat transfer controlled cooling stage consists of several segregated solidification stages [18]. To facilitate the analysis of the temperature history and physical state of droplets during flight, the following assumptions are made. (1) The degree of undercooling in the solidification of metal droplets is ignored, that is, when droplets are cooled to their solidification temperature, the temperature remains unchanged until they are completely solidified. Studies on droplet undercooling [19] show that a droplet with a diameter smaller than 200 μm has an obvious undercooling phenomenon during rapid cooling, which means droplet nucleation begins when it reaches a certain temperature below the solidification temperature. However, due to the oxidation effect of trace oxygen in the environment on the surface of metal droplets, heterogeneous nucleation occurs on the surface of metal droplets, reducing the droplet undercooling [20]. For the convenience of calculation, the undercooling during droplet solidification is ignored. (2) The segregated solidification phenomenon of alloys is ignored. (3) The temperature transfer between droplets, the thermal gradient of the ambient medium, and the change in ambient temperature are ignored. (4) There is no fusion in the process of uniform droplet deposition. Under the above assumptions, the cooling process of metal droplets can be represented by the following three stages. (1) Cooling in the liquid state. At this stage, the droplet enthalpy changes due to convection and radiation heat transfer between the droplet and the environment. Neglecting thermal radiation, the thermodynamic equilibrium equation of the droplet can be written as

44

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

| ( ) )| ( 6 h Td − Tg + σs−b ε Td4 − Tg4 dTd =− dt ρl Cl Dd

(2.59)

where T g is the ambient gas temperature, cl is the specific heat capacity of the droplet in liquid state, ρ l is the droplet density, σ s-b is the Stefan-Boltzmann constant, ε is the droplet emissivity, h denotes the convective heat transfer coefficient of the droplet as h=

) kg ( 0.33 2 + 0.6Re0.5 g Prg Dd

(2.60)

where Pr g is the Prandtl number, which is calculated by the following equation Prg = μg cg /k g

(2.61)

where μg , k g , and cg represent the absolute viscosity, thermal conductivity, and specific heat capacity of the gas, respectively. (2) Heat transfer-controlled solidification. When the droplet temperature reaches the solidification temperature, it is assumed that the temperature remains unchanged due to the latent heat of crystallization released by the liquid, leading to the heat balance equation as ) Δh f d fr 6h ( = Td − Tg csl dt csl ρl Dd

(2.62)

where Δhf is the latent heat of crystallization per unit mass of the metal, f r is the solidification fraction of the droplet. f r = 1 denotes the droplet is completely solidified, while f r = 0 means the droplet is completely liquid. The convective heat transfer coefficient h is determined by Eq. (2.60). At this time, the specific heat capacity is that of the liquid–solid state, which can be expressed as csl = cs f + cl (1 − f )

(2.63)

At this stage, the heat released by the droplet from the latent heat of crystallization (left side of Eq. (2.62)) is balanced with the heat transmitted to the air (right side of Eq. (2.62)), which means the droplet temperature remains constant. The droplet solidification fraction can be calculated by Eq. (2.63). When the solidification fraction of the droplet is 1, it is completely solidified, and the heat conduction-controlled solidification ends. (3) Cooling in the solid state. The solid phase cooling stage begins after the droplet is completely solidified. The calculation equation for the droplet temperature change in this stage is the same as that in the liquid phase cooling stage, where only the liquid specific heat capacity needs to be replaced with the solid one.

2.5 Fundamental Theory for Uniform Metal Droplet Deposition

45

2.5 Fundamental Theory for Uniform Metal Droplet Deposition 2.5.1 Non-Dimensional Analysis of Metal Droplet Impact Behavior Molten metal droplets go through impact, spread, bounce/deposit on the substrate or the pre-deposited droplets in the deposition process, which is a complex coupling process of droplet deformation, heat transfer, and solidification. Currently, there is no mature theoretical system to accurately describe metal droplets’ deposition and impact behavior, which is usually described qualitatively by some dimensionless parameters. Table 2.1 shows the dimensionless parameters describing the deposition and impact process of metal droplets. Among them, Oh is defined as the ratio of viscous force to surface tension force, characterizing the proportion of fluid viscosity to its surface tension during droplet deformation; We is appointed as the ratio of local inertial force to surface tension force, which is used to characterize the proportion of local element inertial force during droplet spreading; Stefan number is a dimensionless number representing the difference between the substrate temperature and the melting point of metal droplets; Prandtl number is the ratio of momentum diffusivity to thermal diffusivity; τ osc is the droplet oscillation time scale, which is used to describe the time magnitude of droplet oscillation; τ sol is the solidification time scale, which is used to describe the time magnitude of droplet solidification. According to the Oh and We numbers during droplet impact, the impact and spreading of droplets under unsolidified conditions can be divided into four deposition types: inviscid impact-driven deformation region, highly viscous impactdriven deformation region, inviscid capillarity-driven deformation region, and highly Table 2.1 Dimensionless parameters during the deposition and impact of metal droplets

Dimensionless parameters

Expressions

Ohnesorge number

Oh =

√ μl ρl σ Dd

Weber number

We =

ρl u 2d Dd σ

Stefan number

Ste =

cl (Tm −Tg ) Δh

Superheat

( ) βsuper = (Td − Tm )/ Tm − Tg

Prandtl number

Pr d =

Oscillation time scale

τosc =

Solidification time scale

τsol =

μl cl kd

/

ρl Dd3 σ

Dd2 ( 1 4α Ste

+ βsuper

)

Notes Δh is the latent heat of fusion; T m is the melting point of the droplet; k d is the thermal conductivity of the droplet; α is the thermal diffusivity

46

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

Fig. 2.16 Four different regions characterizing the droplet deposition behavior under different Oh and We

viscous capillarity-driven deformation region (Fig. 2.16). Various typical time scales in each zone are shown in Fig. 2.16 [21]. Region I (inviscid, impact-driven). In this region, droplet spreading is driven by the pressure of impact and resisted primarily by fluid inertia. Droplet diameter and impact velocity control the time scales of the short droplet spreading process, where viscous effects are weak. Droplet spreading is followed by a long period of underdamped oscillation, which is gradually stopped due to the fluid viscous effects. Region II (inviscid, capillarity-driven). Impact velocity effects in this process are negligible. Most of the spreading is driven by the unbalanced capillarity force near the contact line and resisted by inertia. In this region, the droplet impact velocity has little effect on its final spreading. Droplet spreading is accompanied by interfacial oscillations with a time scale of the same order as the spreading timescale. The radial spreading inertial force in this region is balanced by the pressure difference caused by the capillary force. Region III (highly viscous, capillarity-driven). Droplet spreading is driven by the unbalanced capillarity forces on both sides of the contact line, and resisted by viscosity. Impact velocity has a negligible effect. At the same time, the droplet surface is overdamped under the action of high viscosity, i.e., its surface oscillation is almost imperceptible. The pressure difference due to capillary force is balanced by fluid viscous force. Region IV (highly viscous, impact-driven). Droplet spreading is driven by the dynamic pressure of impact and resisted by viscous shear. The capillary force is negligible. Oscillations are absent on the droplet surface. Radial pressure due to impact is balanced by the viscous resistance.

2.5.2 Non-Isothermal Impact and Spreading Behaviors of Metal Droplets Compared with other droplets (water, alcohol, etc.), metal droplets exhibit two major differences in the deposition and impact process: (1) crystallization and solidification

2.5 Fundamental Theory for Uniform Metal Droplet Deposition

47

occur, and (2) local solidifications determine the morphology. Under non-isothermal conditions, the impact process of metal droplets includes four stages, namely motion, spreading, recoil or oscillation, and solidification [22], as shown in Fig. 2.17. (1) The morphology changes in the droplet motion stage (Fig. 2.17a) and spreading stage (Fig. 2.17b) are similar to that of ordinary droplets. At low We, the spreading of metal droplets with low viscosity is dominated by their capillary forces and balanced by the fluid inertial forces. While for high We, the spreading of droplets with high viscosity is dominated by the impact pressure and balanced by the fluid inertial forces.

Fig. 2.17 Schematic diagram of the deformation and solidification process of molten metal droplets. a Motion stage. b Spreading stage. c Recoil or oscillation stage. d Solidification stage

48

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

(2) If the heat and kinetic energy of the metal droplet are large enough, the droplet may retract and recoil due to incomplete depletion of kinetic energy (Fig. 2.17c). (3) If the kinetic energy is insufficient to realize droplet bouncing, it enters the oscillation solidification stage (Fig. 2.17c), during which the solidified layer keeps growing upward. Since the solidified layer is combined with the deposition substrate, the oscillation occurs only in the unsolidified area above the solidified layer until its complete solidification (Fig. 2.17d). To achieve accurate printing of metal parts, firstly, it is necessary to avoid the recoil phenomenon and lead to only equilibrium oscillation of metal droplets during deposition. The threshold of metal droplet bouncing can be analyzed by energy conservation. Secondly, the post-solidification morphology of droplets is a fundamental parameter for forming parts. The geometry morphology and its influencing factors of the droplet after impact are further analyzed below. (1) Initial moment before impact. The total energy at the initial moment before impact is the sum of the kinetic energy (KE1 ) and surface energy (SE1 ) of the droplet, which are ( KE1 =

)( π 3) 1 2 ρl u d D 2 6 d

(2.64)

S E 1 = π Dd2 σ

(2.65)

(2) Maximum spreading state. When the droplet reaches the maximum spreading radius Dmax , the kinetic energy is zero, and the surface energy (SE2 ) is 2 SE2 = π Dmax σ (1 − cos αd )

(2.66)

where ad is the droplet advancing contact angle. The deformation energy loss (W 2 ) due to viscosity is W2 =

1 π 2 ρl u 2d Dd Dmax √ 3 Re

(2.67)

Droplet solidification stops its spreading, at which time the kinetic energy in the solidified layer is lost. If the solidified layer has average thickness sd and diameter d s when the droplet is at its maximum extension, then the loss of kinetic energy (ΔKE2 ) is ΔKE2 =

(π 4

ds2 sd

)( 1 2

) ρd u 2d

(2.68)

From the conservation of energy, we get KE1 + SE1 = SE2 + W2 + ΔKE2

(2.69)

2.5 Fundamental Theory for Uniform Metal Droplet Deposition

49

Then the maximum spreading factor is Dmax = Dd

/ 3 Wesd∗ 8

We + 12 + 3(1 − cos αd ) + 4 √We Re

(2.70)

where sd * is the dimensionless solidified layer thickness (sd * = sd /Dd ). Poirier et al. [23] derived the solidification layer thickness sd * as a function of Stefan number and Peclet number based on a one-dimensional heat conduction model without thermal resistance: / t ∗ γs 2 sd∗ = √ Ste (2.71) Peγ1 π where Pe = u d Dd /α,

(2.72)

γs,l = ks,l ρs,l cs,l

(2.73)

Then the maximum spreading factor is | | Dmax | / =| Dd We · Ste

We + 12 3γs 2π Peγ1

+ 3(1 − cos αd ) + 4 √We Re

(2.74)

The three terms in the denominator of the right-hand side of Eq. (2.74) represent the effects of solidification, surface tension, and viscous dissipation on spreading, respectively. The second term is √ negligible ) to the other ( compared √ two terms. If the solidification constant Φ = γs /γ1 Ste/ Prd < 1, solidification effects on spreading can be neglected. With the increase of impact velocity, the spreading radius becomes larger, and the effect of solidification on spreading becomes more pronounced. (3) Maximum retraction state. If the droplet is not solidified after its maximum spreading state, the surface tension drives the liquid droplet to retract. When the droplet retraction reaches the highest position (i.e., the maximum retraction state), the retracted molten droplet is in the shape of an inverted water droplet (Fig. 2.18). At this time, the kinetic energy of the droplet is zero, and the total energy includes the potential energy (PE3 ) and surface energy (SE3 ), i.e., {hr PE3 = πρl g

yx 2 dz 0

(2.75)

50

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

Fig. 2.18 Schematic diagram of the droplet shape and size in the maximum retraction state

⎡h / ⎤ ( )2 {r 1 d x dz − Dr2 cos αr ⎦ SE3 = 2π σ ⎣ x 1 + dy 8

(2.76)

0

where x = f(z) defines the droplet profile at this time; hr and Dr are the droplet height and its contact diameter with the deposition substrate in the maximum retraction state, respectively; ar is the receding contact angle. (4) Recoil state. When the droplet retracts until the bottom diameter Dr becomes zero, the liquid column breaks away from the substrate under surface tension, leading to the droplet bouncing. It is assumed that the droplet becomes a sphere at the instant of detachment from the substrate, its surface energy (SE4 ), kinetic energy (KE4 ), and potential energy (PE4 ) are, respectively SE4 = SE1 = π Dd2 σ 1 πρl Dd3 KE4 = 12

(2.77)

{h cb u cb dz

(2.78)

0

1 PE4 = πρl Dd3 gh cb , 6

(2.79)

where ucb is the droplet recoil velocity, hcb is the recoil height. (5) Equilibrium oscillation state. If the droplet does not bounce after retraction, but gradually consumes its energy on the substrate to reach an equilibrium state after repeated oscillation. Then the kinetic energy is zero and the potential energy is negligible, leading to the total energy as the surface energy (SEequ ), namely

2.5 Fundamental Theory for Uniform Metal Droplet Deposition

SEequ =

51

( ) 2 π 2 Dequ − cos αv σ 4 1 + cos αv

(2.80)

where av is the equilibrium contact angle, Dequ is the equilibrium spreading diameter of the droplet, which is | Dequ = Dd

4 sin αv tan2 (αv /2)(2 + cos αv )

|1/3 (2.81)

Substituting Eq. (2.81) into Eq. (2.80), the surface energy at the equilibrium state can be obtained as SEequ

| | |1/3 | 4 sin αv 2 π 2 − cos αv = σ Dd 4 tan2 (αv /2)(2 + cos αv ) 1 + cos αv

(2.82)

From the above equation, it is clear that the equilibrium surface energy is determined by the initial droplet diameter and its wetting effect on the solid surface. However, for metal droplets, the oscillation energy would eventually be dissipated due to solidification. According to the law of energy conservation, the droplet total energy before and after the impact is equal, namely KEi + SEi = SEm + Wd + ΔKEs

(2.83)

where SEm is the droplet surface energy, W d is the work done against viscosity, ΔKEs is the kinetic energy loss. The energy is normalized as follows )−1 ( We 4 SEm Wes∗d + = 1+ √ SEi + KEi 8(1 − cos αv ) 3 (1 − cos αv ) Re ( √ )−1 Re Wd 3 3√ − cos α ) (1 v = Res∗d + = 1+ SEi + KEi 32 4 We

ψSEm =

(2.84)

ψWd

(2.85)

ψΔKEs

( )−1 ΔKEs 8(1 − cos αv ) 32 1 = = 1+ + √ SEi + KEi Wes∗d 3 Res∗d

(2.86)

Equations (2.84–2.86) show the proportions of residual surface energy, work done against viscosity, and energy loss of solidification layer in the total energy of the droplet after impact, respectively. By comparison, we can determine whether the droplet rebounds or not. For example, when the droplet temperature and substrate temperature are high, the heat transfer behavior at the contact interface slows down, resulting in smaller ψ ΔKEs . In this case, the “pinning” effect of the local solidification

52

2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

Fig. 2.19 Normalized surface energy, work done to overcome viscous resistance, and energy loss due to solidification versus impact velocity

layer becomes weak, and the surface energy ψ SEm increases correspondingly, causing droplet bounce. Figure 2.19 shows the variation of ψ SEm , ψ W d , and ψ ΔKEs with impact velocity. While ψ W d and ψ ΔKEs increase with the increase of impact velocity, ψ SEm and the tendency of droplet bounce gradually decrease. This is because the higher impact velocity accelerates the radial spreading speed of the metal droplets, leading to a shorter heat transfer time at the contact interface. Accordingly, the thickness of the local solidified layer decreases while the spreading area increases obviously. The volume of the local solidified layer shows an increasing trend, which promotes the suppression of the “pinning” effect on bouncing behavior. In the equilibrium oscillation stage, if the metal droplet deposits and spreads without bouncing, and the coupling effect of droplet oscillation and solidification is ignored, the final solidification geometric contour of the metal droplet can be approximated as a spherical cap with a regular shape. It can be characterized by the parameters of contact angle av , maximum bump width W d , bump height hbump , spreading radius Rb , and radius of the crown Rc . Figure 2.20 gives the cross-section calculation models with two different contact angles. During droplet-based bump deposition, a single droplet can be considered as a uniform sphere with a diameter Dd before it is deposited onto the substrate. According to the conservation of mass, the volume of the undeposited spherical droplet is equal to that of the spherical cap after deposition, namely ( )3 || )2 | ( ( ( Dd 4 1 | π) π) π + Rc 3Rb2 + Rc sin αv − + Rc = π Rc sin αv − 3 2 6 2 2 (2.87)

2.5 Fundamental Theory for Uniform Metal Droplet Deposition

53

Fig. 2.20 Definition of geometric profile parameters of the solidified spherical cap-shaped metal droplet bumps. a av < 90°. b av > 90°

The relationship of parameters in the bump deposition contour can be expressed by Eqs. (2.88–2.90) [24], which can be used for the preliminary selection of the droplet scanning step. ( ) 13 4(sin αv )3 1 Dd 2 (1 − cos αv )2 (2 + cos αv )

(2.88)

( ) 13 4 1 R c = Dd 2 (1 − cos αv )2 (2 + cos αv )

(2.89)

Rb =

| Ds = 2Rb = Dd sin αv

4 (1 − cos αv )2 (2 + cos αv )

| 13

, 0◦ < αv ≤ 90◦

(2.90)

This chapter summarizes the relevant fundamental theories and computational models involved in the ejection, flight, impact, and solidification processes of uniform metal droplets. These theoretical models can be used to solve or estimate the related behaviors of the metal droplet-based 3D printing process. However, it is noteworthy that the molten metal is also affected by such factors as molten metal oxidation, wetting between molten metal and nozzle wall, wetting and spreading between molten metal and substrate, surface roughness of the substrate, and alloy composition segregation in the process of spraying and printing. The models established so far cannot accurately describe the complex behavior involved in the metal droplet ejection and deposition process, which needs to be further studied by combining the basic theories of metal solidification, fluid mechanics, heat transfer, and welding metallurgy.

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2 Fundamental Theory of Uniform Metal Droplet Ejection and Deposition

References 1. McCuan J. Retardation of Plateau-Rayleigh instability: a distinguishing characteristic among perfectly wetting fluids. ArXiv Preprint Math. 1997;30:970–1214. 2. Rayleigh L. On the instability of jets. Proc Lond Math Soc. 1878;1(1):4–13. 3. Schweitzer PH. Mechanism of disintegration of liquid jets. J Appl Phys. 1937;8(8):513–21. 4. Tseng AA, Lee MH, Zhao B. Design and operation of a droplet deposition system for freeform fabrication of metal parts. J Eng Mater Technol Trans ASME. 2001;123:74–84. 5. Li L. Theoretical modeling and numerical simulation of uniform droplet spray process. Master Thesis. 2006. pp. 1–6 6. Suzuki M, Asano K. A mathematical model of droplet charging in ink-jet printers. J Phys D Appl Phys. 1979;12:529–37. 7. Luo J, Qi LH, Yang F, Li L, Jiang XS. Modeling of droplet charging in droplet spray process. Acta Aeronautica Et Astronautica Sinica. 2007;28:217–21. 8. Brandenberger H, Nussli D, Piech V, et al. Monodisperse particle production: a method to prevent drop coalescence using electrostatic forces. J Electrostat. 1999;45:227–38. 9. Raichel DR The science and applications of acoustics[M]. Springer Science & Business Media; 2006. 10. Bogy DB, Talke FE. Experimental and theoretical study of wave propagation phenomena in drop-on-demand ink jet devices. IBM J Res Dev. 1984;28(3):314–21. 11. Luo J, Qi L, Tao Y, et al. Impact-driven ejection of micro metal droplets on-demand. Int J Mach Tools Manuf. 2016;106:67–74. 12. Holländer W, Zaripov SK. Hydrodynamically interacting droplets at small Reynolds numbers. Int J Multiph Flow. 2005;31(1):53–68. 13. You CF, Qi HY, Xu XC. Research progress and application analysis of Basset force. Chin J Appl Mech. 2022;2(19):31–3. 14. Vojir DJ, Michaelides EE. Effect of the history term on the motion of rigid spheres in a viscous fluid. Int J Multiph Flow. 1994;20(3):547–56. 15. Liu H, Rangel RH, Lavernie EJ. Modeling of droplet-gas interactions in spray atomization of Ta-2.5 W alloy. Mater Sci Eng A. 1995;191(1):171–184. 16. Zhao ZN. Heat transfer. Beijing: Higher Education Press; 2002. p. 123–31. 17. Li HP, Tsakiropoulos P. Droplet dynamic and solidification progress during rotating disk centrifugal atomization. Chin J Nonferrous Metals. 2006;16:793–9. 18. Bergmann D, Frtsching U, Bauckhage K. A mathematical model for cooling and rapid solidification of molten metal droplets. Int J Thermal Sci. 2000;39:53–62. 19. Clyne TW. Numerical treament of rapid solidification. Metall Mater Trans B. 1984; 15B:369– 381. 20. Li Y, Wu P, Ando T. Continuous cooling transformation diagrams for the heterogeneous nucleation of Sn-5 mass% Pb droplets catalyzed by surface oxidation. Mater Sci Eng, A. 2006;419:32–8. 21. Schiaffino S, Sonin A. Molten droplet deposition and solidification at low Weber numbers. Phys Fluids (1994-present). 1997;9(11):3172–3187. 22. Aziz SD, Chandra S. Impact, recoil and splashing of molten metal droplets. Int J Heat Mass Transf. 2000;43(16):2841–57. 23. Poirier DR, Poirier EJ. Heat transfer fundamentals for metal casting: 2nd minerals, metals and materials society, Warrendale, Pennsylvania, USA, 1994. 24. Qi L, Chao Y, Luo J, et al. A novel selection method of scanning step for fabricating metal components based on micro-droplet deposition manufacture. Int J Mach Tools Manuf. 2012;56:50–8.

Chapter 3

Devices and Equipment for Uniform Droplet Ejection

3.1 Introduction Controllable ejection of uniform metal droplets is a prerequisite for metal dropletbased 3D printing. However, due to the high temperature of molten metals and the strong corrosivity of some liquid metals, designing devices that produce the critical requirements for metal droplet ejection is a standing challenge in metal dropletbased 3D printing. This chapter discusses metal droplet ejection devices and testing platforms for different application fields developed by our group in recent years. The devices and platforms discussed include the continuous droplet trains ejection device, the pneumatic drop-on-demand ejection device, the piezoelectric drop-ondemand ejection device, the stress wave-driven drop-on-demand ejection device, the controlling system of metal droplet ejection and deposition, and the key-parameter acquisition system. This chapter specifies the application range of developed metal droplet-based 3D printing devices and platforms, laying a foundation for selecting and designing metal-based printing equipment in multiple application fields.

3.2 Brief Introduction of Equipment for Uniform Metal Droplet Ejection Uniform metal droplet ejection is affected by several parameters such as the excitation waveform, the melting temperature, the ejection pressure, the nozzle diameter, and their coupling interaction. Therefore, the experimental equipment has the following main functions: (1) Heating and melting metal materials. The equipment can melt metals for ejection. It can heat the crucible to an elevated temperature and keep the temperature stable during the metal droplet ejection process. (2) Controllable ejection of tiny metal droplets. For the continuous uniform droplet stream ejection, small mechanical vibrations are applied to break the laminar © National Defense Industry Press 2023 L. Qi et al., Metal Micro-Droplet Based 3D Printing Technology, https://doi.org/10.1007/978-981-99-0965-0_3

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jet in the Rayleigh instability mode and produce uniform metal droplets. For the drop-on-demand ejection, a vibration pulse is applied to eject a certain volume of metal fluid from the nozzle and form uniform metal droplets. (3) Control of uniform droplet deposition position and printing trace. By coordinating the motion of the three-dimensional platform and the ejection process, accurate landing, and smooth movement, the equipment controls the metal droplet deposition position and printing traces. (4) Acquisition of process parameters for the droplet ejection and deposition. To provide a selection basis of experimental parameters for droplet 3D printing, this equipment collects high-speed microscopic images during droplet ejection and deposition, temperature variation during droplet deposition, pressure pulse width, mechanical vibration, etc. (5) Low oxygen protection during metal droplet ejection. The printing environment is filled with inert gas (argon gas) to protect the metal jet and droplets from oxidizing during the ejection process. The schematic diagram of the uniform metal droplet ejection equipment which was designed and developed according to the above-mentioned overall functions is shown in Fig. 3.1. The modules with dashed lines are applied according to the selected driving method. The modules mentioned will be described in detail in the subsequent chapters. Pictures of the equipment are shown in Figs. 3.2, 3.3 and 3.4. The droplet printing equipment for low-melting-point metals (Fig. 3.2) has a maximum operating temperature of up to 600 °C. This equipment is used for printing uniform solder ball arrays, interconnector soldering, etc. The lightweight metal droplet printing equipment (Fig. 3.3) has a maximum operating temperature of 1000 °C. This equipment is used to print metals such as magnesium and aluminum. The droplet printing equipment for high-melting-point metals (Fig. 3.4) has a maximum temperature of 1200 °C. It is used to eject metal droplets with higher melting points like copper, gold, and other high-melting-point metals. The equipment for uniform metal droplet ejection comprises three parts: metal droplet generator, ejection deposition control system, and key-parameter acquisition system. The metal droplet generator consists of a vibration pulse generator, pressure control equipment, a crucible, and a nozzle assembly. According to the different methods for metal droplet ejection, the droplet generator can be sorted into several types, such as continuous droplet stream generator, pneumatic pulse driven generator, piezoelectric vibration pulse driven generator. The generators will be described in detail in subsequent sections of this chapter. The droplet ejection and deposition control system consist of a droplet ejection control subsystem and a droplet deposition control subsystem. The droplet ejection control subsystem is utilized to eject uniform metal droplets and coordinate the droplet ejection process with the substrate motion. This subsystem consists of a droplet ejection control program, a vibration generation module, an air pressure control module, and a temperature control module. Among them, the vibration generation module is only implemented in the uniform droplet spray, piezoelectric driven

3.2 Brief Introduction of Equipment for Uniform Metal Droplet Ejection

57

Fig. 3.1 Schematic diagram of the constituents of the platform for uniform metal droplet ejection

Fig. 3.2 Equipment for uniform solder droplet printing

on-demand, and stress-wave driven on-demand ejection systems. The droplet deposition control system mainly consists of a droplet charging deflection module (only for uniform droplet spray), a motion control module, etc. This subsystem is used to control the droplet deposition position and printing trajectories. The details of

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Fig. 3.3 3D printing equipment for aluminum alloy droplets

this subsystem will be explained in the following chapters. This section only briefly describes the hardware configuration of this subsystem. The parameter acquisition system is employed to acquire the key process parameters in the metal droplet ejection and deposition process. The key process parameters include the mechanical vibration created by the piezoelectric or stress-wave excitation device, the fluctuation of the pneumatic pressure pulse, droplet images in the ejection process, the temperature variation during the droplet deposition process, and the metal particle diameter. The above system is in an inert gas-protected environment. The reason is that the oxidation layer formed on the metal jet surfaces prevents the metal jet from breaking up as the metal jet is ejected into an environment with high oxygen content. Two types of equipment maintain a low oxygen environment: the vacuum chamber and the glove box. (1) Vacuum chamber. The environment can be built by repeatedly vacuuming the chamber and refilling high-purity inertial gas. Because a high-level vacuum system requires expensive chambers and vacuum pumps. this method is costly. In addition, it is not easy to operate the equipment inside the vacuum chamber since it should be sealed to build the high-level vacuum. (2) Glove box. In the glove box, the inertial gas is first filled and then circulated via a circulating purification system. The oxygen in the inert gas is further removed by the oxidation reaction of the copper catalyst. In this way, the oxygen content in the overall environment is maintained at a low level. Since the gas circulation of the glove box does not need a vacuum system, the

3.3 Device for Continuous Uniform Droplet Streams Ejection, Charging, …

59

Fig. 3.4 3D printing equipment for high melting point alloys droplets such as copper and gold droplets

cost is relatively lower than the vacuum system. Additionally, the equipment in the box can be directly operated through rubber gloves, which is very convenient for the experimental operation.

3.3 Device for Continuous Uniform Droplet Streams Ejection, Charging, and Deflection 3.3.1 Device for Ejecting Continuous Uniform Droplet Streams 1. The overall design of the droplet streams ejection device The device for producing continuous uniform droplet streams has a working temperature up to ~ 400 °C. It is mainly utilized to eject low melting point materials such as paraffin wax and lead–tin alloy. The ejection device consists of

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the main body, the crucible and nozzle assembly, the heating furnace, the cooling water case, and the vibration excitation system. The main body of the device is made of stainless steel. The upper part of the device’s main body contains the piezoelectric transducer and positions the vibrating rod. The upper part has a gas inlet to supply the driving pressure. The main body is also packaged with the cooling water case to protect the piezoelectric transducer from the hightemperature crucible. The lower part of the main body is connected to the stainless steel crucible and the nozzle assembly. The ruby nozzle is bonded to the nozzle assembly by the high-temperature ceramic binder. A heating furnace is fixed outside the crucible to melt the metals. The temperature of the metal in the crucible is measured by a thermocouple inserted in the liquid metal and is utilized to feed back the temperature signal to the temperature controlling system. The entire ejection device is installed in the 3D printing equipment through a connecting ring to ensure accurate positioning. The material of the crucible should be able to withstand high temperature and corrosion of molten metals. Stainless steel meets the requirements for ejecting the lead–tin alloy droplets. The upper part of the crucible is connected to the main body via the screw thread to form an enclosure cavity. The lower part is connected to the crucible bottom by the screw thread. The thin graphite sealing ring is used between the crucible and the nozzle assembly to ensure the sealing performance at elevated temperature. 2. Design of Nozzles The nozzle size and the inner shape of the nozzle significantly influences the stable ejection of droplets. Based on the selection of different nozzle sizes and internal geometries, the velocity distribution of the fluid flow inside the nozzle is varied leading to different average jet velocities. Due to the friction on the inner nozzle surface and the viscous force inside the liquid, the fluid velocity is unevenly distributed in the radial direction when the fluid flows out of the nozzle channel: the velocity is slow near the wall and is relatively fast at the center. This process can redistribute the fluid energy and result in jet divergence. Research in the literature illustrate that stable jets are mainly laminar jets, which can be obtained by controlling the Reynolds number, improving the shape of the flow channel, and adopting a smaller flow channel length. The ideal nozzle requires effective energy conversion, that is, effective conversion of the pressure energy into the fluid kinetic energy. In the droplet ejection process, local pressure loss occurs due to the sudden change in the cross-sectional area of the flow channel inside the nozzle, the roughness of the inner nozzle surface, and the viscous friction of the fluid. Assuming the nozzle flow channel is a round pipe, as the fluid in the pipe moves in a laminar flow, the pressure loss along the track can be expressed as [1]: ΔP =

32μl ln u n dn2

(3.1)

3.3 Device for Continuous Uniform Droplet Streams Ejection, Charging, …

61

Fig. 3.5 Schematic diagram of nozzle geometry parameters

where, μl is the fluid viscosity, un is the liquid flow speed, ln is the length of the flow channel, and d n is the diameter of the flow channel. The above equation illustrates that the pressure loss along the nozzle channel is directly proportional to the liquid viscosity, the channel length, and the flow speed. This equation also illustrates that the pressure loss is inversely proportional to the square of the channel diameter. According to the above equation, the pressure loss inside the nozzle can be reduced by the following aspects: (1) Use nozzles with a small aspect ratio channel. (2) Polish the nozzle’s inner surface to reduce the friction between the liquid and the inner channel wall; (3) Design nozzles with a smooth internal transition to reduce the local loss of liquid pressure; (4) Ensure the perpendicularity of the nozzle hole to form symmetrical constrained wetting. However, limited by the existing processing methods, the commonly used nozzle shape is shown in Fig. 3.5. The main parameters of the inner nozzle geometry are the nozzle diameter d n , the nozzle channel length ln , and the nozzle shrinkage angle α n . The aspect ratio of the nozzle channel. The nozzle channel aspect ratio Rn is defined as the ratio of the nozzle channel length ln to the nozzle diameter d n (Rn = ln /d n ). The aspect ratio is a dimensionless number that characterizes the inner geometry of the cylindrical section of nozzles. The state of the jet flow (i.e., laminar, or turbulent) significantly influences the stability of the jetting process. Because of the frictional force on the inner channel surface and the internal viscosity of the fluid, the velocity distribution at different jet sections keeps changing along the flow direction. The section distance L from the inlet a–a to c–c is the initial length of the pipe flow (Fig. 3.6). In the initial section, the uniform velocity distribution in the transitional section is continuously transformed from a uniform distribution into a parabolic one. Then, the pipe flow develops into a complete pipe flow after the length of the initial section. When the aspect ratio of the nozzle channel Rn is large enough, the jet will develop into a complete pipe flow inside the nozzle channel; that is, the “thickness” of the boundary layer reaches the radius and fills the entire nozzle channel. As a result, the

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Fig. 3.6 Schematic diagram of the flow at the inlet section of the round pipe

jet is relatively stable, resulting in a considerable breakup length. On the other hand, when the aspect ratio Rn is less than 1 and the flow inside the nozzle has not yet fully developed, the jet can easily form droplets out of the nozzle [2]. Shrinkage angle. The shrinkage angle α n is the contraction angle of the streamline of the liquid stream (Fig. 3.7a). In this book, the shrinkage angle is defined as the conical angle at the entrance of the nozzle channel. A suitable shrinkage angle can have a converging effect on the jet energy. For 15° < α n < 90°, the change of shrinkage angle does not significantly affect jet flow patterns. However, a small shrinkage angle can form small turbulent areas (Fig. 3.7a) inside the nozzle and a large shrinkage angle creates vortex flows in the recirculation zone of the nozzle channel (Fig. 3.7b). Therefore, finding a proper shrinkage angle is essential to keep the liquid flow stable inside the nozzle channel. Yoshizawa proposed that the optimal value of the shrinkage angle α is approximately 100° at a low flow speed, and this angle is about 30° at a high flow speed. In addition, according to the design criteria of the Venturi flowmeter, the value of α n at high speed can be calculated to be 21°. Whelan [3] demonstrated that nozzles with a large shrinkage angle and a large depth of the nozzle entrance result in a smooth nozzle flow, which can avoid the occurrence of vortices in the fluid recirculation area. For a low flow rate, such nozzles can reduce pressure loss effectively. Therefore, for different ejection conditions, it is necessary to select an appropriate shrinkage angle α n to achieve a stable flow inside the nozzle and reduce the pressure drop inside the nozzle channel. Nozzle channel shape. When the fluid flows through a sudden contraction of the nozzle channel, it produces reverse flow and induces turbulence. Inside vortex flows formed by the backflow creates rotating fluid particles with irregular collisions. Those irregular fluid dynamics not only aggravate the internal friction of the fluid but also cause collisions among fluid particles, resulting in the consumption of the flow energy and causing a great resistance to the fluid flow. A suitable nozzle channel shape can not only effectively avoid vortex flows generated by the sudden contraction of the nozzle channel but also prevent recirculating flow regions formed by the

3.3 Device for Continuous Uniform Droplet Streams Ejection, Charging, …

63

Fig. 3.7 Schematic diagram of the influence of the contraction angle α on the nozzle channel fluid

separation of the boundary layer and the nozzle wall (Fig. 3.8a). In addition, if the liquid flow rate is fast and the liquid pressure is lower than the air separation pressure at the current temperature, cavitation occurs in the recirculating flow region. This degassing process forms bubbles, making the nozzle flow discontinuous. Research by the Korea Institute of Machinery and Materials showed that nozzles with an arc transition shape channel (Fig. 3.8b) [4] could reduce the internal friction of the fluid and avoid the recirculating flow region.

Fig. 3.8 Schematic diagram of nozzle flow path; a The area where the flow path shrinks and pulses; b The nozzle structure with arc transition

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3 Devices and Equipment for Uniform Droplet Ejection

Fig. 3.9 a Schematic diagram of the structure of the nozzle assembly, b picture of the outlet surface of the ruby nozzle

Droplets and jets can be stably ejected by carefully considering the nozzle channel resistance and machinability of nozzles. The shape of the ruby nozzle and its assembly used in this book are shown in Fig. 3.9. 3. Design of Structure of the Piezoelectric Exciter A metal jet breaks into a uniform droplet stream under a specific frequency of external disturbance. This external disturbance is generated by a piezoelectric exciter and is transferred by a solid rod waveguide. The piezoelectric exciter used here is a typical piezoelectric transducer. The alternating driving voltage is converted into mechanical vibration by piezoelectric ceramics according to the inverse piezoelectric effect. This vibration is transmitted to the molten metal via the solid rod waveguide to induce the mechanical vibration for breaking metal jets. This piezoelectric transducer consists of three parts: the sandwich piezoelectric stack, the ultrasonic exponential solid horn, and the rod waveguide. The structure of the piezoelectric transducer is shown in Fig. 3.10. The piezoelectric sandwich stack consists of axially vibrating annular piezoelectric ceramics pre-tightened on an aluminum alloy bottom via a long bolt. The piezoelectric exciter is connected to the crucible top via a flange located at the nodal point of the rod waveguide. The flange and the crucible form a sealed cavity. When the driving voltage is input to the exciter, the vibration amplitude of the piezoelectric ceramic stack can be expressed by Δδ = nd33 U , where d 33 is the piezoelectric strain coefficient, and U is the amplitude of the input voltage. n is the number of annular piezoelectric ceramics. The ultrasonic exponential solid horn is a cone shaft which amplifies the weak mechanical vibration to provide an excitation signal for the jet breakup. The ultrasonic exponential solid horn transfers the vibration via the flange (Fig. 3.10). In the vibration transferring process, the solid rod waveguide is a rod with one fixed end and one free end. The connecting flange is designed between the excitation source and the cone-rod at the nodal point. That means the flange does not vibrate during the vibration transferring process. Assuming both ends of the solid horn are made of the same material, and the cross-section is circular, the amplification factor of the vibration amplitude is [5]:

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65

Fig. 3.10 Schematic diagram of the piezoelectric transducer

( M=

D1 D2

)2

/

(

sin(k1l1 ) 1 +

D1 D2 tan(k1l1 )

)2 (3.2)

By taking the derivation of Eq. (3.2), the maximum amplitude amplification factor of the solid horn can be calculated as: Mmax =

D12 D22

(3.3)

When the resonance frequency of the piezoelectric exciter is f = 15 kHz, the diameters of the cone shaft are D1 = 30 mm and D2 = 100 mm, and the magnification factor of the solid horn M max is 9 according to Eq. (3.3). By taking the initial vibration amplitude of the piezoelectric sandwich stack equal to 4 μm, the velocity and stress inside the solid rod waveguide can be calculated from the vibration velocity equation and boundary conditions shown below [5]: { u(x) = { |T (x)| =

0.377 cos(18.48x) (0 ≤ x < 0.085) −3.93 sin(18.48x − 1.57) (0.085 ≤ x ≤ 0.17)

15 × 106 sin(18.48x) (0 ≤ x < 0.085) 135 × 106 cos(18.48x − 1.57) (0.085 ≤ x ≤ 0.17)

(3.4)

(3.5)

Since the flange does not vibrate, the vibration speed can be zero at this point. According to Eq. (3.5), the stress on the left side of the flange T x=0.085 = 15 MPa and the stress on the right side of the flange T x=0.085+ = 135 MPa (Fig. 3.11). There is a rapid stress change in the sudden change of the cross-sectional area on the rod waveguide. However, the maximum stress is less than the yield strength of 45 steel,

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Fig. 3.11 Vibration velocity and stress distribution in the rod waveguide

meaning that 45 steel can meet the strength requirement. To avoid stress concentration, a round-off transition was adopted at the joint surface to reduce the sudden stress change inside the rod waveguide and improve its life.

3.3.2 Charging and Deflection Device for the Continuous Uniform Droplet Stream Due to the high deposition rate of the uniform metal droplet stream, a charging and deflection device is developed to control the droplet deposition process by selectively charging and deflecting the droplet stream. The droplet charging and deflection device scheme is illustrated in Fig. 3.12. The droplet charging and deflection device mainly consists of a pair of charging electrodes, a pair of deflection electrodes, and the charging control system. In addition, this charging and deflection device needs to be coordinated with the three-dimensional motion platform and the droplet image acquisition subsystem to control the droplet deposition process and measure the droplet deflection process. Charging and deflection electrodes. Those electrodes are mainly used to generate electrostatic fields for the uniform droplet charging and deflection. Figure 3.13 shows the uniform droplet stream generation, charging, and deflection device. Figure 3.14 illustrates the schematic diagram of the charging and deflection electrodes placed directly down the droplet generator. The charging electrodes are a pair of vertical parallel square metal plates insulated with the crucible. They are

3.3 Device for Continuous Uniform Droplet Streams Ejection, Charging, …

67

Fig. 3.12 Schematic diagram of uniform metal droplet stream ejection test platform

both connected to the positive pole of the charging circuit. The negative pole of the charging circuit is connected to the metal crucible and finally connected to the metal melts via the metal crucible. Metal jets should break between the charging plates to charge a certain amount of charge by electrostatic induction. The amount of charge is controlled by the voltage amplitude, which is modulated and output by the charging circuit. Deflection electrodes are placed under the charging electrodes. They are a pair of parallel metal plates connected to the positive and negative poles of a 4000 V DC voltage source, respectively. A deflection field is formed between the parallel metal plates. A low-power high-voltage electrostatic generation module generates the high voltage for deflection. The strength of the electrostatic field can be regulated by adjusting the electrode spacing. When charged metal droplets pass through the deflection electrode, it is deflected laterally by the Lorentz force. Charging control system. The uniform droplet charging control system is mainly utilized to generate droplet charging voltage. The charging data can be set according to the test requirements to modulate the charging voltage waveform (shown by the square wave on the left side of Fig. 3.14). The principal diagram of the charging voltage modulation circuit is shown in Fig. 3.15, which mainly includes a charging data processing module and a pulse generation module. The former module consists of a Microprogrammed Control Unit (MCU) chip and a Complex Programmable Logic Device (CPLD) chip. The pulse generation module consists of a D/A conversion chip and a signal amplifier. This circuit generates a series of voltage pulses for charging each metal droplet.

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Fig. 3.13 Device for uniform droplet stream ejection with the charging and deflection electrodes

Fig. 3.14 Schematic diagram of the charging and deflection electrodes

In this circuit, the charging data processing module receives, stores, and sends charging data. The working principle is as follows: The charging data (8-bit binary data, the value of which determines the charging pulse amplitude) is first calibrated according to the standard voltage. Then those data are transferred to the MCU through a serial port and stored in the MCU’s memory unit. When droplets are charged, a

3.3 Device for Continuous Uniform Droplet Streams Ejection, Charging, …

69

Fig. 3.15 The principal diagram of the charge voltage modulation circuit

logic code in CPLD accesses the corresponding address in the memory unit, reads the charging data according to the charging sequence, and then sends them to the pulse generation module to generate charging pulses. The frequency of the charging pulse is determined by the frequency of the TTL signal for the droplet production. The logic code presets the charging sequence in CPLD. The pulse generation module converts the charging data received from the MCU into charging voltage pulses. The working principle of this module is: The D/A conversion chip converts 8-bit charging data (in hexadecimal format) into weak analog voltage pulses. Those pulses are amplified by an operational amplifier, turning a high-speed CMOS transistor on and off rapidly. Since the CMOS transistor works in the linear state, the weak analog voltage pulse can control the output voltage amplitude, forming a series of square charging pulses with controllable frequency and the voltage amplitude. The charging data are 8-bit hexadecimal data. The value of those data determines the charging voltage amplitude. The relationship between the data value and the voltage amplitude should be calibrated before operation. As the input data is the maximum data FFH, the maximum output voltage is obtained. In this case, the CMOS transistor is open completely. That means the resistance of this transistor is zero. Therefore, the output terminal grounds, and the output voltage is 0 V. As the charging data is C8H, the CMOS transistor works in the linear working region. A resistance exists in the drain-source junction. The output voltage of 300 V can be obtained. The output voltage is measured as the charging data is inputted sequentially, as shown in Fig. 3.16. There is a linear relationship between the charging data and the output voltage when the charging data ranges from D7H to F5H. The output voltage increases approximately 8 V as the charging data increases 1 bit. The measurement results demonstrate that the transistor has good linearity in this range and the resolution of the output voltage is 8 V. As the charging data increases from C2H to D7H, the output voltage does not increase linearly with the increasing charging data. Therefore, it is more convenient to use the charging data inside the linear region for determining the charging voltage.

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Fig. 3.16 Relationship between D/A input data and charging voltage

3.4 Design and Implementation of the Pneumatic Pulse-Driven Drop-On-Demand (DOD) Droplet Ejection System 3.4.1 Pneumatic Pulse-Driven DOD Droplet Generator for Tin Solder 1. Design of pneumatic pulse-driven DOD droplet generator for tin solder The picture of the pneumatic drop-on-demand tin solder droplet generator is shown in Fig. 3.17. The working temperature is around 400 °C. The main components of the droplet generator are the vent valve, the solenoid valve, the T-joint, the crucible (Fig. 3.18a), the resistance furnace, etc. The crucible inside the resistance furnace is used to melt the metal. The small nozzle is assembled at the crucible bottom to eject micro metal droplets. The upper section of the crucible is equipped with a T-joint. One end of the T-joint is connected to the crucible top to form a resonance cavity. The other end of the T-joint opens to the atmosphere via a vent valve. The center end of the T-joint is connected to the gas source through the solenoid valve. The solenoid valve is opened and stopped quickly by the droplet ejection signal to form a pressure pulse. Driven by this pressure pulse, metal droplets can be formed by ejecting the molten metal liquid through the small nozzle. 2. Design of Crucible and Orifice Since the pressure pulse is not very strong, a crucible with a smooth cone-shaped bottom is utilized to concentrate the applied pressure. In this book, such a crucible is made from a quartz glass tube with a streamlined cone-shaped end (Fig. 3.18a). First, a quartz tube is pulled aside to form a closed cone-shaped lot while heating its center by a high-temperature acetylene flame. During this process, the coneshaped end’s axis strictly coincides with the crucible axis when the tube is being

3.4 Design and Implementation of the Pneumatic Pulse-Driven …

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Fig. 3.17 Picture of the pneumatic pulse-driven DOD droplet generator for tin solder [6]

drawn. Then, the close end is grinded, polished, and burned to form a small orifice. In this way, a quartz glass crucible with a high-quality orifice at its bottom can be obtained. Figure 3.18b shows the profile of the crucible bottom, which is a smooth streamlined shape. Figure 3.18c demonstrates the appearance of the end surface. A complete round nozzle outlet can be observed. The crucible and the orifice should be cleaned after the orifice is manufactured (i.e., grinded, burned, and polished). The impurities inside the crucible’s inner surface and the orifice should be carefully removed to ensure the stable ejection of metal droplets. The cleaning process consists of: (1) Washing the crucible cavity and orifice by using anhydrous ethanol. (2) Cleaning the inner and outer walls of the crucible by using a mixture of hydrochloric acid and distilled water. (3) Ultrasonically cleaning the orifice soaked into the anhydrous ethanol to remove the residual impurities on the inner surface and the orifice surface. (4) Drying the crucible to avoid cracking of the glass crucible caused by moisture residues.

3.4.2 Pneumatic Pulse-Driven DOD Droplet Generator for Aluminum Alloy 1. Design of the DOD droplet generator

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Fig. 3.18 Side views of a the crucible, b the cone shape bottom and the orifice. c Bottom view of the crucible end surface [7]

Since the pneumatic DOD droplet generator is driven by pressure pulses and there is no mechanical actuator inside the crucible, the generator works at a high working temperature. A DOD droplet generator is designed according to the solder droplet generator mentioned in the last section. The schematic diagram is illustrated in Fig. 3.19a. The working temperature can be up to 1200 °C. The crucible and the orifice plate for ejecting aluminum droplets are made of high purity graphite and are connected to the connecting plate by a flange. The upper part of the connecting plate is assembled with a vent pipe and a sheathed thermocouple. The vent pipe is similar to the T-joint used in the solder droplet generator. One end of the T-joint is connected to the connecting plate. The other end is connected to the gas source via a solenoid valve. A pressure gauge is installed on the vent pipe to measure the pressure fluctuation inside the crucible (see Sect. 3.7 for details). Figure 3.19b shows the picture of the aluminum droplet generator. The uniform droplet generator is mounted inside the induction furnace and is fixed inside the oxygen-free glove box via a connecting plate. A water-cooling case is located on the top of connecting plate. For ejecting metal droplets, the cooling water is first pumped into the cooling case and keeps circulating during operation. Then, the induction furnace is turned on. After the crucible temperature rises to the working

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Fig. 3.19 a Schematic diagram of aluminum droplet generator, b Picture of aluminum DOD droplet generator

temperature, the metal droplet ejection is carried out. As the droplet ejection finishes, the induction furnace is stopped first. Then the cooling water circulation is maintained until the induction furnace’s internal temperature drops to the room temperature. 2. Design of Crucible and Orifice Since the aluminum liquid has strong corrosiveness and is easily oxidized. Aluminum melts can etch the inner surfaces of the crucible and the orifice to form small craters. Meanwhile, oxide impurities are produced to clog the small orifice. Both of the factors above affect the stable ejection of aluminum droplets and disturb the flight trajectory of the metal droplets. Therefore, crucibles and orifices are made of corrosion-resistant materials. Simultaneously, the whole system should work in an oxygen-free environment. In this book, the crucible and orifice are made of high pure graphite to meet the corrosivity resistance requirements and induction heating requirements. The crucible consists of several parts, shown in Fig. 3.20. The upper section of the crucible is a necked section to form a pneumatic resonant cavity. The cavity volume can be changed by varying the length and the inner diameter of the neck section. The resonant frequency of the pressure fluctuation can be changed by varying the cavity dimension to analyze the characteristic of the metal droplet ejection. A thermal insulation material is fixed outside the necking section to enhance the thermal insulation. The lower section of the crucible is the melting section, which joins the orifice plate with a graphite nut at the bottom. The graphite paper ring is placed between the orifice plate and the crucible to achieve a tight seal to prevent molten metal leakage. According to the basic requirements of nozzle design mentioned in Sect. 3.3.1, the orifice plate is also made of high purity graphite to meet the corrosion resistance requirement of aluminum alloy liquids. The inner surface of the orifice plate tightly contacts with the crucible bottom for sealing.

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Fig. 3.20 Graphite crucible

The picture of the processed orifice is shown in Fig. 3.21. Because the orifice has a burr outlet after being machined, it needs to be post-processed by grinding and polishing. A water jet is always utilized to wash the orifice and remove impurities and the burr on the orifice’s inner wall or outlet surface. Figure 3.21 demonstrates that, after being polished, there is no residue inside the orifice. The orifice outlet has a clear and regular circle shape, which is suitable for the stable ejection of uniform aluminum droplets.

(a) Before processing

(b) During processing

(c) After processing

Fig. 3.21 Comparison of the orifice outlet (upper) and the orifice inlet (lower) before and after the post treatment

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3.5 Piezoelectric Pulse-Driven DOD Droplet Generator The main body of the piezoelectric pulse-driven DOD droplet generator is an ejection cavity made by a capillary glass tube. The capillary nozzle is at one end of this tube, and the other end connects to the metal liquid reservoir. The liquid metal fills the ejection cavity and the capillary nozzle by back pressure. A piezoelectric sleeve is glued outside the capillary tube. The capillary tube and the piezoelectric sleeve are both located inside the protected shell. The picture of the DOD droplet generator developed by MicroFab Inc. is shown in Fig. 3.22 [8, 9]. This generator can eject materials like tin solder, polymer, and organic materials. The droplet diameter and velocity are depended on the orifice size, liquid properties, the driven pulse frequency, and the pulse width. Piezoelectric pulse-driven DOD droplet generator for ejecting high-temperature metals is developed in this book (Fig. 3.23). This generator mainly consists of a piezoelectric ceramic actuator, a solid rod waveguide, a cooling water case, a crucible, and an orifice assembly. The piezoelectric ceramic actuator is separated from the high-temperature heating zone by the solid rod waveguide, which transfers the mechanical vibration inside the liquid metal. Induction heating heats the metal droplet generator. The upper section of the generator is a stainless-steel water-cooling case, which protects the temperaturesensitive piezoelectric ceramic actuator. The lower section of the generator is the graphite crucible, the orifice assembly for ejecting high-temperature metal liquid. This generator can eject metal droplets at 1200 °C. The ejected droplets have a diameter close to the orifice diameter. The piezoelectric pulse vibration equipment is the core part of the ejection equipment, which mainly consists of the piezoelectric actuator and the solid rod waveguide. This solid rod is made of ceramic, graphite, or heat-resistant alloy to transfer the Fig. 3.22 Piezoelectric pulse-driven DOD droplet generator developed by MicroFab Inc

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Fig. 3.23 Picture of piezoelectric pulse-driven DOD droplet generator for aluminum droplets

vibration from the piezoelectric actuator to the molten metal and protect the actuator from the high-temperature molten metal. Therefore, the solid rod waveguide should have good high-temperature stiffness, good corrosion resistance, and light weight. Protecting the piezoelectric actuator from the high working temperature is the key point for successfully ejecting metal droplets since the piezoceramic should work at a temperature less than half of its Curie point. The performance of the piezoelectric actuator decreases rapidly as the working temperature exceeds its safe operating temperature. Worse, the failure of the piezoelectric actuator will be caused by piezoceramic depolarization at high temperatures. Therefore, for the generator, multiple heat insulation methods like the cooling water case and the asbestos insulation layer have been used to protect the piezoelectric actuator. The asbestos insulation layer is installed between the crucible and the piezoelectric actuator to minimize the thermal radiation and thermal conductivity from the high-temperature crucible. The cooling water case made of stainless steel maintains the working temperature of the piezoelectric actuator. The crucible and the orifice plate structures are similar to those of the pneumatic solder droplet generator. The difference is that pure graphite is utilized in this generator. The ceramic filter inside the crucible is designed to remove the oxidation and impurities inside the metal liquid and prevent the clog of the small orifice. Since the crucible and the orifice plate easily react with the aluminum liquid and are contaminated with the aluminum oxide, the lower section of the crucible, the orifice plate, and the rod waveguide are designed to be replaceable. Stable droplet ejection can be maintained by replacing all the expendable components.

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3.6 Stress Wave-Driven DOD Droplet Generator The stress wave-driven DOD droplet generator consists of an electromagnetic coil, an impact rod, a solid rod waveguide, a crucible, and an orifice assembly. After applying a current pulse to the coil, the coil generates an electromagnetic pulse to move the impact rod down forwards. After impact, a compressive wave is generated inside the solid rod. This pulsed wave is transferred into the liquid metal for ejecting metal droplets. Since the solid rod insulates the electromagnetic coil from the high-temperature area, the working temperature can be up to 1200 °C. The diameter of droplets produced by this generator is 0.5 ~ 1 times the nozzle diameter. Therefore, the droplet ejection speed can be up to 1 ~ 3 m/s. A distance adjusting mechanism is installed in the upper part of the electromagnetic coil to adjust the impact energy. By using this structure, the moving distance of the impact rod can be controlled by adjusting the impact rod position. In addition, the momentum of the impact rod at impact can be controlled. That is, the stress wave amplitude can be controlled to achieve controllable metal droplet ejection. The impact between the impact rod and the solid rod waveguide can cause the contact areas to deform and abrase after several impact cycles. The contact areas need to be polished to eliminate the instability of the transferred stress wave. In this way, the stable ejection of metal droplets can be ensured.

3.7 Parameter Acquisition and Control System of the Metal Droplet Ejection and Deposition 3.7.1 Control System for Uniform Metal Droplet Ejection and Deposition 1. Temperature Control System Since metals used in 3D printing have different melting points, the heating temperature of the droplet generator is also different. Resistance heating and induction heating are adapted according to the requirements for melting different materials. For lower melting point metals such as lead, tin, tin–lead alloy, and other lead-free solders, the resistance furnace can meet the requirements for droplet ejection. The electrical schematic diagram of the heating system is shown in Fig. 3.24. This system consists of a temperature controller, a thermal couple, a phase shift trigger, a triode AC switch (Triac for short), an electric resistant furnace, etc. The principle of the temperature controller is that the temperature controller outputs a 0 ~ 5 V signal to drive the phase shift trigger. Then, the phase shift trigger sends a series of PWM pulses to trigger the Triac into conduction and control the alternating current, which

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Fig. 3.24 Temperature control circuit

flows through the Triac and the electric furnace. This way the power of the electric resistance furnace can be adjusted. The electric resistance furnace is an inductive device which may generate a current surge when the heating circuit is turned on or switched off. This current surge may destroy the Triac. Therefore, a RC circuit is connected in parallel between two ends of the Triac to protect the Triac and the phase shift trigger, as shown in Fig. 3.24. A thermocouple measures the temperature of the resistance furnace. The measured signal is then transferred into the temperature controller via the temperature compensation wire. The temperature controller calculates the difference between the measured value and the preset value, and the temperature difference outputs to control the phase shift trigger. Meanwhile, the temperature controller outputs a 4 ~ 20 mA current (or a 1 ~ 5 V voltage) to the data acquisition system via an A/D conversion module. Induction heating is generally used for high melting point metals. During heating, a surface current is formed on the surface of the conductive surface of objects under the induction of the inductance coil. The surface current of the conductor produces heat for melting the metals. High purity graphite has good electrical conductivity and good corrosion resistance to metal melts. Therefore, the high purity graphite crucible can eject droplets of active metals like aluminum, magnesium, copper, etc. For an induction heater, the inductance coil size depends on the structure and size of the external furnace body and the internal crucible. This size determines the final inductance, which can be calculated by [10] Li =

ai2 n 2 (μH ) 50(ai + 2bi + 1.3bi ci /ai )

(3.6)

where ai is the average diameter of the induction coil, bi is the coil height, ci is the coil thickness, and n is the number of coil turns (Fig. 3.25). 2. Pressure Control system Constant pressure is applied to the crucible to eject metal jets. When producing a continuous uniform droplet stream, the applied pressure determines the droplet speed. It also determines the optimal disturbance frequency required for the jet

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Fig. 3.25 Structure design of the induction heating furnace

to break into the uniform metal droplets. Therefore, it is essential to adjust and control the applied pressure accurately. When the diameter of the orifice is small, the capillary force of the molten metal inside the orifice becomes apparent. To successfully eject the molten metal from the small orifice, the applied pressure should overcome the surface tension of the molten metal inside the small orifice. That is, the applied pressure needs to meet the following relationship: Δp >

4σ dn

(3.7)

where, Δp is the driving pressure, σ is the liquid surface tension, and d n is the nozzle diameter. For example, the surface tension of pure aluminum molten liquid is about 0.9 N/m. Assuming the nozzle diameter to be 100 μm, the minimum pressure for the metal jet ejection is 36 kPa. If the fluid weight of the crucible does not affect the ejection pressure and the diameter of the nozzle is much smaller than the diameter of the crucible, according to the jet velocity prediction model, the relationship between the applied pressure and the jet velocity can be obtained: Δp = 0.775ρl u 2j

(3.8)

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Fig. 3.26 Schematic diagram of pneumatic control module

The metal jet ejection process is sensitive to the fluctuation of the applied pressure. To improve the accuracy of the pressure regulation, a precision electric proportional valve is utilized to manipulate the applied pressure (measuring range from 0 to 100 kPa) for droplet ejection, as shown in Fig. 3.26. To protect the pneumatic components from contamination, the high-pressure nitrogen gas flows via a gas filter after it comes from the pressure reducing valve. The ejection of jets is controlled by turning on and switching off the solenoid valves 1 and 2. If the pressure is just utilized to generate a small static pressure to maintain the interface position inside the nozzle, the ejection pressure can be controlled by the precision electrical proportional valve. The ejection pressure control subsystem mainly consists of a compressive gas source, a pressure reducing valve, a precision pressure regulation valve, a pressure gauge, PU pipes, etc. After opening the cylinder valve, the inert gas enters the crucible through the pressure reducing valve and the pressure regulation valve sequentially. The precision electrical proportional valve is utilized to adjust the pressure inside the crucible. A digital pressure gauge is installed in the gas circuit to show the pressure value. 3. Printing Trace Control System The printing trace control system consists of an industrial control computer, a motion control card, several servo motors, and their drivers, a three-dimensional motion substrate, etc. The slicing software transfers the printing traces into numerical control codes. Then those codes will be input into the motion control card to control (Fig. 3.27) servo motors, achieving motion in three-axis (in x, y, and z directions). Meanwhile, the motion platform coordinates the metal droplet ejection’s start and stop. Metal droplets are printed on the substrate according to the preset traces.

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Fig. 3.27 Composition of metal microdroplet print track control system

Figure 3.27 shows the schematic diagram of the motion control system, which consists of an industrial personal computer (IPC), a motion controller, an adapter board, three servo drivers, three servo motors, and two optical gratings, and one encoder. The multi-axis motion controller communicates with the IPC through Ethernet and has several digital I/O interfaces for transferring digital signals. The motion controller connects to servo drivers through the adapter board. The adapter board optically isolates the position feedback signal, the limit signal, the alarm signal, the pulse signal, the reset signal, the position comparison signal, and other signals from the motion card to protect its I/O interface. Servo drivers drive motors to move the three-dimensional motion platform in preset traces. The three-axis motion platform’s X, Y, and Z axes are precision motorized linear translation stages. The travel of the X-axis and the Y-axis is 200 mm, respectively. The travel of the Z-axis is 150 mm. The X and Y axes measure the real-time displacement via the linear optical grating and then feedback this displacement to the motion controller to form a closed loop control. In this way, the position of the X and Y axes can be accurately controlled. The accuracy of the Z-axis is a little lower than the X-axis and the Y-axis since the feedback is based on the motor spindle speed by the encoder (Fuji YM523756) to form a half closed-loop control. 4. Software for Controlling Droplet Ejection and Deposition To achieve droplet ejection and accurate deposition, the control software should have the following functions: (1) Real-time measurement and display of experimental parameters such as the droplet size, the crucible temperature, and the ejection pressure; (2) Real-time setting, operation, and storage of ejection parameters; (3) Real-time control of droplet generation process; (4) sound and light alarm, and power emergency shutdown. A flowchart of the control software is shown in Fig. 3.28. Each module of the control software is initialized at the beginning. Then, after the ejection temperature T is set, the temperature measurement and control module

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Fig. 3.28 Flowchart of the droplet ejection and deposition control software

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83

is activated to melt the metal. After that, the ejection pressure Δp is applied to eject molten jets via the small orifice. The perturbation signal is output to break metal jets into uniform droplets. In the process of executing the control software, each channel is scanned in sequence to display parameters such as the ejection temperature, the ejection pressure, and the excitation frequency and stored in the computer. Meanwhile, the software compares measured parameters with preset values. If the preset value is not reached, the corresponding regulating program is activated to control the corresponding experimental parameters. This software controls the metal droplet ejection process until the time when the experiment ends, or an abnormal situation happens (an emergency stop happens). In the case of an abnormal situation, the perturbation and heating processes are first stopped, then the applied pressure is released. At last, the control software is completed. The architecture of the software used to control the droplet ejection, and deposition is shown in Fig. 3.29. First, the software selects and opens the measurement and control devices and configures the device parameters. Then, the software acquires the data in sequence and transfers them to corresponding data process modules to output control signals. The software is shut down after all the measurements or control processes are finished. The software operation interface is shown in Figs. 3.30 and 3.31, respectively. The parameters for the droplet generation process can be easily monitored via this interface.

Fig. 3.29 Architecture of the control software for metal droplet ejection and deposition

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Main UI Excit. Temp. Press. Parameter setting

Molten droplet ejection Frequency f

Charge Control

Temperature T

Pressure P Deflection Control

Droplet deflection Charge pulse Deflection voltage Deflection distance

Gas Release

Deposition Deposition temperature x location y location

Run

z location

Fig. 3.30 Main operation interface of the control software for metal droplet ejection and deposition Choice of the vibration signal Basic signal

Arbitrary signal

Parameters of the input signal Amplitude

Frequency

Offset

Duty cycle

Signal output Start time

Signal phase

Step

Phase Signal function

Sampling information Sampling rate

Signal output

Channel

Sample Num. Signal save

Fig. 3.31 Operation interface of the perturbation signal module

Path

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3.7.2 Key Parameters Acquisition System of the Droplet Ejection and Deposition 1. Vibration measurement system of the solid rod waveguide A laser Doppler vibrometer measures the vibration at the free end of the solid rod waveguide. The laser Doppler vibrometer emits a laser beam to irradiate the surface of the vibrating rod end. The Doppler shift effect extracts the vibration speed, frequency, amplitude, and other parameters from the reflected laser. The vibration measurement system is utilized to obtain the influence of the width, amplitude, and other parameters of the pulse signal on the vibration waveform of the rod waveguide, which is driven by the piezoelectric pulse or the stress wave pulse. The measurement results are used to analyze uniform droplet ejection behaviors and guide the selection of droplet ejection parameters. 2. Pressure acquisition system of the droplet generator Two pressure acquisition systems are adopted in this book to collect two types of pressure: constant and pulse. The former is applied to eject jets for the continuous droplet stream generation and maintain the liquid interface position during the piezoelectric pulse-driven droplet ejection and the stress wave-driven droplet ejection. The latter one is primarily used to eject a single droplet. The constant pressure acquisition system consists of a precision pressure reducing valve, a precision pressure regulating valve, a vent valve, a pneumatic pressure sensor, and a pressure signal transmitter. During droplet ejection, the compressed gas flowing out of the precision pressure reducing valve is regulated according to the experimental requirement by the precision pressure regulating valve. The pressure value is measured using the pressure sensor, which then inputs to the transmitter and the pressure controller in sequence. Finally, the pressure controller regulates the applied pressure by comparing the feedback pressure value with the preset one. The pressure pulse acquisition system measures the rapid pressure fluctuation inside the droplet generator. This system consists of a piezoelectric pressure sensor, a charge amplifier, and a high-speed data acquisition card, as shown in Fig. 3.32. The piezoelectric pressure sensor is placed on the vent or the upper cover of the droplet generator. The piezoelectric ceramic in the sensor measures the weak pressure pulse. Measured signals are amplified by the charge amplifier and are transmitted to the data acquisition card for data recording. Because the pressure pulse is relatively short, the high-speed data acquisition card should be synchronized with the droplet ejection signal to record the short duration pressure pulse. Figure 3.33 illustrates the pressure pulse collected by the pressure pulse acquisition system. The inner diameter of the vent tube is approximately 9 mm, its length is about 11.5 cm, and the volume of the resonant cavity is about 55 ml. Figure 3.33a illustrates the typical waveform of pneumatic pulses for ejecting droplets. The peak value of the pulse is about 15 kPa, and the pressure duration is approximately 100 ms. Figure 3.33b illustrates curves of pressure pulses recorded with different trigger signal widths on the solenoid valve and with the applied pressure of 150 kPa. The results illustrate that the amplitude of the pulse changes as a function of the

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Fig. 3.32 Schematic diagram of the pressure pulse acquisition system

pulse width. Meanwhile, the peak time moves slightly as the pulse width varies. The influence of the trigger signal on the pressure pulse will discuss later. 3. Droplet image acquisition system for uniform droplet ejection High-speed photography is a direct method to study the process of droplet ejection, jet breakup, and flight trajectory of droplets. Generally, both high frame rate photography and stroboscopic photography are utilized to capture droplet images: High frame rate photography combines the high rate frame with a short shutter time to record videos of the high-speed droplet motion. In Fig. 3.34a, the high frame rate photography consists of a CCD camera, a stereomicroscope, a high brightness light source, and a personal computer. For instance, if the high droplet flight speed is approximately 1 m/s, the short camera shutter of 1/4000 ~ 1/8000 s and a 10,000 lm light are required to obtain burr-free droplet images. However, due to the high frame

Fig. 3.33 Pressure pulses generated inside the generator. a Typical pressure pulses. b Pressure pulses with different trigger signals

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Fig. 3.34 Schematic diagram of high-speed photography system: a High frame rate photography system. b Stroboscopic photography system

rate, the number of images acquired in a short period is relatively large, and the recorded time is relatively short. Stroboscopic photography is a technique that exposes the object images on the CCD sensor at equal time intervals using a flashing strobe light, leaving snapshot of objects at different positions. Then a complete droplet ejection and deposition process can be obtained by combining those images in sequence. Stroboscopic photography, shown in Fig. 3.34b, consists of a CCD camera, a stereomicroscope, an image acquisition card, and a stroboscopic light source. The CCD camera has a global digital shutter, which has the shutter time between 1/110 and 1/110000 S. The stroboscopic light source is a high-speed LED light source, which has the minimum fluorescent lifetime of 0.5 μs. During photography, the CCD camera and the light source are synchronized by an external TTL signal. In the above system, the exposure time τ should be determined to obtain clear droplet images. For the high frame rate CCD system, the exposure time is mainly determined by the shutter time. For the stroboscopic shooting system, the exposure time is determined by the pulse width of the stroboscopic flash. τ=

2 × si ze o f Camera pi xel Dr oplet velocit y × Lens optical magni f ication

(3.9)

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Droplet images captured by the CCD camera need to be image processed to obtain critical parameters such as jet length and droplet diameter. The image processing procedure includes the following steps. (1) Image calibration. An objective micrometer with a minimum scale of 0.001 mm is used to calibrate captured images. The pixel accuracy (μm/pix) equals the value of the scale length divided by the pixel number. Since the droplet diameter ranges from millimeters to centimeters, droplet images should be captured with a magnification of 0.7× ~ 1×. When the droplet diameter is hundreds of microns, it is more appropriate to use the 2× magnification to capture droplet images. (2) Median filtering. Captured images often have noises due to factors such as random uneven illumination and the intense light reflected from measured objects. The median filtering method can be adapted to remove image noises. The procedure for median filtering is: A square filter window with a side length of 5 pixels is moved inside images. The gray levels of all pixels inside this window are sorted. After that, the gray value of the center pixel ( )of the window is then replaced with the median value (i.e., yi, j = median f i, j ). (3) Image segmentation. Image segmentation separates measured objects from the background based on the image threshold. First, the gray distribution of the image is calculated. As shown in Fig. 3.35, peak 1 and peak 2 in the gray histogram are gray values of the measured object and the background, respectively. The valley between the two peaks is the characteristic threshold (T ) of the image. Supposing the gray scale of the original image is gray(x, y), the image can be divided into background and measured object areas by threshold (T ) { g(x, y) =

Fig. 3.35 Image segmentation by Peak-valley method with the image feature threshold

gb (x, y), gray(x, y) ≤ T go (x, y), gray(x, y) > T

(3.10)

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Fig. 3.36 Parameter measurement of uniform droplet streams: a original image, b median filtered image, c measurement of the jet length, d measurement of the droplet diameter

where gb (x, y) is the gray value of the image background, and g0 (x, y) is the gray value of measured objects. (4) Parameter measurement. Figure 3.36 demonstrates that, in the generation of uniform droplet streams, the jet length L 0 can be directly measured from captured images. The droplet diameter Dd is calculated by the formula Dd = √ 2 Sd /π , here Sd is the measured droplet area. The jet velocity u d can be calculated by the formula u d = λ f , where λ is the distance between two adjacent droplets, and f is the droplet generation frequency. 4. Transient temperature measurement system for droplet deposition process To measure the rapid temperature changes at different points on the substrate and printed parts, a multi-channel transient temperature acquisition device is designed and built, as shown in Fig. 3.37. This system consists of a droplet positioning device, a thermocouple probe array, a multi-channel transient temperature acquisition instrument, and some auxiliary devices. First, the droplet positioning device finds the initial deposition position of printed droplets. Then, metal droplets are printed on the top of thermocouple probes. The thermocouple converts the temperature to a weak thermoelectric potential signal, which is amplified and then recorded by the multi-channel transient temperature acquisition instrument. The droplet temperature at different deposition distances can be obtained by placing the thermocouple probe at the corresponding deposition distance. Fine chromium and nickel alloy wires are welded to form a tiny thermocouple joint. Such a small thermocouple joint can rapidly respond to the temperature change by placing the tiny temperature joint (so call thermocouple probe) at the droplet deposition location. Then, the transient temperature acquisition system measures and records the

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Fig. 3.37 Schematic diagram of the temperature measurement system

rapid temperature variation. The average value of the recorded temperature is taken as the metal droplet deposition temperature. A thermocouple nodes probe array is set on the deposition substrate (Fig. 3.38), which can measure temperature changes during metal droplets or parts deposition. A small hole array is pre-drilled on the deposition substrate at preset locations. Tiny thermocouple probes are inserted into the small holes from the lower side of the substrate, ensuring that measurement probes are exposed on the substrate surface. Meanwhile, the thermocouples are glued and insulated from the metal substrate by using the ceramic adhesive. To accurately measure the temperature change process of the droplet deposition, the droplet needs to be accurately positioned on the top of thermocouple probes.

Fig. 3.38 Schematic diagram of the thermocouple and deposition substrate

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Fig. 3.39 Microscopic shooting platform of CCD camera

5. Deposited metal droplet morphology measurement system The final morphology of deposited metal droplets is an important parameter to determine the printing step, layer thickness, and printing speed, since the droplet morphology has a great influence on the surface and the inner quality of printed parts. The droplet morphology can be measured by using the droplet morphology acquisition method. As shown in Fig. 3.39, this system is designed and built by using a CCD camera equipped with a monocular microscope, a multi-axis stage with three translation stages and one goniometer stage, and a LED light source. To obtain a clear droplet profile, the CCD camera is titled horizontally with a small angle against the LED light source. In this way, the light can illuminate the droplet surface and obtain a clear droplet profile. The solid angle of the deposited metal droplet is a crucial parameter in determining their final morphology (Fig. 3.40) and should be precisely measured. After the droplet image is recorded, the LB-ADSA module (Low Bond Axisymmetric Drop Shape Analysis plug-in) of the open-source software ImageJ is used to measure droplet solid angles. In the LB-ADSA module, the influence of gravity on the droplet morphology is not considered, and droplets are assumed to spread uniformly. The solidification angle is calculated by fitting the measured droplet profile with a polynomial line. The steps are as follows: before calculation, the droplet images are enhanced by several imaging preprocessing methods to improve the image quality, such as brightening and sharpening. Then the LB-ADSA plug-in is loaded, and the preset measurement curve is adjusted to fit the droplet profile. After that, the solidification angle of the deposited metal droplets can be calculated.

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Fig. 3.40 Schematic diagram of the measurement results of the solidification angle of the droplet a the case where the solidification angle is greater than 90°; b the case where the solidification angle is equal to 90°; c the case where the solidification angle is less than 90°. The test material is a lead–tin alloy (ZHLZn60PbA), and the deposition substrate is a silver-plated ceramic substrate

References 1. Samuel JD, Steger R, Birkle G, et al. Modification of micronozzle surfaces using fluorinated polymeric nanofilms for enhanced dispensing of polar and nonpolar fluids. Anal Chem. 2005;77(19):6469–6474. 2. Sohn H, Yang DY. Drop-on-demand deposition of superheated metal droplets for selective infiltration manufacturing. Mater Sci Eng A. 2005;392(1–2):415–21. 3. Whelan BP, Robinson AJ. Nozzle geometry effects in liquid jet array impingement. Appl Therm Eng. 2009;29(11–12):2211–21. 4. Payri R, Garcia JM, Salvador FJ, et al. Using spray momentum flux measurements to understand the influence of diesel nozzle geometry on spray characteristics. Fuel. 2005;84(5):551–61. 5. Chen G. Design of ultrasonic transducer. China Ocean Press; 1984. p. 45. 6. Li Y. Research on pneumatic drop-on-demand ejection technique for rapid soldering of microcircuit. Master Dissertation. Northwestern Polytechnical University; 2010. p. 9. 7. Luo J, Qi L, Zhou J, et al. Modeling and characterization of metal droplets generation by using a pneumatic drop-on-demand generator. J Mater Process Technol. 2012;212(3):718–26. 8. Hayes DJ, Wallace DB, Boldman MT. Picoliter solder droplet dispensing. Int J Microcircuits Electron Packaging. 1992;16:173–80. 9. Chen DD, Zhang HT, Jiang HX, Cui JZ. Quantitative analysis of microsegregation in DC cast 7075 aluminum alloy. J Mater Metall. 2011;10(3):220–5. 10. Pan TM. Modern induction heating device. Metallurgical Industry Press: 1996. pp. 130–131.

Chapter 4

Uniform Metal Droplet Continuous Ejection and Printing Process Control Technology

4.1 Introduction Uniform droplet streams with highly uniform size and high generation rate can be obtained by utilizing the Rayleigh instability. Furthermore, the uniform droplet stream can print metal blanks after being controlled by the charge and deflection. This chapter focuses on uniform metal micro-droplet continuous ejection deposition behavior and control technology, including uniform droplet ejection behavior and its parameter influence law, uniform metal micro droplet charging dispersion behavior and flight trajectory control technology, uniform metal micro droplet deposition control, etc. This chapter aims to lay a foundation for 3D printing of metal parts via uniform metal droplet continuous ejection.

4.2 Research on Uniform Droplet Continuous Ejection Behavior and Its Influencing Factors For uniform metal droplet continuous ejection technology, the charging and deflection method is used to control the droplet deposition position and suppress the droplets coalescence phenomenon during their flight. Therefore, this section focuses on the control method of droplet charges, charged droplet dispersion behavior, and deflection trajectory control method.

4.2.1 Numerical Simulation of Continuous Uniform Droplet Ejection Process and Research on Influencing Factors During the metal jet break into droplets, the velocity field, the pressure field, and the temperature field are complex and difficult to be solved accurately by using analytical © National Defense Industry Press 2023 L. Qi et al., Metal Micro-Droplet Based 3D Printing Technology, https://doi.org/10.1007/978-981-99-0965-0_4

93

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4 Uniform Metal Droplet Continuous Ejection and Printing Process …

methods. Numerical simulation and droplet ejection testing experiments reveal the formation mechanism of metal droplets. This helps explore the main influencing parameters, and expounds the change law of related state parameters and the influence mechanism in the jet breakup process as the selection of uniform droplets ejection parameters follows. 1. Numerical modeling and analysis of on-demand ejection of uniform Tin–Lead alloy droplets The process of jet breakup and uniform droplet formation is a fluid–solid coupling process. The physical model is shown in Fig. 4.1. In the process of jet ejection and breakup, the fluid flowing through the orifice satisfies the conservation laws of mass, momentum, and energy. The motion and energy equations of fluid can be expressed as: [1] Mass conservation equation: ∂ρl + ∇ · (ρl u) = Sm ∂t

(4.1)

Momentum conservation equation: ( ρl

) ( ) ∂u + ∇ · (uu) = −∇ p + ∇ · τ + ρl g + F ∂t

Energy conservation equation: Fig. 4.1 Physical model of droplet ejection. z is axis coordinate, the vertical down direction is the positive direction, r is the radial coordinate

(4.2)

4.2 Research on Uniform Droplet Continuous Ejection Behavior and Its …

( ρl c

) ∂T + ∇ · (T u) = ∇ · (kl ∇T ) + ST ∂t

95

(4.3)

where u is the velocity vector, S is the source term, m is the mass, T is the temperature, ∇p is the pressure gradient, ρ l is the material density, c is the specific heat capacity, and k l is the fluid thermal conductivity. The above system of equations is hard to be solved analytically. The numerical simulation method is often adopted to obtain the evolution of physical fields during a jet breakup. The Volume of Fluid (VOF) is a common method that is used to numerically solve the control equations in fluid mechanics. The basic principle of VOF method is to calculate the volume ration function between two fluids in the grid element in order to determine the interface of two-phase flow. During simulation, the computational region is divided into a series of nonrepeating control volumes and the differential equations shown in Eqs. (4.1–4.3) are integrated discretely. The VOF method has advantages of clear physical meaning including the ability to handle complex geometries, and accurate solving results. The VOF method is described in detail as follows: By introducing a generic variable φ, the control Eqs. (4.1–4.3) can be unified accordingly: ∂(ρl φ) + ∇ · (ρl uφ) = ∇ · (\ · ∇φ) + Sφ ∂t

(4.4)

where the terms from left to right are the transient, convective, diffusive, and source terms, respectively. Integrating Eq. (4.4) over time for the control volume (labeled p): t+Δt { {

ΔV

t

∂(ρl φ) d V dt + ∂t

t+Δt { {

∇ · (ρl uφ)d V dt t

ΔV

t+Δt { {

=

∇ · (\ · ∇φ)d V dt + t

ΔV

(4.5)

t+Δt { {

Sφ d V dt t

ΔV

where ΔV is the volume of the control body p. Here, the transient term is t+Δt { {

t

ΔV

The convective term is

( ) ∂(ρl φ) d V dt = ρ 0P φ P − φ 0P ΔV ∂t

(4.6)

96

4 Uniform Metal Droplet Continuous Ejection and Printing Process … t+Δt { {

∇ · (ρl uφ)d V dt ΔV

t

t+Δt {

=

| | (ρl u r ) R A R φ R − (ρl u r ) L A L φ L + (ρl u x )U AU φU − (ρl u x ) D A D φ D dt

t

(4.7) The diffusion term is t+Δt { {

∇ · (\ · ∇φ)d V dt ΔV

t

t+Δt { |

\R A R

= t

| φR − φP φ P − φL φU − φ P φP − φD dt − \L A L + \U AU − \D A D (δr ) R (δr ) L (δx)U (δx) D (4.8)

The source item is t+Δt { {

t+Δt {

Sφ d V dt = t

ΔV

(Sc ΔV + S P φ P ΔV )dt

(4.9)

t

Substituting Eqs. (4.6–4.9) into Eq. (4.2) and adopting the first order windward scheme, the volume cell discrete equation is obtained as: aP φP =

NS E

aE φE + bP

(4.10)

Es

where E s expresses the interface of the control body p, a P = S P ΔV , a E = De + max(0, −Fe ), a P φ P =

NS E Es

Ns E

a Es + ΔF +

Es

a Es φ Es + b P , b P =

ρ 0P ΔV Δt

ρ 0P ΔV Δt

−

+ SC ΔV .

\e Besides, Fe = (ρv)e and De = (δx) represent the convective mass flux and diffusive e conductivity at the interface, respectively. In Eq. (4.2), the pressure gradient ∇p is used as the source term to determine the velocity distribution. Meanwhile, the velocity also satisfies the mass conservation equation (Eq. 4.1). In this way, the pressure and velocity fields are coupled together. The pressure and velocity fields are solved by using the pressure implicit operator partitioning algorithm (PISO). The calculation process consists of three steps: first, the flow field is initialized, the momentum equation and the continuity equation are

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97

solved under the calculation time step Δt. Secondly, after iteration, the flow field velocity distribution u and pressure distribution p are obtained. Lastly, the temperature distribution in the flow field is obtained by solving the energy equation, as shown in Fig. 4.2. In the jet breakup process, the boundary wall motion, the multiphase fluids flow, and the evolution of free surfaces are involved. The controlling equations are solved

Fig. 4.2 Numerical solution process

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4 Uniform Metal Droplet Continuous Ejection and Printing Process …

to calculate the evolution of the liquid surface morphology, velocity and pressure distributions, and other parameters during the jet breakup. The moving mesh model. Moreover, the moving mesh model is used to couple the vibrations of the transferring rod into simulation of fluid field in the crucible. When using the moving mesh model, the motion region should be specified, and the initial mesh and the boundary motion method should be defined. In this case, the integral form of the generalized scalar conservation equation for a control body (with moving boundaries) can be expressed as: d dt

{

{ ρl φd V +

(

) u − ug d A =

∂V

V

{

{ \∇φd A +

∂V

Sφ d V ,

(4.11)

V

where u is the fluid velocity vector, ug is the grid velocity of the moving grid, Γ is the diffusion coefficient, S φ is the source term, and ∂V is the boundary of the control body. The time derivative term on the left-hand side of Eq. (4.11) can be expressed by a first-order backward differential at different moments and nodes. d dt

{ ρl φd V = V

(ρl φV )n+1 − (ρl φV )n Δt

V n+1 = V n +

dV Δt dt

(4.12)

(4.13)

According to the law of grid conservation, Eq. (4.13) can be calculated by the following equation: d

dV = dt

{ ug · d A = ∂V

nf E

u g, j · A j ,

(4.14)

j

where nf is the number of face grids of the controlling volume, and Aj is the area vector of area j. Then, u g, j · A j =

δV j Δt

(4.15)

where δV j is the volume of space swept by control volume surface j in the time interval Δt. Three models can be used to calculate the mesh dynamics: the spring-smooth model, the local redraw model, and the dynamic layer model. The spring-smooth model needs to meet the conditions of unidirectional movement and movement perpendicular to the boundary. The local redraw model needs to locally adjust the mesh as triangle mesh. The dynamic layer model needs to meet: (1) The grid adjacent to the moving boundary must be quadrilateral or volume grids; (2) In the area outside the sliding

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99

grid interface, the grid must be surrounded by a single-sided grid area. Due to the reciprocating motion of the rod, the moving boundary should be parallel to the boundary of the flow field. The local grid should be the structural grid. Therefore, the dynamic layer model is usually used to update the dynamic grid when the metal jet ejection and breakup process is simulated. The dynamic layer is increased or decreased according to the height change of the adjacent layer of the moving boundary. That is, adjacent grid layers j merge or split according to the height h of the mesh layer. While cells in a grid layer are expended, the maximum critical cell height at which cells can be split is expressed as: h max = (1 + αs )h r e f

(4.16)

While cells in the grid layer are gradually compressed, and the minimum critical cell height which can be combined is expressed as h min = αc h r e f

(4.17)

where href is the reference cell height, αs is the splitting factor, αc is the merging factor. If Eq. (4.16) is satisfied, the i layer is split into two layers h0 and h-h0 . When Eq. (4.17) is satisfied, the layers of i and j are merged. Tracking free jet surfaces. In the process of jets breaking into droplets, surfaces of jets and droplets are free surfaces. Those morphology changes with the movement of the flow field. Therefore, the surface morphology of jets and droplets at different times and positions is simulated to illustrate the process of jets breaking into droplets. The VOF method tracks and reconstructs the free surface of jets by solving the momentum equation and processing the fraction of the target fluid that passes through the control body. Define the function fr' as the ratio of the target fluid volume to the grid volume. In the calculation region, the space of the ejected fluid is Ω 1 , the space occupied by the gas is Ω 2 , the intersection is Γ , then: C(x, 0) =

⎧ ⎨

0 x ∈ O2 0 < fr' < 1 x ∈ \ ⎩ 1 x ∈ O1

(4.18)

When 0 < fr' < 1, the grid contains a liquid and gas interface. The average density of volume fractions is: ( ) ρv = fr' ρg + 1 − fr' ρl

(4.19)

The controlling equation for the function fr' is ∂ fr' + u∇ fr' = 0 ∂t

(4.20)

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4 Uniform Metal Droplet Continuous Ejection and Printing Process …

The value of fr' can be solved by Eq. (4.20). Then, the jet surface is updated by using the Youngs interface reconstruction technique [2]. During jet ejection, We is close to 1–10, indicating its surface tension action cannot be neglected. During solving the volume fraction and reconstructing liquid– gas interfaces, the fluid surface tension enters the calculation as a source term of the momentum equation. This source term can be expressed as [3] Fvol = σi j

2ρκi αi ρi + ρ j

(4.21)

where σ ij is the surface tension coefficient, α i is the gradient of the i phase volume fraction, ρ i is the volume fraction density of i phase, κ i is the curvature at interface i. Grid division and boundary condition setting. Assuming that the jet and droplets are axisymmetric, the droplet ejection model can be simplified into a two-dimensional axisymmetric model (Fig. 4.3). The simulation area is the fluid area inside the crucible and the orifice, and the gas area is 20 mm below the nozzle. The velocity and pressure change greatly inside the orifice and the gas area. The dense quadrilateral grid structure is used to ensure the calculation accuracy. Since the fluid velocity inside the crucible changes slightly, the larger unstructured grid can improve the calculation efficiency. The boundary condition for the gas environment is set as the pressure outlet boundary, which has the relative pressure of zero. The boundary condition on the metal liquid surface is set as the pressure inlet boundary, at which the pressure magnitude is the applied pressure for liquid ejection. Finally, the centerline of the jet model is set as the symmetry axis. Both the crucible and orifice walls are set as stationary wall boundaries. If the crucible and the orifice are kept at a constant temperature, they are designated as temperature boundaries with the following heat fluxes on their walls: ( ) q = h f Tw − T f + qrad

(4.22)

where hf is the heat transfer coefficient of the fluid, T w is the wall temperature, T f is the local fluid temperature, qrad is the radiant heat flux. The vibration transferring bar is set as a moving wall boundary with the displacement of pb = Av sin(2π f t)

(4.23)

The corresponding speed can be expressed u b = 2π Av f cos(2π f t),

(4.24)

where Av is the perturbation amplitude, f is the perturbation frequency, and t is time. The wall of the vibration transferring rod is set as the thermal flux boundary with the wall temperature of:

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Fig. 4.3 Modeling area meshing and boundary conditions

Tw =

q − qrad + Tf hf

(4.25)

The metal used in metal droplet ejection and simulation is lead–tin alloy (Sn40w.t.%Pb). In the molten state of the alloy, the ejection parameters and physical property parameters are listed in Tables 4.1 and 4.2, respectively. Assuming that: (1) The density of droplets does not change during the droplet ejection process, that is, the metal jetting process is incompressible flow; (2) The jetting process is an isothermal process, indicating the physical parameters do not change during jet ejection; and (3) The metal jet is the laminar flow and during the process, no turbulence is generated. Table 4.1 Simulation parameters Crucible diameter d c /mm

Nozzle diameter d n /μm

Perturbation frequency f /kHz

Perturbation amplitude Av /μm

Ejection pressure Δp/kPa

20 ~ 40

50 ~ 150

2 ~ 60

2 ~ 200

30 ~ 100

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Table 4.2 Physical properties of materials Material

Liquidus Solid temperature Density ρl , kg/m3 Viscosity μl , Pa·s temperature T s , °C T l , °C

Sn-40%wt.Pb 183

188

N2

8520

0.00133

1.25

1.69 × 10–5

Material

Surface tension σ , N/m

Latent heat of fusion L l , J/kg

Thermal Conductivity kl , W/(m·K)

Specific heat cl , J/(kg·K)

Sn-40%wt.Pb

0.48

47,560

31.7

212.9

After establishing the above model, the metal jet ejection and droplet formation process can be systematically simulated, providing an effective method for releasing the parameter influence law. 2. Analysis of dynamic behaviors of metal jet breakup The continuous uniform droplet stream is ejected in the low-oxygen environment. The device is shown in Fig. 3.13. The images of uniform droplet streams are taken by the stroboscopic photography system, as shown in Fig. 3.34. The photography system is calibrated with an objective micrometer to measure key parameters such as the jet breaking length and the droplet diameter. When the ejection pressure is 45.6 kPa, the predicted jet velocity is 2.6 m/s by using the jet velocity prediction equation. The jet flow state can be characterized by using the Reynolds number (Re = ρu D j /, determining the type of flow pattern as laminar or turbulent while flowing through a pipe / with a the critical value that is approximately 2300), and the Oh number (Oh = / D j , characterizing the proportion of viscosity in the fluid motion). General metal jets, which have the Re number of 700–1000 and the Oh number of 0.0017, can be taken as low viscosity laminar jets. For different perturbation frequencies, the jet morphology can be totally different, resulting in completely different types of droplet morphology (Fig. 4.4. illustrates the droplet morphology, where the simulated jet is truncated into three segments in the jet direction). When the perturbation frequency f is 2 kHz, the ejected droplets are not uniform. Three different types of droplets are produced. Uniform spherical droplets, satellite droplets, and merged droplets, as shown in Fig. 4.4a, b. Uniform droplets are produced from the necking and breaking of the jet. The droplet diameter is in the same order of magnitude as the jet diameter. Satellite droplets are formed by the contraction of slender filaments between the jet and droplets. The diameter of satellite droplets is much smaller than that of main droplets. Super large droplets are created by the coalescence of main droplets due to different droplet velocities during flight. Figure 4.4c, d show images and simulated results of a jet broken into uniform droplets for the applied perturbation frequency f of 3.89 kHz. This frequency is the optimum perturbation frequency (3.89 kHz) calculated from the Rayleigh jet instability theory mentioned in Chap. 2.

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Fig. 4.4 Jet breakup morphology at different frequencies a and b f = 2 kHz, c and d f = 3.89 kHz

To quantitatively analyze the uniformity of the ejected spherical droplets, the simulated volume fraction along z-axis direction is listed as shown in Fig. 4.5. The volume fraction of 1 means the total liquid state. The uniformity of droplets can be characterized by measuring the z length through the liquid region (or with the volume fraction of 1). When jets break randomly, the z lengths are unequal where the volume fraction is 1, meaning that the droplet size is not uniform. When uniform droplets produce, z lengths along the fraction volume of 1 and 0 are the same with each other, meaning that the droplet size and the droplet spacing are uniform. Assuming that droplets are uniform spheres, it can be calculated that the average droplet diameter is about 290 μm, and the droplet center spacing is about 250 μm. To analyze the influence of the perturbation frequency on the droplet formation process in detail, droplet streams are ejected under the disturbance frequency f of 0, 2, and 3.89 kHz respectively. The produced metal droplet streams are photographed at different times. The captured images are shown in Fig. 4.6. Figure 4.6a illustrates that, for f equal to 0, the process for a jet breaking into droplets is extremely unstable, indicating that a slight random disturbance exists when the external excitation signal is not applied. Due to such random disruption, the disturbance on the jet surface grows randomly along the jet, the jet breakup length and jet morphology keep changing during jet breakup. At t = 3 s, the jet

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Fig. 4.5 Liquid volume fraction along the jet axis for different perturbation frequencies: a f = 2 kHz; b f = 3.89 kHz

Fig. 4.6 Jet and droplet patterns for different frequencies. a f = 0 Hz, b f = 2 kHz, c f = 3.89 kHz

begins necking after flying a long distance, and finally breaks into droplets. At t = 3.5 s, the jet is not observed in the high-speed image since its breakup length is very short. The ejected droplet stream contained microsatellite droplets between main droplets. At t = 4 s, the jet breaks into main droplets with the droplet spacing of 540 ~ 820 μm. The change of droplet size is relatively small compared to other times. Since droplets are uniform, it can be deduced that the perturbation frequency at this moment is close to the optimal perturbation frequency. At t = 4.5 s, the jet appears necking with a slender filament, the droplet spacing is quite different (0.35 ~ 1.1 mm), and the droplets coalescences phenomenon appear accordingly. Figure 4.6b indicates that, for f equal to 2 kHz, the difference between the jet break lengths decreases at different times compared to Fig. 4.6a. However, the jet break process is quite irregular, leading to changes of breakup patterns over time. Many satellite droplets and coalesced droplets appear in the droplet stream.

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Figure 4.6c indicates that, for f = 3.89 kHz, the jet breaks into a uniform droplet stream. The jet break lengths are like each other at t = 3 s, t = 3.5 s, t = 4 s, and t = 4.5 s. Meanwhile, the droplet streams have uniform droplet spacing since the jet breaks into a droplet in a disturbance wavelength under optimal external excitations. In this case, the droplet size is also uniform, the adjacent spacing varies between 520 and 580 μm, indicating that the uniform metal micro droplet formation process is stable. The above studies show that, when the external perturbation is not applied, the growth rate of perturbation on the jet surface is not stable, the droplet pattern formed by jet breakup is also unstable. The parameters such as the jet breakup length, the droplet size, and the droplet spacing cannot be precisely predicted and controlled. When a non-optimum external perturbation is applied, the randomness of jet breakup is suppressed to some extent. However, the irregular break pattern still presents in this case. When the non-optimum external perturbation is applied, the random disturbance on the jet surface is completely suppressed. The growth rate of the disturbance on the jet surface is constant, resulting in stable jet breakup and droplet streams with the uniform size and spacing. Numerical simulation of the jet breakup process can further reveal variation of physical fields like the velocity and pressure fields inside jets. The jet velocity and pressure changes at different axial positions can be obtained by setting sampling points at different positions along the simulated jet axis. As shown in Fig. 4.7a, for f = 0 Hz, at the orifice hole (z = 0), the jet velocity and pressure do not change over time. Instead, the driving gas pressure mainly determines the pressure and velocity in this case. As the jet moves away from the orifice hole, for instance at z = ~ 3.5 mm, the jet velocity decreases significantly. The jet starts necking under the action of surface tension, resulting in an increase in the internal pressure (Fig. 4.7b). However, as the ejection time increases, the jet velocity gradually increases away from the orifice, and the internal pressure changes without obvious regulation. When the excitation frequency is 2 kHz, the jet velocity and pressure inside the nozzle orifice change periodically (Fig. 4.7c, d). The changing frequency is equal to the external perturbation frequency, indicating that the pressure and velocity here are dominated by the driving pressure and the external excitation. As the jet leaves the orifice hole, the velocity and pressure inside the jets change randomly. When the excitation frequency is 3.9 kHz, the velocity and pressure inside the orifice variate periodically. One droplet is generated in each cycle. In Fig. 4.7a, c, and e, the average jet velocity inside the orifice is 3 m/s. The simulation results show that, the amplitude of the jet velocity variation inside the orifice reaches 1 m/s when the perturbation frequency is the optimum frequency. The internal perturbation frequency is the same in other sections of the jet. When the perturbation with the optimum frequency is applied, the excitation signal causes resonance inside the orifice, and finally forces jets to break into uniform droplet streams. According to the classical Rayleigh jet instability theory, the loading excitation frequency significantly affects the growth rate β. The relationship between the dimensionless wave number κ = d j f /vj and the disturbance growth rate can

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Fig. 4.7 Variations of velocity and pressure at different positions on the jet axis under different excitation frequencies, a and b f = 0, c and d f = 2 kHz, e and f f = 3.9 kHz

be solved according to the classical Rayleigh jet instability theory. The comparison between simulated jet breakup lengths and dimensionless wave numbers under different disturbance frequencies is shown in Fig. 4.8. The figure shows that when the dimensionless wave number κ increases gradually, the variation trends of the jet length L and the disturbance growth rate β are opposite. When β increases from zero,

4.2 Research on Uniform Droplet Continuous Ejection Behavior and Its …

107

Fig. 4.8 The jet breakup length and the disturbance growth rate β as a function of the dimensionless wave number κ

the time for the disturbance propagating along the jet is gradually reduced. If the jet velocity vj holds constant, the time for the jet breakup length gradually decreases. That is the jet break length reduces as β increases. For the optimum wave number κ opt = 0.705 (for f opt = 3.9 kHz and vj = 2.6 m/s), the disturbance growth rate β reaches the maximum value and L reaches the minimum value around 7.10 mm. As the wave number κ moves away from the optimal value, jet length L increases again. Figure 4.9 shows the relationship between the excitation frequency and droplet diameter obtained by numerical simulation. The change tread is close to the predicted result based on Rayleigh jet instability theory. As the excitation frequency increases, the average droplet diameter decreases from 300 μm (f = 2 kHz) to 250 μm (f = 4.7 kHz). Meanwhile, the droplet diameter deviation gradually decreases. When the optimal frequency is applied, the droplet diameter with the minimum size deviation is obtained. The uniform droplet diameter is 283 μm, which deviates 0.2% from the predicted value of 284 μm, showing that the jet breakup process can be predicted by the Rayleigh jet instability theory. Generally, uniform droplets with the size variation less than 4% can meet the requirement of metal parts manufacturing [4].

4.2.2 The Influence of the Experimental Parameters on the Metal Jet Breakup Process Due to effects of nozzle defects, impurities, oxidation, and other factors, jetting problems, such as skew jets, swing jets, interruption of jet ejection, and failure of jet breakup, can be observed. Those problems make the ejection of uniform droplet stream process unstable and reduce the uniform droplet deposition accuracy. The metal jet ejection process is affected by the coupling effect of many factors, as illustrated in Fig. 4.10. For instant, if the molten metal liquid contains lots of impurities, the “dirty” metal liquid may contaminate the orifice and change states of the jet stream, or even clog the orifice and break the jet ejection process. Second,

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4 Uniform Metal Droplet Continuous Ejection and Printing Process …

Fig. 4.9 Relationship between the droplet diameter and the excitation frequency (Sn40w.t.%Pb)

oxygen in the test environment will cause an oxidation reaction on the surface of metal jets, which directly changes the chemical composition and physical properties of jet surfaces. Furthermore, the asymmetric wetting between the liquid metal and the orifice wall will also affect jetting behaviors. In addition, the applied pressure directly affects the jet velocity. Jets with the high jet velocity break in the wind-induced breakup mode (atomize into metal droplets of different sizes) and fail to break into uniform droplets. Otherwise, with a slow jetting velocity, the jet is susceptible to interference from nozzle deflects, impurities, and other factors, causing improper jetting behaviors such as swinging and deflection of the jet direction. Therefore, to achieve stable jet ejection, the influence mechanism of various experimental factors on the ejection process should be solved. This section

Fig. 4.10 Schematic diagram of influencing factors of metal jet ejection process

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109

combines numerical analysis and droplet ejection experiment to explore the influence of the above test parameters on the breakup behavior of metal jets. 1. The effect of the nozzle diameter on the jet breakup The diameter of the orifice hole has the significant influence on the droplet diameter. This section investigates effects of different combinations of the nozzle diameter and the excitation frequency on the ejection morphology of uniform droplets. When the nozzle diameter is 50 μm, the diameter of produced uniform droplets is about 95 μm (Fig. 4.11a, b). When the nozzle diameter increases to 100 μm, the droplet diameter increases significantly (Fig. 4.11a–d). As the nozzle diameter increases to 150 μm, the ejected uniform droplet diameter increases to 283 μm (Fig. 4.11e, f). In conclusion, as the diameter of the nozzle hole increases, the uniform droplet diameter increases linearly. The ratio of the droplet diameter to the orifice diameter is approximately 1.9. Figure 4.12a shows that the uniform droplet diameter does not change obviously if the applied perturbation frequency varies slightly when the jet breaks uniformly. Simultaneously, the diameter of produced droplets does not change significantly when the applied pressure changes (Fig. 4.12a). The ejection velocity increases along with the increase of applied pressure (Fig. 4.12b). 2. Influence of the ratio of the orifice depth to diameter The aspect ratio of the orifice R is defined as the ratio of the orifice depth to its diameter ho /d o (where ho is the nozzle thickness and d o is the orifice diameter). Uniform droplet ejection process is simulated numerically and experimental tested with different orifice aspect ratios. When the applied pressure is 45.6 kPa and the excitation signal frequency is 3.89 kHz, the uniform droplet ejection parameters with different orifice aspect ratios are listed in Table 4.3. Fig. 4.11 Uniform droplets produced at different orifice diameters

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Fig. 4.12 a The variation of the diameter of uniform droplets, b The relationship between the initial flight velocity of produced uniform droplets and the applied pressure

Table 4.3 Uniform droplet ejection parameters under different orifice thicknesses Serial number (simulated)

Orifice aspect ratio

Perturbation amplitude μm

Serial number (experimental)

Orifice aspect ratio

Perturbation current mA

(a)

1

4

(b)

1

50

(c)

2

4

(d)

2

50

(e)

10

7.5

(f)

10

90

The simulated results show that when the orifice aspect ratio increases from 1 to 2, uniform droplets can be produced when the perturbation signal has an amplitude of 4 μm. In this case, the jet length increases from 1.25 to 1.86 mm (Fig. 4.13a, c). When the thickness of the orifice hole increases to 10, the perturbation amplitude needs to increase to 7.5 μm for producing uniform droplets. Here, the jet breaking length increases to 5.2 mm (Fig. 4.13e). As the aspect ratio of the orifice increases, the jet breakup length gradually increases (Fig. 4.14), and the droplet spacing decreases (Fig. 4.15). Uniform droplet streams production can be ensured by increasing the excitation amplitude. The experimental and simulated results have the same changing trend. With the same orifice diameter, the orifice thickness decreases, and the perturbation amplitude required to produce uniform droplet streams also decreases. 3. Effects of ejection pressure on droplet ejection To understand the influence law of ejection pressure on uniform droplets generation, the ejection pressure is changed in droplet ejection experiments and simulations with the same orifice diameter. According to the Rayleigh jet instability theory, the change of the optimal perturbation frequency is calculated and listed in Table 4.4 when the ejection pressure increases from 30 to 80 kPa. Under those parameters, the comparison of uniform droplet streams obtained by experiment and simulation is shown in Fig. 4.16. The jet breakup length increases from 1.276 to 2.085 mm (Fig. 4.17). The experimental and simulated results have the same

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Fig. 4.13 Patterns of uniform droplets under different aspect ratios of orifice holes

Fig. 4.14 Jet breakup length under different orifice thicknesses

change trend, indicating that, under different gas pressures, the increase of the jet velocity increases the jet breakup length. Figure 4.18 also shows that the spacing of uniform droplets does not change significantly as the ejection pressure increases. The reason is that the increase in the ejection pressure increases the axial velocity of the jet (Fig. 4.18), the optimal perturbation frequency for uniform droplets generation also increases accordingly (for details, see the formula (2.16) in Sect. 2.2.1). Furthermore, since the droplet spacing S is proportional to the jet surface disturbance wavelength λ (λ = uj /f), the

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Fig. 4.15 The droplet spacing of uniform droplets versus the perturbation amplitude under different orifice aspect ratios

Table 4.4 Ejection parameters of uniform lead–tin alloy droplets (the material is Sn-40 w.t.%Pb) Serial number (Simulation)

Ejection pressure kPa

Perturbation frequency kHz

Serial number (Simulation)

Ejection pressure kPa

Perturbation frequency kHz

(a)

30

3.16

(b)

32

3.13

(c)

45.6

3.89

(d)

45.6

3.89

(e)

60

4.48

(f)

60

4.16

(g)

80

5.18

(h)

80

5

Fig. 4.16 Uniform droplet patterns produced by using the parameters listed in Table 4.4

change of λ is small as uj and f increase simultaneously, resulting in a small change in the droplet spacing (Fig. 4.17). Therefore, it is difficult to change the droplet spacing directly by changing the driving pressure. The above experimental results show that the jet breakup length and droplet flight velocity can effectively increase by increasing the applied gas pressure when uniform

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Fig. 4.17 Variation of the jet breakup length and the droplet spacing under different ejection pressures

Fig. 4.18 Influence of ejection pressure on the jet axis velocity

droplet streams are generated. However, the effect of increasing gas pressure on the droplet spacing is not significant. 4. Effects of excitation frequency on uniform streams generation The previous study [5] shows that, when the perturbation frequency of the molten metal jet varies slightly around the optimal frequency, the metal jet can also break into uniform droplet streams, except that the jet breakup length is longer at the optimal perturbation frequency. In the simulation, the ejection pressure (Δp = 45.6 kPa) and perturbation amplitude (Ap = 2.5 m) remain constant, with an optimal frequency being 3.89 kHz. If the perturbation frequency f changes slightly (from 3.7 to 4 kHz), uniform droplet streams can be obtained (Fig. 4.19).

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At this time, the jet break length L opt decreases first, and then increases with the increase of the perturbation frequency f (Fig. 4.20). The droplet spacing S gradually decreases with the increase of f . During this process, the droplet flight velocity does not change obviously with the increases of f . In summary, the frequency taken to achieve uniform droplet ejection is not a constant value but varies within a range. When the excitation frequency is adjusted in a Fig. 4.19 Uniform droplet streams are obtained when the perturbation frequency changes slightly

Fig. 4.20 Variation of the jet breakup length and the droplet spacing under different perturbation frequencies

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small range, the jet breakup length and the droplet spacing both changes accordingly. The initial droplet flight velocity and the uniformity of the droplet size do not change. 5. The effect of the surface oxidation on the breaking process of metal jets Oxidation of molten metal jets can change its surface physical properties, leading to the change of jetting state. The influence law of metal oxidation on jet breakup can be qualitatively analyzed by conducting ejection experiments under different oxygen contents. After the tin solder (Sn-40% w.t. Pb) is placed in a stainless-steel crucible and heated up to 270 °C to be completely melted, the molten metal is ejected into the atmosphere and the low-oxygen environment, respectively. The test parameters are listed in Table 4.5. In the first group, the jet is not loaded with perturbation, and the ambient oxygen content is 21% (atmospheric environment), 10 ppm (i.e., μL/L), and 500 ppm respectively. The low-oxygen environments are achieved by a sealed glove box. In the second group, all other test parameters are kept constant, and a vibration frequency of 15 kHz is applied. Meanwhile, the excitation current is adjusted to obtain different perturbation amplitudes, and the effects of frequency and amplitude on the jet breakup behavior are studied in the environment with different oxygen contents. Figure 4.21 is a metal jets picture taken with a high-speed CCD and SEM. Those pictures show that the breakup patterns of the metal jet under different oxygen contents are different. In the low-oxygen environment, the jet breaks into an irregular droplet stream under the effect of the weak perturbation (Fig. 4.22a, b). At those conditions, a small number of oxides disperse on the jet surface. Since the small oxides isolate with each other, the effect of oxides can not suppress the growth of the weak jet surface perturbation. Therefore, the influence of molten metal oxidation on metal jet breakup can be ignored. In this case, metal jets break freely and satellite droplets can be observed in the droplet streams. With the increase of the oxygen content, the oxidization effect changes the breaking behavior of metal jets. Metal jets become irregular droplet chains (Fig. 4.22c). In this condition, the oxides on the jet surface form a large oxide film, Table 4.5 Parameters for jetting in different conditions With perturbation (frequency as 15 kHz)

Without perturbation Serial Oxygen number content (a)

10 ppm

Perturbation Perturbation Serial Oxygen frequency current/mA number content kHz

Perturbation Perturbation frequency current/mA kHz

0

15

0

(d)

10 ppm

60

(b)

500 ppm 0

0

(e)

500 ppm 15

60

(c)

21%

0

(f)

21%

15

60

(g)

21%

15

100

0

Notes driving pressure is 30 kPa, nozzle diameter is 140 μm

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Fig. 4.21 Metal jet breakup patterns in the environment with a the oxygen content of 10 ppm, b the oxygen content of 500 ppm, c the oxygen content of 21% (atmosphere)

Fig. 4.22 Metal jet ejection under the conditions of Table 4.5. a Oxygen content is 10 ppm. b Oxygen content is 500 ppm. c, d Oxygen content is 21% (atmosphere)

which inhibits the growth of jet surface perturbations, resulting in the change of the jet breakup. Therefore, when the inertia force of jets is smaller than the force required for the deformation of the oxide film, jets could not break and finally solidify into solid metal filaments. When the sinusoidal perturbation signal of the frequency of 15 kHz and the current of 60 mA is applied, jet breakup patterns of the metal jet are different from that without applying external perturbation. In Fig. 4.22a and b, jets can produce a uniform droplet in each perturbation period. When the oxygen content is high (Fig. 4.22c), even varicose veins are formed on the jet surface, jets finally solidify into a long bead-string fiber since the oxidation inhabits the jet breakup. By further increasing the energy of the applied perturbation (in Fig. 4.22d, the disturbance current increases to 100 mA), jets break into short bead-string fibers

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irregularly. The reason for the jet breakup may be caused by the breakup of oxides under extensive perturbation. Since this jet breakup does not satisfy the Rayleigh jet instability, uniform metal droplets cannot be obtained. From the above analysis, the conclusion can be drawn that the oxides produced under different oxygen contents can inhibit the growth of the small jet surface perturbation and change the jet breakup patterns. By increasing the energy of the external perturbation, metal jets can break into short filaments but difficult to form uniform droplet streams. 6. Influence of impurities on the droplet ejection Jetting process can be disturbed when the impurities inside the molten metal block the orifice or attach to the orifice. This is a common problem for causing the failure of capillary jets ejection. The reason is that the impurities inside the crucible or melts adhered to the orifice during the ejection process, resulting in the change of jet patterns during ejection. Therefore, impurities are factors that should be carefully avoided for the stable ejection of metal jets. To eliminate or reduce the blockage or jet deflection caused by impurities, the raw metal blocks, crucibles, and orifices must be cleaned before jet experiment: (1) Remove oxides and impurities on the surface of the raw metals. The metal blocks are first melted and then poured into mold through a ceramic filter to remove the oxides or impurities on their surfaces. (2) Clean the crucible and the orifice. The crucible and orifice are washed by using an ethanol bath with ultrasonic vibration. Then the crucible and orifice are cleaned with deionized water to remove impurities. Jetting experiments have been carried out with market supplied tin solders (Sn40w.t.%Pb) and cleaned (or not) using the method listed above. During jets ejection, the crucible is located inside the low-oxygen environment with the oxygen content of 10 ppm. The heating temperature is set at 250 °C and the crucible holds 20 min at this temperature before ejection. The driving pressure and the perturbation frequency are set as 45.6 kPa and 3.89 kHz, respectively. The high-speed CCD pictures of uniform metal droplet streams are shown in Fig. 4.23. The uniform metal droplet streams can be generated by using non-treated tin solders but easily deflect during ejection. In our experiment, the deflection angle of jetting remains 5.8°. When the treated solder is melted and ejected, uniform metal droplet streams are ejected vertically down. These experimental result show that the stability of jetting can be improved and negative effects on the jetting process can be avoided by removing impurities inside the raw metals and carefully cleaning the crucible and orifice. 7. Effect of wetting behaviors between raw materials and the nozzle wall In the jetting process, the molten metal may wet the nozzle material. This wetting plays a significant role in jets formation. Here, two materials (i.e., brass and ruby, which have different wetting behaviors between liquid tin solder) are used for the jetting process to investigate the effect of nozzle wetting on metal jets ejection.

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Fig. 4.23 Jets breaking into uniform droplet streams from a untreated raw metal blocks, and b metal blocks with impurities being removed

Sn-40%wt.Pb liquid is ejected to form jets through a brass nozzle with different driving pressures and perturbations. The ejection parameters are shown in Table 4.6. When the driving pressure is low, the uniform droplet stream deflects (Fig. 4.24a). The tilted angle is approximately 12.3°. When the air pressure is increased to 80 kPa, the deflection angle of the droplet decreases to 2.75°. After the driving pressure increases to 100 kPa, the excitation frequency increases to 5.8 kHz, the uniform droplet stream does not deflect. When the ejection pressure reduces to 40 kPa, the jet disappears. The molten metal liquid spreads over the nozzle plates, resulting in the failure of the jet ejection (Fig. 4.24b). After that, the jet cannot rebuild when the ejection pressure increases to 100 kPa again.

4.2 Research on Uniform Droplet Continuous Ejection Behavior and Its … Table 4.6 Experimental parameters for ejecting tin solder droplets using copper nozzles

The serial number (a)

Ejection pressure, kPa 40

119 Perturbation frequency, kHz 1.85

(b)

80

2.6

(c)

100

2.95

(d)

40

/

Fig. 4.24 Photographs of uniform droplet streams ejected via nozzles with different materials. Uniform droplet streams generated via the brass nozzle with a the driving pressure of 40 kPa, and the disturbance frequency of 1.85 kHz; b the driving pressure of 80 kPa and the disturbance frequency of 2.6 kHz. c The driving pressure of 100 kPa and the disturbance frequency of 2.95 kHz. d Solder liquid accumulates outside the copper nozzle, resulting the failure of the uniform droplet ejection. e Stable uniform droplet streams are generated via the ruby nozzle

The ejection experiments show that, the liquid metal may accumulate at the outer surface of the nozzle plate since the tin solder liquid wets the brass very well. The wetting between the melt and the nozzle surface increases contact area of the metal liquid, resulting in the excessive inertial force for forming metal jets. Figure 4.24e is uniform droplet streams generated via the ruby nozzle with a diameter of 150 mm. The driving pressures of 40 and 80 kPa, and the perturbation frequency of 3.7 and 5.18 kHz are applied to obtain the left stream and the right stream, respectively. The results show that uniform metal droplet streams can be obtained without obvious deflection. The results show that since the wettability between ruby and tin solder liquid is poor (the wetting angle is greater than 90°), molten metal does not accumulate outside the nozzle plate during jets ejection, which benefits the stable ejection of uniform metal droplet streams. According to the above research, jets may fail to build or deflect when the liquid wets the outside of the nozzle. Uniform droplet streams can still form under the optimal perturbation. But, the deposition accuracy loses when the droplet stream

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deflection occurs. Therefore, it is suitable to choose the non-wetting materials for avoiding instability of jetting.

4.3 Charging and Deflection Control of Uniform Metal Micro Droplet Stream For controllably printing continuous ejected uniform metal droplets, it is necessary to charge and deflect uniform droplets for controlling of the droplet deposition position and suppressing droplet coalescence phenomenon during flight. This section focuses on the droplet charging control method, the charged droplet dispersion behavior, and the deflection trajectory control method.

4.3.1 Control of Droplet Charge of Uniform Metal Micro Droplets 1. Micro droplet charge detection device The accuracy of droplet charge determines the accuracy of droplet deflection distance. To precisely control droplet deposition position, the droplet charge should be first detected, and influence of test parameters on the droplet charge should be also understood. Figure 4.25 is the schematic diagram of the uniform metal droplet charge detection device. The working principle is that charged droplets are continuously deposited in a Faraday cup (double-layer metal cup, the inner and outer cups are insulated with each other. The inner cup is connected to the detection circuit). A small current is formed through the connecting circuit by discharging collected droplets in the inner cup. Since the charge of deposited droplets and their spacing is uniform, the average charge on each droplet can be deduced by detecting the average current generated by discharging. In this way, the droplet charge can be measured. According to the Rayleigh linear instability theory, the frequency of uniform droplet generation is the same as the excitation frequency. Therefore, the frequency of charged droplets deposited on the Faraday cup equals the droplet generation frequency (that is, the droplet deposition frequency is the same with the frequency of the excitation signal). Assuming that the droplet deposition frequency is notated as f and the detected current is notated as i, the droplet charge Q can be expressed as: Q = i/f

(4.26)

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Fig. 4.25 Schematic view of the droplet generation and charge apparatus

From Eq. (4.26), the average droplet charge can be easily measured via measuring the small current i generated by the droplet discharge in the Faraday cylinder. The principle of the detection circuit is shown in Fig. 4.26. The amplifying circuit consists of two OP129 operational amplifiers, which have the advantages of high measuring current resolution and low circuit noise. However, because the induced current is weak, the circuit is susceptible to being disturbed by electromagnetic interference and noise from the circuit system itself. To suppress the signal noise, a well-designed low-noise pre-amplifier circuit first amplifies the weak current and drives the post-amplifier to work. The outside feedback of the circuit is realized by a primary amplifying circuit working in a short-circuit mode. Assuming that the input signal of this circuit is the current signal I in and the output signal is the voltage signal V out , the voltage output of the detection circuit can be expressed as: Vout = −R f · Iin /(1 + j · f / f h ),

(4.27)

f h = 1/2π R f C f ,

(4.28)

where

and f is the signal frequency, Rf is the feedback resistance, and C f is the feedback capacitance. f is generally set below 10 kHz, much smaller than f h . Therefore,

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Fig. 4.26 Schematic diagram of the current detection circuit [6]

Eq. (4.27) can be simplified as Vout = −Iin · R f

(4.29)

In Fig. 4.27, R1, R2 and C1 and the amplifier shown in the left of the figure make of a basic internal feedback circuit. The gain of the amplifier can be adjusted by changing the values of R1 , R2, and C 1 . For the direct current, the capacitor C 1 in this amplifier circuit is in open condition. At this case, the gain of the open loop of the amplifier is calculated by multiplying the open gain of the two amplifiers. By adjusting R1 /R2 , the noise bandwidth and system noise can be reduced. In the droplet charge detection circuit, the C f , which is parallel to the external feedback resistance Rf , is used to reduce the noise bandwidth. C f can be calculated by Eq. (4.27). Fig. 4.27 Droplet charge as a function of the charge voltage

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2. Measurement of the droplet charge Figure 4.27 demonstrates measured charges of water droplets generated under different excitation frequencies. In these experiments, the nozzle diameter is 150 μm, the ejection pressure is 25.8 kPa, and three applied perturbation frequencies are 4.8 kHz, 5.8 kHz, and 7.8 kHz, respectively. Measured results show that droplet charges are close to each other at different charge voltages for the perturbation frequency equal to 5.8 and 4.8 kHz. The reason lies in that for the perturbation frequency of 5.8 and 4.8 kHz, the droplet diameters, which mainly determine the charge amount, are almost the same according to the classic Rayleigh jet instability theory mentioned by Eq. 2.15 in Chap. 2. Figure 4.27 also demonstrates that the charge of droplets is linearly proportional to the charging voltage. When the charging voltage is 300 V, the measured average charge reached the maximum among the measured results for both frequencies. Meanwhile, the standard deviation of the measured results is also very large. For the perturbation frequency of 7.8 kHz, the measured droplet charge differs greatly from the results in the above two conditions. The droplet charge does not have a linear relationship with the charging voltage. The reason is that jets do not work in the Rayleigh instability model under this condition. Liquid jets do not break into uniform droplets, resulting in non-uniform droplets and non-uniform droplet charge. The measured results also show that the droplet charge does not have a linear relationship with the charging voltage. The average measured charges of droplets are smaller than those in uniform-droplet conditions. 3. Effect of charging on the droplet size uniformity Metal droplets are ejected by using different parameters to reveal the effect of charging on the uniformity of the droplet size. These parameters are: the deposition distance of 3 cm, the ejection temperature of 543 K, and the combination of pressure and perturbation frequency of 110 kPa-11.5 kHz. The picture of collected metal droplets and the corresponding diameter distribution are shown in Fig. 4.28. Figure 4.28a shows that lots of medium particles mixed with several large-size merged particles are obtained. The statistics of the particle diameter (Fig. 4.28b) show that the number of merged particles is small. The standard deviation of the particle diameter is 22 μm. Merging droplets can be eliminated by charging metal droplets and generating a classic repulsive force between charged droplets. In the experiment, the ejection pressure of metal droplets is 110 kPa, the frequency is 11 kHz, and the deposition distance is 10 cm. A cup filled with the vacuum pump oil is used to collect metal droplets ejected under the above parameters. After droplets are solidified in the oil, the diameter of obtained metal particles is measured and counted. The picture of obtained metal particles and the diameter deviation are shown in Fig. 4.29. The droplet picture shows that the obtained metal particles are uniform (Fig. 4.29a). The diameters of about 320 droplets are counted (Fig. 4.29b). The droplet particles with a diameter between 160 and 170 μm account for more than 85% of the total number of measured particles. The standard deviation of the measured metal particle diameter

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Fig. 4.28 Collected metal particles at the deposition distance of 5 cm. a Metal particles; b Statistics of the particle diameter

Fig. 4.29 Picture and the size distribution of uniform metal particles produced by charging droplet streams. a Picture of uniform particles. b Statistics of the particle diameter

is 13 μm, demonstrating the high uniformity of particles. Compared to the results shown in Fig. 4.28, the results confirmed that charging metal droplet steams can eliminate the merging droplets and produce uniform metal particles.

4.3.2 Study on the Dispersion Behavior of Charged Uniform Droplet Stream Dispersion of charged droplet streams is caused by inclined electrostatic repulsive forces between charged droplets. Due to factors such as nozzle defects and impurities, a small distance exists between the droplet’s initial position and the droplet stream axis when jets break into uniform droplets. After droplets are charged, electrostatic repulsive forces between charged droplets have the horizontal component. This component will finally force droplets to fly off the droplet stream axis and

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cause dispersion. This dispersion generates a random deviation of the droplet deposition regarding the desired position, decreasing the droplet deposition accuracy. This section mainly investigates the influence mechanism of droplet dispersion behaviors on the droplet deposition accuracy under different parameters. This investigation is conducted by combining the charged droplet dispersion flight physical model (established in Sect. 2.2.2) and the charged uniform droplet stream dispersion experiment. The experimental device for measuring the dispersion of charged uniform droplets is shown in Fig. 4.30. The ejected liquid used in this experiment is red ink, the ejection pressure is 25.8 kPa, and the perturbation frequency is 5.7 kHz. The deposition position is set as 30, 35, 40, 45, and 50 cm directly down the nozzle. A white paper is placed on the deposition substrate to illustrate the position of dispersed droplets. Droplets arrive on the white paper to form a dispersed droplet pattern by horizontally moving the recovery tank with a narrow slot in the middle. To quantitatively study the dispersion position of the charged droplets, the dispersed droplet pattern is recorded at the deposition distance of 40 cm and 50 cm. The dispersed deposition distance of charged droplets can be calculated by using the theoretic model established in Sect. 2.2.2, Chap. 2. The calculated droplet deposition patterns at these two deposition distances are shown in Fig. 4.30c and f, respectively. The origin of the coordinates is located directly below the nozzle. Droplets are distributed in a nearly circular area. The distance from the left of the droplet dispersion area to its right is about 2 cm at the deposition distance of 40 cm. The distance from the dispersion area top to its bottom is about 2.5 cm. At the deposition distance of 50 cm, droplets are dispersed into a nearly circular area with a diameter of approximately 4 cm. Since the shape of the droplet deposition area is not a perfect circle, a special characterization method is proposed to calculate the diameter of dispersion area. First, the circular area filled with dispersed droplet is equally divided into 10 sectors after dispersed droplets deposit on the substrate. In each sector, the droplet dispersion radius is measured as the distance between the center and the farthest droplet. Then, the average value of this dispersion radius in ten circular sectors is taken as the dispersion radius Rdis . By using the proposed method, the measured dispersion radii are 1.1 cm and 1.9 cm, respectively, when the deposition distances are 40 cm and 50 cm. Figure 4.31 illustrates the above experimental results. At the deposition distance of 40 cm, the dispersion area is small and droplets are mostly concentrated in the center of the dispersion area. The droplet dispersion area has a nearly elliptical shape, the distance between the upper and lower boundaries of the deposition pattern is the major axis which is up to 3 cm, and the distance between from the left to right is minor axis which is less than 2 cm. The dispersion radius Rdis , taking as the average value of ten measurements, is 1.2 cm, as shown in Fig. 4.31b. The theoretically predicted value is 1.1 cm, as shown in Fig. 4.31c. Figure 4.31e shows that the dispersion radius Rdis measured at the deposition distance of 50 cm differs from the predicted result of 1.9 cm by only 0.14 mm. The experimental and predicted values are in good agreement.

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Fig. 4.30 Schematic diagram of the charged droplet dispersion process

Figure 4.32 shows average measured dispersion radii (Rdis ) and the responding standard deviations at five deposition distances of 30, 35, 40, 45, and 50 cm. The predicted dispersion radius (Rdis ) as a function of the deposition distance is also shown in this figure. For the deposition distance Z = 50 cm, the predicted value is in good agreement with the experimental one. The standard deviation of the deposition radius Rdis is small. However, when the deposition distance decreases, the difference between the predicted droplet dispersion diameter and the measured value increases. Meanwhile, the standard deviation of the dispersion diameter is also increased. For example,

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127

Fig. 4.31 Comparison of deposited droplet patterns with the predicted ones at the deposition distance of 40 cm (upper three figures) and 50 cm (lower three figures). a, d Deposited droplet patterns. b, e Extracted droplet patterns. c, f Predicted droplet patterns

Fig. 4.32 Measured and predicted radii (Rdis ) of the dispersed area as a function of the deposition distance Z

when the deposition distance is 30 cm, the measured dispersed diameter is 0.28 cm, and the standard deviation is about 0.13 cm. This phenomenon is caused by droplet splashing occurring by massive droplets deposited in a small area when the deposition distance is small. The droplet splashing also increases the standard deviation of the measured diameter. Figure 4.32 also shows that the critical deposition distance of the charged droplet stream without dispersion is 27 cm. That is to say, the dispersion radius is smaller than the droplet radius when the deposition distance is less than

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4 Uniform Metal Droplet Continuous Ejection and Printing Process …

27 cm. On the contrary, the deposition distance is larger than 27 cm, the droplet dispersion radius increases rapidly. Dispersion behaviors of metal droplets with different diameters are studied by using Sn-40 w.t.%Pb alloy as the ejection material. The dispersion threshold is defined as the dispersion radius equal to the droplet diameter. For the ejection pressure of 45.6 kPa, the calculated parameters like the droplet diameter, the droplet charge, and the ejection velocity are shown in Table 4.7. The predicted dispersion radii as functions of the deposition distance for different droplet sizes are shown in Fig. 4.33. The dispersion behavior of charging droplets with diameters of 90.4 and 121 μm is apparent. In those cases, the critical deposition distances, where the dispersion radius exceeds one droplet diameter, are 6.4 cm and 9.7 cm, respectively. Furthermore, the increase rate is fast for droplets with a diameter of 190 and 217 μm. Meanwhile, the critical deposition distances are 42.4 cm, 43.9 cm, and 53.9 cm for droplets with diameters of 190 μm, 217 μm, and 290 μm, respectively. For achieving accurate printing, droplet deposition distances should be shorter than the critical distances. Otherwise, unpredictable position perturbations will appear. Droplet streams with droplet diameters of 90.4 and 121 μm have short critical deposition distances. Droplets with diameters of 190, 217, and 290 μm have Table 4.7 Charge of droplets produced under different parameters

Fig. 4.33 Dispersion radii (Rdis ) of charged metal droplets as functions of the deposition distance Z

Droplet diameter (μm)

Droplet initial velocity (m/s)

Droplet charge (pC)

90.4

2.050

− 0.776

121

2.298

− 1.163

190

2.441

− 1.798

217

2.485

− 2.241

270

2.64

− 2.976

4.3 Charging and Deflection Control of Uniform Metal Micro Droplet Stream

129

long critical deposition distances, and the deposition distances to achieve accurate deposition are also relatively long. The results also show that the droplet dispersion behavior significantly affects deposition accuracy when the droplet diameter is close to 100 μm or less, showing an obvious size effect.

4.3.3 Implementation and Control of Deflected Flight of Charged Uniform Micro Droplets The charging voltage waveform and the physical properties of the ejected material have a great influence on the deflecting trajectory of charged droplets or droplet deposition position. The experiment parameters are listed in Table 4.8. The metal used in the experiment is the lead–tin alloy material (Sn-40 w.t.%Pb), which is polished carefully to remove the surface oxide and impurities. The ejection temperature is set at 250 °C. According to the Rayleigh jet instability theory, the experimental parameters for ejecting uniform water droplets are calculated: the ejection pressure is 25.8 kPa, and the excitation frequency is 2.84 kHz. The experimental parameters for ejecting uniform lead–tin alloy droplets are: the ejection pressure is 45.6 kPa, and the excitation frequency is 2.84 kHz. The perturbation frequency is 3.89 kHz. Charging pulses for droplet charging and deflection are generated by a charging circuit and loaded on the two charging electrodes by a shielded-twisted-pair cable. The frequency of charging pulses generated by the charging circuit is the same as the jet perturbation frequency for droplet generation. The amplitude of charging pulses can be modulated on demand. One of the deflection electrodes is connected to the positive pole of a high-voltage source. Another deflection electrode is ground to form a strong deflection electrostatic field and realizes the deflection control of charged droplets. A high-speed photography system is used to capture images of droplet deflection. The shooting area is 10 × 10 cm below the nozzle. The deflection experiment is conducted by using uniform water droplet streams obtained according to the parameters illustrated in Table 4.8. The images of the uniform water droplet streams before and after deflection are shown in Fig. 4.34a Table 4.8 Experimental parameters for charging and deflection with different materials

Ejection materials

Water

Tin–lead alloy 45.6

Ejection pressure (kPa)

25.8

Perturbation frequency (kHz)

2.78

Deflection voltage (V)

4000

Amplitude of charging pulses (V)

300

3.89

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4 Uniform Metal Droplet Continuous Ejection and Printing Process …

and b, respectively. Coalescence among droplets is not observed. The dispersion of the droplet stream is not apparent. During deflection, chaos of the droplet deflection can be randomly observed, as shown in Fig. 4.34c. The reason lies in that, factors, such as impurities inside the orifice, and disturbance of the perturbation signal, could randomly destroy the uniform droplet generation process. As a result, chaos happens in the droplet deflection process (Fig. 4.34c). To verify the feasibility of the droplet charging and deflection, four different charge pulses are used for charging droplets. These are ladder-shaped pulses, interval laddershaped pulses, square pulses, and amplitude-modulated square pulses. Droplets are deflected after being charged accordingly to reveal the influence of charging on the droplet deflection. Figure 4.35a is the schematic diagram of the ladder-shaped pulses. Each voltage change period corresponds to a droplet generation period so that uniform droplet formation and charging process can be coordinated. The lowest amplitude of charging pulses shown in Fig. 4.35a is 150 V. The highest value is 290 V. The amplitude variation is 20 V and the amplitude of charging pulses changes periodically. Figure 4.35b is a high-speed picture of the deflected droplet stream. Droplets are deflected to the left under the action of the electrostatic force. This picture shows that the distance between adjacent droplets is about 1–2 droplet diameters. As a result, deflected droplets easily coalesced with each other during the deflection process. Figure 4.36 is the schematic diagram of interval ladder-shaped pulses and the high-speed image of the droplet stream deflected by using those charging pulses. Figure 4.36a shows that the period of charging pulses is the same as the droplet generation period. The amplitude of charging pulses changes stepwise. Charged droplets space with uncharged droplets alternately to expand the deflected droplet spacing. Fig. 4.34 High-speed images for deflection of water droplet streams. a un-deflected uniform droplet stream. b deflected uniform droplet stream. c Chaos of the deflected uniform droplet stream at the deposition distance z equal to 84 mm

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131

Fig. 4.35 Ladder-shaped charging pulses and the deflected droplet stream. a Schematic diagram of the ladder-shaped pulses. b High-speed picture of the deflected droplet stream

Fig. 4.36 Schematic diagram of interval ladder-shaped pulses and the high-speed image of the deflected droplet stream. a Interval ladder-shaped pulses. b High-speed image of the deflected droplet stream

Figure 4.36b shows the high-speed images of the deflected droplet stream. The droplet spacing is increased, which can effectively eliminate the droplet coalescence. Figure 4.37 shows the deflection of the droplet stream charged by square charging pulses. The width of square pulses equals one droplet production period. The amplitude of each pulse is the same (Fig. 4.37b). Under those charging pulses, the spacing between charged droplets increases, resulting in the decrease of the electrostatic repulsive force among droplets. Therefore, deflected droplets have the same fly trajectory, and their deflection distance is basically the same when depositing. It can be considered that droplets are subjected to balanced electrostatic forces and keep the fly trajectory stable.

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Fig. 4.37 Schematic diagram of square pulses and the high-speed image of the deflected droplet stream. a Square pulses. b High-speed image of the deflected droplet stream

Figure 4.38 shows the shape of the amplitude modulated square pulse and the highspeed image of the corresponding deflected droplet stream. Figure 4.38a shows that the charging pulse amplitude varies between 150, 200, 250, and 300 V sequentially. Figure 4.38b shows that the deflection distance is about 1 mm with the maximum (300 V) charging voltage. The deflection distance varies correspondingly when the charging amplitude changes. Since droplets are charged alternatively, droplets suffer weak unbalanced electrostatic repulsive forces. Therefore, the deflected droplets can form a perfect “ladder”-shaped queue during flight. The metal droplet charging and deflection experiments are conducted after water droplets are successfully deflected. The single-droplet-charging and double-dropletcharging square pulses are used to achieve different types of droplet deflection, as

Fig. 4.38 Schematic diagram of amplitude modulated square pulses and the high-speed image of the deflected droplet stream. a Amplitude modulated square pulses. b High-speed image of the deflected droplet stream

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133

Fig. 4.39 Droplet streams deflected with different charging pulses. a Deflection of droplet stream charged with single-droplet-charging pulses. b Deflection with double-droplet-charging pulses. c Comparison of measured and predicted deflection trajectories

shown in Fig. 4.39a and b. Those pictures are taken at a distance of 7.3 ~ 8.4 cm down from the nozzle. Figure 4.39a shows that, when the droplet stream is charged by single-dropletcharging square pulses, trajectories of deflected droplets are stable and agree well with predicted ones. The main reason is that electrostatic forces on each charged droplet are almost the same, resulting in similar trajectories. Figure 4.39b shows the picture of the droplet deflection by using double-dropletcharging square pulses. The high-speed image clearly shows that, trajectories of droplets, charged simultaneously, are different. This phenomenon is caused by different electrostatic repulsive forces on two adjacent charged droplets, leading to different deflection distances during flight. Figure 4.39c shows the predicted and measured droplet deflection distances as functions of the deposition distance in the above two charging models. The measured results demonstrate that the balance of electrostatic repulsive forces on charged droplets is an important factor for achieving controllable droplet deflection. Figure 4.40 shows that droplets are charged with amplitude-modulated square pulses, of which the amplitude changes to 150, 200, 250, 300 V sequentially. Figure 4.39a illustrates deflected droplets. This picture is taken at the distance z ranging from 63 to 73 mm. The droplet stream on the left is the un-deflected droplet stream, while on the right is the deflect stream. Figure 4.40b demonstrates the comparison of the measured and predicted trajectories of deflected droplets. Theoretical droplet trajectories are calculated by ignoring the electrostatic repulsive force among droplets. The measured deflection distance is slightly larger than the predicted one. The average difference between the theoretical and measured results is 0.05 mm under the amplitude of charging pulses at 300 V. Differences are 0.078 mm, 0.08 mm, and 0.067 mm for the charging pulses with amplitudes of 250 V, 200 V, and 150 V, respectively.

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Fig. 4.40 Deflection of the metal droplet stream charged with amplitude modulated square pulses. a Picture of the deflected droplet stream. b Measured and predicted deflection trajectories of droplets

The difference between the theoretical and experimental results of the droplet deflection distance by using the above charging methods is less than 0.1 mm, proving the validity of the proposed droplet dynamic models.

4.3.4 Temperature History of Uniform Metal Droplets During the Deflection Flight The temperature of uniform metal droplets continuously cools down during the droplet charging and deflection process. Since different-sized droplets have special flight speeds and trajectories, their temperature histories should be different from each other. This section focuses on modeling and analysis of thermodynamics during droplet deposition, including temperature field evolution, material phase changing, etc. Furthermore, the temperature and physical state of droplets while depositing is predicted to guarantee the internal quality of printed parts. Sn-40w.t.%Pb alloy is used to study thermodynamic behaviors of the droplet during the flight process. The thermal properties of Sn-40w.t.%Pb alloy are listed in Table 4.9. During the test, the inner diameter of the orifice is 100 μm. The ejection pressure is 45 kPa. The frequency is set to 6 kHz. The initial temperature is set at 300 °C. In theoretical calculation and experimental measurement, the origin of the coordinates is located at the center of the orifice outlet. The positive direction of the z coordinate is consistent with the ejection direction. Figure 4.41 shows measured results and the theoretical curve of the droplet temperature as a function of the deposition distance. The droplet temperature is measured at the deposition distances (Z) equal to 5, 10, 15, 30, 40, and 45.8 cm. During measurement, a thermocouple is used to measure the droplet temperature and the highest response temperature is recorded as the measured result.

4.3 Charging and Deflection Control of Uniform Metal Micro Droplet Stream

135

Table 4.9 Material thermal properties of Sn40w.t.%Pb alloy Material

Specific heat in solid state cL (J/(kg·K))

Specific heat in liquid state cS (J/(kg·K))

Melting point T L (K)

Latent heat ΔH f (J/kg)

Sn60/Pb40

186.2

212.9

456

47,560

Fig. 4.41 Droplet temperature T d as a function of deposition distance Z

In the liquid state cooling stages (for Z = 5 and 10 cm), measured results are about 20 K higher than the theoretical calculation. The reason mainly lies in that the ambient gas temperature used in the calculation differs from the real condition. In the theoretical model, the ambient gas temperature is set at room temperature and is assumed to be constant during deposition. However, in the experiment, the gas on the droplet fly trajectory is continuously heated by hot metal droplets. Therefore, measured droplet temperatures are higher than theoretical values due to the small temperature difference between the environment gas and droplets. Figure 4.41 also shows that the measured and predicted temperatures agree well when metal droplets transfer from the liquid state to the solid state (Z ~ 0.1–0.45). In this thermal stage, the heat latent released during droplet solidification compensates thermal losses of droplets. As a result, the droplet temperature is the melting point of droplets. When metal droplets deposit, their deposition temperatures and thermal states determine the internal quality of printed parts. Therefore, precise prediction of the thermal history of droplets is necessary for achieving high-quality microstructures. According to the theory for predicting metal droplet kinetics and thermodynamic behaviors in Sects. 2.4.1 and 2.4.2, Chap. 2, flying velocities, flying trajectories, and thermal histories of ejected tin–lead droplets are calculated with the nozzle diameter of 50 μm, 70 μm, 100 μm, 120 μm, and 150 μm, respectively. Before calculating the droplet fly trajectory, thermal history, and solidification process, the droplet velocity should be first calculated as a function of the deposition

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4 Uniform Metal Droplet Continuous Ejection and Printing Process …

Fig. 4.42 a Droplet flying velocity V d as a function of the deposition distance Z. b Predicted flying trajectories of different size droplets

distance. Figure 4.42a illustrates the relationship between the velocity of deflected droplets and the deposition distance. For droplets with a diameter of 90.5 μm, the droplet velocity increases from 2.05 m/s (initial velocity) to 2.22 m/s inside the electrostatic deflection field. Droplets slow down dramatically after flying out of the electrostatic deflection field. The droplet velocity decreases to 1.2 m/s after depositing 25 cm, showing that the effect of gravity is less than the droplets’ gas drag. For droplets with the diameter of 121 μm, the velocity variation trend is like that of 90.5 μm diameter droplets except the small amplitude of variation. When the droplet diameter is larger than 190 μm, droplets accelerate gradually during fly. For instance, the velocity of droplets with 270 μm diameter increases from 2.52 to 3.02 m/s. Deflection trajectories of charged droplets with different sizes can be obtained by integrating corresponding droplet fly velocity curves. As shown in Fig. 4.42b, smallsize droplets have great deflection distance. For example, at the deposition distance of 30 cm, the deflection distance of the 90.4 μm diameter droplet exceeds 10 cm, while the deflection distance of the 270 μm diameter droplet is only 1.3 cm. The predicted results show that a great difference exists among the deflection distance of different sizes of droplets. Based on theoretical velocity curves and deflection trajectories of deflected droplets, the temperature history and solidification fraction of droplets can be calculated with the five above-mentioned droplet sizes. In the calculation, the initial droplet temperature is set at 300 °C. The assumption is that, when the droplet temperature drops to the metal melting point (183 °C), droplets start the solidification process. Droplets keep their temperature constant until being totally solid (i.e., the solid fraction of droplets is 1). After that, droplets start the solid phase cooling. Droplet temperature histories of different-sized droplets as a function of the deposition distance are shown in Fig. 4.43a. Here, small droplets have a rapid cooling rate and start the nucleation faster than large-sized droplets.

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137

Fig. 4.43 a Droplet temperature as a function of the deposition distance Z. b Solid fraction as a function of Z

While printing, if droplets are in a liquid state, it is easy to cause printing drawbacks such as collapse, and deformation. Meanwhile, if droplets are totally solid, printing droplets could bounce off without remelting deposited ones. Therefore, while depositing, droplets should be in a proper temperature range to avoid the above-mentioned defects. The proposed model can provide a guide for selecting the deposition distance of printing parts (or for controlling the droplet deposition temperature). The relationship between temperature and deposition distance of droplets of different diameters is shown in Fig. 4.43a. The figure shows the small diameter droplets cool faster, then solidify and crystallize earliest. When the part is deposited, if the droplet temperature is too high and it is entirely liquid, it may cause defects such as collapse and deformation of the part. If the droplet is completely solidified, the droplet cannot be remelted with the deposited droplet and bounce. Therefore, when the droplet is deposited and formed, the droplet needs to be in a suitable temperature range to avoid the defects mentioned above. The built model can provide a basis for selecting the deposition distance when the metal droplet is formed. Figure 4.43b shows the relationship between the droplet solidification fraction and the deposition distance. Different-sized droplets begin to solidify at different deposition distances. The deposition distances of droplets with a diameter of 90.5 μm and 121 μm begin to solidify at the deposition distance of 2.5 cm and 4.5 cm, respectively. Meanwhile, for droplets with a diameter of 180 μm, 217 μm, and 270 μm, this distance is 11.2 cm, 14.5 cm, and 22.1 cm, respectively. Different-sized droplets solidify completely at different deposition distances. For instance, when the droplet’s initial temperature is 300 °C, straight fly-down droplets with a diameter of 90.5 μm have only 6 cm deposition distance for solidification. According to the theoretical calculation, for achieving good deposition results, the deposition distance should not exceed 8.5 cm for 90.5 μm diameter droplets, or between 11 and 40 cm for 190 μm diameter droplets.

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4 Uniform Metal Droplet Continuous Ejection and Printing Process …

4.4 Free Forming by Continuous Ejection of Uniform Metal Droplets and Its Controlling Method 4.4.1 Influencing Factors and Research Methods for Free Forming by Continuous Droplet Ejection Many experimental parameters exist and affect each other in the continuous deposition of metal droplets to free-form parts. This section analyzes the experimental parameters involved in metal droplet printing based on previous research. Meanwhile, experimental research are also conducted to find the parameter influence law and the proper forming parameter combination to achieve precise parts printing. 1. Influencing factors for free forming by continuous droplet ejection The influencing factors of the forming process of micro metal parts can be classified into metal droplet deposition parameters and deposition substrate parameters (Fig. 4.44). The droplet ejection parameters include droplet flight speed, size, temperature, and solid phase fraction when depositing, etc. The deposition parameters mainly include substrate motion speed, temperature, thermal conductivity, and surface material, etc. Droplet ejection and deposition parameters determine the dynamic and thermal droplet behaviors such as wetting and spreading, remelting, cooling, and solidification. Furthermore, these parameters determine the dimensional accuracy, shape accuracy, internal metallurgical quality, and mechanical properties of printed parts. 2. Research Methodology Because of the complex interaction among the above parameters, it is difficult to control the shape and quality of internal metallurgical bonding of formed parts through a certain parameter. Therefore, in this section, by designing a multifactor orthogonal experiment, the influence of the three main parameters, i.e.,

Fig. 4.44 Influencing factors of free forming of metal droplet deposition

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139

nozzle diameter, droplet ejection temperature, and substrate movement speed, on the characteristic dimensions (i.e., wall thickness and layer thickness) of the formed small metal pipes are analyzed. In the above three parameters, the orifice diameter determines the droplet diameter and the initial ejection and deposition speed. The orifice diameter also indirectly affects the dynamic droplet behaviors while droplets deposit. Therefore, the orifice diameter is taken as an important considering factor. The thermal states (i.e., deposition temperature and solid fraction) of the metal droplet during deposition determine the remelting depth between deposited metal droplets and the solid substrate or the solidified metal layer. The thermal states affect the shape of printed parts significantly and are also considering factors. The movement speed of the substrate directly determines the shape of the printed metal lines. A slow substrate speed may cause multiple droplet accumulation, resulting in bulging molten pools and changing the shape of printed metal lines. On the contrary, a fast substrate speed may cause overlapping failure and defects on the printed metal lines. Table 4.10, the L9 (34) orthogonal test table by selecting the three levels of three factors for estimating the influence level of parameters. Here, three levels of the orifice diameter are 50 μm, 100 μm, and 150 μm, respectively. The three levels of the droplet ejection temperature are taken as 230 °C, 250 °C, and 270 °C, respectively. The substrate motion speed is taken as 0.5, 1, and 5 mm/s. The investigation index is the layer thickness or the wall thickness of formed parts, which characterizes the minimum dimensions formed in the vertical or horizontal directions (i.e., vertical dimensional resolution and horizontal dimensional resolution). A series of thin-walled metal tube-forming experiments are conducted according to the experimental parameters shown in Table 4.10. In experiments, the ejection Table 4.10 L 9 (34 ) Orthogonal test table and the experimental results of metal tube formation Test number

Experimental parameters Orifice diameter

Ejection temperature

Evaluation index Substrate motion speed/mms−1

Layer thickness/mm

Wall thickness/mm

1

1(50)

1(230)

1(0.5)

0.52

0.62

2

1(50)

2(250)

2(1)

0.38

0.78

3

1(50)

3(270)

3(5)

0.26

0.71

4

2(100)

1(230)

2(1)

0.70

1.60

5

2(100)

2(250)

3(5)

0.42

1.35

6

2(100)

3(270)

1(0.5)

0.65

1.65

7

3(150)

1(230)

3(5)

0.75

1.91

8

3(150)

2(250)

1(0.5)

0.83

2.18

9

3(150)

3(270)

2(1)

0.96

2.45

140

4 Uniform Metal Droplet Continuous Ejection and Printing Process …

pressure is set to 60 kPa, the deposition distance is approximately 10 cm. The excitation frequency is calculated according to the Rayleigh instability theory. When the test is completed, the layer thickness and the wall thickness of printed parts are measured, respectively. The average of ten measurements is taken as the final evaluation index.

4.4.2 Parameter Control of Free Forming by Continuous Ejection of Uniform Metal Droplets Under the combination of the above three minimum parameters (sample No. 1), the formed part has the thinnest wall thickness, about 0.6 mm (Fig. 4.45). In this experiment, the ejection temperature is low (230 °C), metal droplets solidify immediately after contact with the substrate and obtain initial deposition layers with obvious porosity (Fig. 4.45b). Meanwhile, due to the low substrate motion speed (0.5 mm s−1 ), many droplets are deposited in the same position, resulting in a large local heat input. Later deposited droplets remelt solidified ones to form a molten pool, producing local bulges under the action of fluid surface tension (Fig. 4.45c). Local bulges lead to the uneven height of deposited metal tracks, resulting in the fluctuation of subsequent deposition layers. The average position error of the layer center is about 0.6 mm in the same layer. The maximum error can reach 1 mm. The thickness of each layer is uniform except the initial deposition layer, which has 0.5 mm thickness and is thicker than other layers. When the nozzle diameter is taken the largest size, the temperature is set to the highest one, and the substrate motion speed is slow (sample No. 9), the average layer thickness and wall thickness of the formed sample are relatively large ( i.e., 0.95 mm and 2.45 mm, respectively, as shown in Fig. 4.46). Printed results show that a small amount of metal liquid overflows between deposited layers. The reason may lie in that the deposited liquid metal cools down slowly due to the thick deposition layer. The deposited liquid metal, with good fluidity, easily flows down, and finally solidifies between the layers. As a result, the overall surface quality of this sample

Fig. 4.45 No. 1 sample [7]. a Front view if the printed sample. b Initial layer contacting with the substrate, c Picture of sample. The scale bar is 1 mm

4.4 Free Forming by Continuous Ejection of Uniform Metal Droplets and Its …

141

is better than that in No. 1. No obvious macroscopic surface fluctuation and local bulges are observed. Flat and smooth metal layers can be obtained. When the parameters are taken as the smallest nozzle, the highest temperature, and the fastest substrate moving speed (sample No. 3), a small tube is printed with the finest shape (i.e., the thinnest wall thickness, the smallest layer thickness, as shown in Fig. 4.47a). Its average wall thickness and layer thickness are approximately 0.7 mm and 0.26 mm, respectively. Each layer has relatively uniform thickness, which forms a uniform layered morphology, as shown by the enlarged side view in Fig. 4.47b. Since the substrate temperature is low, droplets solidify quickly while spreading, resulting in irregular shapes at the tube bottom (Fig. 4.47c). The part is cut and polished radially at 11 mm from its bottom. The cross-section shows that the formed part has a uniform wall thickness and a regular ring shape, without obvious defects such as pin holes and cold shuts (Fig. 4.47d). To study the significant influence of experimental factors on each index, variance analysis is conducted on the results of the orthogonal test. Table 4.11 demonstrates that the orifice diameter has a great effect on the layer thickness of the sample,

Fig. 4.46 No. 9 sample [7], a front view, b top view

Fig. 4.47 No. 3 sample, a Picture of the metal tube. b Enlarged side view. c Bottom layer. d Cross-section at 11 mm from the tube bottom

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4 Uniform Metal Droplet Continuous Ejection and Printing Process …

the movement speed of the substrate has a significant effect on the layer thickness, and the ejection temperature has an important effect on the layer thickness. Table 4.12 demonstrates that the diameter of the nozzle hole has a great effect on the wall thickness of the sample, and the speed of the substrate movement and the ejection temperature both have a significant effect on the wall thickness. Variance analysis shows that when other test parameters remain unchanged, the droplet size is the main factor affecting the wall thickness and the layer thickness. Large-size metal droplets contain more thermal energy during deposition. Since the solidification time is relatively long, unsolidified large droplets easily coalesce during the printing process, which deteriorates the accuracy of formed parts’ shape and dimension. Therefore, to achieve high-resolution printing, a small size orifice should be used to print small metal droplets. Meanwhile, the moving speed of the substrate should be increased accordingly to avoid the coalescence of molten metal liquid. The mentioned samples are printed by direct deposition of uniform metal droplets without charging and deflection. The shape of the parts is simple. For printing complex parts, the ejected metal droplets need to be charged and deflected for controlling the printing traces. To verify the effectiveness of the charge and deflection on the droplet deposition, a trapezoidal charging voltage pulse (Fig. 4.48a) is used to print a solder bump array combined with movements of the motion platform. In the Table 4.11 Variance analysis of factor effect on the layer thickness Source of error

Sum of Degree Mean squares of of squared deviations freedom deviation

Orifice diameter

0.445267

2

0.222633 351.53

Ejection 0.015267 temperature

2

0.007633 12.05

Substrate speed

0.0266

2

0.0133

Error

0.001267

2

0.000633

F Value Fα critical Significance Optimal value solution

21

F0.01 (2,2) = 99 F0.05 (2,2) = 19 F0.1 (2,2) =9

1

A1

3

B2

2

C3

Table 4.12 Variance analysis of factor effect on the wall thickness Source of error

Sum of Degree Mean F Value Fα critical Significance Optimal squares of of squared value solution deviations freedom deviation

Orifice diameter

3.28762

2

1.64381

875.40

Ejection 0.08276 temperature

2

0.04138

22.04

Substrate speed

0.12382

2

0.06191

32.97

Error

0.00376

2

0.00188

F0.01 (2,2) = 99 F0.05 (2,2) = 19 F0.1 (2,2) =9

1

A1

2

B1

2

C3

4.4 Free Forming by Continuous Ejection of Uniform Metal Droplets and Its …

143

test, the droplet ejection temperature is approximately 563 K. The orifice diameter is 150 μm, the ejection pressure is 45 kPa. The excitation frequency is between 3 and 4.5 kHz. The amplitude of the applied charging pulse voltage gradually increases as 150, 200, 250, and 300 V. The deposition substrate is made of copper. The droplets are deposited in a drop-on-stop model. That is, metal droplets are not deflected and deposited on the substrate while moving. They are directly deposited into the recycling tank to be recycled. After the substrate moves a certain distance and stops, droplets are deflected and deposited on the substrate by applying charging voltage pulses. Figure 4.48b illustrates the deposition results. Uniform molten metal droplets print an array of bumps with a spread diameter of 500 μm on the copper substrate. Each row of the bump array consists of four droplets by charging and deflection. The distance between each row is approximately 3 mm. Experimental results show that charging pulses can control the deposition of a single mono-sized metal droplet individually. However, results also show that the metal droplet deposition process is highly susceptible to disturbance since the spacing between deflected metal droplets is not very uniform. Figure 4.49 demonstrates a printed result by charging and deflection using a wide charge voltage pulse. Here, deflected droplets are deposited on the left, and undeflected droplets are deposited on the right. In the experiment, 100 charged and 100 uncharged droplets are interval between each other, while the deposition substrate moves back and forth. Other parameters are the same as those in the previous droplet ejection. After printing multi-layer by metal droplets, a parallel “wall”-like part is obtained. This part demonstrates that deposited droplets are evenly divided into two streams. The gap between the two deposited “walls” are clear, showing the feasibility and stability of metal droplet deposition by charging and deflection. Figure 4.49 shows the stable deposition of metal droplets by using a broad charging pulse. The charging pulses used for this deposition are shown in Fig. 4.50a. The charging voltages are 400, 200, and 0 V. The substrate moves in a circle. The charging

Fig. 4.48 Charging and deflection of metal droplets [8]. a charging voltage pulse, b metal droplet array printed by droplets charging and deflection

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4 Uniform Metal Droplet Continuous Ejection and Printing Process …

Fig. 4.49 Printed results by charging and deflecting of metal droplets [8]

voltages switch between 0, 200, 400 V in the first 4 turns; in the last 6 turns, the charging voltages switch between 0 and 400 V. Therefore, the number of layers of metal microdroplets deposited under different charging voltages is 10, 4 and 10, respectively. The number of layers of metal droplets deposited under different charging voltage conditions is 10, 4, and 10 layers, respectively. Figure 4.49b shows the three intersecting regular pentagons obtained under the above deposition strategy. The side length of the regular pentagon is 5 mm. The deposition time is 12 s, the surface is smooth, the wall thickness is uniform, no

Fig. 4.50 Droplet deposition using charge deflection control [9]. a Charge pulse, T ' is the time for one week of substrate rotation, approximately 0.5 s. b Staggered orthogonal pentagon shaped using a wide charge pulse approach

References

145

defects such as local swelling. Due to the accumulation of metal droplets during the multilayer deposition of the parts on both sides, the wall thickness of the pentagon with 10 layers is larger than the four in the middle. The deposition results clearly show that the deposition and forming process of uniform metal droplets can be effectively controlled by coordinating the charging voltage pulse and the substrate movement.

References 1. Kundu PK, Cohen IM, Dowling DR. Fluid mechanics. Singapore: Elsevier; 2013. 2. Youngs DL. Numerical methods for fluid dynamics. New York: Academic; 1982. 3. Brackbill JU, Kothe DB, Zemach C. A continuum method for modeling surface tension. J Comput Phys. 1992;100(2):335–354. 4. Alvarez R, Carlos J. Control of the UDS process for the production of solder balls for BGA electronics packaging. Vet Rec. 1997;114(10):91–2. 5. Schummer P, Tebel KH. Production of monodispersed drops by forced disturbance of a free jet. Ger Chem Eng. 1982;5:209–20. 6. Shu D, Qi L, Luo J, et al. Design and realization of measurement system for charge on the droplet in uniform droplet deposition. Chin J Sci Instrum. 2008;29(10):2150–5. 7. Jiang X. Study on the generation of uniform metal droplet flow and its stable ejection. Xian: Northwestern Polytechnical University; 2010. 8. Luo J. Charge deflection and control of uniform metal droplet for micro-part spray forming. Xian: Northwestern Polytechnical University; 2010. 9. Luo J, Qi L, Zhou J, et al. Study on stable delivery of charged uniform droplets for freeform fabrication of metal parts. Sci China Technol Sci. 2011;54(7):1833–40.

Chapter 5

On-Demand Ejection and Control of Uniform Metal Droplets

5.1 Introduction On-demand ejection of uniform metal droplets is the process of forcing tiny molten liquid metal out of a nozzle by applying a pressure pulse to form a single metal droplet. The size and initial velocity of the metal droplet depends on the shape of the pressure pulse. In this chapter, the technical features of drop-on-demand (DOD) ejection technologies utilizing Pb–Sn alloy and aluminum alloy as the ejection materials, and driven by pneumatic pulse, acoustic pulse, and stress-wave pulse are studied by combining numerical and experimental research. The influence of parameters such as the droplet size, size uniformity, and the range of controllable ejection parameters that produce uniform metal droplets are obtained for the above three ejection-driven models in order to lay the foundation for the selection of uniform metal droplet ejection technology.

5.2 On-Demand Ejection Behavior of Metal Droplets Driven by Pneumatic Pulse and the Influence of Parameters 5.2.1 Research on On-Demand Ejection of Uniform Tin–Lead Alloy Droplets Metal drop-on-demand ejection driven by a pneumatic pulse is a complex nonlinear hydrodynamic process. It is difficult to establish analytical models for describing breakup behaviors of metal jets. Fortunately, during the metal jet ejection, the evolution low of physical fields (i.e., the velocity and pressure fields) can be observed based on numerical simulation and experimental tests of metal droplet ejection. The

© National Defense Industry Press 2023 L. Qi et al., Metal Micro-Droplet Based 3D Printing Technology, https://doi.org/10.1007/978-981-99-0965-0_5

147

148

5 On-Demand Ejection and Control of Uniform Metal Droplets

simulated and experimental results can be used to understand the mechanism of the metal droplet formation and serve as a guide for parameter selection. 1. Numerical modeling and analysis of on-demand ejection of uniform Tin–Lead alloy droplets A numerical model was first established to reveal the mechanism of metal droplet on-demand ejection driven by pneumatic pulses and, additionally, to observe the influence of specific parameters on droplet ejection. The continuity equation and momentum conservation equations of the metal fluid’s motion under a pneumatic pulse are the same as those of the continuous jetting process in Chap. 4 (see Eqs. (4.1) and (4.2) for details). This section uses the VOF method to solve the continuity and momentum conservation equations numerically. The solution method and the reconstruction method of the liquid’s free surface are detailed in Sect. 4.2.1. This section focuses on the physical modeling methods of pneumatic pulse-driven droplet on-demand ejection. In pneumatic pulse-driven metal droplet on-demand ejection, the crucible is made of a short quartz tube. One end of the quartz tube is contracted to form a small nozzle. The profile of its inner surface is a complex streamline, which is difficult to describe using simple geometry. In the experiment, the tin alloy can be easily “demoulded” from the crucible after the molten alloy has solidified. The shape of the inner surface could be reflected by the outline of the solidified alloy, and thus the inner shape of the nozzle could be easily obtained by measuring the outline of the solidified alloy. Figure 5.1a shows the outline of the solidified Pb–Sn alloy block taken out of the crucible. The crucible and the nozzle can be described by using a two-dimensional axisymmetric model since they are axisymmetric. The cylindrical coordinate system is established with the middle of the left side of the alloy block as the origin (the z-axis is the axis of symmetry, and the r-axis is the radial coordinate). The z-axis is the symmetry axis of the nozzle internal model, and an image edge finding algorithm is used to obtain the outer contour of the alloy block. The internal nozzle geometry model can then be built by reconstructing the contour (Fig. 5.1b).

Fig. 5.1 Nozzle inner contour modeling. a The morphology of the inner surface of the nozzle obtained by photography. b The extracted crucible inner surface profile data. c The local profile of the nozzle inner surface determined by an extrapolation method

5.2 On-Demand Ejection Behavior of Metal Droplets Driven by Pneumatic …

149

Because the wetting angle between the Pb–Sn alloy liquid and the inner wall of the quartz crucible is about 160° (the metal liquid does not wet the quartz surface), the solid Pb–Sn alloy liquid cannot totally fill the tiny nozzle hole under the effect of surface tension. Therefore, Fig. 5.1b does not perfectly reflect the inner shape of the small nozzle near the nozzle outline. The established nozzle geometry model needs to be further improved hence, after obtaining the internal nozzle profile, the four points near the right side are linearly fitted to obtain a linear profile expression. Then the x coordinate of the nozzle outlet (shown as the rightmost point in Fig. 5.1c) can be calculated by extrapolation using the measured nozzle diameter. In this way, a complete geometry model of the nozzle area can be established. Several assumptions are made before conducting the simulation of Tin–Lead alloy droplet ejection: (1) Density, viscosity, and surface tension of the liquid metal are considered as constants since the temperature varies only slightly in the droplet ejection process. (2) The liquid flow during ejection is considered to be laminar. (3) The liquid metal is taken as an incompressible Newtonian fluid. That is to say the density, viscosity, and surface tension of the liquid metal are considered to be constant. 2. Determination of the initial and boundary conditions A 2D axisymmetric model is established to simulate droplet generation, as shown in Fig. 5.2a. Here, the initial zone and mesh conditions are also illustrated. In Fig. 5.2a, the nozzle domain O1 has the initial condition of liquid metal. Unstructured meshes are used to adapt to the complex inner surface of the nozzle. A rectangular area directly below the nozzle is the droplet generation domain, which is initialized as the gas domain O2 . The width and length of this domain are 1 cm and 2 cm, respectively. This droplet generation domain is divided by dense and uniform structured meshes to accurately simulate the change of the droplet contour. Boundary conditions are schematically shown in Fig. 5.2b. The axis of the nozzle and the left edge of the gas domain are set as the axis of symmetry. Inner surfaces of the nozzle and crucible are set to a no slip wall condition. The top of domain O1 is considered as the gas pressure inlet, where measured pneumatic pressure pulses are loaded. The bottom and right sides of the gas domain O2 are set as pressure outlets. The pneumatic pressure pulse for ejecting uniform Tin–Lead alloy droplets is measured by using a piezoelectric pressure sensor. The sensor is directly connected to the crucible through the top cover of the droplet generator. The measured pressure waveform is applied to the inlet pressure boundary after filtering the signal noise. Here, the measured pressure can be represented by using a Fourier series with multiple sinusoidal and cosinoidal harmonics with different frequencies: P(t) = A0 +

m E n=1

An cos(2nπ f t) +

m E n=1

Bn sin(2nπ f t)

(5.1)

150

5 On-Demand Ejection and Control of Uniform Metal Droplets

(a)

(b)

Fig. 5.2 Schematic diagram of 2D axisymmetric model and boundary conditions a 2D axisymmetric model of nozzle and droplet generation domains, b boundary conditions

where An and Bn are the coefficients of the Fourier series, and f is the perturbation frequency. The above parameters can be calculated from measured results of the pressure pulse. The order of the Fourier series, m, is generally taken as 15 for the pneumatic pulse. Since the piezoelectric sensor cannot operate at the temperature required for melting metal, the pressure fluctuation is measured at room temperature. During this measurement, the crucible is filled with water of a volume equal to that of the melted metal during metal droplet generation. The measured results are approximate to the pressure fluctuation for metal droplet ejection. The typical pressure curve is plotted in Fig. 5.3. The ejection material is Sn–Pb alloy (ZHLZn60PbA) with a melting point of 456 K. The density, surface tension, and kinematic viscosity of the liquid metal at the ejection temperature (T ) are linearly estimated by [2] X = X m + (T − Tm )(d X/dT )

(5.2)

where X and X m are the density, surface tension, and dynamic viscosity of the liquid metal at the ejection (T ) and melting temperature (T m ), respectively. dX/dT is the corresponding rate of change describing the variation of material properties with the change of temperature. To ensure the alloy is completely melted during ejection, the heating temperature is set to 550 K at the crucible. The corresponding material properties for Sn–Pb alloy (ZHLZn60PbA) in the liquid phase at this temperature are summarized in Table 5.1.

5.2 On-Demand Ejection Behavior of Metal Droplets Driven by Pneumatic …

151

Fig. 5.3 Fitting of the pressure fluctuation [1] (the pulse width of the driven signal is 200 μs)

Table 5.1 Pb–Sn alloy property parameters Material

Density of liquid metal, ρ l (Kg/m3 )

Surface tension of liquid metal σ l (N/m)

Dynamic viscosity of liquid metal, μl (Pa.s)

ZHLZn60PbA

8474.4

0.494

0.0013

The wetting angle between the Pb–Sn alloy liquid and the internal wall of the quartz crucible and nozzle is an important boundary condition that should be determined before simulation. The wetting angles between the Pb–Sn alloy of different compositions and the quartz glass are slightly different (Fig. 5.4) [3]. When the weight content of Sn in the alloy is around 60% (near the eutectic zone), the wetting angle between the melted alloy and quartz surface is about 130°, which changes slightly with variations in temperature above the melting point. 3. Simulation results and analysis (1) The forming mechanism of a single metal droplet Figure 5.5 shows the simulated results of the single Pb–Sn alloy droplet ejection process. The metal jet is ejected from the nozzle within 11–14 ms after the pressure pulse is applied. When the jet starts emerging from nozzle, its tip rapidly contracts into a spherical shape (Fig. 5.5a–d). Meanwhile, the bottom of the jet begins necking (Fig. 5.5c). This necking increases as the jet length increases (Fig. 5.5d). At a time of 15 ms, the jet’s neck is equal to the jet radius and the spherical jet tip separates from the jet and forms a spherical droplet (Fig. 5.5e). Figure 5.5f shows that when the droplet breaks from the jet, a droplet with relatively high spherical shape is formed without the forming of a thin filament behind the formed droplet. The simulated results indicate that the metal droplet forming process is dominated by the surface tension of the molten liquid, but not by its viscosity. The pressure and velocity fluctuations inside the nozzle are shown in Fig. 5.6. The simulated results reveal that, at the beginning, the pressure and velocity oscillate with

152

5 On-Demand Ejection and Control of Uniform Metal Droplets

Fig. 5.4 The influence of the composition and temperature of the Pb–Sn alloy on the wetting angle of the quartz surface [3]

Fig. 5.5 Droplet generation process driven by a pneumatic pressure pulse

a frequency of ~ 500 Hz inside the nozzle. The frequency of this oscillation is larger than that of the applied pneumatic pulse (on the order of tens of Hertz), indicating that this oscillation may be caused by the free oscillation of the free surfaces of the liquid under the combination of surface tension and gravity. In our simulation model, free surfaces are located both at the upper liquid surface in the crucible and at the lower liquid surface inside the small nozzle. Therefore, at the beginning of the simulation, the molten liquid begins oscillating due to the release of the liquid’s free surface. The oscillation is too small to eject metal liquid out of nozzle. This small oscillation disappears when the pneumatic pulse is applied inside the crucible and has no effect on the metal droplet ejection.

Pressure in the nozzle kPa Velocity in the nozzle m/s

5.2 On-Demand Ejection Behavior of Metal Droplets Driven by Pneumatic …

0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2

153

t2=11.34ms t3=15ms

t1=11.53ms

6 4 2 0 -2 -4 0

2

4

6

8 10 12 14 16 18 20 22 24 26 28 30

Time ms

Fig. 5.6 Velocity and pressure disturbance in the nozzle

Figure 5.6 also shows that the time of peak velocity and pressure comes at t 2 = 13.43 ms inside the nozzle. Compared with the time of peak pressure (t 1 = 11.53 ms) inside the crucible, peak velocity, and pressure are delayed by 1.9 ms. The jet breaks into droplets when the velocity and pressure inside crucible begin to decrease (at t 3 = 15 ms), meaning that a metal droplet is formed after the time that peak pressure is achieved. The reason being, as the applied pressure decreases, the spherical jet tip keeps going while the jet tail slows down, leading to detachment of droplets. Figure 5.6 shows that the internal pressure of the nozzle fluctuates slowly. Its fluctuation period is much longer than the droplet ejection period. Therefore, it can be deduced that the pressure pulse has little effect on the capillary disturbance on the jet surface. The jet surface disturbance comes mainly from the random disturbance caused by the free contraction of the jet tip. Figure 5.7 illustrates the variations of jet pressure, jet axial velocity distribution, and droplet outline before and after droplet generation. Figure 5.7a illustrates that the initial velocity of the jet is 0.5 m/s. Figure 5.7d shows the axial velocity of droplet is 0.4 m/s after detaching from the jet. The reduction in velocity is due to the transfer of the liquid’s kinetic energy into the surface energy during the droplet forming process. Figure 5.7b and e illustrate that the pressure inside the droplet is relatively small (less than 4 kPa) and uniformly distributed. This is the main reason for the small change in droplet shape during formation. Figure 5.7c and f show that the droplet shape changes slightly before and after formation. Simulation results show that metal droplets keep a spherical shape during their formation because of the uniform distribution of the internal pressure and velocity

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Fig. 5.7 The pressure and velocity disturbance inside jets and droplets. a, b, and c axial velocity distribution, pressure distribution, and droplet shape before droplet formation and d, e, and f after droplet formation

fields. This phenomenon benefits the production of mono-sized spherical metal particles. The morphology of ejected metal droplets is different from that of fluids with higher viscosity, such as ink [4]. Simulation and experimental results also show that metal droplets have a low ejection velocity (approximately 0.4 m/s), which leads to instability in the ejection of droplets. That is, the adherence of oxide skins, and impurities or defects on the nozzle outlet can lead to dispersal of metal droplets from the flight axis, affecting the accuracy of droplet deposit. (2) The effect of nozzle diameter on metal droplet ejection Nozzle size is an important parameter in determining droplet size. Therefore, to customize droplet size, it is necessary to understand the droplet generation mechanism and the parameters that influence it. Figure 5.8 shows the simulated patterns of jets and droplets ejected by using the nozzle diameters, (Dn ), of 100, 120, 150, 200, 220, 260 and 300 μm. The simulated results show that the jet shape from different nozzle diameters are similar. The breakup length remains constant when the nozzle size is equal or greater than 150 μm yet is reduced below a nozzle size of 150 μm. Also, droplet size increases dramatically as nozzle size increases. Figure 5.9 illustrates the relationship between the amplitude of pressure p and the nozzle diameter d n , when generating a single droplet. As can be seen, the amplitude of pressure necessary to generate a single droplet increases exponentially with a decrease in nozzle diameter. The relationship between the desired pressure and the

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155

Fig. 5.8 Simulation of droplet generation from nozzles of different diameters

nozzle diameter can be expressed as: p = 75.6e−dn /47.9 + 4.4

(5.3)

Figure 5.9 also illustrates that the droplet diameter decreases exponentially with a decrease of nozzle diameter, which can be expressed as: Dd = 110.3edn /171.3 + 157

(5.4)

The jet Oh number is between 1.2 × 10−3 and 1.8 × 10−3 corresponding to the 100–300 μm diameter nozzles, showing that viscous force is an insignificant factor in the evolution of the jet when compared to surface tension. When the nozzle diameter

Fig. 5.9 The amplitude of pressure necessary for generating a single droplet and the diameter of the droplet as the function of the nozzle diameter

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5 On-Demand Ejection and Control of Uniform Metal Droplets

decreases from 300 μm to 100 μm, the corresponding We number decreases from 0.46 to 0.02, which illustrates that as nozzle diameter decreases, surface tension dominates the jet breakup process and the effect of inertial force and viscosity on the jet breakup are weak. Figure 5.10 shows the relationship between the dimensionless breakup length L j /d n, the dimensionless droplet diameter (Dd /d n ) and the We number. These simulated results show that when the We number varies between 0.1 and 0.05, these two dimensionless parameters are nearly unchanged. When the We number decreases from 0.1 to 0.01, these two dimensionless parameters increase rapidly, indicating that the jet has a long breakup length and a large volume when the jet velocity is low. The relationship of mentioned dimensionless parameters and the We number can be expressed as: L j /dn = 505e−W e/0.00332 + 2.6

(5.5)

Dd /dn = 250e−W e/0.0057 + 0.57

(5.6)

It should be noted that when the We number decreases from 0.05 to 0.01 (nozzle diameter decreases from 150 to 100 μm), the droplet diameter slightly decreases, while the ratio of droplet diameter to nozzle diameter increases rapidly. At the same time, the pressure amplitude for generating a single droplet also increases rapidly, indicating that decreasing the nozzle size is not a feasible means to reduce droplet diameter. (3) Influence of the amplitude of the pressure pulse During metal droplet ejection, multiple droplets are formed if the amplitude of the applied pressure pulse is continuously increased. In simulation, the

Fig. 5.10 Dimensionless breakup length and diameter as a function of the Weber number

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Fig. 5.11 Metal jet breaks into two droplets with an increase in pressure amplitude

applied pressure pulse can be amplified by multiplying an amplification factor to simulate jet ejection and breakup with an increased pressure pulse. When the pressure amplitude is around 6 kPa, the simulated results illustrate that two droplets break from the jet (Fig. 5.11). As the first droplet is produced, the remaining jet immediately necks and forms the second droplet (Fig. 5.11a, b). The flight velocity and the size of the second droplet is less than the first droplet. The sizes of the second droplet in Fig. 5.11c and d are different to each other, indicating that generation of the second droplet is inconsistent and unstable. The simulation results show that after the first droplet breaks, the tip of the remaining jet rapidly contracts into a spherical shape under the effect of surface tension. The capillary disturbance caused by this contraction aggravates jet necking, producing the second droplet. Since the mechanism of this disturbance is complex, the breakup of the second droplet is random and difficult to accurately control. 4. Experimental influence factors of Pb–Sn alloy droplet ejection on-demand The uniform metal droplet ejection process can be captured by using flash photography. The shutter of the CCD camera is set to remain open. Clear images of ejected droplets are frozen by the flash or strobe. During this process, the CCD shutter, the strobe, and the droplet generator are synchronized by an external trigger. By delaying the strobe triggering time, the time of the evolution of the metal droplet ejection process can be obtained. (1) Single Sn–Pb alloy droplet ejection process.

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5 On-Demand Ejection and Control of Uniform Metal Droplets

The comparison between simulation results and experimental observations using the pressure pulse shown in Fig. 5.3 are given in Fig. 5.12. The breakup time for droplet formation is 18 ms according to the observation. The observed breakup time is about 3 ms later than the corresponding simulated result. This inconsistency between the simulation and experiment could be attributed to such factors as a delay of the triggering signal. Figure 5.12g–i illustrates that the average simulated and experimentally measured droplet diameters are 0.701 mm and 0.689 mm, respectively, demonstrating that the simulated result agrees well with the experimental result. The flying distance of the ejected droplet at the breakup time is approximately 1.318 mm in the experiment, while in simulation this distance is 1.246 mm (Fig. 5.12e). The difference of 0.05 mm also shows consistency between simulation and experiment. Figure 5.13 shows the comparison between simulated and measured results of the droplet flying distance (when the flying distance is measured, the geometric center of droplets is taken as the measuring point and the distance between the droplet center and the nozzle is measured as the droplet flying distance). The comparison shows a small difference between the two sets of values, but the trend is consistent. The simulated and experimental results can be linearly fitted and the slope of the trendline is the initial velocity of the droplets, approximately 0.32 m/s. The above comparison between simulated and experimental results illustrates the accuracy of the established model. Meanwhile, the experimental results also illustrate that the shape of the droplets produced by the pneumatic pulse does not change significantly. Spherical metal droplets are easily formed with a low ejection velocity. (2) The effect of the width of the pressure pulse on metal droplet ejection. In the metal droplet ejection process, the duration and the amplitude of pressure pulses can be varied by changing the pulse width. This is an effective means to control the ejection of the metal droplets. Figure 5.14 shows the metal droplet ejection for different pulse widths (i.e., 0.3, 0.32, 0.35, 1 ms) at a pressure pulse amplitude of 50 kPa. Figure 5.14 shows the three phenomena of metal droplet ejection: retraction, single droplet ejection, and multiple droplet ejection. (1) Retraction: when the pressure pulse is applied in the crucible and the jet inertial force cannot overcome surface tension, the metal jets do not break up into droplets and retract into the nozzle. (2) Single droplet ejection: the jet inertial force overcomes surface tension to form a single droplet without ejecting additional redundant droplets. (3) Multiple droplet ejection: when the jet initial force is significantly larger than jet surface tension, two (or more) droplets can be ejected. Figure 5.14a shows that when the pulse width is small, the liquid meniscus gains kinetic energy and accelerates slowly under excitation of the pressure pulse. After the gas releases from the vent, the pressure inside the crucible gradually decreases to less than one atmosphere. Negative pressure is formed inside the crucible and the liquid meniscus is withdrawn or retracted back into the nozzle without droplet

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159

Fig. 5.12 Comparison between experimental and simulated results of the single Pb–Sn alloy droplet ejection

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5 On-Demand Ejection and Control of Uniform Metal Droplets

Fig. 5.13 Comparison between simulated and measured flying distance

1mm

Fig. 5.14 Metal droplets ejected by using the pressure pulse with widths of a 0.30 ms, b 0.32 ms, c 0.35 ms, d 1 ms, respectively. The corresponding image capture time are 8, 8, 23, 23 ms in sequence

generation. Figure 5.14b shows that when the pressure inside the nozzle increases, the kinetic energy of the jet increases to overcome jet surface tension. A single droplet is formed, leaving a short jet behind. Figure 5.14c shows that as the width of the pressure pulse increases, a second droplet appears but withdraws back to the nozzle. Figure 5.14d shows that with a large pressure pulse, the metal jet breaks into multiple droplets of inconsistent size as the large inertial force overcomes liquid surface tension restriction. Figure 5.15 shows the ejection process of metal droplets under different pulse widths when the supply gas pressure is 28 kPa. The figure shows that as the pulse width increases, the number of metal droplets ejected by the pressure pulse at first increases but then decreases with continued increase in pulse width. When the pulse

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161

width is 0.1 ms, about three droplets can be seen to be ejected. When the pulse width is 0.5 ms, four ejected droplets can be observed. When the pulse width increases to 60 ms, the droplet number reduces to three, and then two, one, and zero for pulse widths of 200 ms, 220 ms, and 260 ms, respectively. The reason for this phenomenon is that when the pulse width is large, the excitation frequency is much lower than the natural frequency of the liquid metal inside the crucible, resulting in “annihilation” of the applied excitation [5]. By adjusting the pulse width properly, the ejection of a single metal droplet can be achieved by breaking jets into one single droplet and having the remaining tail jet retract back into the nozzle. Assume that the threshold pulse width for a single droplet ejection is τ 1 and the threshold for ejecting the second droplet is τ 2 , the range of pulse width for ejecting a single droplet is τ ∈ [τ1, τ2]. (3) The effect of start and stop on metal droplet ejection. The droplet ejection experiments show that metal droplet ejection is unstable at the beginning and the end of the droplet ejection process. In the initial 3 ~ 10 pulses, a single metal droplet cannot be formed. Usually, a large metal droplet with a small one may be ejected simultaneously. Sometimes a single

Fig. 5.15 Effect of pulse width on the formation of a single metal droplet (the delay time for recording images is 12 ms and the supply gas pressure is 28 kPa)

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5 On-Demand Ejection and Control of Uniform Metal Droplets

large metal droplet may be observed. In this case, the metal droplet deposit location varies greatly (Fig. 5.16a). This phenomenon is named “ejection starting phenomenon”. One possible reason lies in the small amount of oxide skin that forms on the surface of the liquid’s meniscus inside the nozzle before ejection. This oxide skin affects the surface tension and viscosity of the liquid metal inside the nozzle. Figure 5.16b shows that the size of the last metal droplet is also very large when the solenoid valve is closed at the end of ejection. The droplet diameter reaches 1 mm (the average diameter of metal droplets is 450 ~ 530 μm), as the solenoid valve which is switched on and turned off regularly, is suddenly closed causing an instantaneous pressure increase in the crucible consequently forcing more liquid metal out of the nozzle. Therefore, to ensure printing accuracy, the droplet generator should be moved out of printing tracks when the metal droplet ejection process begins and ends, and the abnormally ejected droplets recycled. Additionally, when pausing the printing process, it is necessary to continue ejecting droplets so that the liquid metal inside the nozzle can maintain the same oxidization conditions during each ejection. (4) Parameter range for consistent ejection of a single mono-sized Pb–Sn alloy droplet. In metal droplet 3D printing, the size and uniformity of the metal droplets are critical to the accuracy of printed parts. This section introduces the influence of the experimental parameters on the uniformity of the metal droplet size and uniformity in pneumatic pulse-driven ejection. Furthermore, this section seeks

(a)

(b)

Fig. 5.16 Unstable droplet ejection: a small satellite metal droplets (for a pulse width of 230 μs); b abnormally large metal droplets (for a pulse width of 130 μs)

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Table 5.2 The characteristic parameters of the applied pressure waveform in the crucible when a single metal droplet is ejected Supply gas pressure (kPa)

Pulse width τ (ms)

Break time (ms)

Peak time t p (ms)

Peak pressure Pp (kPa)

18

2

12

12

1.6

18

8

12

15

2.5

18

14

12

13

2.1

50

0.32

20

12

5.4

50

0.335

20

11

5.4

50

0.35

20

11

5.5

an appropriate combination of ejection parameters for controllability of the ejecting of a single mono-sized metal droplet. Table 5.2 shows the combination of parameters for forming a single metal droplet under different supply pressures. This table shows the combination of the peak pressure Pp and the pulse width of the peak pressure τ, as well as the peak pressure time t p of the crucible pressure waveform for the ejection of a single metal droplet with a supply gas pressure of 18 and 50 kPa. Here peak pressure times and peak pressure values are measured by using a piezoelectric pressure sensor. When the supply gas pressure is 18 kPa and the pulse width is 2 ms, the gas pressure in the crucible reaches the maximum value (1.6 kPa) at 12 ms and a single metal droplet detaches at 12 ms. When the supply gas pressure is 50 kPa and the pulse width is 0.32 ms, the gas pressure in the crucible reaches the maximum value (5.4 kPa) at 12 ms and a single metal droplet forms and detaches at 20 ms. Table 5.2 shows that with low gas pressures, metal droplets are formed when the gas pressure reaches the peak value in the crucible. With high gas pressures, metal droplets are formed when the gas pressure in the crucible becomes negative. The reason for this phenomenon is that the capillary disturbance on the metal jets, rather than the pressure fluctuations, dominates the droplet detachment process. When similar jet diameters are under different applied pressures, the break time is on the same order of magnitude. However, when large pressures are applied, the ejection velocity becomes relatively high and the fluid inside the nozzle needs more time to decelerate (or retract), and thus the break time becomes relatively longer [6]. Changes in pulse width are an effective method for controlling the ejection of metal droplets. When the solenoid valve is opened and closed, a pneumatic pulse is generated. Jets will retract into the nozzle under the combination of surface tension and the local negative pressure in the cavity if the gas pressure in the cavity is low and no metal droplets are formed. If the gas pressure is high, multiple metal droplets can be formed under a pressure pulse. Figure 5.17 illustrates that by adjusting the pulse width, τ , the range [τ 1 , τ 2 ] for a single metal droplet ejection can be obtained corresponding to different pressure amplitudes and the ejection of a single metal droplet can be effectively controlled.

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Fig. 5.17 Working parameters map for a single metal droplet ejection (circles represent the parameter combination for a single droplet ejection) for pressure amplitudes of 14 ~ 50 kPa

Figure 5.17 illustrates that with a low supply gas pressure, the peak pressure inside the crucible is also low and it is difficult to produce metal droplets. Therefore, the pulse width working range for ejecting a single metal droplet is narrow. For example, for a supply pressure of 14 kPa, a single metal droplet can be generated only when the pulse width is 0.11 ~ 0.2 ms. When the supply pressure increases, the range of the pulse width for ejection of a single metal droplet expands. For example, when the supply pressure is 18 kPa, the pulse width working range (for single droplet generation) is 0.2 ~ 14 ms. However, if the supply gas pressure is too high, changes in pulse width have a great influence on the peak pressure and the working range again becomes narrow. For example, when the supply gas pressure increases to 28 kPa, the pulse width working range is between 0.2 and 0.3 ms. When the applied pressure increases to 50 kPa, the pulse width working range is only 0.32 ~ 0.35 ms, and very difficult to achieve. The uniformity of metal droplets is an important factor to ensure printing accuracy and in determining the process of droplet-based manufacturing of small parts. The uniformity of metal droplets ejected by pneumatic pressure pulses is studied in this section. Metal droplets are ejected with a nozzle diameter of 210 μm, a heating temperature of 280 °C, an ejection pressure amplitude of 18 kPa, and a pulse width of 0.2 ~ 14 ms. The conditions for stable generation of mono-sized droplets are shown in Table 5.3. After the stable and consistent ejection of metal droplets is achieved, the metal particles are randomly collected and the uniformity of the obtained metal particles is analyzed after the solidified particles are photographed. The randomly collected Pb–Sn alloy particles are pictured in Fig. 5.18a. The picture shows that the collected metal particles have good roundness. The diameters Table 5.3 Process parameters for generating single droplets on demand

Applied gas pressure kPa

Pulse width ms

Ball valve Deposition opening angle ° frequency Hz

50

0.2 ~ 14

75

1

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Fig. 5.18 a Picture of solidified particles b and particle size distribution

of approximately 280 metal particles are measured and the size distribution of those particles is shown in Fig. 5.18b. The average diameter of these uniform metal particles is 320 μm, and the deviation in diameter is 3 μm (0.9% of the droplet diameter). Approximately 99% of the diameters of the metal particles are distributed in the range of ± 2.8% of the average diameter, thus proving that droplets produced by pneumatic on-demand ejection, have a concentrated size distribution and consistent uniformity. Figure 5.19 shows the average diameter and the standard deviation of the diameter of the metal particles ejected by nozzles of different diameters. The results show that, driven by gas pressure pulses, the size of metal droplets is determined by the nozzle diameter, and there is a high uniformity of droplet size. Figure 5.19 also shows the relationship between the droplet diameter and the nozzle diameter (Eq. 5.4). When the nozzle diameter increases, the droplet size increases accordingly. The increasing trend is very close to experimental results, indicating the accuracy of the proposed model (Eq. 5.4). In summary, pneumatic pressure pulse driven metal droplet ejection characterized by slow initial velocity results in mild droplet deformation during ejection and spherical metal particles with consistent uniformity in size can be obtained. However, research indicates that the slow fluctuation of the pneumatic pulse pressure results in metal particles nearly twice as large as the nozzle diameter. Furthermore, it is difficult to reduce the diameter of metal droplets solely by reduction in nozzle size.

5.2.2 Research on Ejection of Uniform Aluminum Droplets On-Demand Driven by Pneumatic Pressure Pulse The working principle and structure of the pneumatic aluminum droplet generator are the same as the pneumatic Pb–Sn alloy droplet generator. The difference lies

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Fig. 5.19 The relationship between the droplet diameter Dd and the nozzle diameter d n under the pneumatic pressure pulse

in the use of graphite nozzles and crucibles that are resistant to corrosion from the liquid aluminum. A picture of graphite nozzle plates and a schematic diagram of the crucible structure are shown in Fig. 5.20a, b. An axisymmetric model is built to numerically simulate droplet formation behavior. As shown in Fig. 5.20c, this model is built according to the inner structures of the nozzle and the crucible, including the inlet and outlet pipes, the crucible cavity, and the gas domain where droplets pass under the nozzle. The grid division in the nozzle area and the droplet generation area is shown in Fig. 5.21. The area of the calculation model contains 30,800 structured quadrilateral mapping grids. The nozzle and the droplet generation area below the nozzle are finely divided into 15 square grids along the nozzle radius. Below the nozzle is the droplet generation area, and the grid in this area is the same size as that in the nozzle area. Outside the droplet generation area is the gas domain, where the mesh size is larger than that in the nozzle area. Figure 5.22 shows the boundary conditions of the finite element model. Figure 5.22b is an enlarged view of the nozzle area (the rectangular area shown by the dotted line) in Fig. 5.22a. The boundary number is indexed with capital letters A, B, C, …, S. Boundaries A and ) R are pressure outlets, and gas can flow in through this boundary, ( i.e. η ∇u + (∇u)T n = 0, p = 0. Boundaries B, C, E, F, G, H, I, J, K, M,|P, Q are non-slip | walls, i.e., u = 0; Boundary S is a wetting slip wall, i.e., n · u = 0, t · ∇u + (∇u)T n = 0, n · ninter f ace = cos(θ ). The contact angle θ is defined as 90°, and the sliding length is 25 μm. Boundary D is the pressure inlet. The applied gas pressure pulse is shown in Fig. 5.23, and can be expressed by using a sinusoidal decay function: pn (t) = p p sin(ω0 t) = ae−τ t sin

(π ) t τ

(5.7)

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167

Fig. 5.20 a Graphite nozzle plate for ejecting aluminum droplets, b schematic diagram of the crucible and nozzle structure, and c the axisymmetric model for simulating droplet formation (units: mm)

Fig. 5.21 Structured grid division in calculation areas (nozzle area and its nearby area)

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Fig. 5.22 Finite element model for aluminum droplet-on-demand ejection. a Boundary conditions. b Enlarged view of the rectangular area at the nozzle

This function has a second-order continuous derivative, which can smooth the pressure step changes. Setting the pressure pulse as a smooth function has two advantages [7]: Firstly, it can enhance the reliability and convergence of numerical calculations. Secondly, the real physical system can usually be simplified into a mass-spring-damping system with a pulse input. and damped sinusoidal motion Therefore, it is reasonable to set the pressure disturbance as a second-order decay function.

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169

Fig. 5.23 Waveform of gas pressure pulse and its fitting curve (pulse width is 1 ms, pulse pressure is 100 kPa)

The initial conditions are the level of liquid aluminum below the L surface and above the N surface, as shown in Fig. 5.22. That is, before the pulse is applied, the nozzle is assumed to be filled with liquid aluminum, and the liquid meniscus is at the same height as the nozzle outlet. The gas fills areas above the L surface and below the N surface. In the droplet ejection experiment, pure aluminum is used as the droplet material and high-purity argon is used as the protective gas. The physical properties of materials are shown in Table 5.4. In the aluminum droplet ejection experiment, mono-sized aluminum droplets can be obtained when the supply gas pressure is 70 kPa, the pulse width is 700 μs, the opening angle of the ball valve vent is 75°, the ejection frequency is 1 Hz, and the nozzle diameter is 0.6 mm. The gas pressure as a function of time in the crucible cavity is shown in Fig. 5.24. Simulated results, using this pressure as the initial condition, are also shown in this figure. Figure 5.24 shows that molten metal is ejected from the nozzle under a pressure pulse for a time less than 4 ms. The jet length at the nozzle outlet gradually increases for the time range of 24–33 ms. During the jet elongation process (33 ~ 35 ms), the jet tip contracts into an ellipsoid. When the jet volume is large enough, the effect of gravity on the droplet and inertial force exceed the jet surface tension, resulting in necking at the jet root. This neck grows quickly (35 ~ 38 ms). When this neck Table 5.4 Physical properties of pure aluminum liquid and argon gas for numerical simulation

Density/kg m−3

Dynamic viscosity/Pas

Surface tension/N m−1

Pure aluminum liquid

2368

1.257 × 10–3

0.868

High purity argon gas

1.784

2.217 × 10–5

/

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Fig. 5.24 Pressure pulse in the crucible and time evolution of droplet production under this pressure pulse

increases to the jet radius, the jet eventually breaks to a metal droplet (38 ~ 39 ms). The remaining metal jet becomes a liquid cone under surface tension, and then retracts back to the nozzle under the negative pressure (40 ms). Figure 5.25 shows the production process of a single aluminum droplet captured by the high-speed CCD camera. In this experiment, the nozzle diameter is 600 μm, the applied gas pressure is 75 kPa, and the opening angle of the ball valve is approximately 75 ~ 80°. The droplet images are recorded at the frame rate of 1000 f/s. The pulse width gradually increases from the initial value of 0.75 ms. Figure 5.25 shows that after aluminum droplets are produced, the controllable ejection of a single aluminum droplet can be achieved by carefully adjusting the pulse width. In this experiment, the diameter of ejected droplets is between 1 ~ 1.3 mm, and the ejection velocity is between 0.3 and 1 m/s. Since the initial jet velocity is relatively low, the droplet shape slightly changes during flight. Figure 5.26 shows the generation process of multiple aluminum droplets obtained by high-speed photography. As the pulse pressure amplitude increases, two droplets are generated (Fig. 5.26a) followed by multiple droplet generation (Fig. 5.26b) as pulse pressure further increases. Under these conditions, the droplet ejection process

Fig. 5.25 The evolution of a single aluminum droplet during the ejection process

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171

Fig. 5.26 Multiple droplet ejection. a Ejection pressure ~ 80 kPa, b Ejection pressure ~ 90 kPa

is in an unstable state as it is difficult to control the droplet number and the location of droplet deposit. This type of droplet ejection should be avoided. Figure 5.27 shows simulated results of single aluminum droplet ejection with differing pressure amplitudes. During the simulation, the peak pressure value is gradually adjusted to find the combination of parameters for consistent ejection of a single aluminum droplet. The simulated results are represented by three dimensionless numbers: Dd /d n (Ratio of droplet diameter to nozzle diameter), L d /d n (Ratio of the length to the nozzle diameter when the jet is broken), and t b /t c = t b (ρR3 /σ )1/2 /100 (Ratio of the breakup time to one percent of the droplet capillary time (here, t c = 100(ρR3 /σ )−1/2 )). These dimensionless numbers are used to characterize the droplet diameter, the breakup length, and the breakup time, respectively. The figure shows that with the increase of pulse amplitude, dimensionless droplet diameter and dimensionless breakup time change slightly but the dimensionless breakup length increases. The results indicate that the pulse pressure amplitude has little effect on the breakup time and the droplet size. With a wide pulse width, the dimensionless breakup length increases with an increase in the applied pressure amplitude, but the droplet diameter does not change. In this case, more liquid metal will be retracted back to the nozzle after the jet is broken. With a narrow pulse width, an increase in pressure amplitude has little effect on the metal droplet ejection. Figure 5.28 shows the simulated results of single droplet ejection under different pulse widths. The simulated results show that the pattern of aluminum droplets differs with pulse width. Under narrow pressure pulses, the droplet diameter can be less than the nozzle diameter and droplets with a spherical shape are obtained. Whereas with wide pressure pulses, larger droplets that are easily affected by gravity are obtained and the droplets take an ellipsoidal shape which elongate in the direction of gravity. To quantitatively analyze the influence of the pulse width τ on metal droplet ejection, simulations of the metal droplet ejection process under pressure pulses of different pulse widths are carried out (Fig. 5.29). The simulated dimensionless diameter, dimensionless breakup length, and dimensionless breakup time are considered.

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Fig. 5.27 Influence of the pressure amplitude on the droplet diameter (pulse width τ equal to 0.01 (black) and 0.0001 s (red))

Fig. 5.28 Simulated patterns of aluminum droplets at breakup time under different pulse widths

The results show that for τ = 10 ms, the dimensionless diameter and the dimensionless breakup length decrease exponentially with the decrease of the pulse width. However, when τ is small (to the order of 1 ms), the rate of change of these two parameters is slow. The simulated results also show that when the pulse width is as small as 0.1 ms, the dimensionless droplet diameter is about 1, indicating that the droplet diameter is equal to the nozzle diameter. However, it is very difficult to achieve a pneumatic pulse with the pulse width of 0.1 ms with current pneumatic droplet generators. Generally, the pneumatic pulse width is on the order of 10 ~ 100 ms. Therefore, metal droplets ejected by the pneumatic pulse generally have the diameter larger than the nozzle diameter. The above simulated results show that the pulse width is the main parameter that affects the size of ejected droplets. The amplitude of the pressure pulse has little effect on droplet diameter. However, the pressure amplitude should be adjusted properly:

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173

Fig. 5.29 Dimensionless droplet diameter Dd /d n , dimensionless breakup length L d /d n , and dimensionless breakup time t b /t c as a function of the pulse width τ

if the pulse amplitude is too small, droplets cannot be formed since droplet inertial force cannot overcome the jet surface tension. Conversely, if the pulse amplitude is too large, multiple droplets will be ejected simultaneously, making it hard to eject a single uniform metal droplet on demand. To find the parameter range for ejecting single uniform aluminum droplets on demand, a series of simulations are conducted by varying the pulse width and the pulse amplitude. First, the pulse amplitude increases gradually while the pulse width is set constant. The upper and lower thresholds for single droplet generation with the preset pulse width can be found in this way. Here, the precise threshold is approximated by the average value between two adjacent amplitudes with different ejection results. For instance, the lower threshold for a single droplet ejection is taken as the average value between the two adjacent amplitudes for non-droplet ejection and single droplet ejection, respectively. The upper threshold is found in the same way but between the amplitude for single droplet ejection and the amplitude for multiple droplet ejection. Furthermore, after varying the pulse width gradually, the lower and upper boundaries can be drawn by connecting the obtained upper and lower thresholds, respectively. Finally, the parameter range of pulse amplitude for a single droplet ejection can be calculated. Figure 5.30 shows the pressure amplitude versus pulse width map for single droplet ejection. The simulated results show that with a large pulse width, the range of the pressure amplitude for single droplet ejection is relatively narrow. As the pulse width decreases, this range first gradually increases to reach nearly 10 kPa for τ = 3 × 10–4 s. When the pulse width continues to decrease, the amplitude range gradually decreases. In addition, Fig. 5.30 also shows that as the pulse width decreases, the lower boundary of the pressure amplitude for ejecting a single aluminum droplet rises exponentially. For τ = 1 × 10−4 s, the lower boundary of the pressure amplitude

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5 On-Demand Ejection and Control of Uniform Metal Droplets

Fig. 5.30 Pressure amplitude versus pulse width map for a single aluminum droplet ejection

reaches 80 kPa, which is hard to achieve using a common pneumatic pulse generation system. After obtaining the parameter combination for the ejection of a single aluminum droplet, four nozzles with diameters of 400, 460, 500, and 600 μm are selected to eject aluminum droplets. In these experiments the pulse width is set as 19 ms. The pulse amplitude increases from the lower threshold for τ = 19 ms until uniform aluminum droplet ejection is observed. Droplets are then collected inside an asbestos crucible and size distribution is measured after the aluminum droplets solidify and cool. Figure 5.31a shows the dimensionless droplet diameter as a function of the nozzle diameter. The experimental results illustrate that the aluminum droplets have a diameter triple that of the nozzle diameter, and are produced within a narrow size distribution. Figure 5.31b is a picture of the collected uniform aluminum particles, and clearly displays a perfect spherical shape.

Fig. 5.31 Uniform aluminum particles ejected by pneumatic pulses a Dimensionless diameter of aluminum particles as a function of the nozzle diameter. b Picture of uniform aluminum particles

5.3 Ejection Behaviors of Metal Droplets On-Demand Driven …

175

The simulated results (filled squares) in Fig. 5.31a also show that as the nozzle diameter decreases, the dimensionless droplet diameter rapidly increases, indicating that it is difficult to significantly reduce droplet size by only decreasing nozzle size.

5.3 Ejection Behaviors of Metal Droplets On-Demand Driven by a Stress-Wave Pulse and the Influence of Parameters on Droplet Ejection The stress-wave pulse driven droplet ejection method generates a short stress-wave pulse via the impact of two elastic rods. Such a stress-wave pulse can eject liquid metal from the nozzle and can form a single metal droplet. This section will focus on the metal droplet ejection behavior, influential parameters, influential laws, and potential applications of the stress-wave pulse driven droplet ejection method.

5.3.1 Influence of Parameters of Experiment Device on Metal Droplet Ejection 1. Influence of the travel distance of the impacting rod (S rod ) on droplet ejection The impacting rod hits the vibration transferring rod after being accelerated for a short distance. The travel distance of the impacting rod (S rod ) is defined as the distance between the lower end of the impacting rod and the upper end of the vibration transferring rod (Fig. 5.32a). In the droplet ejection process, the acceleration of the impacting rod can be controlled by adjusting the travel distance of the rod. Since the impacting rod accelerates from a static state, its travel distance directly determines the impact velocity with the vibration transferring rod. This travel distance also has a significant influence on the energy of stress wave pulses for ejecting metal droplets. Figure 5.32 shows Pb–Sn alloy particles ejected under different travel distances S rod . When S rod is set at the maximum value (i.e., S rod_max ≈ 5 cm), the energy generated by the impact of the impacting rod and the vibration transferring rod is relatively large. In this case, satellite metal droplets are easily generated. When S rod is set at the minimum value (i.e., S rod_min ≈ 1 cm), the impact energy is very small, the droplet ejection process is unstable, and droplets are not always generated. Only within a proper range of travel distance can uniform metal droplets be ejected in a stable and consistent manner. In summary, the travel distance of the impacting rod (S rod ) is a significant parameter for controlling the ejection of metal droplets. 2. Influence of the depth of the vibrating cavity (L rod ) on droplet ejection The space between the lower end of the vibration transferring rod and the nozzle inlet is defined as the vibrating cavity and the height of this cavity is defined as the

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5 On-Demand Ejection and Control of Uniform Metal Droplets

Fig. 5.32 Ejection of lead–tin alloy droplets with several different impacting rod travel distances (the nozzle diameter is 100 μm)

vibrating cavity depth, L rod . The metal droplet ejection process can be effectively controlled by adjusting L rod , and thus, change the volume of the vibrating cavity. In stress wave pulse driven metal droplet ejection, a compressive stress wave pulse is transferred along the axis and reflected at its lower end into a tensile wave. During the reflection, a pressure pulse is generated in the fluid near the lower end of the vibration transferring rod. For different values of L rod , there will be differences in the duration and amplitude of the pressure pulse, as well as in the kinetic energy that was converted for droplet ejection. Figure 5.33 shows the metal droplet ejection results for different values of L rod . For a large cavity depth (L rod > 10 mm), the large energy loss from violent impacts results in difficulty in controlling the ejection of metal droplets (Fig. 5.33a). For a small cavity depth (L rod < 1 mm), the energy transferred by the vibration transferring rod is too large and results in generation of satellite droplets (Fig. 5.33c). Only for a proper cavity depth (L rod ∈ [1 mm, 10 mm]), uniform spherical metal particles can be produced by the droplet generator (Fig. 5.33b).

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177

Fig. 5.33 Schematic diagram of the influence of the depth of the vibrating cavity on the ejection of metal droplets (the nozzle diameter is 100 μm)

5.3.2 Effect of Stress Wave Pulse Parameters on Metal Droplet Ejection 1. Effect of Frequency of Stress Wave Pulse on the Metal Droplet Diameter The frequency of the stress wave pulse is the frequency of impact between the impacting rod and the vibration transferring rod. Sn–Pb alloy is used as the ejection material used to study the influence of the pulse frequency on droplet diameter. The ejection pulse frequency is set as 1, 2, 3, 4, 5, 8, 10 Hz. The relationship between the diameter of metal particles and the pulse frequency is shown in Fig. 5.34. Figure 5.34 shows that within a certain frequency range, the diameter of the ejected Pb–Sn alloy droplets decreases exponentially with the increase of the pulse frequency. The relationship can be expressed as: y = 56.81591 + 81.6695 · e−0.61584x

(5.8)

As the impact frequency increases, the impacting rod does not fully retract back to its initial position before the next impact, resulting in reduction of the travel distance of the impacting rod and reduction of the impact energy. Therefore, the energy transferred into metal liquid is small, leading to the ejection of droplets of a small diameter. 2. Influence of the width of stress wave pulses on the droplet diameter The pulse width of the loading pressure pulse is an important factor that affects the ratio of the droplet to the nozzle diameter in the pneumatic and stress wave

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5 On-Demand Ejection and Control of Uniform Metal Droplets

Fig. 5.34 Relationship between the metal particle diameter Dd and the pulse frequency f (the nozzle diameter is 100 μm, the pulse width is 5 ms, the travel distance of the impacting rod is 3 mm, and the vibrating cavity depth is 1.5 mm)

pulse driven on-demand ejection methods. To analyze the influence of the pulse width on the size of metal droplets, the stress wave-driven on-demand ejection device can be separated into two work states: with an elastic connection (the vibration transferring rod is connected to the ejection device through a spring), and with a rigid connection (in which the rod is connected to the ejection device through a rigid ring): (1) Elastic connection: After impact, the vibration transferring rod moves in a damping oscillation motion under the action of a spring. The vibration waveform transmitted to the molten metal is a sinusoidal vibration with attenuated amplitude. The vibration period is determined by the spring stiffness, the mass of the vibration transferring rod, the damping force of the metal rod and other parameters. After measuring the vibration at the end of the vibration rod by using a laser vibrometer, the change in vibration velocity can − t be expressed by the function: v(t) = Ae τdump sin(π t/τ ), where τ dump = 115 μs and τ = 141 μs. Here, the vibration pulse width and the width of the input single pulse are at the same magnitude (Fig. 5.35). (2) Rigid connection: The vibration transferring rod works in the state of elastic vibration, of which the pulse width is too small to be measured. The pulse width can be estimated through the transmission speed of the stress wave. The pulse width of the stress wave depends on the length of the impacting rod (about 3.5 cm), and the transmission speed of the stress wave in the rod is about 5400 m/s, so that the stress wave pulse width τ, which is the time for the stress wave to go back and forth within the impacting rod is ~ 13 μs.

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179

Fig. 5.35 Vibration transferring rod under the spring damping state waveform

It can be seen that the pulse width with a rigid connection is reduced by an order of magnitude when compared to that in the elastic connection. To identify optimal process parameters for individual droplet ejection, a series of droplet ejection simulations are performed with respect to different pulse widths τ and amplitudes U impact . Figure 5.36a shows the ranges of the non-droplet ejection (square), individual droplet ejection (circle), and the multi-droplet ejection (triangle). The solid line and the dashed line show the upper and lower boundaries of the individual droplet ejection range. Figure 5.36b–e illustrates the individual droplet breakup patterns near the lower and upper boundaries with spring and ring connected rods, respectively. For small amplitudes (Fig. 5.36c and e), the droplet has a tear shape at breakup. As the amplitude increases, the tail of the tear shape elongates and the volume of the droplet increases. The breakup time t b becomes larger with the larger pulse widths τ, but breakup time does not depend on the pressure amplitude. When the amplitude exceeds the upper boundary, necking occurs on the tail surface which leads to ejection of a main droplet and a small satellite droplet. Therefore, for this multi-drop ejection range, the size of the droplets becomes inconsistent. The simulated results show that the droplet size is both sensitive to the pulse width and amplitude. The effect of the pulse width on the droplet size is investigated both experimentally and numerically. As shown in Fig. 5.37a, the non-dimensional droplet diameter, defined as the ratio of the droplet diameter to the nozzle diameter, increases as the pulse width increases. The range of this non-dimensional diameter from the lower to the upper boundary is almost 0.4 in this case. For a pulse width exceeding 0.07 ms, the droplets are larger than the nozzle diameter regardless of the pulse amplitude. An example of such droplets is shown in Fig. 5.37b. However, droplets smaller than the nozzle diameter can be produced for a narrow pulse width, especially for pulse amplitudes just above the ejection boundary. The average droplet diameter is

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5 On-Demand Ejection and Control of Uniform Metal Droplets

Fig. 5.36 The range of metal droplet ejection parameters under different pulse widths. a The droplet generation ranges as a function of the pulse width τ and amplitude U impact . b–d Breakup patterns of metal droplets under different vibration amplitudes with τ = 13 μs. e–g Breakup patterns of metal droplets under different vibration amplitudes with τ = 100 μs

predicted to be as low as 0.65 of the nozzle diameters for the pulse widths with the metal-ring connected rod, as shown in Fig. 5.37a. The experiments with the metal ring connected rod verified this prediction. In the experiment, the amplitude of the signal for driving the solenoid is increased gradually to find the lower and upper boundaries of the individual droplet ejection range. Below the lower boundary, no droplet was collected. The lower boundary was identified as a transition to a range without ejection. Above the upper boundary, small satellites are also ejected, and a rapid increase of the standard deviation in size was expected and observed. Therefore, the upper boundary was identified as a transition to a range with much higher standard deviation in the droplet size. As shown in Fig. 5.37a, these measured upper and lower boundaries agree well with the predictions. The experiments also show that the theoretical model overestimates the droplet diameter in the elastic vibration mode. In this case, the statistics of the solidified particle diameters shows that the minimum average droplet is almost 55% of the nozzle in diameter. That means the droplet size can be half of the nozzle diameter in the elastic mode. In the experiment, the frequency is limited to 25 Hz because of the response limitation of the impacting rod. However, since the pulse widths are narrower than 1 ms in both working modes, the proposed generator is still capable of working in the kHz range. In addition, the standard deviations of particle diameter are ~ 7 mm for both modes. The simulations show that the droplet diameter is sensitive to variations in velocity amplitude (as shown in Fig. 5.37a), as the impact occurs between two steel rods. As control of this impact process is still poor, our future work will improve the impact system for better repeatability and higher frequency.

5.4 Comparison of Various Metal Drop-On-Demand Technologies

181

Fig. 5.37 The droplet size increases with an increased velocity pulse width at the individual droplet ejection range. a the non-dimensional droplet diameter Dd /d n as a function of the pulse width at the upper and lower boundaries of the individual droplet ejection range. b Optical images of solidified particles obtained for τ = 115 μs, and c for τ = 13 μs

5.4 Comparison of Various Metal Drop-On-Demand Technologies At present, the documented metal droplet ejection technologies mainly constitute pneumatic pulse driven, piezoelectric vibration pulse driven, and stress wave pulse driven DOD technologies. Among these technologies, pneumatic pulse driven DOD transfers vibration to the fluid via gas, while piezoelectric and stress wave pulse driven methods both transfer vibration to the fluid through a vibration transferring rod. Metal droplet ejection technology can be roughly divided into two types according to the vibration transfer medium. Figure 5.38 summarizes the minimum non-dimensional diameters and the corresponding diameter standard deviations obtained by various metal DOD methods.

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5 On-Demand Ejection and Control of Uniform Metal Droplets

When single-pulse pneumatic ejection is used, the pulse action time is in milliseconds and the diameter of the metal droplets is generally more than twice the nozzle diameter [2, 8] (Fig. 5.38b, c); By modulating the gas pressure, multiple peak pressure pulses appear in a pulse, which force the free liquid surface at the nozzle to eject very small droplets (Fig. 5.38d). However, if the gas pressure pulse-driven ejection frequency is greater than 10 Hz, the gas pressure continuously oscillates slightly, so that the metal droplet ejection is converted to continuous droplet ejection, which does not allow for the ejection of a single metal droplet on-demand [9]. A vibration transferring rod is used to transmit piezoelectric ceramic vibration into the molten metal, which can greatly reduce the pressure action time (generally in the order of hundreds of microseconds). The dimensionless size of the ejection droplets is close to 1 [10, 11] (Fig. 5.38e–g). However, if the vibration transferring rod works in the elastic vibration mode (that is, the vibration transferring rod is rigidly connected to the droplet generator), the vibration transferring rod drives the fluid through a compression wave pulse, which can further reduce the pressure pulse width (up to ten microseconds). The dimensionless size of metal droplets can be close to 0.55 [12], that is, the diameter of ejection metal droplets is half of the nozzle diameter (Fig. 5.38h). Therefore, the dimensionless size of the droplets can be effectively reduced by reducing the pulse width of the vibration pulse.

Fig. 5.38 Comparison of the minimum ratio of the droplet to nozzle diameter obtained with different methods

References

183

References 1. Luo J, Qi L, Zhou J, et al. Modeling and characterization of metal droplets generation by using a pneumatic drop-on-demand generator. J Mater Process Technol. 2012;212(3):718–26. 2. Tseng AA, Lee MH, Zhao B. Design and operation of a droplet deposition system for freeform fabrication of metal parts. J Eng Mater Technol. 2001;123(1):74–84. 3. Demeri M, Farag M, Heasley J. Surface tension of liquid Pb-Sn alloys. J Mater Sci. 1973;9(4):683–5. 4. Kim CS, Sim W, Kim Y, et al. Modeling and characterization of an industrial inkjet head for micro patterning on printed circuit boards. In: Proceedings of the Sixth International ASME Conference on Nanochannels, Microchannels and Minichannels (ICNMM2008), Darmstadt, Germany; 2008. pp. 1–10. 5. Hémon P, Wojciechowski J. Attenuation of cavity internal pressure oscillations by shear layer forcing with pulsed micro-jets. Eur J Mech B Fluids. 2006;25(6):939–47. 6. Bogy DB, Talke FE. Experimental and theoretical study of wave propagation phenomena in drop-on-demand ink jet devices. IBM J Res Dev. 1984;28(3):314–21. 7. Sohn H, Yang DY. Drop-on-demand deposition of superheated metal droplets for selective infiltration manufacturing. Mater Sci Eng A. 2005;392(1–2):415–21. 8. Cheng SX, Li T, Chandra S. Producing molten metal droplets with a pneumatic droplet-ondemand generator. J Mater Process Technol. 2005;159(3):295–302. 9. Amirzadeh A, Raessi M, Chandra S. Producing molten metal droplets smaller than the nozzle diameter using a pneumatic drop-on-demand generator[J]. Exp Thermal Fluid Sci. 2013;47:26– 33. 10. Lee TM, Kang TG, Yang JS, et al. Drop-on-demand solder droplet jetting system for fabricating microstructure. IEEE Trans Electron Packag Manuf. 2008;31(3):202–10. 11. Takagi K, Seno K, Kawasaki A. Fabrication of a three-dimensional terahertz photonic crystal using monosized spherical particles. Appl Phys Lett. 2004;85(17):3681–3. 12. Luo J, Qi L, Tao Y, et al. Impact-driven ejection of micro metal droplets on-demand. Int J Mach Tools Manuf. 2016;106:67–74.

Chapter 6

Uniform Solder Droplet Deposition and Its 3D Printing Technology

6.1 Introduction By using tin–lead alloy, tin–silver alloy, and other tin solders, uniform tin solder droplet printing can direct manufacture uniform micro bump and pillar arrays, microelectronic circuits, and packaging of electronic components. Moreover, tin solder droplet printing can also be used as a demonstration to investigate the parameter combination for metal parts 3D printing. In this chapter, the tin–lead solder is used as the ejection material to investigate physical behaviors and parameter influence laws in tin droplet deposition, including deposition behaviors of a single or multiple droplets, the parameter influence on the morphology of solder bumps and lines, and the corresponding controlling method. Their potential applications are also discussed in this chapter such as droplet-based 3D printing technology for electronic packaging and metal parts forming. This chapter aims to lay a foundation for applying droplet-based manufacturing in microelectronics.

6.2 Deposition Behaviors of Uniform Solder Droplet Deposition and Effect Factors of the Morphology of Deposited Droplets After molten metal droplets deposit and solidify on a substrate, their morphology depends on some important parameters such as substrate temperature and material properties. These parameters also determine the final contour and the surface quality of printed parts. Deposition of molten metal droplets on the substrate involves a series of complex coupling behaviors of dynamics and thermodynamics (i.e., wetting, spreading, heat transferring, and solidification). It is difficult to accurately predict deposition behaviors of molten metal droplets and the corresponding parameter effect lows on droplet final shapes. Therefore, in this section, metal droplet deposition experiments are carried out to investigate droplet deposition behaviors. © National Defense Industry Press 2023 L. Qi et al., Metal Micro-Droplet Based 3D Printing Technology, https://doi.org/10.1007/978-981-99-0965-0_6

185

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

6.2.1 Deposition and Spreading Behaviors of Uniform Solder Droplets In this section, the tin–lead alloy (S-Sn60PbAA) is selected as the ejection material to investigate the spreading and solidification behaviors of solder droplets under different deposition conditions and to reveal the influence of experimental parameters on metal droplets spreading behavior. In the experiment, the piezoelectric pulse driven droplet ejection on-demand generator is used to eject solder droplets. The droplet diameter is approximately 410 µm [1]. The droplet impact velocity measured by the high-speed photography system is approximately 1 m/s. Substrate materials include red copper, stainless steel, titanium, etc. Under this condition, the metal droplet’ We number is 7.05, and the Oh number is 0.001. Figure 2.16 in Sect. 2.5.1 Chapter 2 shows that the spreading behavior of metal droplets locates in the lower part of zone I (inviscid impact-driven region). Here, the viscosity of material has little effect on spreading. The spreading behavior of impacting metal droplets is mainly affected by the droplet inertial force and capillary force. Figure 6.1 shows the high-speed images of a droplet bouncing off a steel substrate. The metal droplet spreads into a flat disk shape when it impacts the substrate. Since the contact angle between the metal droplet and the substrate is large (demonstrating poor wettability with the substrate), the metal droplet bounces off after recoiling. Figure 6.2 demonstrates the deposition process of a tin–lead alloy droplet on a polished red copper substrate. Since the red copper has a large thermal conductivity, molten metal droplet immediately solidifies at the bottom while contacting. Additionally, the tin–lead alloy can react with the red copper substrate surface, produce high-melting-point intermetallic compounds on the substrate surface, and grow into droplets through the bottom. The above two factors suppress the rebound of metal droplets. Figure 6.2b–f illustrate that a small vibration appears on the surface of the metal droplet during the recoiling process, which is accompanied by the solidification process of metal droplets and affects their final morphology.

Fig. 6.1 Process of droplet bouncing off (1 ms per frame)

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187

Fig. 6.2 Deposition and surface impacting process of a metal droplet on the red copper substrate

6.2.2 Effect of Experimental Parameters on Final Shapes of Solidified Micro Droplets In solder droplet deposition experiments, the surface vibration of deposited droplets would cause different final morphology. This phenomenon is not conducive to selecting printing parameters and controlling the surface quality of formed parts. Therefore, the research on the effect of parameters on the droplet surface morphology and depositing metal bumps with a consistent shape is a basis for the application of uniform droplet-based 3D printing. 1. Effect of the substrate material on the morphology of deposited micro droplets A single droplet can be viewed as a perfect sphere before being deposited on the substrate. After deposition and solidification, the droplet has the segment shape. According to the mass conservation law, equations have been established to describe key parameters of the droplet morphology (as shown by Eqs. (2.88)–(2.89), Sect. 2.5.2, Chap. 2). In these equations, the solidification angle is the main parameter that determines the final morphology of droplets. When droplets are deposited on substrates with different materials, the solidification angle determines the final morphology. To analyze the effect of the substrate material on the morphology of deposited droplets, substrates of pure copper, brass, pure aluminum, pure nickel, stainless steel, and titanium alloy0 are selected for droplet deposition experiments. Table 6.1 shows the metal droplet deposition results on substrates with different materials. Since tin solder (tin–lead alloy) droplets bounce on steel and titanium substrates, final deposited droplets have an approximately spherical morphology. Tin solder droplets do not bounce on pure copper, brass, pure aluminum, and pure nickel substrates. The spreading diameters on pure copper and brass substrates are

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

approximately equal to the maximum diameter of bumps, and the solidification angles are less than 100°. While the droplet spreading diameter on aluminum and nickel substrates are smaller, and the solidification angles are greater than 100°. The experimental results show that the wettability of tin solder droplets on pure copper and the brass substrate is better than that on pure aluminum and nickel substrates. Droplets spread more sufficiently on a substrate at better wettability. Therefore, to ensure stable deposition, pure copper and brass substrates are chosen in the tin–lead alloy droplet deposition. 2. Effect of the solidification time on the morphology of deposited solder droplets The deposition process of micro metal droplets is accompanied by the coupling effect of under-damping vibration and layer-by-layer solidification. When the deposition Table 6.1 Experimental results of droplets deposited on different substrates Substrate materials

Whether to Droplet rebound deposition morphology

Solidification The angle/° average height of solidified droplet s/µm

Contact diameter of deposited tin solder droplets/µm

Maximum diameter of deposited tin solder droplets/µm

Pure copper

No

99.66

407.4

473.4

479.8

Brass

No

97.49

402.1

472.3

477.7

Pure No aluminum

102.09

406.4

424.5

476.6

Pure nickel

No

103.431

404.3

427.7

482.9

Stainless steel

Yes

118.44

409.7

381.9

497.9

Titanium alloy

Yes

139.53

441.5

284.1

482.9

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189

parameters are constant, the droplet solidification time is another major factor determining the final morphology of metal droplets. After being deposited on a substrate, the droplet solidification time can be estimated by the solidification time scale τ sol (see Table 2.1 for details). τsol

D2 = d 4α

(

1 + βsuper Ste

) (6.1)

In the experiment, the droplet solidification time can be indirectly controlled by adjusting the droplet deposition temperature. In this way, the droplet deposition morphology of different solidification times can be obtained. Figure 6.3 shows the final bump shapes under different solidification times, which can be divided into three types: “bulb,” “hat,” and “hemispherical”.

Fig. 6.3 Final bump shapes under different solidification rates, which can be divided into three types: “bulb,” “hat,” and “hemispherical”

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Figure 6.3a shows the geometric contour of the bump that takes the “bulb” shape, in which the contact diameter is less than the maximum diameter of the upper part. The reason for forming this shape is that the rapid local solidification (τ sol = 4.2 ms) at the contact line hampered the spreading of the droplet, resulting in a small contact diameter. Figure 6.3b shows the geometric contour of the bump that takes the “hat” shape. A convex edge was formed at the contact line, which was caused by the longer solidification time (τ sol = 4.9 ms) and the droplet spreading at the contact line. Figure 6.3c–f show the geometric profile of bumps that takes the “hemisphere” shape. This is because liquid metal flows away from the solidified metal during the solidification process due to the slower solidification rate (τ sol = 5.7 ms, 6.6 ms, 10.1 ms, and 27.6 ms, respectively). The convex edge was covered, and the final shape was formed like a “hemisphere” due to the surface tension. Figure 6.4 shows the variation between the bump height h and the dimensionless bump height h/Dd with the total solidification time τ sol . A clear threshold that divides the regions of the large and small deviation of the solder bump height can be observed in the range of 6.0–8.9 ms. h decreased sharply when τ sol is less than 6.0 ms, and the final bump shape varies from “bulb” to “hat” and “hemisphere” with the increasing of τ sol . It indicates the fact that the solidification has a marked effect on the bump height under this condition. While h remains stable and all the bumps take the “hemisphere” shape when τ sol is longer than 8.9 ms, h/Dd is also stable at 0.67 at this condition, which shows that the effect of solidification is not obvious. The above researches show that extending the solidification time is beneficial to maintain the consistency of the droplet deposition height.

Fig. 6.4 The relationship between the bump height h and total solidification time τ sol

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191

3. Effect of deposition parameters on the height deviation of droplets According to the conclusion of the last section, the height of deposited droplets h is directly related to the solidification rate. The solidification rate of metal droplets is mainly determined by the droplet temperature T d and the substrate temperature T s . In this section, the droplet and substrate temperature are taken as the main process parameters to study the parameter effect on the height deviation and geometric profile of deposited droplets. Furthermore, the reason for the droplet height deviation will be analyzed. The average value h bump and standard deviation SD of the deposited droplet height hbump are defined as h bump =

n 1E h bumpi n i=1

(6.2)

| 21 | E n 1 (h i − h) SD = i=1 n

(6.3)

The single-factor experiment method is used to analyze the significance of the droplet temperature and the substrate temperature on h bump and SD. The experiment parameters are shown in Table 6.2. In the experiment, more than 300 droplets are collected under each set of parameters, their diameter is measured by using the tool microscope. Figure 6.5 shows the variation of the average height h bump and the standard deviation SD with droplet initial temperature T d and substrate temperature T s . The results illustrate that the bump height deviation is reduced by increasing T d and T s . The high droplet initial temperature or substrate temperature would increase the droplet solidification time, leading to sufficient droplet spread time. However, when the droplet’s initial temperature T d reaches 747 K or the substrate temperature T s reaches 503 K, the average height h bump of the droplet geometric contour suddenly increases, indicating that droplets start to rebound. Then, the droplet solidifies into a spherical-like shape after rebounding several times, which means that the droplet cannot deposit accurately. Figure 6.6 shows the height of droplets deposited at low and high droplet initial temperatures. When the droplet’s initial temperature T d and the substrate temperature T s is low (Fig. 6.6a), the droplet solidification rate is high. The deposited Table 6.2 The depositional parameters of the bump array Serial number

Deposition frequency (Hz)

Deposition distance (mm)

Droplet initial temperature (K)

Substrate temperature (K)

#1

1

10

543, 583, 623, 663, 703, 743

353

623

353, 383, 413, 443, 473, 503

#2

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.5 The effect of the droplet initial temperature and the substrate temperature on the statistical distribution of the bump height

droplets present different geometric contours, which makes a large deviation of droplet height h. This is because when the droplet solidification rate is high, the solidification process is accompanied by vibration, resulting in a random height deviation. When the droplet’s initial temperature T d and the substrate temperature T s is high (Fig. 6.6b), the droplet solidification time becomes long (located in the stable area in Fig. 6.4), which offers droplets sufficient time to stop vibration. As a result, the bump height h is similar, and the geometric contour of the bump array is a uniform “hemispherical” shape.

6.2.3 The Method to Reduce the Height Deviation of Solder Bumps and the Analysis of the Height Accuracy Based on the above discussion, the printed bump height deviation can be suppressed by increasing the droplet initial temperature T d and substrate temperature T s . However, the deposition results still have a slight error. To ensure the consistency of the height of bumps and prevent the effect of vibration on the final droplet morphology, the subsequent post-processing of deposited metal droplets is required. Since ejected droplets have uniform size and the wetting angle between molten metal droplets and substrates is constant under certain conditions, it is possible to use the peak soldering process to “remelt and reshape” the printed metal droplets and obtain metal bumps with uniform shapes and heights. Figure 6.7 shows the comparison of the metal droplet geometric contours before and after “remelting and shaping”. In the experiment, droplets with a diameter of approximately 200 µm are deposited on the brass substrate. After taking pictures, the substrate temperature increases to 533 K and keeps for 30 s to remelt and reshape solidified metal droplets. Then observe the variation of droplet morphology before and after remelting. Due to the low substrate temperature, the solidification rate of directly deposited metal droplets is too fast, which made the deposited droplets present a “bulb” shape with a narrow bottom and a wide upper portion. The enlarged

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193

Fig. 6.6 The final bump shapes under different conditions: a At low temperature, where the final shapes include “hat” and “hemisphere”, the height deviation reaches ± 22. 5 µm; b At high temperature, where all of the final shapes are “hemisphere”, and the height deviation reaches ± 5 µm

picture shows that droplets have ripples on their surface, illustrating the coupling effect of repeated vibration and solidification layer by layer during droplet deposition (Fig. 6.7a). After remelting and shaping, the remelted droplets shrink into a sphere cap with a smooth surface under the action of the surface tension. After cooling and solidification, a spherical cap with regular and smooth geometric contours can be obtained (Fig. 6.7b). After remelting, the droplet shape becomes a regular sphere cap, which can be characterized by the classic spherical cap model [Sect. 2.5.2 of Chap. 2, Eqs. (2.88)– (2.90)]. In this model, the contact angle between droplets and substrates determines the contour shape of droplets. Since the contact angles of tin–lead alloy droplets on pure copper, brass, pure aluminum, and pure nickel substrates are about 60°, 101°, 142°, and 115°, the dimensionless height hbump /Dd of droplet shapes can be solved by substituting the above contact angles into Eqs. (2.88)–(2.90). Figure 6.8 shows the comparison between measured results and the spherical cap model. It can be seen that measured results are in good agreement with the model, indicating the feasibility of the classic spherical cap model to describe the metal droplet shapes after “remelting and shaping”. In the classic spherical cap model, the height h of droplet spherical cap after deposition can be expressed as

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.7 Comparison of metal droplets deposited at low temperature (T d = 583 K, T s = 353 K) and geometric contour shapes after heating and remelting. a Directly deposited metal droplets. b Metal droplets after “remelting and shaping”

Fig. 6.8 Comparison of the model calculation results (curve) and measured results of the metal droplet dimensionless height hbump /Dd versus the dimensionless spreading diameter Ds /Dd (square, circle, and triangle points represent droplets deposited on pure copper, brass, pure aluminum, and nickel substrates respectively)

6.2 Deposition Behaviors of Uniform Solder Droplet Deposition and Effect …

h bump = kbump Dd , kbump =

) 13 ( 4 1 (1 − cosav ) 2 (1 − cosav )2 (2 + cosav )

195

(6.4)

Since the distribution of the droplet diameter obeys the normal distribution Dd ~ N (μd , SDd 2 ), it can be deduced that the final height hbump of the deposited droplet also obeys the normal distribution ) ( h bump ∼ N μh , S D h 2 ,

(6.5)

where μh = kbump

n E

Ddi = kbump μd ,

(6.6)

i=1

⎤(1/2) ⎤(1/2) ⎡ n n E E ( ) 1 1 kbump Ddi − kbump μd ⎦ =⎣ S Dh = ⎣ (h i − μh )⎦ n (i=1) n (i=1) ⎤(1/2) ⎡ n E 1 1 2 ⎣ = kbump (h i − μh )⎦ (6.7) n (i=1) ⎡

2 S D h 2 = kbump S Dd 2

(6.8)

The maximum error Δhbump of the final geometric profile height of the deposited droplet can be expressed as: Δh bump = h bump_max − h bump_min = kbump (Dmax − Dmin ) = kbump ΔDd ,

(6.9)

where k bump is the error coefficient which is determined by the solidification angle av between droplet and the substrate. This value represents the proportional coefficient between the metal droplet size error and the deposition height error. Figure 6.9a shows the variation between the error coefficient k bump and the contact angle av . k bump is always less than 1, indicating that the droplet size error reduces when it transfers to droplet height. The droplet height error is smaller than the droplet initial diameter error. While k bump increases monotonically with the increase of av , indicating big contact angles are not suitable for the reduction of droplet height error. Figure 6.9b shows that the bump height error Δhbump increases with the ejected droplet diameter error ΔDd and the contact angle av . Therefore, improving the droplet size accuracy and selecting a substrate material with good wettability is conducive to reduce the droplet height error.

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.9 The variation between the maximum height error Δh and the error coefficient k with the droplet contact angle θ

6.3 Printing Path Planning of the Metal Droplet and the Effect Factor Printing of traces with a smooth surface and accurate size is the precondition to print complex structures. Proper planning strategy of the printing path is the main factor of efficient printing. In this chapter, the effect of experimental parameters (i.e., droplet temperature, substrate temperature, printing step, scanning strategy, etc.) on the trace printing morphology and the effect of planning the printing path on the forming efficiency will be discussed.

6.3.1 Effect of Sequential Printing Parameters on the Morphology of Printed Traces Sequential printing means that droplets are printed adjacently on the substrate to form traces (Fig. 6.10). Effect parameters of the trace’s final morphology mainly include droplet diameter, droplet temperature, substrate temperature, printing step, and ejection frequency. In the printing process, droplet diameter and droplet temperature are constant. Therefore, the present work aims to study the effect of printing frequency, substrate temperature, printing step, and scanning pattern on the morphology of printing traces. 1. Sequential printing method and the definition of effect parameters During the sequential printing process, the micro-droplets are set to sequentially deposit on the substrate along the scanning pattern (raster-scan) to fill a cross-section of the layer, as shown in Fig. 6.11a and b. The space between two centers of adjacent deposited droplets is defined as the scanning step W, which is expressed by W x and W y in the x and y directions, respectively, as shown in Fig. 6.11c. The ratio of the droplet diameter to the maximum width of the overlapped section between two

6.3 Printing Path Planning of the Metal Droplet and the Effect Factor

197

Fig. 6.10 Schematic diagram of traces printed by the sequential printing method

adjacent deposited droplets is defined as the overlapping ratio η (η = L x /Dd ), here L x is the maximum width of the overlapped section between droplets a and b, and Dd is the droplet diameter. In the trace printing process, the x direction step W x affects the trace forming quality. In the process of one-layer printing, the y direction step W y also needs to be considered. If both W x and W y are not properly selected, printing parts might have low forming accuracy and even defects like internal holes. Figure 6.12 shows the control principle of the scanning step W x . f is the droplet ejection frequency, V is the substrate velocity, N is the ejection number of droplets, and S is the substrate displacement within n seconds. The relationship between these parameters is expressed as: S = nV = Wx N = Wx n f Using Eq. (6.10), W x can be expressed as:

Fig. 6.11 Schematic diagram of the droplet printing step and the overlapping rate

(6.10)

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.12 Schematic diagram of the control model of W x

Wx = V / f

(6.11)

Equation (6.11) shows that the scanning step W x can be controlled by the substrate velocity V and the ejection frequency f . According to the definition of the overlapping ratio, the overlapping ratio ηx in the x direction can be expressed as: ηx =

Lx Dd − W x V Wx = =1− =1− Dd Dd f Dd Dd

(6.12)

Equation (6.12) shows that the overlapping ratio ηx is related to W x and Dd . The scan step W y in the y direction can be controlled by adjusting the spacing of two adjacent lines Ds (Fig. 6.13d). Figure 6.13a is the STL model of the illustrated part. Figure 6.13b, c, and d are the scanning paths in one layer when the value of the droplet spread diameter (Ds ) is 0.1 mm, 0.3 mm, and 0.5 mm, respectively. 2. Calculation model of the optimal scanning step for sequential printing Assumed that when the metal droplets are deposited continuously, the molten metal liquid in the overlapping section of two adjacent droplets can fully spread and fill the gap between them. The optimization model of the scanning step can be established according to the law of conservation of mass and the optimal scanning step in the x and y directions can be calculated. Calculation model of the optimal scanning step W XP . When the droplets are deposited to form a metal line in the x direction, the shape parameters of solidified droplets (i.e., contact angle av , maximum bump width W d , bump height hbump , spreading radius Rb , and radius of the crown Rc as shown in Fig. 2.20, Chap. 2) on the substrate are set constant. As the gap between two adjacent droplets is filled (as shown in Fig. 6.14a), the W XP is defined as the optimal scanning step. The calculating model of scanning step W XP is illustrated in Fig. 6.14. When droplet 2 overlaps droplet 1 with the scanning step W XP , the sunken section of two adjacent droplets (Fig. 6.14a-4) would be sufficiently filled up to form the ideal shape 5 (Fig. 6.14a-5)

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199

Fig. 6.13 Schematic diagram of the scanning step W y . a STL model of parts. b, c, d scanning paths for Ds = 0.1 mm, 0.3 mm, and 0.5 mm, respectively

by the overlapping section 3 (Figs. 6.14a-3). Furthermore, to simplify the calculation, the ideal shape 5 is divided into three parts: two half-spherical caps 6, 8, and one abnormal cylinder 7 (Fig. 6.14a). According to mass conservation, the volume of a single droplet is equal to the volume of an abnormal cylinder 7. Then, the W XP and Z XP can be expressed as follows: Vdr op = V7

(6.13)

4 Dd 3 | π | π ( ) = av Rc2 + Rb Rc sin(av − ) W X P 3 2 2

(6.14)

Fig. 6.14 Calculation models of the optimal scanning step W XP

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

W X P = F(av , Dd ) = | 3 (1−cosa

v

2π Dd (0 < av < 180o ) | 23 4 (av − sinav cosav ) )2 (2+cosa )

(6.15)

v

ηx p = 1 −

WX P Dd

(6.16)

Equation (6.15) shows that the optimal scanning step W XP is only determined by the droplet diameter Dd and the solidification angle av . Figure 6.15 shows the calculated results of scanning steps W XP for different values of the solidification angle av and the droplet diameters Dd . It can be seen that the optimal scanning step W XP is linearly proportional to the droplet diameter Dd when the solidification angle is the same. The relationship between the optimal scanning step W XP and the solidification angles av is nonlinear when the droplet diameter is constant. The optimal scanning step for forming a layer is defined as W YL (Fig. 6.16b). The calculated model of W YL is shown in Fig. 6.16. Figure 6.16a shows that the molten metal in the overlap section of two metal lines can be filled up by the gap between two adjacent lines when line 1 and line 2 overlap with the optimal scanning step W YL . Figure 6.16b shows the cross-section of two deposited lines. The area of curve-side-triangle CDE should be equal to the area of curve-side-triangle ACB according to the conservation of mass. Furthermore, they can be converted into the area of quadrangle ABMN, which is equal to the sum of AME and BND. Then, based on Fig. 6.16b, W YL and ZYL can be expressed as follows:

Fig. 6.15 Scanning step W XP versus the droplet diameter and the solidification angles

6.3 Printing Path Planning of the Metal Droplet and the Effect Factor

201

Fig. 6.16 Calculation model of optimal scanning step W YL in the y direction

S AB M N = S AM E + S B N D | | | ) ) π )| π) + RC = av Rc2 + r R b Rc sin av − WY L RC sin av − 2 2 WY L = F(av , Dd ) | | 13 Dd (1−cosa )42 (2+cosa ) (av − sinav cosav ) v v (0 < av < 180o ) = 2(1 − cosav ) ηY L = 1 −

WY L . Dd

(6.17) (6.18)

(6.19) (6.20)

Equation (6.19) shows that the optimal scanning step W YL is related to the droplet diameter Dd and solidification angle av . Figure 6.17 shows the variation of scanning steps W YL with av and Dd . It is observed that the relationships among the optimal scanning step W YL , the droplet diameter Dd and the solidification angles av are similar to those in Fig. 6.15. Thus, it is known that the optimal scanning steps W XP and W YL are only related to the droplet diameter Dd and the solidification angle av . The W XP and W YL can be calculated when the droplet diameter and the solidification angle are known. 3. Experiments of sequential printing of metal droplets A series of printing experiments of traces, planes, and three-dimensional structures are conducted to validate the calculation model of the optimal scanning step. Tin– lead alloy (S-Sn60PbAA) and the pure copper are used as the ejection material and substrate material, respectively. Trace printing experiment. To verify the correctness of the W xp calculation model, different scanning steps are used to print traces in the x direction. The experiment parameters are shown in Table 6.3.

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.17 Variation of the scanning step W YL with the solidification angles and the droplet diameter

Table 6.3 Experimental parameters for trace deposition Parameters

Value

Parameters

Value

Droplet temperature T d (°C)

270

Ejection frequency f (Hz)

1

Substrate temperature T s (°C)

90

Substrate movement speed V (mm/s)

Deposition distance Hs (mm)

5 ~ 10

Solidification angle av (º)

121.5

Droplet diameter Dd (µm)

400

(a) (b) (c) (d) (e) (f)

0.90 0.75 0.60 0.37 0.294 0.20

In the lines printing experiment, the droplet diameter Dd (400 µm) and the solidification angle av (121°) remain unchanged. The optimal scanning step W XP is 294 µm and the overlapping ratio ηxp is 26.5%, according to Eqs. (6.15) and (6.16). In experiments, the ejection frequency f is set as 1 Hz, and the velocity of substrate V is set as 0.9, 0.75, 0.6, 0.370, 0.294, and 0.20 mm/s, respectively. The corresponding scanning steps W x are 900, 750, 600, 370, 294, and 200 µm according to Eqs. (6.3) and (6.4). Figure 6.18 shows the deposited traces for different scanning steps. When W x is 900 and 750 µm, the droplets cannot form lines due to the large space of two adjacent droplets. When W x is 600 and 370 µm, the adjacent droplets appear to partially overlap. But the quality of lines is not optimal because of the loose structure and wavy surface. When W x is equal to W XP (294 µm), the deposited line with a compact structure and smooth surface is obtained. With further reduction of the scanning step to W x (200 µm), the deposited droplets grow upwards and could not form a line. The experimental results show that, with the change of scanning step from large to

6.3 Printing Path Planning of the Metal Droplet and the Effect Factor

203

Fig. 6.18 Deposited traces for different scanning steps W x . a W x = 900 µm. b W x = 750 µm. c W x = 600 µm. d W x = 370 µm. e W x = 294 µm. f W x = 200 µm

small, four overlapping states are observed: separate, partial overlapping, sufficient overlapping, and arched traces. When W x = W XP , perfect overlapping results are obtained, which verifies the correctness of the W XP calculation model. In the process of micro droplet printing, the substrate temperature is another parameter that should be considered. Figure 6.19 shows the printed traces under different substrate temperatures and scanning steps. It can be seen that when the substrate temperature is 453 K, the partial surface of printed traces is very smooth. However, the traces formed under six scanning steps all appear local agglomeration phenomena which easily appear at the starting position. With the increase of the droplet spacing, the agglomeration phenomenon gradually increases from one place to multi places, indicating that this parameter cannot assure printing quality. When the substrate temperature is 373 K, adjacent droplets are in poor fusion state. The trace surface is rough and has an obvious “scallop” shape. This is due to the fact that droplets solidify rapidly and form a spherical shape with wrinkles when depositing at this temperature, resulting in the rough surface of printing traces. When the substrate temperature is set at 403 or 433 K, and the scanning steps between droplet is larger or smaller than the optimal printing step, the surface of printed traces appears partial sunk- or scalloped-shaped, resulting in poor surface quality. When the proper scanning step is selected, the quality of the line surface is better than that on the low-temperature substrate, however, the scalloped surfaces can be still observed. Figure 6.19 shows that when the substrate temperature are 433 and

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.19 The effect of substrate temperature (T s ) and droplet step (L) on the trace shape printed by sequential printing

403 K, the remelting between deposited droplets at 433 K is better than that at 403 K. The printing quality is also better than lines formed at lower substrate temperatures. Trace morphology shows that even if the remelting between droplets is perfect, the single droplet morphology can still be seen on the trace, resulting in surface roughness. The “scallop” shape of the printed line surface is still hard to avoid even the optimal parameter is used. Layer printing verification experiment. To verify the correctness of the W YL calculation model, different scanning steps (W x + W y ) are used to carry out layers printing. Table 6.4 lists the process parameters of deposition experiments of layers. In the deposition, droplet diameter Dd (700 µm) and solidification angle av (120.5°) remain unchanged. According to Eqs. (6.15), (6.16), (6.19), and (6.20), the calculated optimal scanning step W YL is 620 µm and overlapping ratio ηYL is 11.4%. The ejection frequency f is set to 1 Hz, the velocity of substrate V is set to 0.514 mm/s, and the scanning step W y is set to 1000, 850, 750, 700, 620, and 600 µm, respectively. Figure 6.20 shows the results of layer printing under different values of W y . When W y is 1000, 850, 750, and 700 µm, the printed layer contains many holes because the adjacent two lines can not overlap sufficiently. When W y is equal to the optimal printing step (W YL = 620 µm), the adjacent lines overlap sufficiently and appropriately, the printed layer with the high density and good flatness can be obtained. When W y decreases to 600 µm, the adjacent two lines overlap excessively due to the small scanning step. Deposited droplets grow spatially, resulting in the surface arching.

6.3 Printing Path Planning of the Metal Droplet and the Effect Factor

205

Table 6.4 Parameters of the layer printing experiment Parameters

Value

Parameters

Value

Droplet temperature T d (°C)

270

Ejection frequency f (Hz)

1

Substrate temperature T s (°C)

90

Substrate movement speed V (mm/s)

0.514

Scanning step W y /(mm)

(a) (b) (c) (d) (e) (f)

Deposition distance Hs (mm)

5 ~ 10

Solidification angle av (º)

120.5

Droplet diameter Dd (µm)

700

1.0 0.85 0.75 0.70 0.62 0.60

Fig. 6.20 The layers printed in different scanning steps W y . a W y = 1000 µm. b W y = 850 µm. c W y = 750 µm. d W y = 700 µm. e W y = 620 µm. f W y = 600 µm

To characterize the compactness, the porosity of deposition layers (P) is defined as the ratio of the porosity area to the cross-section area. The calculated results of the porosity in different scanning steps are shown in Fig. 6.21. It can be seen that when the scanning step W y is 620 µm, the porosity P has the smallest value.

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.21 Porosity P of layers deposited for different values of scanning step W y

6.3.2 Line Formation Experiment by Using the Alternate Printing As mentioned above, during sequential droplet printing, the trace surface easily forms the scalloped surface. To print lines with smooth and neat surfaces, an alternate droplet printing method is proposed. The principle of alternate printing is shown in Fig. 6.22. A discrete droplet array is firstly deposited on the substrate with a droplet interval to locate the initial position of traces (called “anchoring”). After that the substrate is moved back, second-layer droplets are deposited at center gaps of the printed droplet array. Deposited droplets remelt solidified droplets and spread under the capillary force [2] to fully fill gaps and finally form a uniform and smooth trace. 1. Calculation of the maximum and the optimal droplet center-to-center distance for alternate deposition When a molten droplet is filled between two anchored droplets, the final morphology of the printed short trace varies from the initial droplet center-to-center distance (or scanning step of the first layer). Therefore, it is necessary to find the suitable range of the scanning step. When the scanning step of anchored droplets is maximum (L max ), droplets are just overlapped. If the solidification angle of deposited droplets is less than 90°, L max is the step in which the filling droplet just contacts with the edges of solidified droplets at two sides after spreading (Fig. 6.23a). If the solidification angle is greater than 90°, L max is the step in which the filling droplet contacts with the maximum diameter of the deposited droplets (Fig. 6.23b). The maximum step represents the threshold of the scanning step for printing continuous traces. Only

6.3 Printing Path Planning of the Metal Droplet and the Effect Factor

207

Fig. 6.22 Schematic diagram of alternate printing by using uniform droplet deposition

when the droplet printing step is less than the maximum step, printed droplets can be overlapped. The maximum droplet center-to-center distance L max , which form efficient filling between two adjacent anchored droplets, can be expressed as | L max = 2Ds = 2Dd

Fig. 6.23 Schematic diagram of the maximum step of alternate printing. For printing continuous traces, the filling droplet a contacts with bottom diameter of the anchored droplet when the droplet solidification angle is less than 90°, b contacts with the maximum diameter of deposited droplets when the solidification angle is larger than 90°

4(sinav )3 (1 − cosav )2 (2 + cosav )

| 13

, av ≤ 90◦

(6.21)

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

| L max = 2Dc = 2Dd

4 (1 − cosav )2 (2 + cosav )

| 13

, av > 90◦

(6.22)

To calculate the optimal step of alternate printing, droplet morphology parameters (av , Rb , and Rc ) are assumed to be constant and filling droplets are assumed to be totally fill gaps of anchored droplets. When overlapping of filling droplets is in the ideal condition, the scanning step of anchored droplets is the optimal droplet distance L opt . According to the mass conservation law, the gap volume is twice of the single droplet volume in this case. Then, the following equations can be obtained V6 = 2Vd , L opt

) π )| π Rc 2 + Rb Rc sin av − = V6 π 2

|a

v

(6.23) (6.24)

Combining Eqs. (6.23) and (6.24), L opt can be expressed as √ 3 L opt =

4 π Dd [(1 − cosav )2 (2 + cosav )]2/3 (av − sinav cosav )−1 3

(6.25)

Equation (6.25) shows that the optimal scanning step of anchored droplets only relates to the initial diameter and solidification angle of printed droplets. The optimal anchored droplet distance linearly increases with the initial droplet diameter when the solidification angle is the same. 2. Effect laws of the trace morphology printed by alternate printing Figure 6.24 shows three-droplet traces printed at 400 °C, and the scanning step is 5 ~ 15 mm. When the substrate temperature is 175 °C (close to the droplet melting point of 183 °C), peaks arise in the center of three-droplet traces. In this case, printed metal droplets are coalesced due to the action of surface tension, which is hard to form uniform traces. When the substrate temperature is between 100 and 150 °C, and the scanning step is slightly smaller (Fig. 6.24d) or larger (Fig. 6.24f) than the optimal step, the morphology of three-droplet traces presents fluctuations. When the scanning step is small, printing traces are slightly protruding upward at their centers. When the scanning step is large, printing traces are sunk at their centers. When the scanning step is the optimal step (Fig. 6.24e), the volume of the filling droplet is equal to the gap between two adjacent anchored droplets. The gap can be fully filled after the liquid metal completely spread under the action of surface tension. Finally, the trace with uniform width and height is formed after solidifying. When the substrate temperature decreases between 50 and 100 °C, the remelting between the filling and anchored droplets decreases because of the rapid cooling of the deposited droplets on the low temperature substrate. As a result, three-droplet traces show obvious scallop shapes for all different printing steps L (Fig. 6.24g–i). At this substrate temperature, no matter how the printing step changes, the morphology of the

6.3 Printing Path Planning of the Metal Droplet and the Effect Factor

209

Fig. 6.24 Typical side and top views of three-droplet traces printed in the alternate sequence for different combinations of the printing step (L) and the substrate temperature (T s )

overlapped traces is scallop. In this case, the top views of the three printing droplets show that when the droplet distance is small, printing traces have the protruding wave shape in the printing direction. When the droplet distance is optimal, printing traces have a concave shape. When the scanning step is large, printing traces also have a concave shape in the printing direction. In addition, Fig. 6.24d–i show some common phenomena on the surface of the deposited droplets. For instance, the overlapping section of the filling and anchored droplets have a wrinkle morphology. Droplets have “crater” in their top center. Figure 6.25 shows the image of three printed droplets when the substrate temperature is approximately 100 °C. Figure 6.25a shows that the surface of the anchored droplets presents “scale” shapes. This is due to the fact that droplets vibrate and solidify simultaneously on the low-temperature substrate, resulting in deposited droplets with the surface full of “shallow pits”. Along the moving direction of the substrate, waved surface can be observed between filling droplets and anchored droplets. The wave becomes dense close to filling droplets. Figure 6.25b shows a “small shallow pit” on the top of the molten droplets. This is due to the fact that, when filling molten droplets deposit, anchored droplets restrict molten filling droplets, which spread towards solidified sections on both sides under the effect of surface tension, and finally, a “small shallow pit” is formed on the top surface.

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.25 Local morphology of three printed droplets. a Morphology of an anchored droplet. b Morphology of a filling droplet after solidification

To quantitatively analyze the effect of printing parameters on the morphology of three droplets, the height deviation ΔH (Fig. 6.26) of three droplets is proposed to describe the fluctuation of the top surface. For a small printing step (Fig. 6.26a), the filling droplet bulges, ΔH is defined as the height difference between the peak of filling droplets and the joint valley between overlapped droplets. For a large printing step, the filling droplet collapses (Fig. 6.26b). In this condition, ΔH is the height difference between the top of anchored droplets and the joint of overlapped droplets. During printing three-droplet traces, the droplet ejection may be affected by external perturbation, uneven spreading of filling droplets, leading to the asymmetry of printed three-droplet traces. Here, the height difference ΔH l and ΔH r of three-droplet traces in the left and right sides are measured respectively, and the average value is taken as the final height difference ΔH of printed results. Figure 6.27 shows the relationship between the height difference of three-printed droplet traces and the scanning step at different substrate temperatures. Each height difference is calculated from ten measured results under the same experiment parameters. By fitting the measured results, we found that the variation tend basically fits

Fig. 6.26 Schematic diagram of measuring the height difference ΔH of three printed droplets. a the solidification angle is smaller than 90°, b the solidification angle is larger than 90°

6.3 Printing Path Planning of the Metal Droplet and the Effect Factor

211

Fig. 6.27 Height differences of three-droplet traces as functions of printing steps of anchored droplets at different substrate temperatures

with a quadratic curve. When the substrate temperature is constant, the height difference of three-droplet traces decreases with the printing step. On the contrary, when the printing step exceeds a threshold, the height difference increases again. The reason lies in that filling droplets causes bulging sections in the middle part and finally results in the height difference when the interval between anchored droplets is too small. However, with the increase of the distance between anchored droplets, the volume of gaps increases, resulting in the decrease of height difference. When the distance between the anchored droplets is close to the optimal distance, the smallest height difference can be obtained. As the printing step of anchored droplets keeps increasing, filling droplets begin to collapse, resulting in the increase of the height difference. Figure 6.27 also shows that when the substrate temperature is approximately 100 °C, the minimum height difference is about 45 µm. This result shows that it is difficult to obtain the traces with the high-quality surface on the low-temperature substrate. When the substrate temperature is 150 °C, the minimum height difference is about 15 µm, and the surface is smoothest. Comparing three groups results with different substrate temperatures, the biggest height difference is observed regardless the change of the printing step when the substrate temperature is 100 °C. In addition, when the substrate temperature is 120 and 150 °C, the height difference is smaller than that at the substrate temperature of 100 °C. As well as the height difference at two substrate temperatures is not significant with different droplet printing steps. Figure 6.28 shows the different non-uniform metal traces, which are deposited by using the alternate printing method. Figure 6.28a shows the trace is printed on a substrate with a temperature of T s that is equal to the solder melting point T m (453 K) and the printing step of 570 µm. The side view shows an obvious smooth surface in the trace. The liquid metal accumulates at the bulging section under the action of surface tension. The top view shows that the width of the printing traces slightly shrinks at the neck section, indicating the stability of the printing process.

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.28 Four types of typical shapes printed by alternate deposition (the top view is taken by SEM; the side view is taken by CCD camera with a microscope lens). a a wave-shaped metal trace printed for the T s equal to the melting point; b a scallop-shaped metal trace printed at the low substrate temperature and small droplet spacing; c a sunk-shaped trace printed at the high substrate temperature and the droplet spacing is larger than the optimal printing step; d a broken trace printed for the droplet space is larger than the maximum printing step

In this case, all the printed traces have a waved surface regardless of the choice in the printing step (ranging from 350 to 800 µm). Figure 6.28b shows a printed scallop-shaped trace which is printed for the substrate temperature of 100 °C and the printing step of 460 µm. The side view illustrates that the scallop-shaped trace is obtained due to the rapid droplet solidification when the substrate temperature is low and the printing step is small. The volume of filling droplets exceeds the gap between anchored droplets, resulting in the formation of bulging shapes between anchored droplets. The top view illustrates the shrinkage of trace width is not obvious, indicating that traces printed on the 100 °C substrate have good stability. Figure 6.28c shows a sunk-shaped trace printed at substrate temperature of 140 °C and the printing step of 600 µm. The side view illustrates that the sunk-shaped trace is formed due to the large printing step between anchored droplets. Here, filling droplets solidify slowly after depositing on the high temperature substrate. The height of filling droplets becomes lower than that of anchored droplets since the volume of filling droplets is not enough to fill the space between two anchored droplets. The top view also shows that the height of filling droplets collapses in a certain degree after depositing and solidifying between anchored droplets. In addition, “small shallow pits” can be observed in the middle of filling droplets on both scallop-shaped and sunk-shaped traces. Figure 6.28d shows a broken trace printed at the substrate temperature of 140 °C and the printing step of 1080 µm. The side view shows that, a broken trace is formed due to the large gap between anchored droplets. Filling droplets break and contract at both sides under the action of surface tension after printing on the substrate.

6.3 Printing Path Planning of the Metal Droplet and the Effect Factor

213

When the substrate temperature is 160 °C and the droplet spacing is 500 µm, the metal traces with the uniform and smooth surface can be obtained (Fig. 6.29a). In this case, the second-layer droplets fuse the overlapped section, and completely fills the gap, which significantly decreases the scalloped shape. Figure 6.29b and c show the detailed surface texture of the uniform metal trace. A trace with the neat and smooth surface is obtained by using the proposed method. No obvious wave shape is observed. The surface profile of the printed metal trace is quantitatively characterized using a 3D confocal microscopy, as shown in Fig. 6.29d. A uniform height can be observed. The cross-section profile in the y-direction shows an arched curve with a sunk top in Fig. 6.29e. Figure 6.29f is the axial section of the printed trace. By taking the sample length of 2 mm, the top surface roughness Ra of the trace is calculated by Ra =

(|Z 1 | + |Z 2 |+ · · · +|Z N |) N

(6.26)

where N is the number of sample points and Z N is the height of the Nth sample point.

Fig. 6.29 Metal trace with the smooth top surface formed by alternate printing. a Side view of the trace, the length of the trace is about 2 mm. b Enlarged side view of the selected section of the metal trace. c SEM morphology of the selected trace section. d 3D scanning results of the metal trace. e Cross section of the metal trace. f Variation of the height of the printed metal trace

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.30 A map of the substrate temperature T s and the printing step L demonstrating different traces for the alternate printing

From the above equation, the roughness of the trace Ra is about 5 µm, which is about 1.8% of the droplet diameter. In Fig. 6.30, the solid line is the prediction curve of the optimal printing step L opt of anchor droplets, which is calculated from Eq. (6.24). The dotted line is the prediction curve of the maximum printing step L max , which is calculated from Eqs. (6.20) and (6.21). This Figure summarizes the parameter windows for printing five typical traces at different substrate temperatures and printing steps. Five typical trace morphologies mainly include wave, scallop, sunk, uniform, and broken traces. When the substrate temperature is close to the melting point of droplets, wave-shaped traces always exist regardless the variation of the printing step, indicating that this is not a conducive parameter for printing uniform traces. When the substrate temperature is 160 and 130 °C, traces with uniform morphology (defined as traces with the surface roughness Ra ≤ 5 µm) can be printed. However, at a substrate temperature of 160 °C, the process window of the printing step is more wide than that at the substrate temperature of 130 °C. In this case, the printing step is close to the optimal printing step. For the substrate temperature is 150 and 120 °C, all printed traces have scallopedshaped morphology when the printing step is less than the optimal printing step. When the printing step is larger than the optimal one, printed traces have sunk-shaped surface. When the printing step keeps increasing, the printed traces break. When the substrate temperature is less than 100 °C, the formed traces are scallopshaped regardless the change of the printing step. This is because the filling molten droplet cools faster when the substrate temperature is low. Since the remelting ratio between the filling and anchored droplets is small, filling droplets show an upward bulge shape. However, when the printing step is too large, printed traces will break. Figure 6.31 summarizes the comparison of the surface roughness (Ra) and dimensionless roughness (Ra/Dd ) of metal traces, which is printed by metal droplets from literature and this work. In literature, Fang et al. [3] printed thin-wall parts combined with 10 layers of lines by using pure tin droplets with diameter of 750 µm. The roughness of this part Ra is about 63 µm, and Ra/Dd is 8.4%. Lass et al. [4] printed thin-wall parts by using Sn95Ag4Cu droplets of the 144 µm diameter. The roughness Ra is about 20 µm, and Ra/Dd is 13.9%. Qi et al. [5] printed tin solder traces by using

6.3 Printing Path Planning of the Metal Droplet and the Effect Factor

215

Fig. 6.31 Comparison of the top surface roughness Ra of metal traces formed by different printing methods

400 µm-diameter solder droplets in 2012 [5], and 290 µm-diameter droplet in 2015 [6]. The roughness of the printed parts Ra is about 17 µm and 9 µm, respectively. The corresponding dimensionless roughness (Ra/Dd ) is 4.25 and 3.2%. All the above metal traces are printed by using dropwise sequential droplet printing method. Using the proposed alternate printing method, 270 µm-diameter tin solder droplets are used to print traces on the silver substrate after the printing parameters are optimized. As a result, the surface roughness Ra is about 5 µm (corresponding to the dimensionless roughness (Ra/Dd ) of 1.8%), indicating that the proposed printing method can improve the surface quality of printing traces. From the above comparison and analysis, the scallop-shaped surface is suppressed by using the droplet alternate printing method. The surface quality of the printed traces is significantly improved compared with the sequential dropwise printing method. At the same time, droplet alternate printing can effectively disperse the thermal stress, which helps reduce the thermal stress concentration. However, the efficiency of alternate printing is lower than sequential printing. Meanwhile, this method requires high stability of droplet ejection. Therefore, in droplet-based printing, the sequential printing method can be used when the requirement of printing surface quality is not high. When the high surface quality is required and the stress concentration needs to be reduce, the alternate printing method is more suitable.

6.3.3 Controlling of the Deposition Path of Micro Metal Parts by Using Uniform Metal Droplet-Based Printing Metal parts can be rapidly formed by printing uniform metal droplets drop-by-drop, line-by-line, and then layer-by-layer. Before printing, the printing path should be first calculated. That is the model of the formed parts is discretized layer-by-layer

216

6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

to obtain the profile data of layers. Then, the droplets printing path can be planned accordingly. Therefore, the precondition of uniform metal droplet 3D printing is to develop the data processing software to conduct the slicing processing and obtain droplets printing path. This section mainly focuses on the data processing software of metal droplet 3D printing. 1. Printing path generation software and its system architecture Based on the characteristics of the metal droplet deposition process, the overall function and module division of the data processing software are established, as shown in Fig. 6.32. The processing software is designed by using a module/component method, which consists of five modules: (1) Data per-processing module. This module mainly realizes STL format data reading, error diagnosis, redundant data filtering, and topological relationship reconstruction. It provides correct model data for subsequent slicing processing and slice contour data acquisition. (2) Slicing module. This module uses split partition, tracing intersection, and other processing algorithms to slice STL format data. The position of contour outlines in each slice is determined by using this module, and then the contour data of each slice is obtained.

Fig. 6.32 Function modules of deposition forming data processing software

6.3 Printing Path Planning of the Metal Droplet and the Effect Factor

217

(3) Optimization module of contour data. This module filters out the redundant data in contour generated in slicing processing. The module removes redundant geometry elements, such as vertices, short edges, and finally obtains the outline data meeting requirements of the droplet deposition process. (4) Printing path generation module. This module generates filling paths by grid scanning according to the contour data of each layer. Then, this module produces a printing file which contains start and stop commands for controlling droplet ejection and G codes for controlling motion of the motion platform. (5) Display module. This module uses virtual vision technology OpenGL to dynamically display STL models, layer contours, filling paths, and deposition paths generated by the above four modules in real time. Functions of above modules are independent. By adopting the open-end design, the software’s overall performance can be improved by upgrading each module separately, meeting the software update requirement for the improvement of the printing technology. The data processing software for the metal droplet ejection deposition process is developed, as shown in Fig. 6.33. The above modules are integrated in the Visual C++ 6.0 environment. The user interface mainly includes title bar, toolbar, status bar, and display area which can effectively realize the functions of the above modules. By using the buttons in the toolbar, following functions can be realized: date files reading and saving, real time display and coordinate change of digital models, slicing process, layer data display and saving, generation of scanning and filling paths, and the output of final printing files. The status bar can display the STL model parameters and slicing information in real time. The display area mainly displays the STL model and layer data obtained by slicing. This software has good interoperability and meets needs of the metal droplet-based manufacturing process. 2. CAD model slicing and contour printing Figure 6.34 shows a slice example of a STL model of a box-shaped part. Firstly, the 3D model is established by using the 3D modeling software. Then, the binary format STL file of this model is output. The STL file size is 500 kb, and contains 9998 triangular patches, 4939 vertices, and 14,997 edges. In the slicing process, the slicing thickness is 0.5 mm, the slicing direction is along the positive z axis. By using the partition and tracing intersection algorithm [7] to slice, a total number of 246 layer contours of the part model are obtained. Contours in each layer are closed, indicating the correctness of the reconstruction module, slicing module, and contour generation module. Figure 6.35 shows the results of slicing, data processing, contour generation, and the final printing parts for different models. The path generation results (middle column) show that the obtained contours are complete and closed, have distinct inner and outer outlines, clean corners, smooth transition curves, and good layered quality. The right column of Fig. 6.35 represents the contours of parts formed by SnPb alloy droplets with a 200 µm diameter. Uniform metal droplets well overlap

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.33 Software user interface

to form complete contours, demonstrating that the software and its corresponding modules can print complete contours. 3. Effect of printing paths on forming efficiency Factors that affect the efficiency of contour filling. In printing a layer, a contour is first printed and its inner region is subsequently filled. The printing efficiency is defined as the ratio of the total filling area to the forming time. The main factors that affect the printing efficiency include the droplet ejection frequency, the platform motion speed, the start-stop times of droplet ejection, the start-stop times of the motion platform, printing paths, and empty jump paths. In the process of filling contours with metal droplets, the scanning path determines the start-stop number of droplet ejection and platform motion, printing paths, and empty jump paths. Therefore, the scanning path is the main factor that affects the forming efficiency. In the forming process, by ignoring the start-stop time of the motion platform, the forming efficiency is determined by the total length of the platform motion path S total for the specified deposition speed and the slice thickness. S total is composed of two parts, namely the droplet deposition path S depd and the empty jump path S jump Stotal = Sdepd + S jump

(6.27)

where the droplet printing path under different scanning models is composed of a series of directed line segments during the filling each layer. Therefore, the length of S depd can be calculated as

6.3 Printing Path Planning of the Metal Droplet and the Effect Factor

219

Fig. 6.34 STL model and slice contours of parts

Sdepd = L n ×

n E

|| P i ||

(6.28)

i=1

En where L n is the total layer number, i=1 || P i || is the droplet printing path in a single layer. For the grid-filling model, the printing process stops droplet En ejection and jumps || P i || and two adjaemptily between any two adjacent directed line segments i=1 cent deposition layers. Therefore, the empty jump length S jump in this model can be calculated as Sjump = L n ×

n−1 E E || || M−1 || P j || + ||Sk || j=1

k=1

(6.29)

220

6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.35 STL model, slicing profile, and path of three parts printed by uniform droplets

where P j is the directed line segments of each empty jump among directed line E M−1 segments P i . L n is the total layer number. k=1 ||Sk || is the empty jump path between layers. The forming of a connecting rod-shaped part is taken as an example to analyze the forming efficiency. Figure 6.36 shows filling paths in the same contour of a micro support part. Those paths are generated with different tilted angles by using the grid scanning method (the line space is 1 mm). The contour has a large aspect ratio and contains seven round holes (Fig. 6.36a). Figure 6.36b, c, and d show the generated filling paths in three different tilted angles (θ = 0°, θ = 60°, and θ = 90°). Blue dotted lines represent empty jump paths, and pink solid lines represent droplet printing paths. According to Eqs. (6.27), (6.28), and (6.29), the start-stop times of droplet ejection, empty jump

6.3 Printing Path Planning of the Metal Droplet and the Effect Factor

221

Fig. 6.36 Deposition paths are generated in different tilted angles by using the grid scanning method

paths, droplet printing paths, and total platform motion paths can be calculated for printing one layer in three different tilted angles. Figure 6.37 shows the comparison of droplet ejection start-stop times and empty jump paths in different rotation angles. Figure 6.38 shows the comparison of the droplet deposition paths and platform motion paths in different tilted angles. By analyzing and comparing Fig. 6.37 and Fig. 6.38, the following conclusions can be drawn: (1) When the droplet diameter and the scanning step are constant, the length of printing paths generated by different scanning methods (for different tilted angles) is approximately the same (430 mm) in the same layer. But the length of empty jump paths is different. The deposited area in each layer should be equal to the cross-sectional area of the part. Therefore, the approximate length of the droplet printing path in each scanning method can be calculated by Eq. (6.30).

Sdepd ≈

Acr oss Dd (1 − ηoverlap )

(6.30)

where Across is the cross-sectional area, and ηoverlap is the overlap ratio (0 < ηoverlap < 1.0).

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.37 Comparison of ejection start-stop times and jump paths in different tilted angles

Fig. 6.38 Comparison of droplet printing paths and total platform motion paths in different tilted angles

6.4 Fabrication of Micro Metal Parts by Drop-On-Demand Printing

223

(2) The length of empty jump paths is an important factor that affects the total path length S total (forming efficiency) of each scanning model. In addition, the startstop time in scanning paths is another important factor that affects the forming efficiency. When the total length of the path is the same, a few break time of the printing path leads to a few start-stop time of the motion platform, a high motion speed, and a high forming efficiency. Otherwise, the above-mentioned printing parameters decrease. Therefore, for the micro support part in Fig. 6.36a, the appropriate scanning method, as shown in Fig. 6.36d, should be selected as the deposition path. By using this method, the motion path of the motion platform is the shortest, and the ejection start-stop times is the least. Due to limited space, the functions of the metal droplet 3D printing software cannot be described in detail in this section. In the following chapters, the selection strategy of printing paths will be explained via specific examples of parts printing.

6.4 Fabrication of Micro Metal Parts by Drop-On-Demand Printing Micro metal parts, especially micro metal thin-walled parts, have important applications in aviation, aerospace, and civil fields. Those parts (i.e., mirror frames, radar waveguides, and heat dissipation fins) are lightweight and have weak stiffness, and are difficult to be manufactured via the traditional cutting process. Uniform metal droplet on-demand ejection printing technology can form thin-walled structures with a thickness of only a single droplet diameter through drop-by-drop deposition of tiny metal droplets. Without the contact force and the limitation of forming dies during printing, micro metal droplet on-demand printing is very promising in manufacturing micro metal parts. While micro metal parts are printed by using uniform micro metal droplet ondemand printing technology, the parameters such as the droplet diameter, positioning accuracy, and the printing path scanning strategy should be considered. When thinwalled parts are printed, geometrical parameters such as the minimum wall thickness and the aspect ratio also need to be considered. Figure 6.39 demonstrates the parameters that affect the manufacturing accuracy of thin-walled parts. In the forming process of thin-walled parts with different structures, each parameter has a different effect, and the required printing path is also different. The printing experiments of micro-finned heat sinks, micro thin-walled honeycomb parts, and micro solid parts will be introduced below.

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.39 Analysis of influencing parameters on the micro thin-walled metal parts forming

6.4.1 Fabrication of Micro-Finned Heat Sinks With the increasing energy density of high-power electronic devices, the cooling performance of heat sinks is demanding. The micro thin-walled finned heat sink with a large specific surface area has become a focus. When it is fabricated by cutting or EDM, the geometric parameters such as thickness, spacing, and aspect ratio of formed fins are limited due to the limitation of cutting tools or machining electrodes. The above issues can be improved by using uniform droplet deposition printing. Table 6.5 shows the experimental parameters of the micro heat sinks. The printing material is lead–tin alloy (S-Sn60PbAA), and the substrate material is brass. The uniform droplet deposition device was driven by a pneumatic pulse. Figure 6.40a shows the STL model of the micro heat sink. The length is 10 mm, the width is 5.2 mm, the height is 1.3 mm, the fin thickness is 0.3 mm, and the width of each channel is 0.4 mm. The heat sink consists of seven flow channels and eight fins. The slicing thickness is 185 µm, and the number of layers is 7. During uniform droplet printing, the path planning method is to scan the bottom layer by line-by-line grid path first (as shown in the solid line path in Fig. 6.40b). Then the fins were printed one by one along the length direction, each fin was printed one layer (as shown in the dotted line path in Fig. 6.40b), and the substrate moved down

6.4 Fabrication of Micro Metal Parts by Drop-On-Demand Printing Table 6.5 Process parameters of deposition forming experiment for micro radiators

225

Parameters

Value

Parameters

Value

Droplet temperature T d (°C)

270

Scanning step W (µm)

175

Substrate temperature T s (°C)

110

Slice thickness H z (µm)

185

Droplet diameter Dd (µm)

235

Deposition layers Ln

7

Platform speed V (mm/s)

0.35

one slicing height. Repeat printing until the whole part is formed (Fig. 6.40c, d, and e). Table 6.6 lists the measurement results of the sample size (sample length, height, wall thickness, and runner width). It can be seen that the relative error of the length and height is tiny, while the relative error of single-wall thickness and the channel width is big. The reason is that the length and height of the formed part are larger than the droplet size, and the size deviation can be reduced by controlling the printing step. However, the single wall thickness and the wall spacing are very small (0.3 mm and 0.4 mm, respectively), which are less than twice the droplet diameter. It is difficult to adjust and control the printing step and other parameters, resulting in large fabrication

Fig. 6.40 Deposition formed micro heat sink. a STL model. b deposition forming trajectory

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Table 6.6 Measurement results of forming dimensions of micro heat sinks Sample length (mm)

Sample height (mm) Number

Measured value

Average size

Relative error

1

1.235

1.243

4.3%

2

1.245

3

1.250

Number

Measured value

Average size

Relative error

10.11

2.1%

1

10.25

2

10.18

3

10.20

Channel width (mm)

Single wall thickness (mm) Number

Measured value

Average size

Relative error

Number

Measured value

Average size

Relative error

1

0.320

0.328

9.3%

1

0.373

0.377

5.7%

2

0.325

2

0.382

3

0.336

3

0.375

errors. Thus, the only way to improve fabrication accuracy is by reducing the droplet size. The experimental results show that uniform metal droplet printing can print micro fins directly, and the error of the overall length and width of the formed sample is tiny. The fin wall thickness and channel width are close to the droplet diameter, but the fabrication accuracy is poor. Thus, it is necessary to improve the accuracy by reducing the droplet diameter. By modifying the model, the fin structures with different shapes and high aspect ratios can be formed quickly. It provides a new method for additive manufacturing to fabricate complex micro fins.

6.4.2 Fabrication of Micro-Honeycomb Parts The metal honeycomb structure is a kind of typical lightweight and high-strength structure. This kind of structure is mostly manufactured by plastic forming and welding. However, the millimeter-sized thin-walled metal honeycomb structure is difficult to manufacture. Table 6.7 shows the experimental parameters for uniform metal droplet printing of micro honeycomb structures. The ejection material was lead–tin alloy (S-Sn60PbAA) and used the pneumatic pulse-driven uniform droplet deposition device for the experiment. Figure 6.41a shows the STL model of the micro thin-walled honeycomb part. The whole part is composed of seven independent small hexagon units. Each unit is 4 mm in height, 0.4 mm in wall thickness, and 2 mm in diameter. The distance between each unit is one wall thickness. Figure 6.41b shows the results of model slicing. The slicing thickness is 192 µm, and the layer number is 21. Figure 6.41c shows the droplet deposition path in any layer, and Fig. 6.41d shows the micro honeycomb

6.4 Fabrication of Micro Metal Parts by Drop-On-Demand Printing Table 6.7 Process parameters of deposition forming experiment for the micro honeycomb structure

227

Parameters

Value

Parameters

Value

Droplet temperature T d (°C)

270

Scanning step W (µm)

256

Substrate temperature T s (°C)

110

Slice thickness H z (µm)

192

Droplet diameter Dd (µm)

312

Deposition layers Ln

21

Platform speed V (mm/s)

0.512

formed by deposition. While planning the printing path, droplets only need to print along the contour to form a thin-walled structure with only one droplet diameter. Table 6.8 shows the average measurement results of the height and thickness of thin-walled honeycomb parts. The results show that the relative error between forming height and design height is 1.5%, and the relative error of forming wall thickness is 4.0%. It can be seen that the fabrication accuracy is great.

Fig. 6.41 Uniform metal droplet deposition printed micro honeycomb parts. a STL model. b Slicing results. c Printing path. d Fabricated micro honeycomb parts

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Table 6.8 Measurement results of forming dimension of the micro honeycomb structure Wall thickness (mm)

Sample height (mm) Test number

Value

Average size

Relative error

1

4.1

3.94

1.5%

2

3.90

Test number

Value

Average size

Relative error

1

0.419

0.416

4.0%

2

0.422

3

3.95

3

0.41

4

4.06

4

0.416

4

3.85

5

0.415

6

3.92

6

0.418

6.4.3 Fabrication of Micro-Squared Parts 3D printing of complex solid parts can be realized using uniform droplets ejection layer-by-layer printing combined with contour and filling path planning. This section shows the printing experiments of the hollow block to preliminarily analyze the printing efficiency, dimensional accuracy, and consistency. It can also verify the feasibility of uniform metal droplet printing for complex parts. The printing sample is a square part with 0.25 cm wall thickness, 1 cm length, and 0.5 cm height (Fig. 6.42a). During the printing process, the inner and outer contours were first printed and then filled line by line. This process was repeated until the solid squared parts were built. Table 6.9 lists the experimental parameters for the printing of squared parts. The ejection material was lead–tin alloy (S-Sn60PbAA) and used a pneumatic pulse uniform droplet deposition device. The nozzle diameter was 150 µm, and the droplet diameter was about 235 µm. Under these parameters, the optimal scanning step (W x = W XP and W y = W YL ) is calculated by Eqs. (6.14) and (6.18). Figure 6.42b shows the filling path planning of a single layer. After printing the inner and outer contours, the layer is filled by grid scanning. The printing step of the filling path is the same as the contour. Figure 6.42c shows the square part printed by the setting scanning step. The results show that the forming part shape is regular, the transitional angle is distinct, and the final forming surface is smooth with slightly raised. Figure 6.42d is the partially enlarged view and the inner section light microscope view of the part. There is no obvious cavity in the formed part, and the metallurgical bonding of droplets is good. Using Archimedes drainage method to measure the consistency of the formed parts, and the result is more than 96%, which indicates the formed part has great consistency.

6.4 Fabrication of Micro Metal Parts by Drop-On-Demand Printing

229

Fig. 6.42 Printed square parts. a STL model data. b layer filling path data. c deposited parts. d partial section micromorphology

Table 6.9 Experimental parameters of square parts printing Parameters

Value

Parameters

Value

Droplet temperature T d (°C)

270

Scanning step in the x-direction Wx (µm)

188

Substrate temperature T s (°C)

90

Overlap ratio in the x-direction ηx (%)

26.4

Droplet diameter Dd (µm)

235

Scanning step in the y-direction Wy (µm)

227

Overlap ratio in the y-direction ηy (%)

11.3

6.4.4 Fabrication of Micro Gears The sample is a spur gear with 11 teeth, 3 mm tooth width, 6 mm root circle diameter, and 10 mm addendum circle diameter (Fig. 6.43a). Table 6.10 shows the experimental parameters of micro gear. The ejection material is lead–tin alloy (S-Sn60PbAA) and used the pneumatic pulse uniform droplet deposition device. The calculation method of the X and Y-direction printing step is the same as in the above sections.

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.43 Experimental results of micro gear deposition. a STL model. b Slicing processing results. c Deposited layer profile. d Formed micro gear

Table 6.10 Technological parameters of micro gear deposition forming experiment Parameters name

Value

Parameters name

Value

Droplet temperature T d (°C)

270

Scanning step in the x-direction Wx (µm)

171

Substrate temperature T s (°C)

110

Scanning step in the y-direction Wy (µm)

201

Droplet diameter Dd (µm)

200

Slice thickness H z (µm)

122

Deposition layers L n

24

Figure 6.43b shows the result of slicing. The layer is filled by a grid scanning path, which prints the contour first and fills the inner space line by line. Figure 6.43c shows the printing contour of the layer. It can be seen that the contour is clear, and the line is uniform, but there is a little overlapping at the tooth root. Figure 6.43d shows the formed micro gear with a clear contour. There are a few droplets deposited on the surface of the formed part. The printed micro gear was compared with the model and measured the tooth width, root circle diameter, and addendum circle diameter. The results show that the relative error between design size and measured results is

6.4 Fabrication of Micro Metal Parts by Drop-On-Demand Printing

231

less than 4%. Using the Archimedes drainage method to measure the consistency of the sample, the result is more than 95%, which indicates the formed part has great consistency.

6.4.5 Fabrication of Micro Racks Figure 6.44a shows the STL model and contour size of a micro rack. The micro rack has nine through holes of different sizes and a shallow step hole. The minimum hole diameter is 1 mm The nozzle diameter is 125 µm, and the droplet diameter is about 200 µm. The ejection material was lead–tin alloy (S-Sn60PbAA) and used the pneumatic pulse uniform droplet ejection device. The experimental parameters are shown in Table 6.11. The calculation method of the X and Y-directions deposition step is the same as the above, and the optimal printing step can be calculated by Eqs. (6.14), (6.15), (6.18), and (6.19). The scanning path of metal droplet deposition is shown in Fig. 6.36b, which uses the grid scanning method. The droplets were deposited dropwise along the short side and line by line along the long side. The formed micro racks are shown in Fig. 6.44c. It can be seen that the inner and outer contour of the

Fig. 6.44 Experimental results of micro racks. a STL model. b Slicing result. c Formed micro racks. d The internal micromorphology

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Table 6.11 Deposition forming experiment parameters of micro racks Parameters

Value

Parameters

Value

Droplet temperature T d (°C)

280

Scanning step in the x-direction W x (µm)

171

Substrate temperature T s (°C)

100

Scanning step in the y-direction W y (µm)

201

Droplet diameter Dd (µm)

200

Slice thickness H z (µm)

122

Deposition layers L n

21

Table 6.12 Measurement results of micro support parts forming dimensions Sample length/mm

Sample height/mm

Number Value Average size Relative error Number Value Average size Relative error 1

2.42

2

2.48

3

2.46

2.45

1.8%

Sample width/mm

1

47.5

2

47.8

3

47.2

47.16

3.1%

Holes diameter/mm

Number Value Average size Relative error Number Value Average size Relative error 1

21.5

1

5.83

2

21.8

21.7

1.5%

2

5.86

3

21.7

3

5.92

5.87

2.1%

sample is distinct, and nine through holes and a shallow step hole can be successfully printed. The micro racks’ surface morphology and enlarged photograph are shown in Fig. 6.44d. The images show that the formed sample has a great consistency and has no obvious cavities, cracks, or any other defects. Table 6.12 shows the measured results of the key dimensions of the small connector. The difference between the printing size and the design size is less than 4%. The density, measured by the Archimedes method is larger than 96%, demonstrating a dense inner structure. The above five printed results demonstrate that complex parts with good dimensional accuracy and a dense inner structure can be obtained by using the uniform droplet printing method.

6.5 Electronic Packaging via Uniform Micro Lead–Tin Alloy Droplet 3D Printing Technology Electronic circuits are developing towards miniaturization, multi-function, largescale direction. As a result, connection pins become denser, and their shapes are more complicated than conventional ones. The interconnection of high-density or complex circuits on small microcircuits becomes a major challenge to the traditional

6.5 Electronic Packaging via Uniform Micro Lead–Tin Alloy Droplet 3D …

233

packaging and soldering processes. If uniform droplets (solder joints) can be accurately printed at desired locations, the uniform metal droplet ejection technology can be used to achieve rapid preparation of tiny solder joints, rapid soldering of circuits, rapid printing of circuits, and microelectronics packaging. This section focuses on possible applications of uniform solder droplet ejection in this field.

6.5.1 Rapid Printing of Ball Grid Array and Solder Column Array A ball grid array (BGA) is a tin solder ball array that is attached to the bottom of electronic packaging substrates. BGAs work as interconnections between circuit I/O ports and printed circuit boards (PCB). Such packaging I/O ports are distributed under electronic packaging in an array of sphere- or column-shaped bumps, which have the advantages of large numbers and high density. To achieve a great electrical combination, flip-chip packaging technology has high requirements on the size accuracy of the bump array. For instance, the bump diameter should be less than 300 µm, the error of the bump height should be less than ± 2 µm, and the space between bumps should not be less than 100 µm. The above requirements should be first met for using the uniform droplet ejection technology in printing bump arrays. According to Sect. 6.2.3, inside the process parameter window that droplets do not bounce, the solidification time can be prolonged, the effect of solidification behavior on the bump height h can be reduced, and the uniformity of the bump height in arrays can be improved via properly increasing the droplet temperature T d and the substrate temperature T s. To find the effect of process parameters on the deposited droplets’ height consistency, a series of bump array printing experiments regarding two factors (i.e., the droplet temperature T d , and the substrate temperature T s ) were carried out. Experiments results show that when droplet temperature T d is 643 K and the substrate temperature T s is 393 K, the printed bump arrays have the best height consistency. The average height h bump is 402 µm, and the standard deviation SD is 4.96 µm. The contours of solder bumps are consistent and present a “hemisphere” like shape (Fig. 6.45). To further reduce the bumps height error and improve the surface smoothness, a 15 × 10 bump array was printed and then treated by the “remelting and shaping” method. After that, the height of the bumps was measured to calculate the mean and the standard deviation of the height distribution. The SEM images of the printed bumps array are shown in Fig. 6.46. The measurement results are shown in Table 6.13. It can be seen from Fig. 6.46a that the bumps are arranged neatly, and the distances are uniform. Figure 6.46b shows that the bump geometric contours are consistent and regular spherical crowns. The measurement of height h is 223 ± 2 µm, which indicates a great consistency. Table 6.13 shows that the diameter deviation of ejected solder droplets is 0.97%. After printing into the bump array, the ratio of the bump

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.45 Printed bump array under the combined parameters of droplet initial temperature T d is 643 K and substrate temperature T s is 393 K. a Uniform bump array printed by solder droplets. b Side view photomicrograph of one row of bumps. c Contour shapes of three droplets

height error to the droplet diameter is reduced by 0.6%, indicating that the deposited bumps have great consistency. The results show that the “remelting shaping” method can effectively smooth the geometric contour and ensure the height consistency of bumps. This method may lay a foundation for the application of uniform droplet ejection technology in microelectronic packaging. In electronic packaging, except for the bump arrays, tin solder column arrays with a certain height are always used as the interconnections of the high-temperature ceramic chip packaging. By depositing several uniform tin solder droplets repeatedly, tin solder column arrays can be easily printed. This process has the advantages of great process flexibility and high efficiency. The introduction for the uniform solder column array printing experiments is listed below. Figure 6.47 shows a tin solder column array deposited by using the piezoelectric pulse on-demand ejection method. The top view shows (Fig. 6.47a) that droplets on the top of solder columns have a uniform size and space, and are in good circularity. The enlarged top view (Fig. 6.47b) shows that droplets can be accurately positioned, and a few droplets have a slight position error. The side view demonstrates that each solder column is combined with 16 droplets. Although the diameter of the solder column is slightly fluctuating, the column height is relatively uniform. The result shows that this method can be used to deposit uniform solder column arrays. Figure 6.48 shows the increase of the solder column height with the increase in the number of deposited droplets. In three cases, the height of solder columns increases

6.5 Electronic Packaging via Uniform Micro Lead–Tin Alloy Droplet 3D …

235

Fig. 6.46 The printed bump array on a brass substrate using the “heating and remelting” method

Table 6.13 Statistics of droplet diameter distribution and bump height distribution results Mean/µm

Standard deviation/µm

Ratio to the initial droplet diameter/%

Initial droplet diameter distribution

203.4

1.98

0.97

Bump height distribution

130.2

1.25

0.614

Error coefficient obtained from experiment k bump

0.64

0.63

/

Theoretical calculation error coefficient k bump

0.67

0.67

/

linearly, and the minimum resolution is the height of one deposited droplet, which is approximately 100 µm (Fig. 6.48a). When the number of deposited droplets is two or three, the height resolution of the solder column is 240 µm and 350 µm (Fig. 6.48b and c), respectively. In the solder column printing process, the final solder column height can also be controlled by varying the droplet diameter, the droplet temperature, the substrate temperature, and other parameters.

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6 Uniform Solder Droplet Deposition and Its 3D Printing Technology

Fig. 6.47 Printed solder column array. a Top view of solder column array. b Partially enlarged view of solder column array. c Side view of solder array

Fig. 6.48 Tin solder columns in different heights

6.5.2 Rapid Printing and Soldering of Electronic Circuits In the research and development of personalized electronic circuits, electronic circuits usually need to be quickly printed and soldered to realize electrical interconnections according to the design. By printing uniform solder droplets on-demand, automatic soldering, and printing for preparing personalized circuits can be achieved, illustrating a novel method for the rapid manufacturing of microcircuits. This section

6.5 Electronic Packaging via Uniform Micro Lead–Tin Alloy Droplet 3D …

237

Fig. 6.49 Inductance coil printed by solder droplets

shows two examples (i.e., inductor coils and flexible gold finger packaging) to illustrate the application of uniform droplet on-demand ejection technology in printing and soldering electronic circuits. Figure 6.49 shows the inductor coil deposited by uniform metal droplets in a spiral track on the polymer substrate. The experimental results show that, in the continuous solder droplet deposition process, the substrate with good thermal insulation performance greatly reduces the heat dissipation of metal droplets. Molten droplets slightly melt the substrate surface to achieve a firm connection and overlap with each other to achieve good metallurgical bonding, and finally form good electrical conductivity. The results show that the uniform solder droplet on-demand ejection technology can facilitate the customization of electronic devices or circuits, providing an effective way for rapid prototyping personalized circuits. Figure 6.50a is a gold finger of a Flexible Printed Circuit that needs to connect to an external copper wire. The width and space of gold fingers are both 0.5 mm. Since fingers are dense, they are hard to be soldered manually. For rapidly soldering the gold finger and the external wire, solder droplets are accurately printed on the side of the copper wire which is first positioned on the finger (Fig. 6.50b). The experimental results show that since the gold finger pins and wires are both at room temperature, the metal droplets solidify quickly after being deposited and remain spherical, which does not completely spread to fill the gap between the wire and the gold finger joint. Good soldering can be achieved by heating and remelting the gold finger pins printed with solder droplets. During this process, the maximum substrate temperature is set at 190 °C, and the holding time is about 20 s. During heating, a small amount of rosin is added to help solder droplets spread. The remelting results show (Fig. 6.50c) that, under the action of the capillary force, the solder droplets are evenly spread on the surface of the wire and gold fingers to form a uniform solder layer, finally achieving good soldering between the wire and pins.

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Fig. 6.50 Soldering copper wire to flexible crucible using DOD technology [8]: a the flexible crucible with dense golden fingers, b solder droplets deposited on the joint of the copper cables and the fingers with uniform distance, and c the finally obtained interconnects after re-melting

References 1. Xiong W, Qi L, Luo J, et al. Experimental investigation on the height deviation of bumps printed by solder jet technology. J Mater Process Technol. 2017;243:291–8. 2. Avron JE, Van Beijeren H, Schulman LS, et al. Roughening transition, surface tension and equilibrium droplet shapes in a two-dimensional Ising system. J Phys A: Gen Phys. 1982;15(2):92291B. 3. Fang M, Chandra S, Park CB. Building three-dimensional objects by deposition of molten metal droplets. Rapid Prototyping Journal. 2008;14(1):44–52. 4. Lass N, Riegger L, Zengerle R, et al. Enhanced liquid metal micro droplet generation by pneumatic actuation based on the starjet method. Micromachines. 2013;4(1):49–66. 5. Qi L, Chao Y, Luo J, et al. A novel selection method of scanning step for fabricating metal components based on micro-droplet deposition manufacture. Int J Mach Tools Manuf. 2012;56:50–8. 6. Qi L, Zhong S, Luo J, et al. Quantitative characterization and influence of parameters on surface topography in metal micro-droplet deposition manufacture. Int J Mach Tools Manuf. 2015;88:206–13. 7. Chao YP, Qi LH, Luo J, et al. Acquisition and experimental demonstration of STL model slice contour data in metal droplet deposition manufacturing. China Mechanical Engineering. 2009;22:2701–5. 8. Luo J, Qi LH, Zhong SY, et al. Printing solder droplets for micro devices packages using pneumatic drop-on-demand (DOD) technique. J Mater Process Technol. 2012;212(10):2066–73.

Chapter 7

Uniform Aluminum Droplet Deposition Manufacturing and Its Controlling Technique

7.1 Introduction Aluminum alloy parts have the prospect for wide application in the aerospace and civil engineering fields due to the advantages of the material’s lightweight and high strength. This chapter focuses on the rules of deposition of uniform aluminum droplets and their influencing factors, laying a foundation for the application of uniform aluminum droplet-based 3D printing technology.

7.2 Deposition Behaviors of Uniform Aluminum Droplets The solidification profile of aluminum droplets on the substrate plays an important role in the forming quality. The substrate material, substrate temperature, droplet temperature, deposition height, etc. could affect droplet morphology, which will be discussed in the following sections.

7.2.1 Impact Behaviors of Aluminum Droplets Aluminum droplets may be directly deposited on the substrate or the surface of solidified metal droplets during deposition. The deposition surface can be divided into the cases of rigid entity, elastic entity, rigid porous body, elastic porous body, and powder (Table 7.1). In most cases, aluminum droplets are deposited on metal substrates, so this chapter only studies the impact and deformation of aluminum droplets deposited on rigid substrates. A pneumatic pulse-driven drop-on-demand ejection device was used in the experiment, the experimental parameters of which are shown in Table 7.2. Firstly, the droplet diameter and velocity should be clarified. A high-speed CCD was used © National Defense Industry Press 2023 L. Qi et al., Metal Micro-Droplet Based 3D Printing Technology, https://doi.org/10.1007/978-981-99-0965-0_7

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7 Uniform Aluminum Droplet Deposition Manufacturing and Its …

Table 7.1 Classification of droplet collision according to the deposition surface

Deposition surface

Surface deformation situation

Liquid infiltration situation

Rigid entity

Not deformed

Not infiltrated

Elastic entity

Deformed and recoverable

Not infiltrated

Rigid porous body

Not deformed

Infiltrated

Elastic porous body

Deformed and recoverable

Infiltrated

Powder

Deformed and unrecoverable

Infiltrated

Table 7.2 Experimental parameters of aluminum droplet ejection and deposition Ejection material

Initial droplet temperature/°C

Deposition height/mm

Substrate temperature/°C

2A12

700 ~ 1000

20 ~ 200

200 ~ 500

to record the deposition and impact process of aluminum droplets on different substrates with a frame rate of 500 fps. The droplet collision velocity was calculated by measuring the droplet position difference on two frames of images (approximately 0.8 m/s in the experiment). Aluminum droplets were then ejected into oil and collected to measure and record their dimensions, yielding a droplet diameter of 0.9 mm with a size error of less than 0.1 mm. A brass plate was selected as the deposition substrate for aluminum droplet deposition experiments. Figure 7.1 shows high-speed images the moment an aluminum droplet impinges onto the substrate. The time before droplet collision is −1 ms (Fig. 7.1a), while the moment of the first image frame after the droplet contacts the substrate is 1 ms (Fig. 7.1b). The time between each subsequent frame is determined in this manner resulting in a time interval of 2 ms. Figure 7.1 exhibits the droplet deforming into a circular disk at the instant of impact (about 1 ms) on the substrate and reaching the maximum spreading radius. Subsequently, the droplet rebounds and approaches the first retraction limit at approximately 3 ms. Although the droplet tends to bounce off the substrate and is stretched vertically into an ellipse (Fig. 7.1c), the droplet always keeps in contact with the substrate. The droplet then enters the equilibrium oscillation stage during which the droplet’s kinetic energy is dissipated by the work done against the viscous force, resulting in reduced droplet deformation. Droplet morphology changes very little after 45 ms (Fig. 7.1m), and exhibits nearly no change after 75 ms (Fig. 7.1n). As depicted in the impact process, the droplet bounces on the brass substrate but, it exhibits adhesion and stable deposition, and does not detach from the substrate. The droplet collision experiment was repeated by increasing the aluminum droplet diameter to 1.2 mm, with the other experimental conditions remaining unchanged.

7.2 Deposition Behaviors of Uniform Aluminum Droplets

241

Fig. 7.1 The deformation process of an impinging droplet on a brass substrate [1]. a − 1 ms. b 1 ms. c 3 ms. d 5 ms. e 7 ms. f 9 ms. g 11 ms. h 13 ms. i 15 ms. j 17 ms. k 19 ms. l 21 ms. m 45 ms. n 75 ms

Figure 7.2 shows that the droplet collision Weber number (We = ρ l d d u2 /σ l ) rises due to the increase of impact velocity, namely the ratio of the droplet inertial force to the capillary force increases, resulting in more pronounced droplet deformation. The droplet reaches the maximum spreading radius at about 3 ms (Fig. 7.2b) with a short spreading time. Then the droplet enters the equilibrium oscillation stage, approaching the first retraction limit at 7 ms (Fig. 7.2d), during which the droplet almost completely detaches from the substrate. After that, the droplet retracts and oscillates on the substrate until it is completely still at 100 ms (Fig. 7.2n). Compared with Fig. 7.1, the collision deformation time is 25 ms longer due to the increase in droplet size. Figure 7.3 shows the evolution of droplet spreading diameter with droplet diameters of 0.8, 0.9, and 1.2 mm. It was found that the larger the droplet diameter, the larger the maximum spreading diameter, and consequently, the longer it takes for the droplet to reach the maximum spreading diameter. Meanwhile, the time for the droplet with a diameter of 1.2 mm to reach the maximum spreading diameter after the first retraction is also longer: about three times that before retraction; and its oscillation amplitude is more obvious than that of smaller droplets. As shown in

Fig. 7.2 The deformation process of an impinging droplet at a critical state. a 1 ms. b 3 ms. c 5 ms. d 7 ms. e 9 ms. f 11 ms. g 13 ms. h 15 ms. i 21 ms. j 27 ms. k 33 ms. l 39 ms. m 45 ms. n 100 ms

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7 Uniform Aluminum Droplet Deposition Manufacturing and Its …

Fig. 7.3 Time evolution curve of the spreading diameter of aluminum droplets

Fig. 7.3, the larger the droplet diameter, the higher its spreading diameter, the greater the number of oscillations and oscillation amplitude. This is attributed to greater kinetic energy during deposition, which needs to be dissipated by greater oscillation, for droplets with a larger diameter. Figure 7.4 shows the bounce of a metal droplet deposited on a stainless-steel substrate (substrate temperature of 400 °C) The droplet diameter is 0.8 mm, and the initial droplet temperature is 900 °C. The droplet deposition height is 20 mm, and the instantaneous velocity at the moment of impact is approximately 1 m/s. The collision results demonstrate that the droplet bounces after impact on the substrate due to the high initial droplet temperature and substrate temperature, resulting in complete separation from the substrate by the droplet after retracting to the first retraction limit. The spreading time of the droplet is less than 2 ms (Fig. 7.4b), while it bounces at 4 ms (between Fig. 7.4c and d) and has completely detached from the substrate at 5 ms (Fig. 7.4d). The droplet rises to the highest point at approximately 67 ms, then falls again, and collides with the substrate for the second time at 111 ms (Fig. 7.4h). The droplet then oscillates on the substrate until it reaches equilibrium (Fig. 7.4n–p). The bouncing of droplets on the substrate or the deposited droplet layer affects printing accuracy, and should be avoided as much as possible. There are two methods to prevent droplets from recoiling. Firstly, by selecting the appropriate crucible temperature and substrate temperature, local solidification of the droplet bottom can be ensured when it contacts the substrate, so that the kinetic energy of the droplet can be rapidly dissipated to achieve precise deposition. Another method is to choose a substrate that has good wettability with the molten droplets, such as a substrate of the same material as the droplets, so that the droplet infiltrates the substrate surface when they come into contact, inhibiting the bouncing behavior of the metal droplet.

7.2 Deposition Behaviors of Uniform Aluminum Droplets

243

Fig. 7.4 Droplet collision, bouncing, and deposition process on a stainless-steel substrate. a − 1 ms. b 1 ms. c 3 ms. d 5 ms. e 15 ms. f 27 ms. g 107 ms. h 111 ms. i 113 ms. j 115 ms. k 117 ms. l 119 ms. m 121 ms. n 159 ms. o 161 ms. p 163 ms

7.2.2 Effect of Process Parameters on the Profile of Deposited Aluminum Droplets In this section, pure aluminum was used as the ejection material and polished brass was used as the deposition substrate. The deposition experiments of aluminum droplets under different parameters (temperature, deposition distance, etc.) were conducted to study the evolution and influencing factors of aluminum droplet morphology. 1. Effect of ejection temperature on the deposition morphology of droplets The parameters of the deposition experiments of aluminum droplets at different ejection temperatures (namely the initial droplet temperature) are shown in Table 7.3, and the corresponding droplet morphology is shown in Fig. 7.5. The experimental results demonstrate that droplet morphology changes significantly with ejection temperature. A low ejection temperature results in a spherical cap with a large solidification angle, while a high ejection temperature leads to a spherical cap with a small solidification angle. Table 7.3 Experimental process parameters about ejection temperature

Process parameters

Value

Droplet diameter/µm

800

Substrate temperature/°C

350

Ejection temperature/°C

750, 800, 850, 900, 950

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7 Uniform Aluminum Droplet Deposition Manufacturing and Its …

Fig. 7.5 The deposition morphology of aluminum droplets at different ejection temperatures (i.e., initial droplet temperatures). a 750 °C. b 800 °C. c 850 °C. d 900 °C. e 950 °C

Multiple droplets were deposited under the same experimental conditions, after which the average solidification angle and standard deviation were measured and calculated (Fig. 7.6). The results show that the solidification angle of aluminum droplets decreases linearly with the increase of the ejection temperature. This is because when the deposition height remains constant, the higher the ejection temperature, the higher the instantaneous droplet temperature when it contacts the substrate, resulting in better droplet fluidity. Under these conditions, the droplet spreading diameter is larger, and the corresponding solidification angle is reduced. Fig. 7.6 The relationship between solidification angle av and initial droplet temperature T d

7.2 Deposition Behaviors of Uniform Aluminum Droplets Table 7.4 Experimental process parameters about deposition height

245

Process parameters

Value

Droplet diameter/µm

800

Ejection temperature/°C

950

Substrate temperature/°C

350

Deposition height/mm

20, 30, 50, 80, 120, 200

2. Effect of deposition height on the deposition morphology of droplets The experimental parameters for the deposition of aluminum droplets at different deposition heights are shown in Table 7.4, and the corresponding droplet morphology is shown in Fig. 7.7. The contact angle between the deposited droplet and the substrate changes with the variation of the deposition height. When the deposition height is small, the droplet temperature (at the moment of impact with the substrate) is high, and the deposited droplet spreads out into a spherical cap with a smaller solidification angle. On the contrary, when the deposition height is large, the droplet temperature (at the moment of impact with the substrate) is low, and faster solidification leads to a spherical cap with a larger solidification angle. By characterizing the solidification angle of multiple aluminum droplets deposited at different deposition heights, the relationship between deposition height and solidification angle can be obtained as shown in Fig. 7.8. The solidification angle increases with the rise of the deposition height. When the deposition height is larger, the droplet flight time is longer, meaning the droplet temperature is lower when it reaches the

Fig. 7.7 The deposition morphology of aluminum droplets at different deposition heights. a 20 mm. b 30 mm. c 50 mm. d 80 mm. e 120 mm. f 200 mm

246

7 Uniform Aluminum Droplet Deposition Manufacturing and Its …

Fig. 7.8 The relationship between solidification angle av and deposition height H s

substrate, resulting in a shorter droplet spreading time and a larger solidification angle. 3. Effect of substrate temperature on the deposition morphology of droplets The deposition morphology of aluminum droplets is significantly altered by the substrate temperature as shown in Table 7.5 and Fig. 7.9. When the substrate temperature is low, the deposition morphology shows a spherical cap with a small spreading diameter and a large contact angle. When the substrate temperature is high, the morphology is a spherical cap with a large spreading diameter and a small contact angle. Figure 7.10 shows the measurement results of the contact angle of the aluminum droplets. The solidification angle decreases linearly with the increase of substrate temperature. This is attributed to the higher substrate temperature leading to a smaller temperature difference between the deposited droplets and the substrate, meaning slower heat transfer between the droplets and the substrate. Under this condition, the droplet spreading time on the substrate is longer, resulting in a larger spreading area and smaller solidification angle. Table 7.5 Experimental process parameters about substrate temperature

Process parameters

Value

Droplet diameter/µm

800

Ejection temperature/°C

950

Deposition height/mm

10 ~ 20

Substrate temperature/°C

200, 250, 300, 350, 400, 450

7.3 Deposition of Aluminum Lines by Uniform Droplets

247

Fig. 7.9 The deposition morphology of aluminum droplets at different substrate temperatures. a 200 °C. b 250 °C. c 300 °C. d 350 °C. e 400 °C. f 450 °C

Fig. 7.10 The relationship between solidification angle av and substrate temperatures T s

7.3 Deposition of Aluminum Lines by Uniform Droplets The quality of the printed lines has significant influence on the forming accuracy of parts. According to the above studies, deposition parameters such as ejection temperature and deposition height could affect the deposition morphology of droplets, which in turn influences the quality of the printed lines. (1) When the printing frequency and droplet spreading diameter remain constant, the main parameter determining the scanning step is the platform velocity. The optimal step distance can be calculated using a theoretical optimal step distance model (Eq. 6.15). Thus, the optimal platform speed can be deduced. The parameters near the optimal speed can be selected to explore the quality of printed lines at different platform velocities.

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7 Uniform Aluminum Droplet Deposition Manufacturing and Its …

(2) During the printing of lines, the newly deposited metal droplet needs to partially remelt the previously solidified droplet to achieve an adequate metallurgical bond. Since the heat carried by a single droplet is limited, the main factor affecting the remelting effect is the substrate temperature, which is selected as the main parameter for investigating the remelting effect.

7.3.1 Effect of Platform Velocity on Printed Lines In the experiment, while the initial droplet temperature, deposition height, and substrate temperature remain constant, the movement speed of the deposition platform changes according to the values shown in Table 7.6. The optimal droplet spacing is 0.68 mm/s as determined by combining the calculation of the optimal step distance and the measurement results of the solidification angle in the previous section. In other words, the ideal motion velocity of the platform should be 0.68 mm/s when the printing frequency is 1 Hz. Figure 7.11 shows the experimental results of printed lines by uniform aluminum droplets under the above parameters. As illustrated, when the moving speed of the deposition platform is large (≥0.9 mm/s), the printed aluminum lines are discontinuous. When the velocity of the platform is less than 0.8 mm/s, continuous aluminum lines can be printed. Different platform speeds result in diverse surface morphologies of the printed lines. When the platform speed is 0.9 and 0.8 mm/s, the surface of line segments has obvious irregularities. When the platform speed is 0.7 and 0.6 mm/s, lines with smooth surfaces and favorable consistency in size are printed. For a platform speed of 0.5 mm/s the surface of the line is smooth but there are local bulges in the line. As for the platform velocity of 0.4 mm/s, obvious wrinkles emerge on the surface of the printed line. The influence of the platform velocity on printed lines can be shown by the spacing of droplets. Larger droplet spacing causes discontinuities in the lines, while smaller spacing leads to lines with bulges or wrinkles. The optimal droplet spacing can be calculated by using the optimal droplet spacing model (Eq. 6.15). Supplemented with experiments for correction, smooth and uniform aluminum lines could then be printed. Table 7.6 Experimental process parameters about platform velocity

Process parameters

Value

Droplet diameter/µm

800

Ejection temperature/°C

950

Deposition height/mm

10 ~ 20

Substrate temperature/°C

350

Platform velocity/mm s−1 1.5, 1.2, 1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4

7.3 Deposition of Aluminum Lines by Uniform Droplets

249

Fig. 7.11 Line morphologies deposited by uniform aluminum droplets at different platform velocities. a 1.5 mm/s. b 1.2 mm/s. c 1 mm/s. d 0.9 mm/s. e 0.8 mm/s. f 0.7 mm/s. g 0.6 mm/s. h 0.5 mm/s. i 0.4 mm/s

7.3.2 Effect of Substrate Temperature on Printed Lines The substrate temperature plays a significant role in the metallurgical bonding and fusion morphology of metal droplets. To investigate the influence of substrate temperature on metal lines, printing experiments of metal lines were carried out at different substrate temperatures. In the experiment, the moving speed of the deposition platform was set at the optimal value determined in the previous section (0.7 mm/s), and the ejection temperature and deposition height were kept unchanged. The specific process parameters are given in Table 7.7 with the corresponding printed lines shown in Fig. 7.12. Theoretically, favorable droplet overlapping can be achieved with optimal droplet spacing. However, when the substrate temperature is high (Fig. 7.12a and b), the droplets cannot solidify in time resulting in discrete lines due to droplet coalescence. With an appropriate substrate temperature (relatively low), the droplet will partially solidify after being deposited on the substrate and the next deposited droplet partially remelts with the previous droplet to form a continuous line, as shown in Fig. 7.12c–i. Figure 7.13 exhibits the scanning electron microscope (SEM) images of two overlapped droplets. There are obvious differences in the surface morphology of

250

7 Uniform Aluminum Droplet Deposition Manufacturing and Its …

Table 7.7 Experimental process parameters about substrate temperature during line printing

Process parameter

Value

Droplet diameter/µm

800

Ejection temperature/°C

950

Deposition height/mm

10 ~ 20

Platform velocity/mm s−1

0.7

Substrate temperature/°C

500, 450, 400, 370, 350, 330, 300, 270, 240

Fig. 7.12 Line morphologies deposited by uniform aluminum droplets at different substrate temperatures. a 500 °C. b 450 °C. c 400 °C. d 370 °C. e 350 °C. f 330 °C. g 300 °C. h 270 °C. i 240 °C

the two droplets. The first droplet is deposited directly on the substrate, forming a spherical cap with horizontal ripples. The second droplet, deposited on the side of the first one, solidifies after contacting the underlying substrate and simultaneously remelts with the adjacent droplet locally. The remaining unsolidified molten metal oscillates then solidifies on the surface of the substrate and the previous solidified droplet to form a surface with curved ripples. Figure 7.14 shows the SEM image of the line printed by multiple overlapped aluminum droplets. The aluminum line is formed by overlapping and solidifying

7.4 Drop-On-Demand Printing of Aluminum Pillars by Uniform Droplets

251

Fig. 7.13 SEM images of two overlapped aluminum droplets. a Side view. b Top view

Fig. 7.14 SEM image of multiple overlapped aluminum droplets [2]

several identical droplets point by point, resulting in droplets of similar contour and surface morphology, and indicating repeatability of the printing process. The printed line is relatively uniform with shell-like undulations on the line surface.

7.4 Drop-On-Demand Printing of Aluminum Pillars by Uniform Droplets To realize the printing of parts, it is not only necessary to deposit metal droplets on a horizontal substrate to fabricate aluminum traces or planes, but it is also necessary to stack them drop by drop in the vertical direction to achieve three-dimensional

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7 Uniform Aluminum Droplet Deposition Manufacturing and Its …

fabrication. Based on the single droplet deposition and line printing described in the previous chapters, this section discusses the printing rules of the drop-by-drop accumulation process of metal droplets.

7.4.1 Temperature Change During the Deposition of Aluminum Droplets During the point-by-point deposit of metal droplets, the new incoming droplet can partially remelt the surface of the previously solidified droplet to achieve metallurgical bonding. In this process, the degree of remelting at the interface largely determines the bonding quality between droplets, which consequently affects the mechanical properties of parts. Key factors affecting the remelting of droplets are the initial droplet temperature and substrate temperature. When both temperatures are low, local pores and cold laps may not be avoided at the droplet bonding interface, leading to the formation of a mechanical bond. In this case, cracks are prone to occur under solidification shrinkage and thermal stress. When the initial droplet and substrate temperatures are too high, the interfacial temperature between adjacent droplets is also high, resulting in complete droplet remelting and collapse, and difficulty in guaranteeing accuracy in the forming of the part. Therefore, it is necessary to reasonably match the initial droplet temperature and substrate temperature to ensure favorable metallurgical bonding among droplets, as well as desired component size. In this section, a one-dimensional (1D) heat conduction model for predicting the temperature change of the pillar printing process is established, which is used to analyze the factors affecting the column surface temperature during printing. Moreover, different initial droplet temperatures and substrate temperatures for metal column printing are selected to obtain favorable parameter combinations for adequate metallurgical bonding. 1. Remelting model during droplet printing A schematic diagram of the fusion principle of two droplets is shown in Fig. 7.15. When a metal droplet is deposited and remelted on the surface of a solidified droplet, these two droplets can be assumed as semi-infinite bodies during an infinitesimal time. T inter is the interfacial temperature of two bonding droplets, T d is the initial temperature of the new-incoming droplet, and T surf is the surface temperature of the previously-deposited droplet. By ignoring the interfacial thermal resistance of droplets, T inter can be predicted by the following equation [3].

Tinter

√ √ Tsur f ( cl kd )sur f + Td ( cl kd )d = √ √ ( cl kd )sur f + ( cl kd )d

(7.1)

7.4 Drop-On-Demand Printing of Aluminum Pillars by Uniform Droplets

253

Fig. 7.15 Schematic diagram of the fusion principle of two droplets

where c1 is the specific heat capacity of droplet material, k d is the thermal √ conductivity of droplet material, both of which are affected by temperature; ( cl kd )surf √ is the calculated value using the previously deposited droplet temperature (T surf ); ( cl kd )d is the calculated value corresponding to the newly deposited droplet when the initial temperature is set as T d . 7075 aluminum alloy (Al: 88.9%, Cu: 1.6%, Zn: 5.6%, Mg: 2.5%, Fe: 0.5%) was selected as the experimental material. To simplify the model, the following assumptions are made: (1) When Tinter ≥ T solid (T solid = 450 °C, which is the solidus temperature of droplet material), remelting occurs at the bonding interface of continuously deposited droplets. (2) When T inter ≥ T liqu (T liqu = 680 °C, which is the liquidus temperature of droplet material), the interfacial region of adjacent overlapping droplets may be in the total liquid state. Therefore, given T inter = T solid and T inter = T liqu , according to Eq. (7.1), the relationships among Tinter , T surf , and T d can be established, as shown in Fig. 7.16. In Fig. 7.16, curves 1 and 2 are the calculated critical remelting temperature, by which the graph area can be divided into three parts: no-remelting region, remelting region, and completely remelting region. (1) When the combination of T surf and T d (e.g., T surf = 350 °C and T d = 520 °C) is below curve 1, droplet remelting would not occur. (2) When the temperature combination (e.g., T surf = 600 °C and T d = 680 °C) is above curve 1 and below curve 2, remelting occurs between droplets. The strength of remelting and bonding is gradually enhanced with the rise of T surf and T d . (3) When the temperature combination (e.g., T surf = 650 °C and T d = 700 °C) is above curve 2, the adjacent overlapping droplets may appear completely remelted and lead to collapse and difficulty in ensuring the shape of the fabricated component. 2. Influence factors of the surface temperature of deposited droplets From the above analysis, it is concluded that effective control of T d and T surf is the key to ensuring good metallurgical bonding between adjacent droplets and the building of a perfect part. However, during metal droplet deposition and part manufacturing, many factors could affect the surface temperature T surf , including the substrate temperature T s , droplet temperature T d , ejection frequency f , and height of deposition layer hp , which requires further analysis as shown in Fig. 7.17.

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Fig. 7.16 Remelting temperature condition of T d and T surf when fixing T inter = T solid and T inter = T liqu

Fig. 7.17 Calculation model of the surface temperature of previously-deposited droplets (T surf ) on the top of a column

To investigate the relationships between the deposition process parameters (T d , T s , f , hp ) and the surface temperature T surf , a 1D heat conduction model can be established. In this model, the previously deposited droplet column and the new droplet that is to be deposited are assumed to be a semi-infinite solid system. The heat loss of the droplet due to heat convection and heat radiation to the surrounding environment is ignored. Only the heat conduction between the metal droplet and the

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substrate is considered. Therefore, the thermal energy carried by the new incoming droplet E d and the heat conducted from the column top to the substrate E cond can be respectively represented by Ed = f

ρl π Dd 3 [cl (Td − Tsurf ) + \h] 6

(7.2)

(Tsurf − Ts ) .Ac Rh + Rt.c

(7.3)

E cond =

where Dd is the droplet diameter, ρ l is the droplet density, \h is the droplet latent heat, c1 is the droplet specific heat, Ac is the average cross-section area of the deposited column, Rt, c is the thermal contact resistance between the substrate and previously deposited droplets, Rh is the thermal resistance of the deposited column (Rh = hp /k d ). To achieve stable droplet deposition, it is necessary to maintain a constant temperature at the top of the deposited column. An energy balance must be maintained, which means that the heat carried by the new droplet, E d , is equal to that dissipated by the column and substrate, E cond . f

ρl π Dd3 (Tsurf − Ts ) [cl (Td − Tsurf ) + \h] = Ac 6 Rh + Rt.c

(7.4)

Thus, the relationship between T surf and process parameters (T d , T s , f , and hp ) is established as Tsurf = φ(Td , Ts , f, h P ) =

(h P /kd + Rt.c ) f

ρl π Dd3 (cl Td 6

− \h) + Ts Ac

Ac + (h p /kd + Rt.c ) f

ρl π Dd3 .cl 6

(7.5)

Figure 7.18 shows that T surf has a linear relationship with each deposition process parameter. When the height of the deposition layer, hp , remains constant, T surf rises with the increase of ejection frequency, substrate temperature, and droplet temperature. If other parameters remain unchanged, hp has a significant influence on T surf , which is caused by the increase of thermal resistance and the thermal accumulation at the column top due to the extension of the heat conduction path. For a small hp , the influence of droplet temperature on T surf is not obvious, while that of substrate temperature is more prominent. With the increase of hp , the influence of droplet temperature on T surf becomes more considerable.

7.4.2 Morphology Features of Deposited Pillars The schematic diagram for the droplet deposition of a column is shown in Fig. 7.19, where the droplet radius is Rd and the ejection frequency is f . After depositing a

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Fig. 7.18 Influence factors of surface temperature T surf . a The relationship between T surf and T d at different hp . b The relationship between T surf and f at different hp . c The relationship between T surf and T s at different hp

droplet on the substrate, the deposition platform descends a certain distance to deposit the second droplet, which is repeated until the end of deposition. The radius of the column bottom surface is Rb , and the column radius is Rc , which can be calculated by Eqs. (2.88) and (2.89). As shown in Fig. 7.19a, to acquire a uniform cylinder, the identical deposition conditions for each droplet should be guaranteed, maintaining a constant droplet deposition height. Figure 7.19b illustrates the ideal column deposited by f droplets, and composed of a cylinder with a height of lp and a hemisphere with a radius of r p . According to mass conservation, lp can be expressed as lp =

4 f Rd 3 − 2rp 3 3rp 2

(7.6)

Then the ideal distance for each descent of the deposition platform is Hd =

4 f Rd 3 + r p 3 lp + rp = f 3 f r p2

(7.7)

The above equation demonstrates that the morphology of the deposited droplet column is determined by the droplet radius, Rd , hemisphere radius, r p , and the

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Fig. 7.19 Schematic diagram of pillar forming. a Schematic diagram of pillar forming by droplet deposition. b Critical dimensions of the pillar

distance of each descent of the deposition platform, H d . To obtain an ideal column, the key is to ensure that the deposition conditions of each droplet are consistent.

7.4.3 Pillar Forming by Drop-On-Demand Printing of Aluminum Droplets 1. Printing parameters of pillars by pneumatic pulse-driven drop-on-demand ejection A pneumatic pulse-driven drop-on-demand ejection device was used to fabricate aluminum pillars. The droplet diameter is 800 µm, while the initial droplet temperature and substrate temperature are 950 °C and 350 °C, respectively. Assuming that the solidification angle of the deposited aluminum droplet is 90° and the droplet spreading radius on the substrate is 500 µm, the ideal descent distance can be initially calculated as 0.34 mm according to Eq. (7.7). (1) Effect of deposition height on printed aluminum columns The descending distance of the deposition platform was set as 0, 0.2, 0.3, 0.34, 0.4, and 0.5 mm to study the influence of deposition height on the printed column. The specific process parameters in the experiment are shown in Table 7.8. Figure 7.20 shows the optical and scanning electron micrographs of aluminum pillars printed by pneumatic pulse-driven drop-on-demand ejection under the process

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Table 7.8 Process parameters in pillar forming experiments about intermittent descent distance of deposition platform

Process parameters

Value

Droplet diameter/µm

800

Initial droplet temperature/°C

950

Substrate temperature/°C

350

Intermittent descent distance of deposition platform/mm

0, 0.2, 0.3, 0.34, 0.4, 0.5

parameters shown in Table 7.8. The morphology of the deposited aluminum column is distinct each instance the deposition platform falls by a different descent distance. When the descending distance is 0 and 0.2 mm, the cylinder possesses the characteristics of a thick upper end and a thin lower end (Fig. 7.20a–b). While the descending distance is 0.3, 0.34, and 0.4 mm, the column has an equal diameter throughout (Fig. 7.20c–e). For the descending distance of 0.5 mm, the column possesses a thin upper end and a thick lower end (Fig. 7.20f). The desired falling distance of the deposition platform calculated by Eq. (7.7) is 0.34 mm, which means that consistency in the deposition height for each droplet can be theoretically ensured by moving the platform down by 0.34 mm for the deposit of each droplet. Therefore, when the lowering distance of the deposition platform is 0 mm and 0.2 mm, smaller than the ideal value, the deposition height of the second droplet relative to the first one is reduced by 0.34 mm and 0.14 mm, respectively. The deposition height of the third droplet is smaller than that of the first one by 0.68 mm and 0.28 mm, respectively, which makes the droplet deposition height increasingly smaller. Due to the constant initial droplet temperature, a smaller deposition height causes a higher temperature when the droplet reaches the deposition point, leading to more significant droplet remelting and a larger column diameter. Therefore, the further along in the column printing process, the larger the cylinder diameter, which forms a column with a thick upper end and a thin lower end.

Fig. 7.20 Columns built by depositing aluminum droplets under different intermittent descent distances of the deposition platform. a 0 mm. b 0.2 mm. c 0.3 mm. d 0.34 mm. e 0.4 mm. f 0.5 mm

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When the deposition platform descends by 0.3, 0.34, and 0.4 mm, close to the ideal value, the droplet temperature is nearly consistent when it reaches the deposition point, producing a similar melting volume and droplet diameter after cooling. Consequently, the upper and lower thickness of the deposited column are the same, indicating proper experimental parameters. When the descent distance is 0.5 mm, larger than the ideal value of 0.34 mm, the deposition height becomes increasingly larger. Since the initial droplet temperature is constant, a larger deposition height results in a lower droplet temperature at the deposition position as the printing process proceeds, which remelts a smaller volume of the previously deposited droplets, forming subsequently smaller diameters after cooling. Thus, the further along in the printing process, the smaller the column diameter, resulting in a pillar with a thin upper end and a thick lower end. In summary, during pillar fabrication by droplet deposition, the descent distance of the deposition platform substantially affects the forming process by regulating the deposition height. When the descending distance is small, the droplet deposition height becomes smaller and smaller, forming a column with a thick upper end and a thin lower end. While for a larger falling distance, the droplet deposition height gets increasingly larger, producing a pillar with a thin upper end and a thick lower end. (2) Effect of initial droplet temperature and substrate temperature on printed aluminum columns To reveal the influence of substrate temperature and initial droplet temperature on the deposition morphology of aluminum columns, metal droplet printing experiments under different temperature combinations were carried out. The main process parameters are shown in Table 7.9. During the experiment, the deposition platform remains stationary in the x and y directions, which makes the aluminum droplets pile up one by one according to the deposit position. After each droplet is printed, the deposition platform is lowered by a certain distance in the z direction to maintain the same deposition height of each droplet. The aluminum pillars deposited under the above experimental conditions are shown in Fig. 7.21 [4]. When the initial droplet temperature T d is 660 °C and the substrate temperature T s is 350 °C (Fig. 7.21a), the printed aluminum droplets are spherical. The bonding interface between adjacent droplets is small with weak remelting, forming the bead-like aluminum pillar. With the increase of T d (670, 680, and 690 °C) and T s (370, 400, and 420 °C), the bonding interface between droplets and degree of remelting are gradually enhanced (Fig. 7.21b–d). The deposited droplets Table 7.9 Process parameters of the deposition experiment using 7075 aluminum alloy

Process parameters

Value

Substrate material

Copper

Droplet diameter Dd /mm

1.2

Deposition height H s /mm

5 ~ 10

Initial droplet temperature T d /°C 660, 670, 680, 690, 700, 740 Substrate temperature T s /°C

350, 370, 400, 420, 450, 500

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spread to a disk-like shape, which induces the pillar to gradually approach a cylindrical shape. Favorable spreading of droplets and ideal remelting at the bonding interface are achieved at the temperature combination of T d (700 °C) and T s (450 °C) as shown in Fig. 7.21e, generating an aluminum column near cylindrical in shape. However, excessive temperatures of T d (740 °C) and T s (500 °C) gather a large amount of heat on the top of the aluminum column as shown in Fig. 7.21f. The newly deposited droplet and the previously deposited droplet on the column top are completely fused to form a large droplet, which may lead to local collapse, and the inability to form a uniform column. The above experimental results show that it is of vital importance to select appropriate process parameters to achieve good metallurgical bonding of adjacent metal droplets and to ensure a consistent forming contour and accuracy in part formation. As demonstrated by the experiment, when the initial droplet temperature T d is 700 °C and the substrate temperature T s is 450 °C, droplets achieve good metallurgical bonding. According to Eq. (7.5), it can be calculated that the range of T surf is 450 °C ~ 550 °C at different hp , which means under this temperature combination that T surf is in the remelting region in Fig. 7.16, and droplets can achieve proper fusion. The experimental results agree well with the theoretical model.

Fig. 7.21 Aluminum columns deposited under different ejection temperatures T d and substrate temperatures T s [4]. a T d = 660 °C, T s = 350 °C. b T d = 670 °C, T s = 370 °C. c T d = 680 °C, T s = 400 °C. d T d = 690 °C, T s = 420 °C. e T d = 700 °C, T s = 450 °C. f T d = 740 °C, T s = 500 °C

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2. Printing parameters of pillars by piezoelectric pulse-driven drop-on-demand ejection The droplet diameter printed by pneumatic pulse-driven drop-on-demand ejection is relatively large, resulting in roughly printed parts. The diameter of aluminum droplets can be significantly reduced by using a piezoelectric pulse-driven drop-on-demand ejection device. However, with the decrease of metal droplet diameter, the droplet cooling rate increases, and the process parameters vary accordingly. In this section, a piezoelectric pulse-driven drop-on-demand ejection device was used with ZL104 as the ejection material, and aluminum pillar printing experiments were carried out with a 300-µm-diameter nozzle. The effects of printing frequency, temperature, and deposition height with small-diameter droplets on the deposition process of aluminum pillars were investigated, laying a foundation for the application of highprecision aluminum droplet-based 3D printing technology. (1) Effect of deposition height on printed aluminum columns When the droplet diameter is reduced, the ejection instability has a more significant impact on the printing accuracy. Due to nozzle exit defects, oxidation, uneven wetting, etc., there is a random position disturbance relative to the nozzle radial direction as the metal droplet leaves the nozzle. At the time the metal droplet leaves the nozzle, the droplet velocity can be decomposed into a vertical velocity component and a horizontal velocity component. The horizontal velocity component would cause a deviation between the actual droplet deposition position and the ideal deposition position (called lateral instability), resulting in a deposition error which gradually increases as the deposition height increases. Figure 7.22 exhibits an aluminum pillar formed with a fixed substrate position. At the beginning of the deposition, the substrate is 14.5 cm away from the nozzle, which causes a large deposition position error of aluminum droplets. In this situation, multiple droplets are piled together at the same height (Inset graph 5). With the decrease of deposition height to 6 cm (Inset graph 4), the deviation of the droplet deposition position relative to the center position is reduced, however, there is still a random deviation. When the deposition height is reduced to 5.5 cm (Inset graph 3), the deposition position has only a small deviation from the center position, indicating the improvement of droplet printing accuracy. When the deposition height further decreases to 1.5 cm (Inset graph 1), the stable droplet printing position produces an aluminum column with uniform size and good verticality. The experiment shows that the deposition height is an important parameter affecting the deposition position error of aluminum droplets and forming quality of fabricated parts. (2) Effect of printing frequency on printed aluminum columns Figure 7.23 shows the changes in the diameter of the deposited aluminum pillars under four groups of different ejection frequencies. Since the heat input rate of the aluminum column is largely determined by the deposition frequency of uniform droplets, the final shape of pillars obtained under different deposition frequencies is different. As shown in Fig. 7.23, the diameter of the aluminum pillar increases

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Fig. 7.22 A column printed by depositing aluminum droplets and its partial microscope images. The column height is 13 cm with a height-diameter ratio of 190. (Notes: Inset graphs 1, 2, 3, 4, and 5 are the column sections deposited at deposition heights of about 1.5 cm, 3.5 cm, 5.5 cm, 6 cm, and 15 cm, respectively)

linearly with the rise of frequency, while the height of a single aluminum droplet after deposition decreases linearly. The relationship between aluminum column diameter and ejection frequency can be expressed as Dc = 397.5 + 15.4 f

Fig. 7.23 Variation curve of aluminum column diameter with ejection frequency

(7.8)

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Fig. 7.24 Deposition process of aluminum pillars under different frequencies. a 15 Hz. b 20 Hz

When the ejection temperature remains constant, each droplet carries the same amount of heat. With the increase of the ejection frequency, the heat loss time of aluminum droplets becomes shorter, which is prone to cause heat accumulation on the droplet surface during high-frequency deposition. The surface temperature of the aluminum pillar gradually increases due to heat accumulation. When subsequent droplets are deposited on the top of the aluminum pillar, their spreading diameter and fusion depth increase, leading to a decrease in the height of the deposited aluminum droplet accordingly. If the ejection frequency is too high, the temperature at the top of the aluminum column increases accordingly, and the solidification of the falling droplet becomes difficult, resulting in a collapse phenomenon. Figure 7.24 exhibits aluminum pillars deposited at frequencies of 15 and 20 Hz. It’s seen that the surface of the aluminum pillar is smooth. The aluminum column diameter increases as the height rises, resembling an inverted cone. In addition, the diameter of the aluminum pillar at the same height position deposited under 20 Hz is larger than that deposited under 15 Hz. (3) Effect of droplet temperature on printed aluminum columns The ejection temperature of aluminum droplets (i.e., initial droplet temperature) determines the heat input during deposition, which affects the fusion of aluminum droplets. Thus, the ejection temperature should be kept within a reasonable range. If the temperature is too high, droplet remelting and column collapse occur, while too low an ejection temperature hinders the full fusion between aluminum droplets. Keeping other parameters unchanged, the aluminum pillar deposition experiments were carried out under different initial droplet temperatures of 650 ~ 750 °C. The experimental results are shown in Figs. 7.25 and 7.26. Figure 7.25a illustrates the bead-like structure formed by the accumulation of aluminum droplets when the initial droplet temperature is 650 °C. Under this condition, the spreading diameter of the aluminum droplet is small. The diameter of the aluminum column is 385 ± 5 µm and the height is 300 µm. When the ejection temperature increases to 750 °C, the spreading diameter of a single aluminum droplet increases to 423 ± 5 µm, while the

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height of a single aluminum droplet after deposition decreases to about 240 µm. The surface of the aluminum column also shows a bead-like shape, but irregularities are significantly reduced. Figure 7.26 shows the diameter of the aluminum column with a variation of ejection temperature, where the diameter of the aluminum pillar increases linearly with the rise of ejection temperature. The relationship can be expressed as Dc = 150 + 0.36Td

(7.9)

Fig. 7.25 Optical microscope images of aluminum pillars deposited at different initial droplet temperatures (Notes: The nozzle diameter is 300 µm, and the deposition height is 15 mm). a 650 °C. b 750 °C

Fig. 7.26 Diameter of the aluminum column as a function of droplet temperature

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From the above experimental results, it’s seen that the deposition height mainly affects the deposition position accuracy of aluminum droplets, while the ejection temperature and frequency influence the thermal state during aluminum droplet deposition. Therefore, to ensure printing quality and accuracy, it is necessary to reasonably select parameters such as deposition height, initial droplet temperature, and ejection frequency. Based on the above experiments and analysis, a combination of appropriate parameters is determined with a deposition height of 15 mm, an initial droplet temperature of 750 °C, and an ejection frequency of 6 Hz. An aluminum column part was printed under this combination of parameters, and the deposition process shown in Fig. 7.27. As can be seen, the ejection process of aluminum droplets is stable. The diameter of the aluminum column is consistent at different heights, indicating good forming quality. Figure 7.28 shows SEM images of the printed aluminum column. The aluminum droplets have precise deposition positions, favorable uniformity and stability, and uniform transition in the droplet bonding region.

Fig. 7.27 Image sequences of droplet flying and deposition process during pillar forming. The time interval between adjacent images is 1 ms

Fig. 7.28 SEM images of an aluminum column (Notes: The nozzle diameter is 300 µm, the ejection frequency is 6 Hz, the droplet temperature is 750 °C, and the deposition height is 15 mm). a Overall view of the aluminum column. b Drawing of partial enlargement of the aluminum column

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7.4.4 Forming of Thin-Walled Aluminum Parts The above studies demonstrate that the deposition morphology of aluminum droplets can be controlled by adjusting parameters such as the initial droplet temperature, deposition height, and substrate temperature. To be specific, the deposition morphology of lines can be regulated by changing the horizontal velocity of the deposition platform and the substrate temperature. The deposition morphology of pillars can be controlled by varying the intermittent descent distance of the deposition platform. Therefore, the forming of complex parts can be achieved by properly adjusting the process parameters. The aluminum droplet printing and part forming experiment was carried out using a pneumatic pulse-driven drop-on-demand ejection device. In the experiment, the ejection frequency is 1 Hz, and the deposition height is 10–20 mm. The initial droplet temperature and substrate temperature are 950 °C and 350 °C, respectively. The platform velocity and intermittent descent distance of the deposition platform are 0.7 mm/s and 0.34 mm, respectively. The diameter of aluminum droplets is ~ 800 µm. During deposition, the deposition platform movement occurs along a predetermined path and the droplet deposition occurs along this scanning path. After the deposition of one layer is completed, the deposition platform moves down by a certain distance and is followed by the deposition of the next layer, and repeated until the end of the printing. From the appearance of the deposited aluminum part (Fig. 7.29a) and the partially enlarged view (Fig. 7.29b), it is observed that the surface morphology of the aluminum part shows favorable consistency. This indicates that adequate parts can be printed by selecting reasonable process parameters.

Fig. 7.29 Tubular parts deposited by aluminum droplets. a Photo of aluminum parts. b SEM image of partial enlargement

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The pneumatic pulse-driven drop-on-demand ejection technology can realize the controllable deposition of aluminum droplets with large diameters, which is advantageous in improving the forming efficiency but disadvantageous in forming precision. As a comparison, the piezoelectric pulse-driven drop-on-demand ejection technology can eject and deposit aluminum droplets with small diameters, thereby improving the accuracy and reducing the surface roughness of the fabricated parts. It can be used for the building of thin-walled parts such as tiny horn waveguides, heat dissipation cavities, and specially shaped shells. Here, 7075 aluminum alloy was used to print a thin-walled horn pipe fitting with an inclination angle of 75°. Two kinds of deposition conditions were selected for comparative experiments to investigate the influence of process parameters on the forming quality of parts. (1) With the aluminum droplet diameter of 450 µm, ejection frequency of 1 Hz, initial droplet temperature of 700 °C, substrate temperature of 200 °C, deposition height of ~ 10 mm, platform velocity of 10 mm/s, and an intermittent deposition platform descent distance of 0.2 mm, the resultant part sample is shown in Fig. 7.30a. (2) By changing the ejection frequency to 10 Hz, and substrate temperature to 400 °C, and maintaining the other parameters constant, the resultant fabricated part is shown in Fig. 7.30b. Comparing the experimental results in Fig. 7.30a and b, it can be found that an increase of ejection frequency and substrate temperature can significantly improve the degree of fusion between droplets, and reduce surface roughness. As shown in Fig. 7.30b, when the aluminum droplet diameter is 450 µm, the surface roughness (Ra) of free-formed thin-walled parts can reach 10–15 µm under ideal remelting conditions. Fig. 7.30 Thin-walled aluminum parts formed by piezoelectric ejection. a Substrate temperature of 200 °C, ejection frequency of 1 Hz. b Substrate temperature of 400 °C, ejection frequency of 10 Hz

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7.5 Forming of Aluminum Solid Parts Solid parts can be directly formed by controlling the layer-by-layer deposit of aluminum droplets, as illustrated in Fig. 7.31. In the same layer, aluminum droplets are deposited using a raster scanning pattern, where the deposit trajectories of aluminum droplets are adjacent reciprocating lines. After one layer is printed, the substrate descends by the thickness of one layer to deposit the second layer. The process is repeated until a 3D solid part is built. The pneumatic pulse-driven drop-on-demand ejection technology is used to fabricate solid parts. The process parameters are listed as follows: a nozzle diameter of 0.5 mm, an initial droplet temperature of 700 °C, a substrate temperature of 450 °C, a droplet diameter of 1.2 mm, a deposition height of ~ 5 mm, an ejection frequency of 1 Hz, and a platform speed of 1 mm/s. In addition, the step distances in the x and y directions are 0.85 mm and 1 mm, respectively, and the layer spacing is 2 mm. During deposition, after droplets are deposited in a horizontal line, the platform moves laterally for a set distance. Then a second line is deposited on the side of the existing line (the scanning direction is opposite). A certain overlap ratio between two adjacent lines is ensured to form a dense layer, and a metal layer can be thus deposited by repeating the above process. Figure 7.32a exhibits a 7075-aluminum alloy solid part created by the pneumatic pulse-driven drop-on-demand ejection method. The length × width × height of the fabricated part is 60 mm × 16 mm × 8 mm. The part has flat surfaces and a clear outline. The right end of the part is slightly irregular, which might be caused by the concentration of thermal stress. Figure 7.32b shows the optical micrograph of the upper surface of the printed part. The deposited metal layer is formed by overlapping and the fusion of several metal lines with different scanning directions. The metal droplets on the layer exhibit an obvious shell-like morphology. The scanning direction of deposited lines can be distinguished by the overlapping order of droplets. The optical micrographs of the front and side of the printed part are shown in Fig. 7.32c and d. During the deposition and formation process of each metal layer, the metal

Fig. 7.31 Schematic diagram of scanning trace for 3D parts deposited by uniform droplets

References

269

Fig. 7.32 Deposited aluminum solid parts. a Overall morphology. b Top view. c Front view. d Side view

droplets can be accurately deposited on top of the solidified droplets to form a shelllike morphology. The droplet surface at the overlapping region exhibits a corrugated morphology. The above forming experiment of aluminum solid parts shows that 3D solid parts can be built through drop-by-drop printing and vertical stacking of layers. The deposition path can be generated by layering the target workpiece model and the planning of a layer scanning trajectory, which can provide a feasible method for the fabrication of complex aluminum parts. In conclusion, aluminum droplet deposition can achieve the printing of thinwalled, solid, aluminum parts, which can provide forming accuracy with minimum wall thickness and outstanding advantages in terms of forming cost. However, due to the limitations in control technology for the stable ejection and precise deposition of aluminum droplets, the technology is still in the laboratory research stage and has yet to enter industrial applications.

References 1. Zeng X. Research on numerical simulation of impact and solidification for droplet deposition on substrate. Xi’an: Northwestern Polytechnical University; 2011. 2. Zuo H. Research on microstructural evolution of uniform molten aluminum droplets during controlled deposition fabrication. Xi’an: Northwestern Polytechnical University; 2015.

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3. Cheng X. Development of a molten metal droplet generator for rapid prototyping. Toronto: University of Toronto; 2002. 4. Chao Y. Fundamental research on manufacturing micro-metal parts based on deposition metal droplet. Xi’an: Northwestern Polytechnical University; 2012.

Chapter 8

Microstructure Evolution and Interface Bonding of Uniform Aluminum Droplet Deposition Manufacturing

8.1 Introduction The deposition process of aluminum droplets involves complex behaviors such as fluid flow, unsteady heat transfer, and solidification. Such behaviors determine the microstructure of printed parts, affecting their final mechanical properties. Therefore, the investigation of these complex behaviors is significantly important in the droplet deposition process. This chapter focuses on the influence of thermodynamics and kinetic behaviors on solidification crystallization and solid phase transformation during the deposition of aluminum droplets. It clarifies the evolution mechanism of microstructure, influence of interface bonding, and causes of various common internal defects, which provides an experimental and theoretical foundation for the fabrication of high-quality aluminum parts.

8.2 Microstructure Evolution of Uniform Aluminum Droplet Deposition During the deposition process of aluminum droplets, sub-rapid solidification (cooling rate of 10 ~ 103 K/s) or even rapid solidification (cooling rate of 103 ~ 106 K/s) occurs due to the rapid quenching effect. The cooling rate is much greater than that in casting (10−3 ~ 10 K/s). Meanwhile, the impact, spreading, and repeated oscillation of aluminum droplets during deposition also affect their solidification process, making their microstructure morphology different from that of slow solidification (e.g., ascast condition). Furthermore, in the drop-by-drop deposition process, the high-temperature metal droplet as a moving point heat source is periodically added to the deposition surface. Through reheating, it remelts with solidified droplets to achieve metallurgical bonding. The deposition parameters directly influence the internal microstructure of © National Defense Industry Press 2023 L. Qi et al., Metal Micro-Droplet Based 3D Printing Technology, https://doi.org/10.1007/978-981-99-0965-0_8

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8 Microstructure Evolution and Interface Bonding of Uniform Aluminum …

the deposited part, which in turn affects the mechanical properties of the printed part and the form of its internal defects. In this chapter, the microstructure morphology of typical deposited parts (single droplets, vertical pillars, horizontal lines, and solid parts) was investigated by metallographic observations, X-ray diffraction analysis, and scanning electron microscope technique. Internal defects and mechanical properties of parts were characterized by combining densitometry, microhardness measurement, and tensile property testing to reveal the relationship between the forming process and the microstructure, mechanical properties, and internal defects. 7075-H112 aluminum alloy bars were used as the ejection material. A pneumatic pulse-driven drop-on-demand ejection device was utilized as the printing equipment. The experiment was conducted under a droplet diameter of ~ 1 mm, ejection temperature of 850 °C, ejection frequency of 1 Hz, and brass substrate temperature of 250 °C. When the deposited aluminum droplet on the brass substrate was solidified completely, it was cut vertically from its center to observe the internal microstructure of the solidified droplet. As depicted in Fig. 8.1a, it can be divided into three different regions: the bottom contact region (Fig. 8.1b), the middle directional microstructure region (Fig. 8.1c), and the upper non-directional microstructure region (Fig. 8.1d).

Fig. 8.1 SEM images of the microstructure of a deposited aluminum droplet (longitudinal section). a Overall morphology. b Bottom contact region. c Middle directional microstructure region. d Upper non-directional microstructure region

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Fig. 8.2 Schematic diagram of local contact between an aluminum droplet and the substrate. a Overall view. b Partially enlarged view

The thin bottom contact region is directly in contact with the substrate, which is formed in the droplet impact and spreading stage. Theoretically, since the significant temperature difference between the top and bottom of this region leads to a fast cooling rate, fine grains can be formed. However, in addition to the fine microstructures caused by rapid solidification (Fig. 8.1b), many bottom contact regions show coarse grains without obvious directionality. This is related to the actual contact conditions between droplets and the substrate during spreading. As shown in Fig. 8.2, during the spreading of a liquid aluminum droplet, some local point contacts between the droplet and the substrate appear due to the influence of substrate roughness and trapped air [1, 2]. This results in relatively low heat conduction efficiency and more heat exchange by convection within the droplet, forming coarse grains without obvious directionality. A small number of directional dendrites can be observed at the bottom center of the aluminum droplet as illustrated in Fig. 8.3a. The formation reasons are as follows. During deposition, the relative motion velocity between the melt and the substrate in the bottom center region of the droplet is approximately zero, and the thermal convection effect is not significant. The favorable interfacial contact conditions [1] lead to a relatively high thermal conductivity and a significant solidification rate. At the same time, the high-temperature melt preferentially nucleates at the interface contact point (Fig. 8.3b), which grows rapidly in the opposite direction of the heat flow, eventually forming directional dendritic crystals. When the droplet bottom gradually solidifies to produce a local solidification layer with a certain thickness, the heat between the solidified layer and the unsolidified liquid is exchanged by heat conduction. Therefore, as shown in Fig. 8.1c, the middle part of the droplet mainly contains directional dendrites, whose growth directions are opposite to the heat flow direction (i.e., perpendicular to the substrate and upward). The longitudinal-section image in the middle area of the solidified droplet is shown in Fig. 8.4a. The middle area is made up of small sheet-like primary α-Al dendrites which are arranged regularly in parallel. The second phase is distributed between dendrites. As illustrated in the horizontal-section image parallel to the substrate (Fig. 8.4b), the average distance between primary dendritic arms is ~ 5 μm. The dendritic branches of these microstructures are underdeveloped, closing to the cellular morphology.

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Fig. 8.3 SEM images of the microstructure at the bottom of the deposited aluminum droplet. a Center of the bottom region. b Solidification region at the contact point

Fig. 8.4 SEM images of the directional microstructure in the middle of the deposited aluminum droplet. a Longitudinal section. b Horizontal section

The upper part of the solidified droplet is a non-directional region (Fig. 8.1d), which contains a large number of coarse dendrites, presenting a non-directional equiaxed crystal morphology. When a large volume of molten metal is dispersed into droplets, a small number of heterogeneous nucleation cores can be involved in the droplets. As a result, the columnar dendrites in the droplet middle area tend to grow in the opposite direction of the heat flow continuously. However, the internal shear force caused by droplet spreading and oscillation tears the growth tips of columnar dendrites, which provides additional nucleation points for the unsolidified molten metal [3]. Secondly, as the solidification front continues to move up, the temperature gradient of the droplet gradually decreases, which reduces the solidification rate accordingly, forming turning dendrites or even coarse equiaxed dendrites at the upper part of the droplet. In addition, the free surface of the droplet generates surface nucleation sites due to the adhesion of impurities, oxidation [4], and the rise of torn solid crystal nuclei, which produces microstructures growing from the surface to the inside of the droplet, as shown in Fig. 8.5.

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Fig. 8.5 Coarse dendritic microstructures stemmed from surface nucleation sites

8.2.1 Microstructure Evolution of Uniform Aluminum Droplets During the Vertical Pileup Figure 8.6 illustrates the internal microstructure of the second aluminum droplet deposited vertically on the surface of a solidified aluminum droplet, which is the same as the single droplet deposited on the substrate (Fig. 8.1). The microstructure of the stacked droplet can be also divided into three regions: the bottom contact region, the middle directional microstructure region, and the upper non-directional microstructure region. The bottom contact region (Fig. 8.6b) is still dominated by homogeneous and fine equiaxed grains without obvious orientation, which can be attributed to the favorable interface conditions between two vertically stacked droplets. The solidified droplet surface can provide a large undercooling and sufficient nucleation conditions for the crystallization of the subsequently deposited droplet so that grains can be refined. The directional microstructure region (Fig. 8.6c) in the middle of the droplet is significantly narrowed, where columnar dendrites are coarsened. While in the upper part of the droplet, the non-directional microstructure region (Fig. 8.6d) becomes wider, showing thick secondary dendrite arms of equiaxed dendrites. This indicates that the solidification time of the deposited droplet increases and the temperature gradient at its top decreases due to the increase of thermal resistance. During the vertical deposition of droplets, subsequent droplets may have a significant thermal effect on the solidification microstructure of the contact area below them. When the second droplet is deposited on the top of a solidified droplet, the heat carried by the second droplet is rapidly transferred to the substrate through the first one, making the upper surface of the first droplet undergo a quick heating–cooling process in a very short time. In the following deposition process, the first droplet

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Fig. 8.6 Microstructures of the second vertically-deposited aluminum droplet (longitudinal section). a Overall morphology. b Bottom contact region. c Middle directional microstructure region. d Upper non-directional microstructure region

experiences multiple sharp heating–cooling cycles. The upper surface temperature of the first droplet exhibits periodic changes with the period as the droplet ejection interval. When aluminum droplets are successively deposited to build a vertical column (Fig. 8.7), the first droplet would go through multiple heating–cooling processes. To investigate the influence of the number of thermal cycles on the deposited part, we need to observe the microstructure of deposited droplets. As shown in Fig. 8.8a, the single aluminum droplet deposited on the substrate is not affected by the thermal cycling effect, showing small dendrites. The field of view inside the droplet is dark after chemical corrosion, where no apparent grains can be distinguished. After the second droplet is deposited on the top of the first one, the first droplet undergoes one thermal cycle, changing non-equilibrium fine dendrites to grains close to equilibrium (Fig. 8.8b). The first droplet has undergone two thermal cycles with the deposition of the third droplet. As depicted in Fig. 8.8c, the field of view inside the droplet brightens gradually, where grains and grain boundaries become clear. As the number of thermal cycles continues to increase, the microstructure changes are no longer noticeable, indicating that the microstructure is stabilized (Fig. 8.8d).

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Fig. 8.7 Different numbers of vertically stacked aluminum droplets (Notes: The droplet temperature is 1173 K, the substrate temperature is 300 K, and the ejection frequency is 1 Hz)

Fig. 8.8 Microstructures of the first deposited aluminum droplet under different numbers of thermal cycles. a Direct deposition (Zero cycles). b One cycle. c Two cycles. d Three cycles

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The evolution of the second phase distribution of the first deposited aluminum droplet under different thermal cycle times is shown in Fig. 8.9. It is observed that before the deposition of the second droplet, second phase grains in the first droplet are evenly distributed along the dendrite growth direction (Fig. 8.9a). As demonstrated in Fig. 8.9b, the instantaneous heat transfer of the second droplet leads to coarser and fewer second-phase grains without obvious distribution direction in the first droplet. As the number of thermal cycles continues to increase, the size of the second phase grains in the first droplet does not increase. However, the distribution characteristics along the grain boundary contour become more obvious (Fig. 8.9c and d). It indicates that small second-phase grains in the crystal are segregated at the grain boundary, making the overall field of view brighter and the grain boundary more evident. The interlayer heat accumulation effect of droplets has a significant impact on the profile, internal microstructure, and mechanical properties of printed columns. Figure 8.10 shows the appearance and top region microstructure of 1D columns (diameter of ~ 1.2 mm) deposited at different ejection frequencies. Note that the columns were vertically stacked by 40 aluminum droplets with a droplet temperature of 1173 K and substrate temperature of 300 K. When the ejection frequency is 1 Hz, the vertical column presents an obvious bead-like contour with its top area mainly composed of fine dendrites (Fig. 8.10a). The backscattered electron (BSE) image (Fig. 8.10b) demonstrates that second-phase grains are small and

Fig. 8.9 Backscattered electron (BSE) images of the first deposited aluminum droplet under different numbers of thermal cycles. a Zero cycle. b One cycle. c Two cycles. d Three cycles

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dispersed in this area. When the ejection frequency increases to 3 Hz, the column height decreases, and the top radial diameter increases. While the proportion of second-phase grains is reduced, the grains are enlarged significantly and not evenly distributed (Fig. 8.10c and d). It manifests that a micro molten pool forms at the interface between two successively deposited droplets at the column top, leading to the obvious coarsening of solidification microstructures. As shown in Fig. 8.10e and f, for the ejection frequency of 7 Hz, the printed column becomes shorter and thicker, producing a dendritic network structure similar to the as-cast condition. In summary, with an increment of the ejection frequency, the heat accumulation effect gets more prominent, causing more significant microstructure coarsening and composition segregation. As shown in Fig. 8.11, the interface bonding situations at different positions of the deposited vertical column are distinct. There are clear cold laps and interface gaps at the contact interface between the first and second droplets (Fig. 8.11a). The cold laps between the second and third droplets become less obvious (Fig. 8.11b) and disappeared between the third and fourth droplets (Fig. 8.11c). The shared crystal grains crossing the contact interface could be observed in the partially enlarged view (Fig. 8.11c). We can conclude that the interface bonding between deposited droplets varies with the increase in vertical height. Due to the thermal accumulation effect, the microstructure and phase composition of vertically deposited columns differ along the height direction (Fig. 8.12). At a distance of 20 mm from the substrate, there is a large directional columnar crystal region in the solidified droplet. Non-directional equiaxed crystals only exist near the droplet bonding area, where some residual cold laps could be observed (Fig. 8.12a). For a distance of 50 mm, the temperature difference between the deposited droplet and the column top declines, which weakens the directional growth tendency of grains, increasing the number of non-directional equiaxed crystals (Fig. 8.12b). The second phase distribution at different heights of the vertical column is shown in Fig. 8.13. There are mainly a large number of round grains and a few needle-like microstructures at a distance of 20 mm from the substrate. The small crystals are uniformly dispersed in the aluminum matrix (Fig. 8.13a). With the increase of vertical deposition height to 50 mm, the melt solidification process becomes relatively slow, leading to the obvious coarsening of second-phase grains and a certain continuous distribution trend. The segregation phenomenon is thus intensified (Fig. 8.13b). The thermal accumulation effect of droplets affects not only the microstructures of deposited parts but also their local mechanical properties. Microscopic hardness tests were carried out at different heights of the deposited columns as shown in Fig. 8.14. In the experiment, an automatic turret microhardness tester (HXP-1000TM/LCD) was utilized to measure the local Vickers hardness of the sample with a load of 200 g and a loading time of 15 s. Five points were measured for each target position. The measurement results were obtained by removing the maximum and minimum values and averaging the remaining values. During microhardness tests, the distance between two adjacent test points or the test point and the edge should be at least three times the indentation diagonal length. The results show that with the rise of the column height, the average microhardness increases immediately and then decreases.

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Fig. 8.10 Profiles and microstructures of vertical columns under different ejection frequencies. a Metallograph for 1 Hz. b BSE image for 1 Hz. c Metallograph for 3 Hz. d BSE image for 3 Hz. e Metallograph for 7 Hz. f BSE image for 7 Hz

The microhardness at the lower part of the pillar is relatively low, which is due to the cold laps and interface gaps. When the vertical height increases, the solidification time of newly deposited droplets becomes longer, which improves the bonding condition between droplets and reduces the microhardness fluctuation. However, since the thermal accumulation effect makes the internal grains grow up, the microhardness of this region decreases somewhat.

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Fig. 8.11 Interface bonding situations in varied regions of the stacked column. a Interface of the first and second droplets. b Interface of the second and third droplets. c Interface of the third and fourth droplets

Fig. 8.12 Microstructures of the vertical column at different heights (Notes: The aluminum droplet temperature is 1173 K, the droplet diameter is ~ 1 mm, the substrate temperature is 623 K, and the ejection frequency is 1 Hz). a 20 mm from the substrate. b 50 mm from the substrate

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Fig. 8.13 BSE images of the vertical column at different heights (Note: The printing conditions are the same as Fig. 8.12). a 20 mm from the substrate. b 50 mm from the substrate

Fig. 8.14 Variation of local microhardness of aluminum column with height (Note: The printing conditions are the same as Fig. 8.12)

8.2.2 Microstructure Evolution of Lines Deposited by Uniform Aluminum Droplets During the deposition of horizontal lines by uniform aluminum droplets, the heat transfer surface is not a flat or gently curved surface, but a nearly L-shape composite surface composed of the underlying substrate (or solidified droplets) and a neighboring droplet of the same layer. Hence, the microstructure of the horizontal printing of aluminum droplets is different from that of the vertical pillar. In the contact interface between two horizontally overlapped aluminum droplets (Fig. 8.15a), the growth direction of dendrites is different due to the competitive selective growth mechanism. Some dendrites continue to extend into the interior of the droplet, while others gradually stop growing. During the solidification of molten metal, the growth direction of cellular and eutectic microstructures is parallel to the heat flow direction, while that of dendrites is the preferred orientation closest

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Fig. 8.15 Competitive growth phenomenon of microstructures in the contact area of two horizontally overlapped aluminum droplets. a Microstructures in the contact area. b Schematic diagram of the competitive growth

to the heat flow direction. When two droplets contact to form intragranular bonding (Fig. 8.15b), the epitaxial growth at the droplet boundary is evident. Crystal structures with unfavorable orientation soon stop growing, while those with favorable orientation (i.e., crystallization direction in line with the temperature gradient or heat dissipation direction) continue to evolve. Note that the crystal structure of aluminum is face-centered cubic with its preferred orientation as direction [5]. Eventually, the orientation of crystal structures extending into the melt is essentially the same. Figure 8.16 shows the microstructure of the second aluminum droplet printed horizontally. Similar to the internal microstructure of a single droplet deposited on the substrate, fine dendrites appear as shown in Fig. 8.16a. The difference is that the microstructure growth direction of the overlapped droplet is not consistent. Dendritic structures close to the substrate grow vertically upward (Fig. 8.16b), whereas those close to the adjacent droplet grow horizontally (Fig. 8.16c). Microstructures within the above two regions converge into the melt and eventually grow diagonally upward (Fig. 8.16d). A schematic diagram of the dendritic microstructure evolution in a horizontally overlapped aluminum droplet is illustrated in Fig. 8.17. The deposition surface for a horizontally overlapped droplet is a curved composite surface consisting of the substrate below and the contact interface of the previously deposited droplet in the same layer. Most of the heat in the high-temperature melt is transferred through the substrate contact interface, where the microstructure growth direction is vertical upward, namely direction. The same-layer contact interface also provides the supercooling and growth substrate required for the crystallization of the newly deposited droplet, leading to the microstructure growth direction as direction in this region. With the advance of the solidification front, the curvature of the isothermal surface in the melt gradually decreases, turning slowly from the initial near-L-shape to a gentle arc. Accordingly, the maximum temperature gradient direction, namely the heat transfer direction, is gradually deflected. Crystal structures adjust the growth direction continuously through competitive growth, producing

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Fig. 8.16 Microstructures of the second horizontally overlapped aluminum droplet. a Overall morphology. b Horizontal microstructure region on the right. c Vertical microstructure region at the bottom. d Meeting region of different microstructures at upper left

microstructures growing along the angle direction of / in the upper part of the droplet. Fig. 8.17 Schematic diagram of solidification microstructure evolution in a horizontally overlapped aluminum droplet

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Fig. 8.18 Microstructures of different positions in a horizontal aluminum line. a The third droplet. b The sixth droplet

A horizontally overlapped line was cut along the longitudinal direction to probe the variation of internal microstructures. The overlapping morphology between the third and fourth droplets is shown in Fig. 8.18. Similar to the second droplet (Fig. 8.16), only fine dendritic structures are exhibited, indicating that solidification and crystallization conditions for each droplet are quite close. Moreover, most of the heat carried by new-coming droplets is directly transmitted to the substrate through the lower contact interface. Hence, the coarsening effect on the fine dendrites of adjacent droplets is not significant.

8.3 Influence of Interface Bonding Between Metal Droplets on Printed Aluminum Parts During the printing of 3D solid parts, since the heat dissipation conditions of metal droplets vary, their solidification behaviors are different from the above-mentioned single droplet or line deposition process, forming diverse microstructures. This section focuses on the evolution mechanism of microstructure morphology during the 3D printing of solid parts.

8.3.1 Effect of Interface Bonding on the Microstructure of Aluminum Parts Rectangular 7075 aluminum alloy bulks were printed using the process parameters shown in Table 8.1. In the experiment, three groups of process parameters of aluminum droplet temperature and substrate temperature, noted as Set 1, Set 2, and Set 3, respectively, were taken.

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Table 8.1 Printing process parameters of rectangular aluminum parts Process parameters

Value

Process parameters

Value

Droplet diameter Dd /mm

0.5

Scanning step in the x direction W x /mm

0.8

Ejection pressure P/kPa

60

Scanning step in the y direction W y /mm

1

Ejection frequency f /Hz

1

Droplet temperature T d /K

Set 1 1123 Set 2 1373 Set 3 1423

Deposition height H s /mm

10 ~ 20

Substrate temperature T s /K

Set 1 423 Set 2 573

Substrate material

Cu

Set 3 623

The aluminum part printed under Set 1 (T d = 1123 K, T s = 423 K) is shown in Fig. 8.19a with its partially enlarged view depicted in Fig. 8.19b. It is observed that the outline of the deposited bulk is clear. However, the surface is rough, and the droplet fusion is poor. Further observation of the internal microstructure in the deposited part (Fig. 8.20) shows obvious cold laps in the droplet bonding zone, revealing unfavorable metallurgical bonding. Besides, droplets have solidified before being fully spread out due to the fast solidification rate. There is not enough time to fill the gaps between neighboring droplets, resulting in many hole defects and cracks in the droplet bonding region. As tested by the drainage method, the density of this printed component is ~ 95%. The aluminum component was printed under Set 2 (T d = 1373 K, T s = 573 K) as shown in Fig. 8.21a. The relatively clear outline indicates that the improvement of thermal parameters does not have a significant impact on the stability of droplet ejection and deposition. As demonstrated in the partially enlarged view of the printed aluminum part (Fig. 8.21b), the spreading degree of deposited droplets is significantly larger in the collision process, producing a much smoother solidified surface than

Fig. 8.19 Profile of as-deposited aluminum bulk under Set 1 (T d = 1123 K, T s = 423 K). a Overall morphology. b Partially enlarged view

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Fig. 8.20 Microstructure of the printed aluminum part under Set 1 (T d = 1123 K, T s = 423 K)

Fig. 8.21 Profile of as-deposited aluminum bulk under Set 2 (T d = 1373 K, T s = 573 K). a Overall morphology. b Partially enlarged view

that under Set 1. Droplets are interlaced and overlapped with each other without apparent gaps or holes remaining. Further observation of the microstructure inside the part (Fig. 8.22) shows no triangular holes and other defects in the droplet bonding zone. The density of the part reaches 97% as measured by the drainage method. According to the partially enlarged view (Fig. 8.22b), cold laps in the bonding zone disappear, and the grain boundary is not apparent. The bonding area shown in the rectangular frame in Fig. 8.22b has a bright white band with a width of ~ 20 μm, which are grain structures shared by two droplets. This manifests that in addition to the original intergranular bonding, the contact regions between droplets begin to melt to form intragranular bonding. The bonding strength enhancement between droplets of printed aluminum parts is beneficial to improving their mechanical properties. With the further increase of droplet temperature and substrate temperature under Set 3 (T d = 1423 K, T s = 623 K), the aluminum part was printed as shown in Fig. 8.23. The excessive temperature parameters make the deposited droplets in a paste or even total liquid state for a long time. Thus, droplets fuse and agglomerate with each other

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Fig. 8.22 Microstructure of the printed aluminum part under Set 2 (T d = 1373 K, T s = 573 K). a Low-magnification microscope image. b Partially enlarged view

Fig. 8.23 Profile of as-deposited aluminum bulk under Set 3 (T d = 1423 K, T s = 623 K). a Overall morphology. b Partially enlarged view

under surface tension, eventually forming an irregular solidification profile with a blurred outline, which deteriorates the forming accuracy seriously. Furthermore, as depicted in Fig. 8.24, the internal microstructure shows non-directional coarse equiaxed crystals and large second-phase microstructures at grain boundaries, which is detrimental to the overall mechanical properties of the printed parts. Despite no apparent holes and gaps inside the fabricated part (measured density of 98%), its mechanical property is not high (σ b = 228 MPa).

8.3.2 Effect of Interface Bonding on the Mechanical Properties of Aluminum Parts The interface bonding situation and the degree of fusion between deposited droplets have a significant impact on the mechanical properties of as-deposited aluminum components. Test specimens for mechanical properties were prepared from the parts deposited under the condition of Set 1. It is observed that the sample contains discontinuous triangular holes, which are regularly distributed between two layers of the

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Fig. 8.24 Microstructure of the printed aluminum part under Set 3 (T d = 1423 K, T s = 623 K). a Low-magnification microscope image. b Partially enlarged view

printed structure (Fig. 8.25a). As revealed in the side view of the gauge section (Fig. 8.25b), there are also apparent gap defects between adjacent droplets in the same layer. To sum up, the contact interface is not fused well under the temperature condition of Set 1, presenting a large number of dense gaps and holes, which would significantly reduce the mechanical properties of the tensile specimen (σ b = 159 MPa). Figures 8.26 and 8.27 show the printed samples under the conditions of Set 2 and Set 3. As the substrate temperature and droplet temperature increase, the gap defects are reduced or even disappeared, indicating the improvement of the interface bonding state between aluminum droplets. Thus, it can be deduced that the mechanical properties could be enhanced (σ b = 373 MPa). As displayed in Fig. 8.28, the room temperature tensile properties of aluminum parts deposited under the above three thermal parameter conditions (Set 1, Set 2, and Set 3) were compared with those of extruded rod blanks of 7075 aluminum alloy and as-cast properties of the same grade material [6]. Among the three-parameter combinations, the performance of printed aluminum parts under Set 1 is the worst,

Fig. 8.25 Aluminum tensile specimen deposited under Set 1 (T d = 1123 K, T s = 423 K). a Whole image. b Side view of gauge section

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Fig. 8.26 Aluminum tensile specimen deposited under Set 2 (T d = 1373 K, T s = 573 K). a Whole image. b Side view of gauge section

Fig. 8.27 Aluminum tensile specimen deposited under Set 3 (T d = 1423 K, T s = 623 K). a Whole image. b Side view of gauge section

which is lower than that of as-cast samples. The tensile strength (373 MPa) and elongation (9.95%) of aluminum samples fabricated under the Set 2 condition are the highest, close to the mechanical properties of extruded bars. When the thermal parameters are further increased (under Set 3), the tensile properties of samples are significantly reduced, implying that the droplet fusion under overheating conditions would deteriorate the mechanical properties of parts. As depicted in Fig. 8.29a, the macroscopic fracture image of a tensile specimen of 7075 aluminum alloy rod blank shows an undulating fracture surface. A large number of small dimples with prominent dimple edges are uniformly distributed in local areas (Fig. 8.29b). This indicates that the fracture failure of the sample belongs to the typical ductile fracture with a relatively high elongation of up to 11.2%. Figure 8.30 shows the fracture surface morphology of a tensile specimen under Set 1 condition. A large number of directional tearing ridges and non-directional dimples are observed on most areas of the fracture surface, which is consistent with the internal microstructure morphology and distribution characteristics of deposited droplets. Besides, there are small second-phase particles with the size of about 1 ~ 2 μm in surface dimples of the sample (Fig. 8.31), which might be the T(AlZnMgCu) phase dispersed in the deposited solidification microstructure. It is shown that when the droplet temperature and deposition surface temperature are not enough

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Fig. 8.28 Mechanical properties of aluminum specimens under different process parameters

Fig. 8.29 Fracture surface morphology of 7075 aluminum alloy rod blank. a Overall morphology. b Partially enlarged view

to ensure excellent metallurgical bonding, the fracture surface exhibits distinct pullout curves and pores. It suggests that droplet bonding is mainly mechanical bonding between rough surfaces. In this case, the tensile performance mainly depends on the morphology, size, and distribution of defects such as pores and cold laps at the contact interface, rather than the solidification microstructure inside deposited droplets. In other words, when internal holes appear due to unfavorable droplet bonding, the overall tensile properties of as-deposited aluminum components are relatively poor, even lower than those of casting aluminum alloys with dense interiors. It is concluded that the failure behavior at Set 1 is the mixed mode of interface pull-out and transgranular ductile fracture. The fracture surface morphology of a 7075 aluminum alloy tensile specimen under Set 2 condition is shown in Fig. 8.32a. Defects as displayed in Fig. 8.30, such as pull-out curves and pores are seldom observed in the figure. From the local magnification image (Fig. 8.32b), it can be seen that the local remelting phenomenon of

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Fig. 8.30 Fracture surface morphology of 7075 aluminum alloy tensile specimen deposited under Set 1 (T d = 1123 K, T s = 423 K)

Fig. 8.31 Partial enlargements of fracture surface morphology of 7075 aluminum alloy tensile specimen deposited under Set 1 (T d = 1123 K, T s = 423 K). a Dimples and tearing ridges. b Second-phase particles in dimples

the bonding zone between two adjacent droplets becomes prominent. It suggests that the interface bonding condition between adjacent droplets is improved by the rise of thermal parameters, transforming from mechanical bonding to stronger metallurgical bonding. Moreover, micro-dimples dominate most of the fracture surface of the tensile specimen, which is caused by the decrease of directional columnar crystals and the increase of non-directional equiaxed crystals in deposited droplets under this thermal parameter. The failure mechanism turns from the mixed mode of interface pull-out and transgranular ductile fracture to the single type of transgranular ductile fracture. Figure 8.33a shows the fracture surface morphology of an aluminum sample printed under Set 3 condition. It can be seen that the fracture surface is flat, where individual droplet profiles and solidification microstructures are difficult to distinguish. This indicates that the as-deposited component cools down in the form of shared

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Fig. 8.32 Fracture surface morphology of 7075 aluminum alloy tensile specimen deposited under Set 2 (T d = 1373 K, T s = 573 K). a Overall morphology. b Bonding area between droplets

molten pools rather than separate droplets. The fracture surface shown in Fig. 8.33b belongs to a typical intergranular brittle fracture. This is attributed to that excessive thermal parameters coarsen solidification microstructures of the printed aluminum part, gathering second phase particles at grain boundaries. Thus, the sample under tensile stress breaks along the weakened grain boundaries. Plenty of dimples can also be observed on the side of the fracture bulk structure as demonstrated in Fig. 8.33c. The results show that the failure behavior of printed aluminum parts under Set 3 turns gradually from transgranular ductile fracture (Set 2) to the mixed mode of transgranular ductile fracture and intergranular brittle fracture. Fig. 8.33 Fracture surface morphology of 7075 aluminum alloy tensile specimen deposited under Set 3 (T d = 1423 K, T s = 623 K). a Overall morphology. b Partially enlarged view. c Intergranular dimples

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8.4 Internal Defects and Their Influencing Factors of As-Deposited Aluminum Components According to the above research, inappropriate process parameters can easily generate hole defects in the parts, which would seriously affect their mechanical properties. Common internal defects of printed aluminum parts include holes and internal cracks. This section will discuss the causes and suppression methods of these defects.

8.4.1 Hole Defects Inside Printed Aluminum Parts Based on different formation mechanisms, hole defects can be divided into interstitial pores, gap pores, solidification shrinkage pores, etc., which are discussed separately below. 1. Interstitial pores During uniform metal droplet deposition, if deposited droplets cannot spread out effectively in the bonding zone between droplets in the same layer or between the upper and lower layers, pores not filled with high-temperature melt appear between the contact interfaces, called interstitial pores (Fig. 8.34). Such defects are a common form of defects inside printed parts. They feature irregular shapes, mostly with sharp corners and rough inner walls. The density and mechanical properties of printed parts would be significantly reduced under the condition of a large number of interstitial pores. Therefore, it is necessary to improve the filling capacity of aluminum melts to enhance the mechanical properties of printed parts, which means interstitial pores in printed parts must be eliminated or suppressed as much as possible. When an aluminum droplet is deposited, the higher temperature causes lower viscosity and better fluidity, leading to the deposited droplet with a longer time in the Fig. 8.34 Interstitial pore in an as-deposited aluminum bulk

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Fig. 8.35 Internal morphology of printed aluminum bulks under different droplet temperatures. a 1173 K. b 1223 K

liquid state and better filling ability and spreading degree. The internal morphology of printed parts at different droplet temperatures is exhibited in Fig. 8.35. Under the droplet temperature of 1173 K, several pores can be observed in the printed bulk, showing a low degree of densification. When the droplet temperature is increased to 1223 K, the hole defects are eliminated. Since too low droplet temperature is prone to generate interstitial pores, appropriately increasing the parameter can effectively avoid such defects. The deposition surface temperature greatly determines the cooling rate after the collision of high-temperature droplets and the equilibrium temperature after complete solidification [7]. This parameter affects not only the spreading and solidification process of the first layer of deposited droplets but also the internal heat conduction efficiency of printed parts and the surface contour of deposited droplets. Besides, it has a significant impact on the formation of internal hole defects. The surface of uniform droplet deposition can be divided into two types, namely the pristine substrate and the solidified droplet surface of the last layer. If the initial deposition surface temperature (i.e., substrate temperature) is low, the deposited hightemperature molten droplet would soon reach the solidification temperature and stop spreading. As a result, the high-temperature melt is unable to fully spread and fill solidified droplet gaps, producing more interstitial pores remaining inside the printed part (Fig. 8.36a). If the substrate is properly preheated, droplets have sufficient time for spreading, flow, and filling, which can effectively inhibit the formation of interstitial pores, thereby significantly improving the density of the printed part (Fig. 8.36b). However, the substrate preheating temperature should not be too high. Otherwise, the intensified heat accumulation effect between layers would continuously increase the droplet surface temperature during the printing process, resulting in the collapse phenomenon when the temperature is higher than the liquidus temperature of the aluminum alloy. The overlap ratio refers to the degree of overlap between adjacent droplets or lines, which is one of the foremost parameters to suppress or eliminate the interstitial pores of printed parts. When the thermophysical properties of droplets are constant,

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Fig. 8.36 Internal morphology of printed aluminum bulks at different substrate temperatures. a Without preheating. b Preheating at 573 K

the overlap ratio is mainly determined by the spacing between deposited droplets or lines. Printing results under different overlap ratios of lines are shown in Fig. 8.37. When the line spacing is 1.6 mm, the overlap ratio is ~ 20%, forming numerous interstitial pores inside the printed sample. For the line spacing of 1.4 mm and the overlap ratio of ~ 30%, the degree of densification of the printed part is significantly improved. 2. Gas pores When aluminum or aluminum alloys transform from liquid to solid, the dissolved hydrogen could precipitate due to the decreased solubility, thus forming hole defects called gas pores [8]. Most of these pores are regular spheres or ellipsoids with smooth inner surfaces. During the process of uniform droplet deposition, the fast solidification rate of droplets sharply reduces the solubility of hydrogen, resulting in a large amount of hydrogen precipitation. If the precipitated hydrogen cannot escape in time, it would gather into bubbles and remain in the solidification structure to form

Fig. 8.37 Internal morphology of printed aluminum bulks under different line spacings. a 1.6 mm. b 1.4 mm

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Fig. 8.38 Gas pores in an as-deposited aluminum tensile specimen

spherical gas pores. As demonstrated by the printed aluminum tensile specimen in Fig. 8.38, regular gas pores remain at the clamping end and gauge section, which could seriously affect the mechanical properties of the sample. The potential hydrogen sources in the uniform droplet deposition process include oxide film, surface impurities (oil, dirt, rust, etc.), and impurities in the protective gas. Aluminum or aluminum alloys are prone to oxidization. The surface loose oxide film is easy to absorb moisture and water, converting into an aqueous oxide film (Al2 O3 ·H2 O) or hydrated oxide film (Al2 O3 ·3H2 O), which could decompose and emit hydrogen under high-temperature conditions. Meanwhile, the residual oil, moisture, and other impurities on the surface of original blanks would also precipitate a mass of hydrogen in the high-temperature environment. In addition, although the purity of high-purity argon for environmental protection is 99.9 ~ 99.999%, a small number of impurities such as nitrogen and water vapor remain. All of the above potential hydrogen sources may be the causes of gas pore defects. In summary, the key to inhibiting or eliminating gas pores in the drop-on-demand uniform droplet printing test is to control the potential hydrogen source and reduce the hydrogen content in the aluminum alloy melt. The generation of gas pores in printed parts can be effectively controlled by the pretreatment process of aluminum billets (removing oxide skin and cleaning), ensuring the dryness of the low-oxygen environment, and selecting high-quality inert protective gas. 3. Solidification shrinkage pores As demonstrated by the results of aluminum droplet deposition, in addition to interstitial pores and gas pores, solidification shrinkage pores caused by solidification and shrinkage may also be generated in the deposited aluminum components. In the traditional casting process, due to the liquid shrinkage and solidification shrinkage of alloys, holes often appear in the final solidification part of the casting. Large and concentrated holes are called shrinkage cavities, while small and scattered holes are named shrinkage porosities. During the deposition of a single droplet, shrinkage cavities or shallow pits may be produced near the surface of the solidified droplet caused by solidification shrinkage. Such pores can be eliminated by remelting with subsequently deposited droplets by the reasonable deposition process. However, as depicted in Fig. 8.39, relatively concentrated numerous small shrinkage porosities

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Fig. 8.39 Solidification shrinkage pores in an as-deposited aluminum bulk

can be observed inside deposited components of 7075 aluminum alloy and other aluminum alloys. The effect of such shrinkage porosity on the mechanical properties of printed parts is still unclear and needs further study. In conclusion, hole defects inside printed aluminum parts mainly include interstitial pores, gap pores, and solidification shrinkage pores. Among them, interstitial pores which are relatively more common, have the most significant impact on the performance of parts. Process parameters, such as the droplet temperature, substrate preheating temperature, and overlap ratio, need to be adjusted to suppress or eliminate interstitial pores.

8.4.2 Internal Cracks of Printed Aluminum Parts In addition to hole defects, cracks inside parts are also common internal defects in the forming process. Such defects would reduce the effective bearing area of parts, leading to stress concentration and performance degradation. Common crack defects mainly involve bonding line cracks and thermal cracks. 1. Bonding line cracks The bonding line crack is a split defect connecting the interstitial pore and the interface between droplets, which has two main causes as follows. (1) Cold laps. When two connected droplets are bonded to each other by mechanical bonding rather than local remelting, a close-fitting cold lap without remelting appears as illustrated in Fig. 8.40. The cold lap is essentially different from the continuous grain boundary in the intergranular metallurgical bonding area, which can be observed without chemical corrosion. Due to the relatively low mechanical bonding strength, when two adjacent droplets are subjected to solidification shrinkage or external stress, they are easy to separate along the cold lap surface between them to form macroscopic cracks, which could rapidly expand

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and break under external force. The tensile fracture surface shown in Fig. 8.41 reveals the rippled morphology of the free solidified surface of two unfused droplets. The fracture failure is mainly caused by the peeling along the cold lap surface. (2) Metallurgical bonding zone cracks. The metallurgical bonding can be formed only when local remelting occurs between two connected droplets. Metallurgical bonding is achieved through the mutual diffusion of homogeneous materials. Insufficient diffusion affects the bonding strength of the interface and even forms crack defects. As exhibited in Fig. 8.42a, the cold lap in the bonding region between two droplets is short, indicating favorable remelting and metallurgical bonding between droplets. From the partially enlarged view (Fig. 8.42b), the bonding zone shows micro-cracks, which are usually the source of interface cracking under stress. Both the cold laps and metallurgical bonding zone cracks eventually appear as bonding line cracks extending along the interface, which are difficult to distinguish. Nevertheless, two sides of the metallurgical bonding Fig. 8.40 Cold laps between two connected droplets in a printed aluminum part

Fig. 8.41 Fracture surface morphology of an as-deposited aluminum tensile specimen cracked along the cold lap

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zone crack are often accompanied by the grain morphology that should have been connected (shown by arrows in Fig. 8.43), indicating the formation and subsequent cracking of metallurgical bonding in the grain. In the experiment, it is found that the formation and propagation of the two kinds of crack defects are related to multiple factors such as the thermal stress effect, interface bonding state between droplets, and microstructure morphology. (1) The effect of thermal stress on cracks. The uniform droplet deposition manufacturing process is a typical input process with moving point heat sources. On the one hand, the solidification shrinkage of metal droplets is constrained by the initial low-temperature substrate (or solidified droplet layers), generating internal stresses. On the other hand, due to the periodic deposition of metal droplets, the printed part would be continuously subjected to alternating thermal loads to induce internal stresses. The combination of the above two factors can cause thermal stress concentration at the defects (interstitial pores, gap pores,

Fig. 8.42 Morphology of the interface bonding zone between two connected droplets in a printed aluminum part. a Interface bonding zone. b Partially enlarged view

Fig. 8.43 Metallurgical bonding interface cracking in a printed aluminum part

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Fig. 8.44 Microstructures inside printed aluminum parts under different remelting conditions. a Poor remelting. b Good remelting

solidification shrinkage pores, etc.) inside the deposited components, leading to the generation or expansion of crack defects. Proper preheating of the substrate can effectively reduce the internal temperature gradient of parts and relieve or eliminate their internal thermal stress [9]. (2) The influence of interface bonding state between droplets on cracks. In the uniform droplet deposition manufacturing process, the remelting state of droplets mainly depends on the droplet deposition temperature and substrate preheating temperature. When the two parameters are not properly selected, the remelting depth on the droplet surface is small, forming mechanical bonding between droplets. At this time, there will be obvious cold laps in the droplet bonding zone as illustrated in Fig. 8.44a. Such undesirable bonding defects may expand into bonding line cracks under solidification shrinkage or thermal stress. As revealed in Fig. 8.44b, the bonding line cracks can be eliminated by adjusting the ejection temperature and substrate preheating temperature, which can fundamentally avoid the crack defects caused by the bonding line cracking. (3) The influence of grain growth direction on cracks. Since directional columnar dendrites dominate the microstructure of each droplet in the deposited aluminum components, different grain growth directions between droplets can also cause cracks [10]. Figure 8.45 displays a bonding line crack in the bonding zone of three droplets, where the crack grows along the interface between droplets A and B. However, when the crack extends into the cross-contact area of three droplets, it is forced to turn to the bonding interface between two droplets of B and C rather than the original direction caused by the interlaced local microstructure morphology. Due to the mismatch between the extension direction of the turning crack and the initial stress direction, the bonding interface cracking is slowed down in the changed direction and finally completely suppressed. At this time, the crack may deflect again and propagate to the interior of the solidified droplet along the growth direction of columnar crystals. In other words, strongly directional continuous grain boundaries of columnar crystals provide

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Fig. 8.45 Redirection of a crack inside a printed aluminum part

a convenient path for crack propagation. It can be seen that breaking the directionality of columnar crystals, destroying the continuity of directional grain boundaries, and reducing the crack extension path are the main measures to suppress the propagation of bonding line cracks. Turning dendrites at the top of deposited droplets and staggered stacked microstructures of multiple droplets in the printed part play a certain role in improving the crack resistance of printed aluminum parts. 2. Thermal cracks A thermal crack is a kind of defect produced in the solidification and crystallization of high-temperature metal, which mostly occurs in the high-temperature range close to the solidus temperature. Hot cracks are common but difficult defects to eliminate, which exist in almost all industrial deformed aluminum alloys except Al–Si alloys. This is due to the inherent properties of such alloys, such as a wide solidification temperature range, a large solid–liquid density difference, and a relatively high thermal expansion coefficient. Compared with bonding line cracks, the causes and influencing factors of hot cracks are more complicated. Besides the thermal stress effect, interface bonding state between droplets, and microstructure morphology, the formation and propagation of thermal cracks can be affected by the solidus–liquidus temperature interval width of alloys, content and segregation of impurity elements (sulfur, phosphorus, silicon, etc.), and phase composition. Prevention measures for hot cracks usually need to be determined according to the specific situation. As shown in Fig. 8.46, thermal cracks are also common in as-deposited aluminum components. Compared to bonding line cracks, thermal cracks are relatively minor and irregular, usually extending along dendrite boundaries and sometimes branching. The formation of hot cracks is closely related to the quasi-solid mechanical properties, microstructure, grain boundary state, and solidification process of aluminum alloys. During the solidification and crystallization process, the “liquid film” formed by the alloying element segregation or aggregation of low-melting eutectic structures

References

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Fig. 8.46 Thermal cracks inside a printed aluminum part. a Overall morphology. b Partially enlarged view (after corrosion)

covers the grain surface, weakening the grain boundary strength to form vulnerable zones inside the material. When the molten metal solidifies and crystallizes, tensile stresses can be generated due to volume shrinkage. Once they exceed the material strength, or the shrinkage rate surpasses the elongation rate, thermal cracks can be created along the above weak areas. In summary, common crack defects in printed aluminum parts mainly comprise bonding line cracks and thermal cracks, both of which are affected by factors such as thermal stress, remelting temperature, and the solidification shrinkage rate of molten metal. Compared with minor thermal cracks, bonding line cracks have a greater impact on the overall mechanical properties of as-deposited components. Therefore, more attention should be paid to suppressing and eliminating such defects in the process of metal droplet deposition manufacturing.

References 1. Fukumoto M, Nishioka E, Matsubara T. Effect of interface wetting on flattening of freely fallen metal droplet onto flat substrate surface. J Therm Spray Technol. 2002;11(1):69–74. 2. Bennett T, Poulikakos D. Heat transfer aspects of splat-quench solidification: modelling and experiment. J Mater Sci. 1994;29(8):2025–39. 3. Fukuda H. Droplet-based processing of magnesium alloys for the production of highperformance bulk materials. 2009. 4. Xu Q, Lavernia EJ. Microstructural evolution during the initial stages of spray atomization and deposition. Scripta Mater. 1999;41(5):535–40. 5. Chalmers B. Principles of solidification. 1964. p. 117. 6. Tajally M, Huda Z, Masjuki HH. A comparative analysis of tensile and impact-toughness behavior of cold-worked and annealed 7075 aluminum alloy. Int J Impact Eng. 2010;37(4):425– 32. 7. Xu Q, Gupta VV, Lavernia EJ. Thermal behavior during droplet-based deposition. Acta Mater. 2000;48(4):835–49. 8. Liu JA, Xie SS. Aluminum processing defects and countermeasures. Chemical Industry Press; 2012.

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9. Zhu BL, Hu ML, Cheng L, Xie CS. Research status of cracking in laser cladding layer. Heat Treatment of Metal. 2000;7:1–4. 10. Huang WD, Lin X, Chen J, et al. Laser stereoforming: fast free forming of high performance dense metal parts. Northwestern Polytechnical University Press; 2007.

Chapter 9

Application Prospect of Uniform Metal Droplet-Based 3D Printing

9.1 Introduction Compared with other additive manufacturing technologies, uniform metal droplet ejection technology, which is still in development, has not yet been developed into a mature technical system. However, this technology is playing an increasingly significant role in additive manufacturing due to its unique technical advantages. This chapter discusses the application prospect of this technology based on the existing research of our group at Northwestern Polytechnical University and the latest research progress in China and other countries.

9.2 Preparation of Mono-Sized Spherical Metal Particles With the rapid development of technologies such as metal additive manufacturing, powder metallurgy, advanced microelectronics, mono-sized spherical particles with the diameter ranging from microns to sub-millimeters are required to improve the dimensional accuracy, internal quality, and servicing performances of fabricated parts. Uniform droplet ejection technology (i.e., Continuous uniform droplet ejection technology or Drop-on-Demand ejection (DOD) technology) can efficiently prepare mono-sized spherical metal particles. The continuous uniform droplet ejection technology relies on the principle of the Rayleigh-Plateau instability to perturb laminar capillary jets with a certain frequency and then break jets into uniform droplet streams. Mono-sized spherical particles can be produced by charging such uniform droplet streams. By applying a series of equivalent pressure pulses into the molten metal, the DOD technology forces melts to eject from a small orifice, generating mono-sized spherical metal particles. By using the uniform droplet ejection method, produced particles have a uniform size and a highly consistent internal microstructure since such particles are ejected © National Defense Industry Press 2023 L. Qi et al., Metal Micro-Droplet Based 3D Printing Technology, https://doi.org/10.1007/978-981-99-0965-0_9

305

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with the same parameters and experience the same temperature history. The particles have high sphericity since the molten droplets would shrink into a spheric shape driven by their surface tension. However, because small droplets are ejected through a small orifice, the droplet ejection process is easily influenced by impurities inside the crucible, oxidation of molten metal liquid, and other factors, resulting in droplet ejection instability. Therefore, strict requirements are needed for successful droplet ejection. By ejecting tin–lead solder or lead-free solder droplets using piezoelectric pulses, uniform tin solder balls (Fig. 9.1a) [1], and Ball Grid Array (BGA) [2, 3] can be prepared (Fig. 9.1b). Those highly uniform tin solder balls and BGA can be used as high-density electronic packaging or rapid soldering. Spherical lightweight metal particles (Fig. 9.1c) with uniform sizes, such as mono-sized aluminum or spherical magnesium particles, can be prepared to be used as powder materials for laser beam or electron beam additive manufacturing. Highly uniform metal droplet size can improve the dimensional accuracy and the uniformity of micro-structures of forming parts. Mono-sized spherical copper particles (Fig. 9.1d), produced by the Pulsated Orifice Ejection Method, can be used to fabricate photonic bandgap microstructures [4, 5] for modulation of Terahertz waves. The produced amorphous Fe-based metal glass [(Fe0.5 Co0.5 )0.75 B0.2 Si0.05 ]96 Nb4 spherical particles (Fig. 9.1e) are promising powder materials for powder metallurgy, which fabricates micro parts with excellent mechanical properties [6]. Spherical semiconductor particles (Fig. 9.1f), generated by Pulsated Orifice Ejection Method, can be utilized to fabricate spherical semiconductor integrated circuits with increases the integration degree or miniature spherical solar cells with an extended effective area of photoelectric conversion [7].

9.3 Printing and Packaging of Microcircuits With the increasing need for customization, stereoscopic design, high density, and rapid manufacturing, printing and packaging technologies are required to fabricate personalized microcircuits. Micro circuits or electronic components can be fabricated by continuously ejecting and printing micro metal droplets on the plastic substrates (Fig. 9.2a). Meanwhile, pins of microchips can be rapidly soldered to the micro circuits by spreading solder droplets. Therefore, uniform metal droplet-based manufacturing technology is an effective way to prepare customized micro circuits or packaging. The advantage of the proposed technology is that microcircuits with good electric conductivity can be rapidly obtained benefiting by the metallurgical bond of metal droplets. Furthermore, 3D microcircuits can be directly formed with dropwise deposition of uniform metal droplets. However, since metal droplets, such as copper, gold, and silver droplets, have a large surface tension, it is hard for them to wet common insulating electronic substrates like plastic, FR, and ceramics substrate to achieve good bonding. Insulating substrates, which can stably deposit metal droplets, should be investigated to print microcircuits by metal droplets.

9.3 Printing and Packaging of Microcircuits

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Fig. 9.1 Mono-sized spherical metal particles prepared by uniform micro-droplet ejection. a Uniform PbSn solder particles [1]. b Uniform solder bump array [2, 3]. c Uniform aluminum particles. d Uniform copper particles [4, 5]. e Uniform Fe-based metal glass ([(Fe0.5 Co0.5 )0.75 B0.2 Si0.05 ]96 Nb4 ) particles [6]. f Uniform germanium particles [7]

Fig. 9.2 Microcircuits printed by using mono-sized micro metal droplets. a Schematic diagram of printing process. b Microcircuits printed on polymer substrates (acrylic glass) and conductive test of printed circuits (the lighted LED on the right side)

Stereoscopic microcircuits can be fabricated by the combination of uniform droplet ejection technology with traditional 3D printing technology (Fig. 9.2b). Microelectronic components such as inductance coils and 3D antennas can be formed. Meanwhile, the stereo pins of micro MEMS chips, LED, or thermal-sensitive

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electronic components can be rapidly connected by precisely depositing solder droplets.

9.4 Micron Scaled Metal Parts Printing The requirements of 3D micron-scale metallic parts increase steadily due to the miniaturization and integration of mechanical systems. However, limited by the traditional micro manufacturing methods, fabrication methods for effectively preparing micron-scale metallic parts is still in development. Laser-induced forward transfer (LIFT) prints micron metallic parts by ejecting and printing micron-scale metal droplets. The principle is shown in Fig. 9.3. By focusing ultrashort laser pulses (nanosecond, picosecond, or femtosecond laser pulses) on donors (i.e., glass plates coating with nano-thickness metal films), micron-scale or nanometer-scale metal droplets can be ejected after locally melting metal films on donors. Small metal parts with a micron size can be printed by controlling the deposition of those metal droplets. The advantage of this technology is that the focused ultrashort pulse laser can eject metal droplets with a diameter of microns or nanometers, which print complex metal parts in small sizes and high resolution. This technology can easily form structures with large aspect ratios because of no contact force during the printing process. However, due to the small size of the ejected metal droplets, the deposition efficiency needs to be improved. Additionally, metals used in the existing LIFT technologies are mostly pure metal films. The limited choices of forming metals need to be further expanded. By ejecting gold droplets of a diameter around 1 ~ 3 µm with nanosecond laser pulses, pure gold pillars with a diameter of 5 µm and a height of 860 µm (Fig. 9.4a and b) [8] can be printed. The maximum high-aspect ratio is up to 300. Such parts can be used in areas such as Through Silicon Vias (TSVs) and electronic connections in micro sensors. For an instant, a free-standing thermocouple with a height of only 200 µm was printed by coordinating deposition of gold and platinum droplets Fig. 9.3 Schematic diagram of laser-induced forward transfer

9.5 Micro Thin-Wall Parts Printing

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Fig. 9.4 Small parts printed by using LIFT technology. a Pure gold micro pillars with the diameter of 5 µm [8]. b Enlarged view of the gold pillar. c Free-standing small thermocouple printed by deposition of micro gold and platinum droplets [9]

(Fig. 9.4c) [9]. Such a sensor can be used to detect the temperature in micro flow fields.

9.5 Micro Thin-Wall Parts Printing Micro thin-wall metal parts with a high strength-weight ratio have essential applications in lightweight mechanical systems. However, limited by the small size and low stiffness characteristics of micro thin-wall metal parts, the size accuracy, shape accuracy, and shape complexity of printed thin-wall parts need to be further improved. Uniform metal droplet ejection technology can print micro thin-wall structures with a wall thickness close to the maximum spreading diameter of droplets (Fig. 9.5a). Various thin-wall parts can be rapidly printed by controlling the printing trajectory (Fig. 9.5b, c). The advantage of this technology is that high aspect-ratio, complex shape thinwall parts can be formed since the contact force is absent during the printing process. However, since the droplet deposition direction is vertically downwards, structures with large inclined angles easily collapse during printing. Methods of auxiliary supports and multi-degree deposition are required to increase the complexity of the printed parts. Micro thin-wall metal parts have extensive requirements in fields such as microelectronics, precision optical systems, aviation, and aerospace. Lightweight truss structures, printed by microdroplets of aluminum and magnesium, can be used as reflective mirror frames to achieve rapid movement and precise positioning. Highaspect ratio micro-pin–fin array and dense metal fin array, printed by microdroplets of copper and aluminum, can work as highly effective heat sinks. Those heat sinks

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Fig. 9.5 Thin-walled parts printed by uniform metal droplets. a schematic diagram of the printing process; b the waveguide horn printed by uniform metal droplets; c, d Complex thin-wall parts printed by uniform metal droplets

can improve the heat dissipation efficiency for high-density energy sources such as satellite-borne and air-borne radars, concentrating solar energy cells. Micro thin wall parts like horn antennas and waveguides, printed by micro aluminum droplets, can reduce the weight of satellite radar antennas.

9.6 3D Printing for Functional Parts In advanced mechanical systems (e.g., medical endoscope systems, industrial robots, and deep space detectors), mechanical parts tend to integrate the mechanical performance with special functions like thermal management, electromagnetic shielding, and electric connection. In this way, parts can have abilities of external perception, action, and auto adaptation besides the temperature and load bearing capacity. Uniform metal droplet ejection technology can directly embed heterogeneous functional units such as sensors, actuators, photoelectric channels, and fluid microchannels into parts to rapidly fabricate multifunctional parts according to requirements (Fig. 9.6a).

Fig. 9.6 Printing principle and schematic diagram of functional parts. a Schematic diagram of the embedding process of functional units. b Connecting rods embedded with wires. c Direct-printed non-assembled hinge structures

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The advantage of this technology is that the parts’ functions can be tailored according to the requirement. In this way, the parts’ performance can be significantly improved. However, because of the high temperature of deposited droplets, problems like pores, defects, and fragile interfaces can be formed between the functional units and the base material. Those problems are still under investigation. Figure 9.6b shows an example of a printed functional part. In the printing process of this functional part, flexibly conductive wires are embedded inside to achieve the integration of mechanical properties and electrical signal transmission performance. The overall efficiency of printing functional parts has been improved. Figure 9.6c shows a non-assembled hinge structure printed by metal droplet printing. In the printing process, the hinge pair is formed by changing the tilted angle of fit between the hinge and the hinge mount. This process does not need to prepare supporting structures. It is a novel method for rapidly forming of miniaturized and lightweight connectors.

References 1. Ando T, Chun J, Blue C. Uniform droplets benefit advanced particulates. Met Powder Rep. 1999;54(3):30–4. 2. Liu Q, Leu M C, Orme M. High precision solder droplet printing technology: principle and applications. IEEE; 2001. pp. 104–109. 3. Xiong W, Qi L, Luo J, et al. Experimental investigation on the height deviation of bumps printed by solder jet technology. J Mater Process Technol. 2017;243:291–8. 4. Takagi K, Masuda S, Suzuki H, et al. Preparation of monosized copper micro particles by pulsated orifice ejection method. Mater Trans. 2006;47(5):1380–5. 5. Zhong SY, Qi LH, Luo J, et al. Effect of process parameters on copper droplet ejecting by pneumatic drop-on-demand technology. J Mater Process Technol. 2014;214(12):3089–97. 6. Miura A, Dong W, Fukue M, et al. Preparation of Fe-based monodisperse spherical particles with fully glassy phase. J Alloy Compd. 2011;18(509):5581–6. 7. Masuda S, Takagi K, Dong W, et al. Solidification behavior of falling germanium droplets produced by pulsated orifice ejection method. J Cryst Growth. 2008;11(310):2915–22. 8. Visser CW, Pohl R, Sun C, et al. Toward 3D printing of pure metals by laser-induced forward transfer. Adv Mater. 2015;27(27):4087–92. 9. Luo J, Pohl R, Qi L, et al. Printing functional 3D microdevices by laser-induced forward transfer. Small. 2017;13(9):1–5.