Metal and Bone Drilling - The Thermal Aspects [1st ed. 2019] 978-3-030-26046-0, 978-3-030-26047-7

Table of contents :
Front Matter ....Pages i-xiv
Introduction (Albert J. Shih, Bruce L. Tai, Rui Li)....Pages 1-19
Experimental Analysis of Titanium Drilling (Albert J. Shih, Bruce L. Tai, Rui Li)....Pages 21-50
Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys (Albert J. Shih, Bruce L. Tai, Rui Li)....Pages 51-75
Experimental Analysis of Cast Iron Drilling with Dry and MQL Conditions (Albert J. Shih, Bruce L. Tai, Rui Li)....Pages 77-93
Modeling of Workpiece Temperature and Thermal Expansion in Dry and MQL Drilling (Albert J. Shih, Bruce L. Tai, Rui Li)....Pages 95-115
Thermal Analysis of Bone Drilling in Orthopaedic Surgery (Albert J. Shih, Bruce L. Tai, Rui Li)....Pages 117-131
Model-Based Approach for Predicting Thermal Damage in Bone Drilling (Albert J. Shih, Bruce L. Tai, Rui Li)....Pages 133-147
Advancement of Surgical Bone Drills: A Case Study of Notched K-Wires (Albert J. Shih, Bruce L. Tai, Rui Li)....Pages 149-162
Back Matter ....Pages 163-165

Citation preview

Albert J. Shih · Bruce L. Tai · Rui Li

Metal and Bone Drilling - The Thermal Aspects

Metal and Bone Drilling - The Thermal Aspects

Albert J. Shih • Bruce L. Tai • Rui Li

Metal and Bone Drilling The Thermal Aspects

Albert J. Shih Mechanical Engineering University of Michigan Ann Arbor, MI, USA

Bruce L. Tai Mechanical Engineering Texas A&M University College Station, TX, USA

Rui Li China Aerospace Science and Technology Corporation Beijing, China

ISBN 978-3-030-26046-0    ISBN 978-3-030-26047-7 (eBook) https://doi.org/10.1007/978-3-030-26047-7 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

For my lovely wife, Huishan, and children, Arthur, Brenda, Christopher, and Deanna. –Albert Shih For my lovely wife, Ploy, and son, Dylan. –Bruce Tai For my lovely wife, Xue Zhou, and children, Chuyu and Yuanbao. –Rui Li

Preface

This book summarizes advanced technologies on drilling and demonstrates the evolution of manufacturing from industry to healthcare. Drilling is an art and science. Manufacturing engineers and orthopaedic surgeons understand the importance and challenges of drilling, a seemingly routine process that is often overlooked by people who do not know manufacturing or orthopaedic surgery. Many engineers have dedicated their talent and career to advance the drill design, material, coating, manufacturing, and performance. Every advanced drill is a work of art. New technology is built on these advanced drills, which make high-performance drilling and drilling research possible. Broad applications of titanium alloys in the aerospace, transportation, sporting equipment, and other industries have driven the research in machining of titanium alloys. Drilling, particularly the high-throughput drilling, is important because it is one of the most widely utilized and technically challenging processes for machining of titanium alloys. The drill tip starts to glow due to high temperature after rapid drilling only a few holes in titanium alloys. Compared to measuring the thrust force and torque using a dynamometer, it is more difficult to measure the drill temperature and even more challenging to find the spatial and temporal temperature distributions of a drill during drilling. Chapters 2 and 3 present our pathway, which is built on the drilling research in the past century, to gain in-depth understanding of drill temperature. Another evolution in manufacturing is the emphasis on sustainability and the health and safety of workers in manufacturing plant. A group of dedicated and outstanding manufacturing and machine tool engineers worked together and demonstrated that the minimum quantity lubrication system was as productive as the traditional flood cooling with the central cooling system in a plant and could save the overall cost from the life cycle perspective. That was a milestone achievement. New technical challenges of rising workpiece temperature and the resulted thermal expansion during production with the minimum quantity lubrication give great research opportunities. This work will be presented in Chaps. 4 and 5. We are very fortunate to work with orthopaedic surgeons on the frontier biomedical manufacturing research in bone drilling. We have learned that knowledge vii

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in metal drilling can be applied to study bone drilling. There are many opportunities for innovations in bone drilling. This is a great task for manufacturing engineers and critically important for the future of biomedical manufacturing research to improve the quality and reduce the cost of healthcare. Our bone drilling research is presented in Chaps. 6 to 8. It takes a village to create and finalize a book. We are greatly indebted to the researchers and collaborators who have guided and helped this team in the past decade on drilling research. We started from the late Professor S.M. Wu who was a giant in drilling research since the 1960s at the University of Wisconsin at Madison. Many of his students, particularly Dr. David Stephenson and Professor Jun Ni, continued his legacy and went to great lengths for drilling research in industry and in the University of Michigan at Ann Arbor. Our work is built on their past achievements. In the automotive industry, Drs. Richard Furness and John Agapiou are professors’ professors in advanced drilling. We have learned a lot from them about drilling in high-volume production. Superior drills provided by Kennametal and technical knowledge and support from Dr. Qiang Wu and Parag Hedge made our metal drilling research possible. Outstanding orthopaedic surgeons, particularly Drs. James Holmes, Andrew Palmisano, and Todd Irwin, transformed and guided our bone drilling research. We greatly appreciate the graduate students and visiting scholars who have worked with us in drilling research, including Wenwu Wu, Ali Kazu, Yao Liu, Yiwen Wang, and Barry Belmont. The support from the US National Science Foundation (Program Directors: Drs. George Hazelrigg, Bruce Kramer, and ZJ Pei), US Department of Energy (Program Director: Dr. Raymond Johnson), Ford Motor Company (Dr. William Dowling), Department of Orthopaedic Surgery at the University of Michigan at Ann Arbor, and Springer Nature (Brinda Megasyamalan and Agnes Felema) were critical to make this research and book possible. Ann Arbor, MI, USA  Albert J. Shih College Station, TX, USA   Bruce L. Tai Beijing, China   Rui Li

Contents

1 Introduction����������������������������������������������������������������������������������������������    1 1.1 Work Materials Studied for Thermal Aspects in Drilling ����������������    2 1.1.1 Titanium Alloys��������������������������������������������������������������������    2 1.1.2 Cast Irons������������������������������������������������������������������������������    4 1.1.3 Bone��������������������������������������������������������������������������������������    5 1.2 Metal Drilling: Drill and Metal Working Fluid Delivery������������������    6 1.2.1 Drill Design and Nomenclature��������������������������������������������    6 1.2.2 Through-the-Drill Metal Working Fluid Delivery����������������    6 1.2.3 MQL in Production Drilling ������������������������������������������������    8 1.3 Bone Drilling������������������������������������������������������������������������������������   11 1.3.1 Bone Drill and Kirschner Wire ��������������������������������������������   11 1.3.2 Drill and Spindle for Orthopaedic Bone Drilling ����������������   12 1.4 Inverse Heat Transfer Method and Finite Element Modeling of Drill and Workpiece Temperatures in Drilling ����������������������������   13 1.4.1 Inverse Heat Transfer Modeling�������������������������������������������   13 1.4.2 Drill Temperature and Failure Prediction ����������������������������   14 1.4.3 Workpiece Temperature and Thermal Expansion ����������������   14 1.4.4 Bone Temperature in Drilling ����������������������������������������������   15 1.5 Overview of the Book ����������������������������������������������������������������������   15 References��������������������������������������������������������������������������������������������������   15 2 Experimental Analysis of Titanium Drilling�����������������������������������������   21 2.1 Drills and Drilling Parameters����������������������������������������������������������   21 2.2 Design of Experiments����������������������������������������������������������������������   23 2.3 Results of Low-Speed Drilling ��������������������������������������������������������   26 2.3.1 Effect of Cutting Speed and Coolant������������������������������������   26 2.3.2 Effect of Drill Type ��������������������������������������������������������������   28 2.4 Results of High-Speed Drilling��������������������������������������������������������   28 2.4.1 Effect of Cutting Fluid Supply����������������������������������������������   29 2.4.2 Effect of Feed and Cutting Speed ����������������������������������������   31 2.4.3 Drill Wear in High-Speed Drilling����������������������������������������   31 ix

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2.5 Chip Analysis������������������������������������������������������������������������������������   33 2.5.1 Chip Morphology������������������������������������������������������������������   34 2.5.2 Chip Microstructure��������������������������������������������������������������   34 2.5.3 Chip Hardness����������������������������������������������������������������������   38 2.6 Workpiece Drilled Surface and Subsurface Analysis�����������������������   38 2.6.1 Microstructure on the Workpiece Subsurface of Drilled Hole����������������������������������������������������������������������   40 2.6.2 X-ray Diffraction Analysis����������������������������������������������������   41 2.6.3 Chemical Composition Analysis������������������������������������������   44 2.6.4 Nanoindentation��������������������������������������������������������������������   45 2.6.5 Burr Formation����������������������������������������������������������������������   46 2.7 Concluding Remarks������������������������������������������������������������������������   48 References��������������������������������������������������������������������������������������������������   49 3 Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys������������������������������������������������������������������������������������   51 3.1 Overview of Drill Temperature Analysis Methods ��������������������������   51 3.1.1 Experimental Measurements������������������������������������������������   51 3.1.2 Analytical Modeling ������������������������������������������������������������   53 3.1.3 Inverse Heat Transfer Method����������������������������������������������   53 3.2 IHTM for Drill Temperature Distribution����������������������������������������   53 3.2.1 Step 1: Experimental Inputs��������������������������������������������������   54 3.2.2 Step 2: Drill 3D Geometry����������������������������������������������������   55 3.2.3 Step 3: ECT Identification����������������������������������������������������   55 3.2.4 Step 4: Drill FEM ����������������������������������������������������������������   56 3.2.5 Step 5: Oblique Cutting Mechanics in ECT ������������������������   58 3.2.6 Step 6: Heat Generation��������������������������������������������������������   60 3.2.7 Step 7: IHTM Solution ��������������������������������������������������������   61 3.2.8 Convective Heat Transfer Coefficient (for Wet Drilling)������������������������������������������������������������������   62 3.3 Drill Temperature������������������������������������������������������������������������������   63 3.3.1 Inverse Solutions������������������������������������������������������������������   63 3.3.2 Drill Temporal Temperature Distribution ����������������������������   66 3.3.3 Drill Spatial Temperature Distribution ��������������������������������   67 3.4 Drill Thermo-Mechanical Analysis��������������������������������������������������   67 3.4.1 Drill Deformation�����������������������������������������������������������������   69 3.4.2 Drill Stress and Failure Prediction����������������������������������������   70 3.5 Concluding Remarks������������������������������������������������������������������������   74 References��������������������������������������������������������������������������������������������������   74 4 Experimental Analysis of Cast Iron Drilling with Dry and MQL Conditions������������������������������������������������������������������������������������������������   77 4.1 Overview of Cast Iron Drilling ��������������������������������������������������������   77 4.2 Dry and MQL Drilling of CGI����������������������������������������������������������   78 4.2.1 Drilling Tool and Experiment ����������������������������������������������   78 4.2.2 Testing Methods��������������������������������������������������������������������   80

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4.2.3 Force, Torque, Drill Wear, and Chip Speed��������������������������   82 4.2.4 Summary ������������������������������������������������������������������������������   86 4.3 MQL Deep-Hole Drilling ����������������������������������������������������������������   86 4.3.1 Drilling Tool and Experiment ����������������������������������������������   87 4.3.2 Results of Force, Torque, and Temperature Rise������������������   88 4.3.3 Temperature Distribution and Hole Quality�������������������������   89 4.3.4 Summary ������������������������������������������������������������������������������   92 4.4 Concluding Remarks������������������������������������������������������������������������   92 References��������������������������������������������������������������������������������������������������   93 5 Modeling of Workpiece Temperature and Thermal Expansion in Dry and MQL Drilling������������������������������������������������������������������������   95 5.1 Deep-Hole Drilling Workpiece Thermal Model ������������������������������   96 5.2 Inverse Method 1: Linear Invariant System��������������������������������������   97 5.2.1 Concept ��������������������������������������������������������������������������������   97 5.2.2 A Case Study������������������������������������������������������������������������   99 5.3 Inverse Method 2: Control Point Method ����������������������������������������  103 5.3.1 Concept ��������������������������������������������������������������������������������  103 5.3.2 Case Study����������������������������������������������������������������������������  105 5.4 Workpiece Thermal Distortion����������������������������������������������������������  107 5.4.1 Model Concept and Model Construction������������������������������  107 5.4.2 Experimental Study��������������������������������������������������������������  110 5.5 Conclusions��������������������������������������������������������������������������������������  114 References��������������������������������������������������������������������������������������������������  115 6 Thermal Analysis of Bone Drilling in Orthopaedic Surgery ��������������  117 6.1 Clinical Challenges ��������������������������������������������������������������������������  117 6.2 Comparison of Bone Drills ��������������������������������������������������������������  118 6.2.1 Drilling Test bed and Sample Preparation����������������������������  118 6.2.2 Testing Parameters and Procedures��������������������������������������  119 6.2.3 Drilling Temperature Results������������������������������������������������  120 6.2.4 Discussion of the Results������������������������������������������������������  122 6.3 Heat Accumulation in Bone Drilling������������������������������������������������  123 6.3.1 Testing Setup and Procedures ����������������������������������������������  123 6.3.2 Data Analysis Method����������������������������������������������������������  125 6.3.3 Experiment Results ��������������������������������������������������������������  126 6.3.4 Histology Analysis����������������������������������������������������������������  128 6.3.5 Discussion of the Results������������������������������������������������������  129 6.4 Conclusions��������������������������������������������������������������������������������������  130 References��������������������������������������������������������������������������������������������������  131 7 Model-Based Approach for Predicting Thermal Damage in Bone Drilling������������������������������������������������������������������������������������������������������  133 7.1 Overview of Bone Drilling Thermal Models������������������������������������  133 7.2 Finite Element Thermal Model ��������������������������������������������������������  134 7.2.1 Advection Method����������������������������������������������������������������  134

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7.2.2 Implementation in Multi-Hole Drilling��������������������������������  136 7.2.3 Determination of Heat Source by IHTM������������������������������  137 7.3 Thermal Damage Model ������������������������������������������������������������������  140 7.3.1 A Modified Thermal Dose����������������������������������������������������  140 7.3.2 A Case Study: Multi-Hole Sequential Drilling��������������������  141 7.3.3 Discussion on Simulation Results����������������������������������������  145 7.4 Conclusions��������������������������������������������������������������������������������������  146 References��������������������������������������������������������������������������������������������������  147 8 Advancement of Surgical Bone Drills: A Case Study of Notched K-Wires ����������������������������������������������������������������������������������������������������  149 8.1 Modified K-Wires in the Literature��������������������������������������������������  149 8.2 Design and Manufacturing of Notched K-wires������������������������������  150 8.2.1 Notched K-wire Design��������������������������������������������������������  150 8.2.2 Manufacturing of Notched K-Wires ������������������������������������  153 8.3 Drilling Experiment��������������������������������������������������������������������������  154 8.4 Results and Discussion ��������������������������������������������������������������������  156 8.4.1 Time-Based Analysis and Comparison ��������������������������������  156 8.4.2 Cross-Comparison among Notched K-Wires ����������������������  159 8.5 Conclusions��������������������������������������������������������������������������������������  162 References��������������������������������������������������������������������������������������������������  162 Index������������������������������������������������������������������������������������������������������������������  163

About the Authors

Albert J. Shih  is Professor in Mechanical Engineering, Biomedical Engineering, and Institute of Gerontology at the University of Michigan. He received his PhD from Purdue University in 1991 and was an Advanced Manufacturing Process Engineer at Cummins (1991–1998) and an Associate Professor at NC State University Mechanical and Aerospace Engineering (1998–2002). He has been a Faculty at the University of Michigan since 2003. In 2017, he was the Assistant Director of Education and Workforce in the Advanced Manufacturing National Program Office (AMNPO) at Gaithersburg, Maryland. His research area is manufacturing. He is a Pioneer in biomedical manufacturing, the application of manufacturing technologies to advance the safety, quality, efficiency, and speed of healthcare service and biomedical science. He has 10 US patents and a textbook, Analysis of Machining and Machine Tools, and authored or coauthored over 210 archival journal papers and 120 conference papers in manufacturing and biomedical sciences. He is the Recipient of the Fulbright Scholar, SME Frederick W. Taylor Research Medal in Manufacturing Research, ASME Milton C. Shaw Manufacturing Research Medal, Blackall Machine Tool and Gage Award, Society of Automotive Engineers Ralph R. Teetor Educational Award, and Best Paper Awards in ASME Manufacturing Science and Engineering Conference (MSEC), North American Manufacturing Research Conference (NAMRC), and International Conference on Frontiers of Design and Manufacturing (ICFDM). He is the President of the North American Manufacturing Research Institute (NAMRI) of SME (2019–2020), Fellow of ASME, SME, and CIRP. Bruce L.  Tai  is an Assistant Professor and Mechanical Engineering Industry Advisory Council Faculty Fellow in J. Mike Walker ‘66 Department of Mechanical Engineering at Texas A&M University. He received his PhD in Mechanical Engineering from the University of Michigan at Ann Arbor in 2011 and his MS and BS from National Taiwan University in 2004 and 2006, respectively. He was a Research Faculty Member in the University of Michigan and held a joint appointment in the University of Michigan Health System (2012–2014). He had a long-­ term collaboration with the automotive industry on developing advanced machining xiii

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About the Authors

processes and with surgeons on innovative surgical tools and simulation models. His research interests generally encompass advanced machining processes, additive manufacturing processes, and surgical tools and simulation. His research has been supported by the National Science Foundation, US Department of Energy, and Orthopaedic Research and Education Foundation. He has published over 40 peer-­ reviewed journal papers and over 40 conference papers across the areas of machining, additive manufacturing, and biomedical engineering. He is the Recipient of the Best Paper Awards in ASME MSEC and ICFDM, SME Outstanding Young Manufacturing Engineer Award (2017), and ASME Blackall Machine Tool and Gage Award (2017). Rui Li  is a Professor at China Aerospace Science and Technology Corporation. He received his Bachelor’s degree in Mechanics from the University of Science and Technology of China and his master’s and PhD degrees in Mechanical Engineering from the University of Michigan at Ann Arbor. He has held a number of engineering and engineering management positions in Kavlico Corporation, Elekta, and China Aerospace Science and Technology Corporation (CASC). He has extensive engineering experience in mechatronic system design, machining process, mechanics, finite element simulation, thermal analysis, and materials science. He published over 30 articles and several patents in those areas. He received a number of awards, including Best Paper Award from NAMRI and Best Interactive Presentation Award from the International Astronautical Congress and recognized as a Young Space Leader by the International Astronautical Federation.

Chapter 1

Introduction

Drilling is a machining process to create a round hole in a workpiece using a drill. A drill is a rotating cylindrical tool with cutting edges on the working end. The drill feeds into the workpiece to generate a round hole. Such round hole is a common feature in product design to achieve various functional purposes, such as joining, access, and fluid passages. The size, shape, position, and surface integrity of the drilled holes are determined by the drill and drilling process parameters (particularly the rotational speed and feed rate), as well as the temperature, deformation, surface integrity, and thermal expansion of the drill and workpiece. Drilling is a fundamental machining process and widely used in the manufacturing industry. For example, in automotive powertrain and aircraft component manufacturing, drilling is utilized extensively and often among the final steps that have significant impacts on the quality and cost of the product. High material removal rate (MRR) and long drill life are essential to increase the productivity and reduce the manufacturing cost. To achieve the desired MRR in drilling, high drill cutting speeds (rotational speeds) and feeds per revolution (feed rate) are required. Advanced tool materials (with superior and balanced strength, toughness, and hardness at high temperature), multi-layer wear-resistance tool coatings, drill geometry (design of the chisel edge, cutting edge, flute, and margin of the drill), and manufacturing of the drill are all critical to enable the high productivity and good drill life in production drilling. In addition to the industrial application, drilling is also the most common and fundamental procedure in orthopaedic surgery. Bone drilling is utilized in the fixation of broken bones, joint fusion, and many other surgical procedures. Bone drilling often produces high temperatures and results in the thermal osteonecrosis that affects the post-operative healing and quality-of-life of patients. The work-material deformation and removal mechanism in drilling are complicated due to the coupling of large deformation, high strain rate, high temperature, and potential chemical reaction. At the drill center, the cutting speed is zero. At the chisel edge close to the drill center, the work material is plowed under a negative rake angle. Along the drill cutting edge, the cutting speed, rake angle, and clearance © Springer Nature Switzerland AG 2019 A. J. Shih et al., Metal and Bone Drilling - The Thermal Aspects, https://doi.org/10.1007/978-3-030-26047-7_1

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angle all vary with respect to the distance from the drill center. The outermost point on the cutting edge has the highest cutting speed. The side of the drill, also known as margin, slides on the newly generated hole surface and generates frictional heat. The chips created during drilling have high temperatures and are evacuated via the flutes on the drill. Chip evacuation is critical in deep hole drilling as well as in bone drilling. Materials are critical in drilling from both the work-material and tool-material perspectives. High performance parts demand the use of difficult-to-cut work materials, such as titanium alloys for aerospace and compacted graphite iron and ductile iron for the automotive powertrain. The inherent difficulties in drilling arise from the very advantage that these work materials impart to a wide range of industrial applications: high strength and lightweight for superior performance and energy efficiency. Under extreme force and heat during the high-throughput drilling, the drill-material is critical to the drill life and process capability. In healthcare, knowledge of drill design and heat generation in bone drilling is lagging behind that of metal drilling in the industry. This book addresses the thermal aspects for both metal and bone drilling. Section 1.1 introduces the three work materials (titanium alloy, cast iron, and bone) studied in this book. Section 1.2 reviews the metal drilling and metal working fluid delivery. Section 1.3 discusses the bone drilling and the drill used for the purpose. Section 1.4 presents a summary of the inverse heat transfer method and finite element modeling of drill and workpiece temperatures in drilling. Section 1.5 gives an overview of all the chapters in this book.

1.1  Work Materials Studied for Thermal Aspects in Drilling 1.1.1  Titanium Alloys Titanium (Ti) and its alloys are lightweight, corrosion resistant, biocompatible, and high-temperature materials. Ti has two crystal structures: the hexagonal close-pack (HCP) α phase and body-centered cubic (BCC) β phase [1, 2]. Pure Ti is 100% α at room temperature. The allotropic transformation from α to β phases takes place at the β transus temperature of 883 °C. For Ti-6Al-4V, Vanadium (V) is added to pure Ti to stabilize the β phase by lowering the β transus temperature. Aluminum (Al) is added to increase the β transus temperature. With 6 wt% of Al and 4 wt% V, the β transus temperature of Ti-6Al-4V is 980 °C, beyond which Ti is 100% β. Because Ti-6Al-4V is a two-phase alloy, it can be heat treated and aged to provide exceptional material properties like the high strength–density ratio at elevated temperatures. Generally, higher α content imparts higher creep resistance and high-temperature strength, while higher β content gives higher density and room temperature strength.

1.1  Work Materials Studied for Thermal Aspects in Drilling

3

Although Ti is the ninth most abundant element and the fourth most abundant metal in earth’s crust [3], the extraction and processing cost to produce raw Ti are high due to its high free energy requirement for reduction of oxide [3]. The high cost has limited Ti and its alloys to applications in which the material cost is not a key factor. Ti and its alloys are popular in aerospace (e.g., engine compressor blade and structural frame) [4], military (e.g., armor and submarine hull) [5], medical devices (e.g., bone screw, artificial hip/knee, stent, and dental implants) [6], chemical reactors and piping, sport equipment (e.g., bicycle frame and golf club), and other high-­ end products. For instance, most structural parts of the SR-71 supersonic aircraft (Fig.  1.1a) are made of Ti alloys for the high-temperature, lightweight, and high strength needs. The combination of Ti alloy and carbon fiber reinforced plastic (CFRP) is widely used in new commercial aircrafts for light weighting and fuel efficiency. Other applications of Ti include the golf club driver head and the dental implant, as illustrated in Fig. 1.1b. Figure 1.1c shows the front view of a titanium cannula bone screw and the side views from the cap and screw sides. A high aspect ratio through hole (drilled by deep hole drilling of Ti alloy) allows this screw to be guided by a Kirschner wire (to be discussed in Sect. 1.3) during the orthopaedic surgery. Figure  1.1d illustrates this cannula bone screw with a Kirschner wire through the hole. The poor machinability of Ti alloys has been reported by researchers and summarized in several review articles [7–14]. As shown in Table 1.1, commercially pure (CP) Ti and its alloys have low thermal conductivity and high strength–weight ratio, compared to that of other commonly used materials, such as aluminum alloys.

Fig. 1.1  Applications of Ti alloys: (a) SR-71 aircraft, (b) dental implant bone screw, (c) cannula bone screw, and (d) cannula bone screw and Kirschner wire

1 Introduction

4 Table 1.1  Material Properties of Ti, Ti-6Al-4V, and Aluminum 6061-T4 [2] Material Density (g/cm3) Thermal conductivity (W/m-K) Heat capacity (J/kg-K) Elastic modulus (GPa) Poisson’s ratio Ultimate strength (MPa)

CP Ti 4.5 16.4 523 105 0.37 344

Ti-6Al-4V 4.4 6.6 526 114 0.33 540

Al 6061-T4 2.7 154 894 68.9 0.33 241

Ti  has the highest strength–weight ratio of all commonly used metals of up to 550 °C [15]. Due to the inherent properties of Ti, particularly low thermal conductivity, the drill temperature is high when machining Ti at high MRR. High temperature softens the tool material, promoting rapid diffusion wear [16] and severe tool edge chipping, thus limiting the MRR and productivity. In addition to tool wear and limited productivity, two other technical challenges in the machining of Ti are the long and continuous chip [17], which is difficult to evacuate, and burr formation [18], which is difficult to remove. The research in drilling of Ti and its alloys is still limited. Sakurai et al. [19–21] conducted a series of experiments in the drilling of Ti-6Al-4V. Effects of tool surface treatment, cutting speed, and feed on thrust force and torque [19], benefits of the vibratory motion of the drill [20], and the variable feed for chip ejection [21] have been investigated. Other research in Ti drilling includes the works of Arai and Ogawa [22] in high pressure (7  MPa) cutting fluid assisted drilling and Cantero et al. [23] in dry drilling tool wear and workpiece sub-surface damage. A series of systematic Ti drilling studies conducted by Li et al. [24–28] is the foundation for Chaps. 2 and 3 of this book.

1.1.2  Cast Irons Cast iron is a common, widely used structural material in automobiles, railways, buildings, bridges, etc. In automotive powertrain, gray iron (GI), ductile iron (DI), and compacted graphite iron (CGI) are the most common grades [29]. The morphology of graphite is different in these three iron materials: GI has the long, randomly oriented graphite, DI has the spherical graphite, and CGI has the short, thick, and worm-like compacted graphite [30]. The shape of graphite affects the mechanical and physical properties of GI, DI, and CGI, which are compared in Table  1.2 [30–33]. CGI also has high strength and can achieve 10–30% weight reduction (compared to GI) for diesel engine block applications [34]. Machinability is one of the barriers for large-scale adoption of CGI for automotive powertrain, particularly the engine block and head [35]. Machining of CGI is challenging, compared to that of GI, due to the high tool wear rate caused by the graphite morphology, high strength and

1.1  Work Materials Studied for Thermal Aspects in Drilling

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pearlite content, and the lack of manganese sulfide (MnS) as the lubricant in machining of GI [36, 37]. The high-throughput dry and minimum quality lubrication (MQL) drilling of CGI will be presented in Chap. 4. DI, also known as nodular cast iron or spheroidal graphite iron, has high strength and good ductility. One of the key applications of DI is in the crankshaft (Fig. 1.2), which is a critical engine component with long oil gallery holes to supply engine oil to journal bearings and connecting rods. In the production of crankshaft, MQL has been developed and adopted for deep hole drilling of DI [38]. A series of MQL deep hole drilling research was conducted by Tai et al. [37–39] to study the workpiece temperature and thermal distortion. This study is the foundation for Chaps. 4 and 5.

1.1.3  Bone Bone is a rigid organ made of porous, living material with a layered structure, including a hard outer layer of cortical bone and soft, spongy cancellous bone tissue inside. Bone is a metabolically active material composed of four types of cells, namely osteocyte, osteoblast, osteoclast, and osteoprogenitor cells, for growth, shape, and maintenance of bone. Bone has a network of blood vessels and exhibits blood diffusion and metabolic function, which influences the bio-heat transfer characteristics. Bone is sensitive to heat. Between 43 and 47 °C, thermal osteonecrosis occurs and consequently leads to the bone death [40–45]. Bone properties vary from age, gender, diet, but general ranges are listed in Table 1.3 based on available data in the Table 1.2  Comparison of mechanical and thermal properties of GI, CGI, and DI [30–33] Properties Ultimate tensile strength (MPa) Elastic modulus (GPa) Hardness (BHN) Elongation (%) Thermal conductivity (W/m-K)

Fig. 1.2  Deep hole drilling of oil gallery holes in a crankshaft

GI 150–450 66–143 156–277 1 36–57

CGI 250–575 130–160 179–269 1–3 36–47

DI 350–900 159–176 160–360 2–22 31–37

1 Introduction

6 Table 1.3  Ranges of mechanical and thermal properties of the human cortical bone

Properties Strength (MPa) Elastic modulus (GPa) Density (kg/m3) Specific heat (kJ/kg-K) Thermal conductivity (W/m-K)

Human bones 57.9–107.9 5.4–19.9 0.80–1.6 1.14–2.37 0.16–0.75

literature, including bovine samples used in research. The thermal conductivity of bone is about 100 times smaller than that of the AISI 316 stainless steel tool material for bone drilling. A series of bone drilling studies to investigate the temporal and spatial distributions of bone temperature have been conducted [46–49] and summarized in Chaps. 6, 7, and 8.

1.2  Metal Drilling: Drill and Metal Working Fluid Delivery 1.2.1  Drill Design and Nomenclature Figure 1.3a shows the tip of a traditional twist drill with a straight chisel edge at the drill center. This drill typically has a point angle of 118°, which results in the rake angle of −59° for the plowing action at the drill tip (i.e., chisel point) during drilling. Drill design and manufacturing have advanced significantly from this traditional twist drill. The front, perspective, and side views of a drill used for CGI are shown in Fig. 1.3b–d, respectively. This drill has a spiral point, which can lessen the negative rake angle and plowing at the drill tip. This two-flute drill also has three margins to enhance the stability during drilling and a polished flute surface to reduce the friction force during chip evacuation.

1.2.2  Through-the-Drill Metal Working Fluid Delivery Metal working fluid (MWF) serves three purposes: cooling, lubrication, and chip evacuation. Delivering a steady and continuous supply of the MWF directly to the cutting edges at the drill tip is critical, particularly for deep hole drilling. An ideal way to deliver the MWF is through the body of the drill to the cutting edges at the drill tip. This through-the-drill fluid delivery approach is more effective than the external delivery method. With adequate pressure and controlled temperature of the MWF, it is beneficial in three ways. First, it cools the drill, particularly the tip and cutting edges. Second, it lubricates the cutting edges and helps to reduce the heat generation. Lastly, MWF helps to flush the chips out of drilled hole while reducing

1.2  Metal Drilling: Drill and Metal Working Fluid Delivery

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Fig. 1.3 (a) Traditional twist drill with straight chisel edge, (b) front view, (c) perspective view, (d) side view of a drill with spiral point chisel edge and three margins for CGI drilling (by Kennametal), and (e) drill with slots at exit holes (by Guhring)

the friction and heat generation in the drill flute during chip evacuation. Figure 1.3b shows the tip of a drill with two round through-the-drill holes. Slots can also be ground at the exit holes of the MQL drill (Fig. 1.3e) to aid the delivery of MQF droplets to cutting edges. Spindle with the shaft and tool holder allowing the delivery of MWF is a key element of the machine tool to match to drills in Fig. 1.3b–d with through-the-drill holes. In this book, all metal drilling studies (Chaps. 2 and 3) utilize through-the-­ drill delivery of MWF or air. For industrial drilling of deep holes and/or difficult-to-­ cut materials, through-the-drill delivery of high-pressure MWF is standard and necessary to gain productivity and drill life. The experimental study of Ti drilling [25] showed that the externally supplied MWF could not reach the drilling zone and did not improve the drill life. Under the same drilling condition and using the same drill and same type of MWF, the drill life improved more than seven times with the through-the-drill fluid delivery approach for Ti drilling [25]. For drilling titanium in Chaps. 2 and 3, through-the-drill delivery of MWF is necessary to achieve the desired MRR and drill life.

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1.2.3  MQL in Production Drilling The MQL approach has been implemented and demonstrated to be beneficial to reduce the overall manufacturing cost and achieve positive impacts to reduce the energy use and carbon emission as well as improve workers’ health and plant safety in automotive powertrain production [36, 50, 51]. In conventional flood cooling, the large amount of MWF in the production plant can cause problems with ground contamination, evaporation and dissociation of emulsion, high energy consumption, wet chip disposal, and endangered workers’ health and safety. Factory operating data shows that sustaining and operating a large central MWF delivery system in a plant is expensive, consumes energy, and causes environmental and health concerns. In addition, such central MWF delivery system also occupies floor space and limits flexibility to relocate machines in the production line [36, 50, 51]. MQL is achieved by using a small amount of oil-based MWF mixed with pressurized air to generate droplets that are delivered directly to the drill cutting edge. The flow rate of MWF in MQL is low, typically 10–100 mL an hour, a significant reduction in MWF over conventional flood cooling in machining. A variety of MQL MWF delivery systems have been developed with external nozzles or through spindle and drill internal channels. The external MQL MWF supply is easy to implement and requires no special tools. However, it is inadequate for deep hole drilling because the cutting edges are inside the workpiece. In high-volume automotive powertrain manufacturing, the MWF is delivered internally for MQL. Two different approaches, single- and dual-channel MQL systems, as shown in Fig. 1.4, are available for internal MWF delivery. In the single-channel MQL system, the oil and air are mixed outside the machine and routed through the spindle. This system ­produces

Fig. 1.4  Single and dual-channel MQL systems

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larger MWF droplet size due to long traveling distance for the aerosol stream. Also, the mist quality may be unstable because of inertial and centrifugal force when delivered to the cutting tool tip, particularly for smaller oil holes in the drill. Studies have shown that finer and stable mist is preferred in machining processes because of better lubrication and heat dissipation [52]. In the dual-channel system, the air and oil are mixed near the drill. MWF and air are routed in two parallel tubes through the spindle and mixed close to the tool holder. This way makes less dispersion and dropout of the mixture and delivers the mist with finer and more uniform droplet size than that in the single-channel system, especially for high spindle speed where centrifugal force becomes significant. Also, the dual-channel system has less lag time when changing tools. This is beneficial for machining operations which require multiple tool changes. The dual-channel system has proven to be more robust in production MQL operations. For example, Ford Motor Company is currently using the dual-channel system for machining aluminum prismatic parts, such as transmission cases and valve bodies. A benefit of MQL is that both part and chip remain nearly dry and can reduce the cost of processing chips for recycling [53]. The automotive industry has implemented MQL machining in high-volume production of powertrain components. For example, the first automotive MQL machining operation in Ford Motor Company was for the ductile iron crankshaft oil gallery hole drilling in the early 2000s [51]. In 2005, Ford began applying MQL to aluminum transmission components, and by 2008 had over 200 MQL machines in operation machining aluminum transmission cases, torque converter housings, and valve bodies [51]. MQL machining is Ford’s current standard machining method for powertrain components, and is being implemented in new high-volume powertrain production machining lines globally. MQL saves energy cost in production. The largest energy consumptions in wet computer numerical control (CNC) machines are cutting process (about 25%), MWF system (30–40%), and compressed air (15–20%). The MWF-associated energy consumption is significant in all CNC machining processes. Figure  1.5

a

b 10

Metal working fluid Air

2 0

Others 5 Cycle time

Machining

8

10

6 4 2 0

Feeding Fixed consumption

4

Machining Power (kW)

6

Feeding

Fixed consumption

Power (kW)

8

10

5 Cycle time

10

Fig. 1.5  An illustration of energy consumption between (a) wet and (b) MQL conditions for an identical process (source: Horkos Corp.)

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shows an ideal energy map between a wet and MQL machining operation. In wet machining, the energy consumption is mostly fixed and can only be reduced by improving the cutting efficiency and decreasing the cycle time. For MQL, the MWF-related energy no longer exists, which automatically results in saving in energy. In practice, MQL can achieve higher throughputs than wet approach in many applications, especially in aluminum machining. For example, a study in comparison of drilling oil holes in nodular cast iron crankshaft showed that MQL can yield drill life equivalent to gun drills at higher penetration rates [36, 37]. Although the machining power and air output in MQL drilling could increase, the overall energy decreases with the cycle time as shown in Fig.  1.5b. The MQL requires increased compressed air use compared to wet machining and may reduce the energy benefit achieved through cycle time and MWF pumping improvements. Production and research studies have shown that, with a proper selection of the MQL system and cutting parameters, it is possible for MQL machining to have cost and performance similar to or better than wet conditions [50]. The major cost saving of MQL is from the elimination of flood cooling, which occupies 10%–17% of the total manufacturing cost, as shown in Fig.  1.6. Flood cooling-associated costs include filtration equipment, chiller, piping and pumps, water consumption, and waste water treatment. The MWF system increases both investment and maintenance costs. A case study was conducted by Ford Motor Company to compare two identical transmission modules with MQL and wet, respectively, for a 10-year cycle analysis including downtime cost, maintenance, operating cost, and floor space. The study showed over 15% saving, on average, and a cost reduction in all sectors [50]. Although the initial capital investment for MQL equipment could be substantial, MQL was demonstrated to have an overall cost saving. To completely substitute conventional wet machining, MQL has to deliver three primary functions: lubrication, cooling, and chip evacuation. However, since a small amount of MWF is applied, the heat dissipation in MQL is not as efficient as wet

Fig. 1.6  Potential MQL savings from wet operations in terms of (a) the manufacturing costs and (b) the energy consumption

1.3  Bone Drilling

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condition. The high temperature around the cutting region may cause workpiece thermal distortion and poor dimensional accuracy. For deep hole drilling with MQL, extreme thermal loads make it even more difficult to achieve stringent dimensional tolerances needed by precision automotive powertrain parts. MQL deep hole drilling is one of the most technically challenging processes in production. Deep hole drilling is typically defined by a drilling depth to diameter ratio larger than 10. In automotive powertrain, deep hole drilling process is common in drilling of crankshaft oil holes, transmission valve body spool bores, and engine block oil feed holes. Deep hole drilling is also a high-energy-density machining process which requires good lubrication and cooling to maintain the drill life and hole quality. The heat dissipation at the hole wall surface should be significant for deep hole drilling due to the friction between drill margins and the workpiece, chip accumulated in the drill for evacuation, and heat transferred from high-temperature drill to the workpiece. During drilling, the energy is converted to heat, producing very high temperatures in the deformation zones and surrounding regions of the chip, drill, and workpiece. Filipovic and Stephenson [36] have reported that MQL drilling can yield drill life equivalent to gun drills at higher penetration rates in steel and ductile iron, while the thermal expansion in machining aluminum could be a challenge due to its low heat capacity and high thermal expansion coefficient. Heinemann et al. [54] have shown that, with the external MQL supply, the drill life decreases with an increasing hole depth, whereas low-viscous lubricant with high-­ cooling capacity could help maintain the drill life. Hussain et al. [55] have demonstrated that MQL deep hole drilling is feasible in production with optimal feed and speed. In this book, Chaps. 4 and 5 study MQL deep hole drilling.

1.3  Bone Drilling 1.3.1  Bone Drill and Kirschner Wire Bone drilling is a fundamental skill for orthopaedic surgeons to treat musculoskeletal trauma (e.g., the repair and fixation of bone fracture), sports injuries, and degenerative disease (e.g., the joint fusion for arthritis). The bone drilling is conducted by hand using a hand drill. Figure 1.7a shows a typical battery-powered hand drill (by Stryker, Kalamazoo, Michigan, USA) for bone drilling. The hand drill (including battery) is thermally sterilized by the autoclave with a minimum temperature of 121 °C and pressure above 2 × 105 Pa for about 80 min before surgical operation. Unlike drills used in metal drilling with intricate shape and hard tool material, the design of bone drill is simple, and the tool material is typically stainless steel due to the biocompatibility requirement. For fixation of the fragments of bone, the Kirschner wire, commonly called K-wire, is the most popular choice. K-wires, introduced in 1909 by Dr. Martin Kirschner, are sharpened stainless steel pins widely used in orthoapedics and other medical and veterinary surgical procedures

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Fig. 1.7  Bone drilling and K-wire: (a) a battery power hand-held bone drill, (b) diamond and trocar tip of K-wire, (c) K-wires in the wrist, and (d) change in color of the K-wire tip after bone drilling

[56, 57]. The typical diameter of K-wire ranges from 0.9 to 3.5 mm and lengths of K-wire are 100, 150, and 225 mm. Two common tips for K-wire are the diamond and trocar, as shown in Fig. 1.7b. K-wire is a solid drill without flute to better secure broken bone pieces, as illustrated in Fig. 1.7c. The main function of K-wire is to penetrate and hold bone fragments together (pin fixation) or to provide an anchor for skeletal traction and temporary joint immobilization or definitive fixation of the fracture fragments is small [58]. Typically, the K-wires are often driven into the bone through the skin (percutaneous pin fixation) using a power or hand driller and will be removed once fracture heals about 2–4  months later. As K-wires are used to mechanically invade the human body, worn and inefficient cutting edges or improper operation by surgeons can increase the risk of both traumatic and thermal injuries to the bone and adjacent neurovascular structures [59, 60]. Bone debris could be jammed between the bone and K-wires. The compacted debris generated in the drilling process produces resistive and friction forces on the drill as well as the haptic feedback to orthopaedic surgeons who operate the drill [59, 61].

1.3.2  Drill and Spindle for Orthopaedic Bone Drilling In bone drilling, orthopaedic surgeons rely on their feeling and experience to quickly stop the feed motion of a bone drill immediately after it penetrates the hard-cortical bone to prevent collateral damage to surrounding organs or blood vessels. Hence precise haptic control is necessary for orthopaedic surgeons. A dull bone drill tip may have better haptic control, but it has high friction and generates a significant amount of heat between the bone and the drill [62]. During clinical bone drilling, the K-wire tip often is discolored due to high temperatures (Fig. 1.7d). The heat generated from drilling also causes thermal injury to the bone adjacent to the drilled hole through osteonecrosis.

1.4  Inverse Heat Transfer Method and Finite Element Modeling of Drill…

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All clinical bone drilling procedures are currently conducted with external saline supply for cooling. Through-the-drill saline delivery is not available because the orthopaedic bone drill does not have the coolant-through capability. The depth of bone drilling through the hard-cortical bone is shallow (a few mm thick) before the drill reaches the soft, sponge-like cancellous bone. To suppress the heat generated, studies have shown that drill size, cutting speed, and irrigation with saline (for lubrication and cooling) have significant effects on bone temperature and necrosis [61, 63]. In particular, saline irrigation has shown to significantly decrease drilling temperatures, even under intermittent supply [42, 44]. However, irrigation is not appropriate for some clinical situations. For example, bone drilling to aid in fusion of a joint would be negatively impacted by irrigation because it washes away the cells orthopaedic surgeons try to access by drilling into the subchondral bone. Joint fusion often requires repeated bone drilling sequential passes within a finite region to encourage increased blood flow to aid the healing. The increase in bone temperature and related necrosis in repeated bone drilling are studied in Chap. 7.

1.4  I nverse Heat Transfer Method and Finite Element Modeling of Drill and Workpiece Temperatures in Drilling High temperatures in drilling can lead to many detrimental effects, such as workpiece dimensional errors, shortened drill life, or thermal injury to bone tissue. The infrared thermal camera is not suitable for drill temperature measurement because the cutting region is embedded inside the workpiece during drilling. Since the heat generation rate and drill and workpiece temperature distributions inside the workpiece are difficult to measure directly, numerical modeling becomes an important tool to study temperatures in drilling.

1.4.1  Inverse Heat Transfer Modeling The inverse heat transfer method (IHTM) [64] based on experimentally measured temperature using embedded thermocouples and finite element modeling (FEM) has been developed to analyze the spatial and temporal distributions of the drill and workpiece temperature during drilling. For drill temperature, IHTM utilizes the temperature measured by thermocouples embedded on the drill flank surface as the input to predict the heat flux on the drill chisel and cutting edges. This model estimates the cutting-edge heat generation rate by minimizing the discrepancy between the experimentally measured and FEM-predicted temperature at the thermocouple locations and can provide temperature information for locations where it cannot be measured directly.

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Thermocouples can be embedded in the drill flank surface and routed via shallow grooves on the margin surface of the drill to outside of a stationary drill for drilling a rotating workpiece. It requires careful specimen preparation to avoid damaging the thermocouple during drilling. Thermocouples measure the drill temperature at several points adjacent to the cutting edge. A validation process can be performed by comparing the drill temperature analyzed by FEM to the thermocouple measurements.

1.4.2  Drill Temperature and Failure Prediction The early analytical modeling of temperature distribution in a drill bit, which is represented as a semi-infinite body, utilizes the empirical force equations from a series of oblique cutting tests to calculate heat source and the transient heat transfer analysis to calculate heat partition [65–67]. On the analysis of drill as a finite domain, Saxena et  al. [68] and Watanabe et  al. [69] applied the finite difference method. FEM has been applied by Fuh [70], Chen [71], and Bono and Ni [72–74] to analyze the drill temperature. Using the Eulerian formulation, Strenkowski et al. [75] developed an approach of dividing the cutting edge of a drill into a series of elementary cutting tool (ECT) and applying the oblique cutting model for each ECT to predict the forces and torques in drilling. Li and Shih [24, 26] advanced the FEM to solve the complete temporal and spatial distributions of the drill temperature and stress during Ti drilling. By applying the modified Mohr criterion for brittle tool material (Chap. 4), the onset of drill failure is predicted in the cutting edge for dry drilling and the chisel edge for wet drilling of Ti-6Al-4V.  FEM results show that the supply of cutting fluid helps to prevent premature drill failure associated with high drill temperature. FEM also indicates that the lower peripheral cutting speed and higher feed can reduce the drill temperature while maintaining the same MRR, but the chisel edge would undergo increasingly higher stresses. Accurate FEM predictions of drill temperatures and stresses can assist the choice of optimal process parameters for optimal productivity and cost.

1.4.3  Workpiece Temperature and Thermal Expansion The FEM analysis of work-material deformation in drilling is challenging due to the complexity of drill geometry and difficulty in modeling the work-material deformation under large negative rake angle cutting at the drill chisel edge. Using the updated-Lagrangian formulation, Guo and Dornfeld [76, 77] investigated drilling burr formation with a split point drill, Min et al. [78] developed the 2D burr formation model for a twist drill, and Marusich et  al. [79] analyzed the 3D drilling of Ti-6Al-4V using a twist drill.

References

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The thermal expansion of the workpiece can lead to errors in the size and location of drilled holes. The hole geometry often presents a tapered shape after dry drilling with a larger diameter at the exit due to the thermal expansion of the drill and the workpiece [80]. In MQL deep hole drilling, a large amount of heat can be conducted from chips inside the hole to the workpiece during chip evacuation. The thermally induced workpiece distortion causes position errors for subsequent machining operations. A comprehensive FEM thermal model of the workpiece in MQL deep hole drilling has been developed to investigate heat generation and predict workpiece temperature and thermal expansion induced distortion and hole position errors [39].

1.4.4  Bone Temperature in Drilling Bone temperature modeling is mostly based on the metal cutting theory. Thermo-­ mechanical FEM [81] predicts the heat generation in bone drilling based on orthogonal cutting theory. This is the input for the heat transfer FEM to predict the temperature rise and thermal injury to bones while drilling. A numerical model further considering the heat conduction from heated drill bit and chips into the bone has been developed by Lee et  al. [82]. Drill rotational speed, feed rate, and drill diameter have been identified to have the most significant impacts on bone temperature. In Chaps. 6, 7, and 8, the bone temperature in drilling is studied.

1.5  Overview of the Book This book has eight chapters. The drilling with Ti alloys using flood cooling is studied in Chaps. 2 and 3 with focus on the drilling experiments and modeling, respectively. Chapter 4 presents the dry and MQL drilling of CGI and MQL deep hole drilling of ductile iron. Chapter 5 studies the workpiece temperature and thermal expansion in deep hole drilling. Bone temperature in drilling is investigated in Chaps. 6, 7, and 8. Chapter 6 summarizes the bone temperature measurement in drilling experiments, Chap. 7 focuses on the thermal modeling in bone drilling, and Chap. 8 presents a case study using the notched K-wire tip on the bone temperature in drilling.

References 1. Lütjering G, Williams JC (2007) Titanium. Springer, Berlin 2. Donachie MJ (2000) Titanium: A Technical Guide, 2nd edn. ASM International, Material Park 3. Kraft E (2003) Summary of emerging titanium cost reduction technologies. Oak Ridge National Laboratory Report ORNL/Sub/4000023694/

16

1 Introduction

4. Peters M, Kumpfert J, Ward CH, Leyens C (2003) Titanium alloys for aerospace applications. Adv Eng Mater 5:419–427 5. Montgomery JS, Wells MGH (2001) Titanium armor applications in combat vehicles. JOM 53:29–32 6. Brunette DM, Tengvall P, Textor M (2001) Titanium in medicine: material science, surface science, engineering, biological responses, and medical applications. Springer, Berlin 7. Machado AR, Wallbank J (1990) Machining of titanium and its alloys—a review. Proc Inst Mech Eng B J Eng Manuf 204:53–60 8. Ezugwu EO, Wang ZM (1997) Titanium alloys and their machinability—a review. J  Mater Process Technol 68:262–274 9. Yang X, Richard Liu C (1999) Machining titanium and its alloys. Mach Sci Technol 3:107–139 10. Rahman M, Wang Z-G, Wong Y-S (2006) A review on high-speed machining of titanium alloys. JSME Int J Ser C 49:11–20 11. Ulutan D, Ozel T (2011) Machining induced surface integrity in titanium and nickel alloys: a review. Int J Mach Tools Manuf 51:250–280 12. Watanabe I, Kiyosue S, Ohkubo C, Aoki T, Okabe T (2002) Machinability of cast commercial titanium alloys. J Biomed Mater Res 63:760–764 13. Veiga C, Davim JP, Loureiro AJR (2013) Review on machinability of titanium alloys: the process perspective. Rev Adv Mater Sci 34:148–164 14. Zhang PF, Churi NJ, Pei ZJ, Treadwell C (2008) Mechanical drilling processes for titanium alloys: a literature review. Mach Sci Technol 12:417–444 15. Hurless BE, Froes FH (2002) Lowering the cost of titanium. AMPTIAC Q 6:3–9 16. Hartung PD, Kramer BM, von Turkovich BF (1982) Tool wear in titanium machining. CIRP Ann 31:75–80 17. Bermingham M, Kirsch J, Sun S, Palanisamy S, Dargusch MS (2011) New observations on tool life, cutting forces and chip morphology in cryogenic machining Ti-6Al-4V. Int J Mach Tools Manuf 51:500–511 18. Dornfeld D, Kim JS, Dechow H, Hewson J, Chen LJ (1999) Drilling burr formation in titanium alloy, Ti-6Al-4V. CIRP Ann 48:73–76 19. Sakurai K, Adachi K, Ogawa K, Niba R (1992) Drilling of Ti-6Al-4V alloy. J Jpn Inst Light Metals 42:389–394 20. Sakurai K, Adachi K, Ogawa K (1992) Low frequency vibratory drilling of Ti-6Al-4V alloy. J Jpn Inst Light Metals 42:633–637 21. Sakurai K, Adachi K, Kamekawa T, Ogawa K, Hanasaki S (1996) Intermittently decelerated feed drilling of Ti-6Al-4V alloy. J Jpn Inst Light Metals 46:138–143 22. Arai M, Ogawa M (1997) Effects of high pressure supply of coolant in drilling of titanium alloy. J Jpn Inst Light Metals 47:139–144 23. Cantero JL, Tardío M, Canteli JA, Marcos-Bárcena M, Miguélez MH (2005) Dry drilling of alloy Ti-6Al-4V. Int J Mach Tools Manuf 45:1246–1255 24. Li R, Shih AJ (2007) Tool temperature in titanium drilling. J Manuf Sci Eng 129:740–749 25. Li R, Hegde P, Shih A (2007) High-throughput drilling of titanium alloys. Int J Mach Tools Manuf 47:63–74 26. Li R, Shih A (2007) Spiral point drill temperature and stress in high-throughput drilling of titanium. Int J Mach Tools Manuf 47:2005–2017 27. Li R, Shih AJ (2007) Finite element modeling of high-throughput drilling of Ti-6Al-4V. Trans NAMRI/SME 35:73–80 28. Li R, Riester L, Watkins TR, Blau PJ, Shih AJ (2008) Metallurgical analysis and nanoindentation characterization of Ti–6Al–4V workpiece and chips in high-throughput drilling. Mater Sci Eng A 472:115–124 29. Grzesik W, Rech J, Żak K, Claudin C (2009) Machining performance of pearlitic–ferritic nodular cast iron with coated carbide and silicon nitride ceramic tools. Int J Mach Tools Manuf 49:125–133 30. Nayyar V, Kaminski J, Kinnander A, Nyborg L (2012) An experimental investigation of machinability of graphitic cast iron grades; flake, compacted and spheroidal graphite iron in continuous machining operations. Procedia CIRP 1:488–493

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31. Heck M, Ortner HM, Flege S, Reuter U, Ensinger W (2008) Analytical investigations concerning the wear behavior of cutting tools used for the machining of compacted graphite iron and grey cast iron. Int J Refract Met Hard Mater 26:197–206 32. Dawson S, Hollinger I, Robbins M, Daeth J, Reuter U, Schulz H (2001) The effect of metallurgical variables on the machinability of compacted graphite iron. SAE International, V110–5, p 21 33. Lampman S, Moosbrugger C, DeGuire E (2008) ASM handbook: casting, vol 15. ASM International, Material Park 34. Dawson S, Schroeder T (2004) Practical applications for compacted graphite iron. AFS Trans 47:1–10 35. Alves SM, Schroeter RB, Bossardi JCDS, Andrade CLFD (2011) Influence of EP additive on tool wear in drilling of compacted graphite iron. J Braz Soc Mech Sci Eng 33:197–202 36. Filipovic A, Stephenson DA (2006) Minimum quantity lubrication (MQL) applications in automotive power-train machining. Mach Sci Technol 10:3–22 37. Tai BL, Stephenson DA, Shih AJ (2013) Workpiece temperature during deep-hole drilling of cast iron using high air pressure minimum quantity lubrication. J  Manuf Sci Eng 135(031019):1–7 38. Tai BL, Stephenson DA, Shih AJ (2012) An inverse heat transfer method for determining workpiece temperature in MQL deep hole drilling. J Manuf Sci Eng 134(021006):1–8 39. Tai BL, Jessop A, Stephenson DA, Shih AJ (2012) Workpiece thermal distortion in MQL deep hole drilling  - finite element modeling and experimental validation. J  Manuf Sci Eng 134(011008):1–9 40. Eriksson RA, Albrektsson T, Magnusson B (1984) Assessment of bone viability after heat trauma: a histological, histochemical and vital microscopic study in the rabbit. Scand J Plast Reconstr Surg 18:261–268 41. Hillery MT, Shuaib I (1999) Temperature effect in drilling of human and bovine bone. J Mater Process Technol 92:302–308 42. Augustin G, Davila S, Udiljak T, Vedrina DS, Bagatin D (2009) Determination of spatial distribution of increase in bone temperature during drilling by infrared thermography: preliminary report. Arch Orthop Trauma Surg 129:703–709 43. Augustin G, Davila S, Mihoci K, Udiljak T, Vedrina DS, Antabak A (2008) Thermal osteonecrosis and bone drilling parameters revisited. Arch Orthop Trauma Surg 128:71–77 44. Augustin G, Zigman T, Davila S, Udilljak T, Staroveski T, Brezak D, Babic S (2012) Cortical bone drilling and thermal osteonecrosis. Clin Biomech 27:313–325 45. Berman AT, Reid JS, Yanicko DR, Sih GC, Zimmerman MR (1984) Thermally induced bone necrosis in rabbits: relation to implant failure in humans. Curr Orthop Pract 186:284–292 46. Palmisano AC, Tai BL, Belmont B, Irwin T, Shih AJ, Holmes J (2015) Comparison of cortical one drilling induced heat production among common drilling tools. J  Orthop Trauma 29:e188–e193 47. Tai BL, Palmisano AC, Belmont B, Irwin T, Shih AJ, Holmes J (2015) Numerical evaluation of sequential bone drilling strategies based on thermal damage. Med Eng Phys 37:855–861 48. Palmisano AC, Tai BL, Belmont B, Irwin TA, Shih A, Holmes JR (2016) Heat accumulation during sequential cortical bone drilling. J Orthop Res 34:463–470 49. Liu Y, Belmont B, Wang Y, Tai B, Holmes J, Shih A (2017) Notched K-wire for low thermal damage bone drilling. Med Eng Phys 45:25–33 50. Stoll A, Sebastian AJ, Klosinski R, Furness R (2008) Lean and environmentally friendly manufacturing – minimum quantity lubrication (MQL) is a key technology for driving the paradigm shift in machining operations. SAE Technical paper, SP-2208-011128 51. Tai B, Stephenson DA, Furness R, Shih A (2014) Minimum quantity lubrication (MQL) in automotive powertrain machining. Procedia CIRP 14:523–528 52. Tai BL, Dasch JM, Shih AJ (2011) Evaluation and comparison of lubricant properties in minimum quantity lubrication machining. Mach Sci Technol 15:376–391 53. Itoigawa F, Childs THC, Nakamura T, Belluco W (2006) Effects and mechanisms in minimal quantity lubrication machining of an aluminum alloy. Wear 260:339–344

18

1 Introduction

54. Heinemann R, Hinduja S, Barrow G, Petuelli G (2006) Effect of MQL on the tool life of small twist drills in deep-hole drilling. Int J Mach Tools Manuf 46:1–6 55. Hussain MI, Taraman KS, Filipovic AJ, Immo G (2008) Experimental study to analyse the workpiece surface temperature in deep hole drilling of aluminium alloy engine blocks using MQL technology. J Achiev Mater Manuf Eng 31:1–6 56. Franssen BB, Schuurman AH, Van der Molen AM, Kon M (2010) One century of Kirschner wires and Kirschner wire insertion techniques: a historical review. Acta Orthop Belg 76:1–6 57. Nichter LS, Spencer S, Navarrette PM, Kosari K (1992) The biomechanical efficacy of an oscillating K-wire driver. Ann Plast Surg 29:289–292 58. Wassenaar EB, Franssen BBGM, van Egmond DB, Kon M (2006) Fixation of Kirschner wires: a comparison between hammering and drilling k-wires into ribs of pigs. Eur J  Plast Surg 29:153–156 59. Khanna A, Plessas SJ, Barrett P, Bainbridge LC (1999) The thermal effects of kirshner wire fixation on small bones. J Hand Surg Am 24:355–357 60. Karmani S, Lam F (2004) The design and function of surgical drills and K-wires. Curr Orthop 18:484–490 61. Pandey RK, Panda SS (2013) Drilling of bone: a comprehensive review. J Clin Orthop Trauma 4:15–30 62. Wiggins KL, Malkin S (1976) Drilling of bone. J Biomech 9:553–559 63. Bertollo N, Walsh WR (2011) Drilling of bone: practicality, limitations and complications associated with surgical drill bits. In: Klika V (ed) Biomechanics in applications. InTech, London 64. Huang C-H, Jan L-C, Li R, Shih A (2007) A three-dimensional inverse problem in estimating the applied heat flux of a titanium drilling-theoretical and experimental studies. Int J  Heat Mass Transf 50:3265–3277 65. Agapiou JS, DeVries MF (1990) On the determination of thermal phenomena during drilling—part I. Analytical models of twist drill temperature distributions. Int J Mach Tools Manuf 30:203–215 66. Agapiou JS, DeVries MF (1990) On the determination of thermal phenomena during drilling—part II. Comparison of experimental and analytical twist drill temperature distributions. Int J Mach Tools Manuf 30:217–226 67. Agapiou JS, Stephenson DA (1994) Analytical and experimental studies of drill temperatures. J Eng Ind 116:54–60 68. Saxena UK, DeVries MF, Wu SM (1971) Drill temperature distributions by numerical solutions. J Eng Ind 93:1057–1065 69. Watanabe K, Yokoyama K, Ichimiya R (1975) Thermal analyses of the drilling process. J Jpn Soc Precis Eng 41:1078–1083 70. Fuh KH (1987) Computer aided design and manufacturing of multi-facet drills. PhD dissertation, University of Wisconsin at Madison 71. Chen W-C (1996) Effect of the cross-sectional shape design of a drill body on drill temperature distributions. Int Commun Heat Mass Transf 23:355–366 72. Bono M, Ni J (2001) The effects of thermal distortions on the diameter and cylindricity of dry drilled holes. Int J Mach Tools Manuf 41:2261–2270 73. Bono M, Ni J (2002) A model for predicting the heat flow into the workpiece in dry drilling. J Manuf Sci Eng 124:773–777 74. Bono M, Ni J (2005) The location of the maximum temperature on the cutting edges of a drill. Int J Mach Tools Manuf 46:901–907 75. Strenkowski JS, Hsieh CC, Shih AJ (2004) An analytical finite element technique for predicting thrust force and torque in drilling. Int J Mach Tools Manuf 44:1413–1421 76. Guo YB, Dornfeld DA (1998) Finite element analysis of drilling burr minimization with a backup material. Trans NAMRI/SME 26:207–212 77. Guo YB, Dornfeld DA (2000) Finite element modeling of burr formation process in drilling 304 stainless steel. J Manuf Sci Eng 122:612–619

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78. Min S, Dornfeld DA, Kim JS, Shyu B (2001) Finite element modeling of burr formation in metal cutting. Mach Sci Technol 5:307–322 79. Marusich TD, Usui S, Aphale R, Saini N, Li R, Shih AJ (2006) Three-dimensional finite element modeling of drilling processes. Presented at the 2006 ASME manufacturing science and engineering conference (MSEC), October 8–11, Ypsilanti, Michigan 80. Kalidas S, Kapoor SG, DeVor RE (2002) Influence of thermal effects on hole quality in dry drilling, part 2: thermo-elastic effects on hole quality. J Manuf Sci Eng 124:267–274 81. Davidson SRH, James DF (2003) Drilling in bone: modeling heat generation and temperature distribution. J Biomech Eng 125:305–314 82. Lee J, Rabin Y (2011) A new thermal model for bone drilling with applications to orthopaedic surgery. Med Eng Phys 33:1234–1244

Chapter 2

Experimental Analysis of Titanium Drilling

Drill temperature is a critical factor in drilling of Ti alloys. As a result of the low thermal conductivity of the Ti alloys as the work-material, most of the heat generated in the tool–chip interface transfers to the tool and generates high drill temperature in drilling of Ti alloys. This chapter outlines experimental study of drilling of Ti alloys. In high material removal rate (MRR) drilling of Ti, the heat is concentrated at the tip of the drill. The temperature is so high that the tool material will visibly change color and start to glow. Such high tool temperature is accompanied by the softening of the tool material and leads to drill wear and low productivity. This chapter will demonstrate that, by the appropriate selection of the drill geometry, tool materials, and drilling process parameters, such as feed and peripheral cutting speed (denoted as cutting speed), the high-performance drilling of Ti alloys is possible. It is also important to recognize that, with the continuing innovations of new drill geometry, materials, and coatings, this chapter presents a pathway for future research. The best drill and drilling process parameters are up to manufacturing engineers to discover. In this chapter, drill geometry, process parameters, and design of experiments are first presented to compare effects of different drills and process parameters, followed by two sections on analyses of chips and workpiece after drilling.

2.1  Drills and Drilling Parameters Figure 2.1 shows four types of 4 mm diameter double-fluted twist drills investigated in this chapter. The conventional drill made of M2 high-speed steel (HSS), a common drill material, is shown in Fig. 2.1a. This drill has a 118° point angle and a 30° helix angle, and straight 0.7 mm chisel edge (web) at the center of the drill. The rake angle at the chisel edge is −59° in this conventional drill design. Figure 2.1b shows a web-thinned point twist drill which also has a 118° point angle and a 30° helix angle. Two web-thinning notches are created at both sides of © Springer Nature Switzerland AG 2019 A. J. Shih et al., Metal and Bone Drilling - The Thermal Aspects, https://doi.org/10.1007/978-3-030-26047-7_2

21

22

2  Experimental Analysis of Titanium Drilling

Fig. 2.1  Top and side view of four types of drill: (a) HSS twist drill (Greenfield Industries 44210), (b) WC-Co Twist drill (Kennametal KWCD00344), (c) uncoated WC-Co spiral point drill (Kennametal K285A01563), and (d) TiAlN coated WC-Co spiral point drill (Kennametal K285A01563)

chisel edge to reduce the thrust force while drilling [1]. The web length of this drill is around 0.45 mm. The tool material is the fine grain tungsten carbide in cobalt matrix (WC-Co). Figure 2.1c is a WC-Co spiral point drill which has an advanced drill geometry design with the S-shaped chisel edge at drill center. This S-shaped chisel edge increases the rake angle (above the −59° of the conventional twist drill shown in Fig. 2.1a) [2, 3] and is expected to have a lower thrust force. The drill has a 135° point angle and a 30° helix angle. The web length is around 0.72  mm. Figure 2.1d shows the TiAlN coated WC-Co spiral point drill with the same shape as the drill in Fig. 2.1c. Tool coating can be applied on the drill surface to reduce the friction and tool wear. The coating is subject to the very high temperature during Ti drilling. Feed and cutting speed are two important process parameters to achieve the desired MRR and productivity in drilling. The use of better drill geometry and tool material with higher hardness (and strength) in elevated temperature, as known as the red hardness, can enable larger feed and cutting speed in drilling. Based on the Machining Data Handbook [4], the recommended maximum feed for turning of Ti-6Al-4V using the WC-Co tool is only 0.40 mm/rev, which is much smaller than those of Al alloys (1.0  mm/rev for HSS and 2.05  mm/rev for WC) and cast iron (0.75–1.00 mm/rev). In drilling, the maximum recommended feed also depends on the drill diameter. For drilling using a WC-Co twist drill with the diameter smaller than 6 mm, the recommended feeds for Al alloys, gray cast iron, and Ti-6Al-4V are 0.18, 0.10, and 0.05 mm/rev, respectively. It is obvious that the recommended feed for machining Ti is expected to be slower by at least a factor of 2. At a given feed, the cutting speed can also be increased to improve the MRR. Depending on the work and tool materials, the cutting speed in machining may vary considerably. Based on the Machining Data Handbook, turning Ti alloys

23

2.2  Design of Experiments

should be below 100 m/min [4] since a high speed creates high tool temperature, which accelerates tool wear and limits drill life [5, 6]. In comparison, cutting speed for Al alloys can be 300 m/min using HSS and 600 m/min using WC-Co tool materials [4]. For gray cast iron, typical maximum cutting speeds range from 40 to 450 m/min depending on the cutting tool. However, the cutting speed of drilling is typically much lower than that of turning given more energy-intensive in a confined space. Using an HSS twist drill with smaller than 6 mm in diameter, the maximum recommended cutting speeds for Al alloys, gray cast iron, and Ti-6Al-4V are 105, 49, and 11 m/min, respectively. Low cutting speeds along with a small feed significantly lower the MRR and productivity of Ti alloys.

2.2  Design of Experiments The thrust force and torque are two key output parameters commonly used to evaluate a drilling process. They can be measured using a dynamometer that allows a high sampling rate for force measurement. Figure 2.2 illustrates the three stages, marked as A, B, and C, in drilling. The thrust force and torque in these three stages will be identified. Stage A occurs when the drill has traveled a distance d, which is called the drill point length, from the initial contact. Neglecting the deformation of the workpiece, the drill cutting edge becomes fully engaged with the workpiece at this stage. When the drill tip reaches the back surface of the plate without considering material deformation, as shown in Fig. 2.2, it is marked as the Stage B. Stage C is defined when the drill cutting edge is disengaged from the workpiece without considering the deformation of the workpiece and burr formation. The torque and force changed throughout the drilling process. Values of thrust force and torque at Stage A, denoted as FA and TA, and maximum thrust force and torque during drilling, denoted as Fm and Tm, respectively, can be compared to quantify different drilling conditions.

Stage B

Stage A

Drill d

Workpiece

Fig. 2.2  Illustration of three stages in drilling

Stage C

24

2  Experimental Analysis of Titanium Drilling

Besides thrust force and torque, another variable indicating the effect of drilling condition is the energy E required to drill a hole. Drilling energy E can be expressed as follows:



E = ∫Fdl + ∫ l

l

2π T dl f

(2.1)

where l is the depth of drilling, F is the thrust force, T is the torque, and f is the feed per revolution. In drilling, E is expected to be dominated by the torque term, which accounts for over 99% of the E. The selection of drill, drilling process parameters (feed and cutting speed), and internal or external supply of cutting fluid have directly impacted the productivity and drill life in drilling of Ti alloys. A systematic investigation of drilling the Ti-6Al-4V using the four drills on thrust force, torque, energy, and chip length. Table 2.1 shows input parameters, including the type of drill, cutting fluid delivery, and two key process parameters, feed and cutting speed, on drilling results, including the drill life, drilling time, FA, TA, Fm, Tm, and E of five sets of drilling experiments, marked as Exps. I, II, III, IV, and V. The workpiece is a 6.35 mm thick Ti-6Al-4V plate. The cutting fluid is the water-soluble CIMTECH 500 metal cutting fluid at 5% concentration. The cutting fluid can be applied internally (from two through-the-drill channels, denoted as Int.) and externally (from outside the drill, denoted as Ext.). Based on the drilling time, the experiments are grouped into low-­ speed drilling and high-throughput drilling. The low-speed drilling group includes Exps. I–III, while the rests belong to high-throughput drilling. Exp. I is the baseline drilling process using the conventional HSS drill (Fig. 2.1a) without cutting fluid. Three levels of cutting speeds and a constant feed of 0.051 mm/ rev are chosen to investigate the effect of cutting speed on HSS drilling of Ti-6Al-4V. Exp. II is conducted with an external cutting fluid supply using the same HSS drill. Two identical cutting speeds and one higher speed (27.4 m/min) are carried out under the same feed of 0.051 mm/rev. Exp. III is to compare results of HSS twist drill with three WC-Co drills (WC-Co twist, WC-Co spiral point, and coated WC-Co spiral point drill) at an identical cutting speed of 18.3 m/min and a feed of 0.051 mm/rev without cutting fluid. For the high-throughput group, Exp. IV uses WC-Co spiral point drills at a high cutting speed of 183 m/min while maintaining at 0.051 mm/rev. The drilling time is only 0.57 s for the 6.35 mm thick plate, which is ten times faster than the low-speed group. Three sets of drilling are conducted under the dry, external cutting fluid supply, and internal (through-the-drill) cutting fluid supply conditions to evaluate the drill life and drilling performance. Using the same WC-Co spiral point drill with internal cutting fluid supply, Exp. V studied the balance of feed and cutting speed on drill life under the same MRR as in Exp. IV. Three combinations of speed and feed are selected to maintain the total drilling time of 0.57 s.

8.1 464– 486 0.39– 0.40 464– 486 0.72– 0.79 426– 455 12–20

12.2 401– 413 0.40– 0.44 0.40– 0.44 0.56– 0.58 391– 400 20–35

6.1 8.1 390 417– 420 0.36 0.40– 0.44 390 420– 434 0.80 0.50– 0.54 453 367– 390 N/A 14–24

0.051 74.9 56.0 15.6 11.6 2 N/A

6.1 430– 446 0.39– 0.41 430– 446 0.70– 0.76 387– 427 14–20

74.9 15.6 N/A

N/A

412

0.79

485

0.3

4.1 400

N/A

453

0.80

390

0.36

6.1 390

0.051 112.1 74.9 23.3 15.6 2 2

III HSS twist drill No 18.3

6.1 233– 255 0.23– 0.32 235– 257 0.76– 0.86 603– 628 25–35

N/A 5.7 290–313

N/A

325–360

48–54

351–375

40–58

358–407

0.42–0.49 0.44–0.57

177–181

0.38–0.42 0.37–0.39

5.7 166–169

N/A

a

0.57 132– 144 0.24– 0.29 166– 201 0.96– 1.31 497– 709 0–5

145– 167 0.28– 0.31 145– 181 0.53– 1.45 504– 574 0–10

0.051 749 156 10 14

172– 202 0.47– 0.53 205– 241 1.02– 1.48 762– 995 18–25

101

IV Coated WC-Co WC-Co WC-Co spiral WC-Co spiral spiral twist point drill point drill point drill drill No Ext Int 183

Ext external cutting fluid supply, Int internal (through-the-drill) cutting fluid supply, No no cutting fluid supply b Through 6.35 mm thick plate

Chip length (mm)

E (J)

Tm (N-m)

Fm (N)

TA (N-m)

56.0 11.6 N/A

0.051 37.2 7.7 N/A

HSS twist drill HSS twist drill No Ext 9.1 13.7 18.3 13.7 18.3 27.4

Drill type Cutting fluid supplya Peripheral cutting speed (m/min) Feed (mm/rev) Feed rate (mm/min) MRR (mm3/s) Drill life (number of holes) Drilling timeb (s) FA (N)

II

I

Exp.

0.57 184– 195 0.72– 0.92 205– 210 1.47– 1.56 1027– 1119 18–30

0.076 749 156 153

258– 292 1.22– 1.34 264– 327 1.72– 3.61 1288– 2415 20–30

205

0.102

WC-Co spiral point drill Int 122 91

V

277– 315 1.26– 1.51 304– 334 2.01– 2.58 1432– 1803 5–15

164

0.152

61

Table 2.1  Experiment process parameter selection, material removal rate, drill life, drilling time, and summary of the thrust force and torque, energy, and length of spiral cone chip

2.2  Design of Experiments 25

26

2  Experimental Analysis of Titanium Drilling

2.3  Results of Low-Speed Drilling 2.3.1  Effect of Cutting Speed and Coolant In Exp I, no obvious wear is observed on the HSS drill after three holes at 9.1 and 13.7 m/min cutting speeds, both with very low MRR. At 18.3 m/min cutting speed, the drill tip melted in the second hole due to high drill temperature. Figure  2.3a shows the thrust force and torque as a function of drilling depth using the HSS drill. The time to reach Stage C (i.e., the time taken by the drill to penetrate the 6.35 mm thick workpiece) is 12.2, 8.1, and 6.1 s at the corresponding cutting speeds, respectively. Variation of thrust forces and torques show similar pattern at three cutting speeds. By increasing the cutting speed from 9.1 to 13.7  m/min, the thrust force rises by about 50 N or 12%. This is because strain-rate hardening outweighs thermal softening [7]. At both speeds, the thrust forces decrease slightly after Stage A. Between Stages B and C, the thrust forces rapidly decrease because the chisel and cutting edges gradually disengage from the workpiece. The torques increase, instead of decreasing as in the thrust force, after Stage A, because the resistance to chip ejection [8] has a more significant effect on torque. Torques begin to decrease after Stage B at 9.1 m/min cutting speed. At 13.7 m/min cutting speed, the torques start to peak after Stage B, i.e., when the drill chisel edge penetrated the workpiece. The difficulty for chip ejection resulting from the chip welding to the drill flute near the cutting edge is the likely cause. This can be confirmed by the difficulty in removing the chip from the drill after each drilling. At the cutting speed of 18.3 m/min, the curves of thrust force and torque last longer past Stage C due to the melting of drill tip. Figure 2.3b shows the thrust force and torque at cutting speeds of 13.7, 18.3, and 27.4 m/min with an external cutting fluid supply in Exp. II. At 13.7 m/min cutting speed, compared to dry drilling, the thrust force and torque are both reduced. At 18.3 m/min, which is the maximum cutting speed in dry drilling, the drill lasts more than three holes with no obvious wear on cutting edges with the external cutting fluid supply. This is a significant improvement of drill life from the dry drilling condition. At both cutting speeds, the benefit of cutting fluid is noted. When the cutting speed is further increased to 27.4 m/min, which is still low for effective MRR, the drill tip melted in two holes. This illustrates the limited cutting speed and MRR of the conventional HSS drill in drilling the Ti-6Al-4V. The TA, FA, Tm, Fm, and E for all drilling tests are summarized in Table 2.1. For the HSS drill, as shown in Exps. I and II, at a cutting speed of 13.7 m/min, the supply of cutting fluid decreases Tm by about 30%, Fm by about 10%, FA by about 10%, and E by 15%. The combination of low energy input and the cooling and lubrication of cutting fluid improves the drill life.

2.3  Results of Low-Speed Drilling

27

Fig. 2.3  Thrust force and torque of HSS. (a) Exp. I without cutting fluid and (b) Exp. II with ­cutting fluid

28

2  Experimental Analysis of Titanium Drilling

2.3.2  Effect of Drill Type Figure 2.4 shows the thrust force and torque for WC-Co twist drill, WC-Co spiral point drill, and coated WC-Co spiral point drill at the same cutting speed of 18.3 m/ min and a feed of 0.051 mm/rev with no supply of cutting fluid. These results, along with those in Exps. I and II, show the benefits of drill geometry and the WC-Co tool material with lower thrust force and torque. For the HSS drill, compared to the WC-Co twist drill, the first hole needs much higher thrust force (390 N) and about the same peak torque (0.8 N-m). This demonstrates the benefit of web thinning to reduce the thrust force in drill geometry design. The benefit of spiral point drill geometry is also obvious. The WC-Co spiral point drill has the lowest thrust force and torque among all four drills tested. The torque curve for WC-Co spiral point drill is particularly stable, maintaining 0.4 N-m after Stage A, which means the chip ejection is not a problem for WC-Co spiral point drill at this cutting speed. In comparison, the torque for WC-Co twist drill continuously increases from about 0.3 N-m in Stage A to 0.8 N-m in Stage B. The TiAlN coating, a technology developed in the 2000s, does not benefit the drilling of Ti-6Al-4V. The torque for coated WC-Co spiral point drill is in the range of 0.37–0.57 N-m. As shown in Table 2.1, compared to the WC-Co twist drill and coated WC-Co spiral point drill, the WC-Co spiral point drill also has lower thrust force (166–181 vs. 233–257 N and 293–360 N) and energy (351–375 vs. 603–628 J and 358–407  J). This phenomenon has also been reported in a review paper by Ulutan and Ozel [9] that, under the high temperature in machining Ti alloys, the tool coating wears quickly due to delamination and do not provide significant advantages over non-coated WC-Co tools on surface roughness, plastic deformations, surface defects, residual stresses, and white layer formation. Tool coatings might even cause other surface problems such as WC cracking and chemical reactions or accelerate the amount of tool wear. However, the coating technology continues to advance. New multi-layer tool coatings have the potential to overcome this significant technical challenge in high-throughput drilling of Ti alloys.

2.4  Results of High-Speed Drilling Results of Exps. I–III indicate that the WC-Co is the tool material and the spiral point drill is the drill geometry for drilling of Ti-6Al-4V. This uncoated WC-Co spiral point drill is used for the high-throughput drilling of Ti-6Al-4V. At a feed of 0.051 mm/rev, the WC-Co spiral point drill can perform at 183 m/min cutting speed under the dry drilling condition. At this high speed, the feed rate can also increase accordingly with the same chip load. It takes only 0.57 s to drill a through hole in the 6.35 mm thick Ti-6Al-4V plate in Exps. IV and V. Effects of cutting fluid and combinations of feed and speed are summarized in the following sections. Further, analyses of hole quality, tool wear, and chip formation are included.

2.4  Results of High-Speed Drilling

29

2.4.1  Effect of Cutting Fluid Supply As shown in the drill life in Table 2.1, under the dry condition, the WC-Co spiral point drill lasts about ten holes at 183 m/min cutting speed and 0.051 mm/rev feed. Figure 2.5 shows the thrust force and torque before drill breakage in dry drilling. The thrust force is about 150–200 N after Stage A. This is the same level of thrust force for the same drill at 18.3 m/min cutting speed, as shown in Fig. 2.4. The torque starts to peak after Stage B, as a result of difficulty in chip ejection due to chip welding to the drill. The same phenomenon is observed during the use of the HSS drill at a cutting speed of 13.7  m/min, as shown in Fig.  2.3. A significant increase in torque (Tm increases by about 30%) but not the thrust force is observed in the last hole before the drill broke catastrophically during drilling. It indicates that the wear Hole number

200 100

A

3rd BC WC-Co Twist

0.8 0.6 0.4

6.1 s

Torque (N-m)

300

2nd

1

WC-Co Twist

400

6.1 s

0.2 0

0 BC

5.7 s

Torque (N-m)

Thrust force (N)

400 300 200 100

A

1

WC-Co Spiral

0

BC WC-Co Spiral

0.8

5.7 s

A

500

0.6 0.4 0.2 0

BC

Thrust force (N)

WC-Co Spiral+Coating 5.7 s

400 300 200 100 0 0

A

1 Torque (N-m)

A

500

BC WC-Co Spiral+Coating

0.8

6.1 s

Thrust force (N)

BC

A

500

1st

0.6 0.4 0.2 0

5

10

Drilling depth (mm)

15

0

5

10

Drilling depth (mm)

15

Fig. 2.4  Exp. III—thrust force and torque of WC-Co Twist, WC-Co Spiral, and coated WC-Co spiral point drill at the cutting speed of 18.3 m/min

2  Experimental Analysis of Titanium Drilling

A

BC

3

0.57 s

Torque (N-m)

Dry

300 200 100 0 400

200 100

Dry

2

1st 5th

1

9th

External

2

1st

1

13rd

5th

0

0

400

3

Internal

Torque (N-m)

Thrust force (N)

Hole sequence

BC

3

External

300

300 200 100 0

A

0 Torque (N-m)

Thrust force (N)

Thrust force (N)

400

0.57 s

30

0

5

10

Drilling depth (mm)

15

Internal

1st

2

50th

1 0

100th 0

5

10

Drilling depth (mm)

15

Fig. 2.5  Exp. IV—thrust force and torque of WC-Co spiral point drill for high-throughput drilling at 183 m/min cutting speed and 0.051 mm/rev feed under the dry and internal and external cutting fluid supply conditions

is concentrated on the periphery of the cutting edges, which is confirmed by visual observation of the drill wear pattern during the test and will be confirmed later in the drill stress analysis in Sect. 3.4. Using external flood cutting fluid supply increases the drill life only slightly to about 14 holes under the same cutting speed and feed as in dry drilling. The high drill rotational speed generates high centrifugal force and prevented the cutting fluid from reaching the cutting zone in the center of the drill. As shown in Fig. 2.5, the thrust force and torque have similar values and patterns as in dry drilling. The increase in torque near the end of drilling is another indication that the chip evaluation is a problem for drilling with external cutting fluid supply. The use of an internal cutting fluid supply significantly increases the drill life to 101 holes at 183 m/min cutting speed and 0.051 mm/rev feed. The cutting fluid supplied through the machine spindle and the drill directly reaches the tool–chip ­interface for effective cooling, lubrication, and, more importantly, assistance in chip ejection. The torque curve does not have the high peak between Stages B and C,

2.4  Results of High-Speed Drilling

31

unlike in the dry and external cutting fluid supply conditions. The peak torque ranges from 1.02 to 1.48 N-m and is reached before Stage B. The thrust force is slightly higher, about 200–240  N, likely caused by the hydrodynamic force with internal cutting fluid supply. As shown by the energy E in Table 2.1, drilling with internal cutting fluid supply requires more energy (762–995 J vs. 497–709 J for dry and 504–574 J for external fluid supply) because of the elevated and more uniform torque curve after Stage A. Exp. IV proves that internal supply of cutting fluid is critical to achieve long life in high-throughput drilling of Ti.

2.4.2  Effect of Feed and Cutting Speed The same MRR can be realized with different combinations of feed and cutting speed. In Exp. V, the balance of feed and cutting speed is studied by maintaining the same feed rate (479  mm/min) and MRR (156  mm3/s) as in Exp. IV.  From the 0.051 mm/rev feed in Exp. VI, the feed is increased to 0.076, 0.102, and 0.152 mm/ rev, which is matched with the cutting speeds of 122, 91, and 61 m/min. These combinations yield different drill life, as shown in Table  2.1. The best drill life is achieved at a cutting speed of 91 m/min and a feed rate of 0.102 mm/rev. Adjusting the feed has a significant impact on drill life. Feed is a process parameter which has been overlooked by drilling researchers. Using the conventional twist drill, the range of feed is limited. For the 4 mm drill, the recommended feed is 0.051 mm/rev. Advanced spiral point drill geometry design and new tool material enable the drill to take a higher cutting force and feed. As shown Fig. 2.6, as the feed increases from 0.051 to 0.076 mm/rev, the thrust force stays at about 200 N. Increasing the feed to 0.102 mm/rev only raises the thrust force to about 260 N for the new drill and 330 N at the end of drill life (205 holes). New drill geometry design can withstand such increase in cutting forces. The lower cutting speed at higher feed helps to reduce the drill temperature, which is beneficial to the drill life. However, there is a limit to the increase in drill life associated with the increase of feed. As the feed increased to 0.152 mm/rev, the drill life (164 holes) starts to reduce due to the high cutting force.

2.4.3  Drill Wear in High-Speed Drilling Scanning electron microscope (SEM) micrographs of the progressive wear of a WC-Co spiral point drill for high-throughput drilling at 61 m/min cutting speed and 0.152  mm/rev feed with internal cutting fluid supply in Exp. V are presented in Fig. 2.7. The drill is removed from the machine and examined after drilling 25, 100, and 164 holes. Four SEM micrographs, the overview of drill point and the close-up views of the chisel edge, middle of cutting edge, and intersection of the margin and cutting edge, as shown by boxes in the overview of the drill tip, are presented.

32

2  Experimental Analysis of Titanium Drilling

Fig. 2.6  Exp. V—thrust force and torque of WC-Co spiral point drill for high-throughput drilling at 0.75 m/min feed rate and 156 mm3/s material removal rate with internal cutting fluid supply

After drilling 25 holes, minimal drill wear is seen. The chisel edge is sharp with slight work-material buildup. The middle of cutting has slight material buildup, as marked by A2. Relatively more significant, but not severe, material buildup is observed near the margin of cutting edge due to the relatively high cutting speed in this area. The energy dispersive X-ray spectroscopy (EDS) analysis of areas A1, A2, and A3 shows identical outcome of Ti, Al, and V in elemental analysis. These are the composition of the Ti-6Al-4V alloy, an indication of the adhesion of work-­ material on the drill. EDS X-ray analysis also has W and C, the composition of the tool material, and O, representing oxidation of the drill material at high temperature. After drilling 100 holes, the tool wear is obvious. On the chisel edge, residual Ti work-material buildup on the surface becomes more apparent. Similar work-­ material buildup is observed in the middle and outside corner of the cutting edge. The corner of the drill margin and cutting edge remain sharp, indicating the drill is still capable of effective drilling. The drill tip at the time of drill breakage at 164 holes has fractured significantly but not molten. Close-up views show that the chisel

2.5  Chip Analysis

33

Fig. 2.7  SEM micrographs of tool wear of the WC-Co spiral point drill at 61 m/min cutting speed and 0.152 mm/rev feed with internal cutting fluid supply

edge and middle cutting edge are both fractured. The corner of drill margin and cutting edge is also severely fractured and no longer sharp. The drill has lost its sharp cutting edge for effective drilling.

2.5  Chip Analysis Chip light emission (sparks) can be observed in some Ti alloy drilling tests. Due to the low thermal conductivity of Ti alloys, the chip temperature is high and subsequently creates oxidation or burning. For HSS drill, the chip light emission is observed at cutting speeds of 13.7 m/min and 27.4 m/min for drilling under dry and external cutting fluid supply condition, respectively. For drilling using the WC-Co spiral point drill, no light emission occurs at the cutting speed below 82.3 m/min. For the same WC-Co spiral point drill at 183 m/min cutting speed, the chip sparked

34

2  Experimental Analysis of Titanium Drilling

in almost every hole drilled in dry drilling and drilling with external cutting fluid supply. When the cutting fluid is supplied internally through the drill at the same cutting speed and feed, no chip light emission is observed initially. In general, chip light mission becomes more frequent as the tool wears out over time. This light emission is usually associated with chip welding, which can be identified by the difficulty to remove the chip in the flutes near the drill tip.

2.5.1  Chip Morphology A continuous chip with three regions, initial spiral cone followed by a steady-state spiral cone and a folded long ribbon chip, can be seen in all Ti-6Al-4V drilling tests in this study. An example of the chip generated by WC-Co spiral point drill at a cutting speed of 18.3  m/min and feed of 0.051  mm/rev in dry drilling is shown in Fig. 2.8a. The close-up view of the initial spiral cone, generated at the start of drilling from the beginning of contact to Stage A, is illustrated in Fig. 2.8b. After Stage A, the steady-state spiral cone chip morphology, as shown in Fig. 2.8c, is generated. Due to the increased resistance to chip ejection, the spiral cone changed to folded ribbon chip morphology. The transition from steady-state spiral cone to folded long ribbon chip occurs early, and the length of spiral cone is short. Close-up views of the chip transition region and the folded ribbon chip are shown in Fig.  2.8d and e, respectively. In dry drilling using WC-Co spiral point drill, the length of spiral cone chip decreases from 48–54 mm to 0–5 mm when the cutting speed increases from 18.3 m/ min to 183 m/min. At a cutting speed of 183 m/min, the use of internal cutting fluid supply can assist chip ejection and increased the length of spiral cone chip to 18–25 mm. In Exp. V, at the same MRR, the drilling condition with the longest drill life also has the longest spiral cone chip length, indicating the improved chip ejection under such drilling condition.

2.5.2  Chip Microstructure Serrated chip formation with the saw-tooth shape surface is commonly observed in orthogonal turning of Ti alloys [10–16]. Surprisingly, the saw tooth is not a common feature on the chip surface in high-speed drilling of Ti-6Al-4V. Figure 2.9 shows the chip microstructure under 183 m/min cutting speed in a dry condition (Exp. IV). As labeled as the point F in Fig. 2.9a and magnified in Fig. 2.9b, the saw teeth can be seen only at the outmost edge of the chip. This region is generated by the outmost point on the drill cutting edge. This saw teeth region is less than 50 μm from the chip edge. It is only a very small part of the whole chip. Other than this narrow region, the saw-tooth formation becomes indiscernible. The free surface on the chip degrades to lamellae [17], as shown by an example

2.5  Chip Analysis

35

Fig. 2.8  Chip morphology of Ti-6Al-4V generated by WC-Co spiral point drill at 18.3  m/min cutting speed and 0.051 mm/rev feed in dry drilling: (a) whole chip and regions of the close-up view, (b) initial spiral cone, (c) steady-state spiral cone, (d) transition between spiral cone and folded long ribbon, and (e) steady-state folded long ribbon

point G in Fig. 2.9a and its close-up view in Fig. 2.9c. This observation is different from Ti chips formed in turning [10–16]. Contrary to the orthogonal cutting, chip in drilling is not generated uniformly along the cutting edge. The rake and inclination angles as well as the cutting speed vary along the drill cutting edge. Near the center of the drill, the strain rate is low, where plowing of the work-material occurs. The strain rate and cutting parameters in this region are not likely reaching the critical cutting condition to initiate the chip saw teeth formation. This and the continuously changing cutting conditions along the drill cutting edge likely inhibit the serrated chip formation in drilling of Ti-6Al-4V. At the outmost region of the drill cutting edge, the chip is less affected by the changing cutting speed and tool geometry. This can explain the saw teeth formation in this narrow region.

36

2  Experimental Analysis of Titanium Drilling

Fig. 2.9  SEM micrographs of chip morphology: (a) spiral cone chip, (b) outer edge of the chip, and (c) inner side of the chip

2.5  Chip Analysis

37

Fig. 2.10  SEM micrographs of chips in (a) Exp. D183 (dry drilling), (b) Exp. W183 (internal cutting fluid supply), and (c) close-up view of regions H (Exp. D183) and J (Exp.W183)

To better observe the chip cross-section, the chip samples are mounted in epoxy, sectioned, polished, and then etched. Figure 2.10 shows the close-up view of the chip-free edge in the dry and wet conditions of Exp. IV, denoted as D183 and W183, respectively. The narrow shear bands initiate from the valley of saw-tooth chips are observed in both drilling conditions. The grain structures are elongated along the both sides of shear bands, clearly identifying the severe plastic shear deformation.

38

2  Experimental Analysis of Titanium Drilling

2.5.3  Chip Hardness The thermal softening and strain hardening are two competing factors which determine the hardness of an indent in the chip. Nanoindentation on the chip cross-­ sections is conducted before etching to minimize the influence of chemical etching. Figure 2.11a shows an example of indents on a chip before etching. The spacing between each indent is about 5 μm. After indentation, the sample is etched to expose the crystal structure and determine if the indent is close to the shear band. An example of etched chip sample is shown in Fig. 2.11b. Two indents close to the shear band are marked by circles in Fig. 2.11b. There is no significant difference of hardness between these two and other indents. Over 140 and 60 indents are made in a similar configuration on the saw-tooth chip cross-sections in Exps. D183 and W183, respectively. The hardnesses of all indents are shown in Fig. 2.12 as a function of the distance to the nearby shear band. Considering the scattering characteristics of nanoindentation results because of the small scale of indents and two-phase structure of Ti-6Al-4V [18], it is concluded that the shear band does not change the nanoindentation hardness in the drilled chip of Ti-6Al-4V. This result is different form that observed of commercially pure (CP) Ti chip at low cutting speed turning [16]. At low cutting speed, the thermal effect is weak, so the strain hardening effect dominates. Besides, the commercially pure Ti is a single-phase material, no phase transformation occurs. In high-speed drilling of Ti-6Al-4V, both thermal effect and phase transformation can occur and counteract the strain hardening effect.

2.6  Workpiece Drilled Surface and Subsurface Analysis In high-throughput drilling of Ti-6Al-4V, the workpiece and chip undergo large deformation at high strain rate and temperature, which can alter the microstructure and material properties of the Ti work-material and chip. The high temperature and

Fig. 2.11  Nanoindentation on the chip cross-sections in Exp. D183: (a) before etch and (b) after etch (circled indents: indents close to the shear band)

2.6  Workpiece Drilled Surface and Subsurface Analysis

39

Hardness (GPa)

5 4 3 2 1 0 0

2

4

6

8

10

12

10

12

Distance from saw tooth valley (mm)

(a)

Hardness (GPa)

5 4 3 2 1 0 0

2

4

6

8

Distance from saw tooth valley (mm)

(b) Fig. 2.12  Chip nanoindentation hardness vs. the distance to the shear band: Exps. (a) D183 and (b) W183

subsequent cooling may cause the β phase decomposition, usually by martensitic transformations, to the α′ or α″ phase. The nanoindentation and metallurgical analysis are conducted on the hole surface. For metallurgical analysis of drilled holes, the workpiece specimen is cut in half axially along each drilled hole. The sectioned specimen is metallographically mounted in epoxy, polished for nanoindentation. Additional etching is needed for SEM analysis. Four etched specimens under the high-throughput drilling conditions selected in Exps. IV and V, marked as Exps. D183, W183, W91, and W61  in Table 2.2, are analyzed.

2  Experimental Analysis of Titanium Drilling

40

Table 2.2  Process parameters of the four high-throughput drilling specimens for metallurgical analysis Exp. Cutting fluid supply Peripheral cutting speed (m/min) Feed (mm/rev)

D183 Dry 183 0.051

W183 Int 183 0.051

W91 Int 91 0.102

W61 Int 61 0.152

Int: Internal (through-the-drill) cutting fluid supply

Mechanical properties of the hole subsurface are affected by the combination of phase transformation, thermal softening, and strain hardening during drilling. This layer is usually called the subsurface layer [10, 19] or deformed layer [11] underneath the machined surface. The subsurface layer adjacent to the hole surface is narrow, only a few μm wide. The nanoindentation is applied to measure the hardness of subsurface layer adjacent to the hole surface.

2.6.1  M  icrostructure on the Workpiece Subsurface of Drilled Hole The polished and etched hole cross-section is examined by a SEM to identify the α and β phases in the subsurface of drilled holes. Figure 2.13 shows the SEM micrographs of the hole cross-section of Exp. D183. As shown in Fig. 2.13a, there is a 10- to 15-μm-thick subsurface layer next to the hole surface. In this layer, there is a gradation of distinct grain boundaries between α and β phases to indiscernible ones from the bulk toward the hole surface. Figure 2.13b shows the high magnification micrograph of the bulk material. Both large and tiny β grains can be observed among the α phase. At the transitional region between the bulk and subsurface layer, as shown in Fig. 2.13c, large β grains are still observable, but most tiny β grains disappear and transform to martensites which have acicular or needle-like shape. This phase transformation is a result of high temperature above β transus temperature and subsequent fast cooling by conduction into bulk and convention to cutting fluid. In the drilling-influenced subsurface layer as shown in Fig.  2.13d, even large β grains disappear. The whole layer is distributed with martensitic grains, but grains are equiaxed, as a result of plastic deformation by rubbing between the drill and hole surface. Because the drilling time is short, the heat-affected zone is significantly narrower than the 125  μm observed in drilling at lower peripheral cutting speed (50 m/min) [20]. Figure 2.14 shows the etched hole surface cross-section of Exps. W183, W91, and W61, which have the same drill feed rate and MRR as in Exp. D183. In Exp. W183, the β structure is observable in regions very close to the hole surface, primarily due to two reasons: less phase transformation above β transus temperature and the following β phase decomposition as a result of a decreased cutting temperature with internal cutting fluid supply. The subsurface layer is about only 3  μm.

2.6  Workpiece Drilled Surface and Subsurface Analysis

41

Fig. 2.13  SEM micrographs of the polished and etched cross-sections of drilled holes in Exp. D183 (dry): (a) hole, subsurface, bulk material, (b) bulk material, (c) transition layer, and (d) subsurface layer

As shown in the high magnification micrograph, the grain structure within the subsurface layer is elongated parallel with the hole edge, indicating the severe plastic deformation. The micrographs of Exps. W91 and W61 show similar features and dimensions as those in Exp. W183.

2.6.2  X-ray Diffraction Analysis The X-ray diffraction (XRD) can quantify the α and β phases and study the phase transformation on the drilled cylindrical hole surfaces. XRD analysis results of as-­ polished bulk material and drilled hole surface of Exp. D183 are shown in Fig. 2.15. The X-ray diffraction pattern of the as-polished bulk material shows that the BCC β phase has a (110) preferred orientation/texture. The HCP α phase is also textured on the (100) and (002) planes. In Exp. D183 (dry drilling), compared to the pattern of as-polished bulk material, the α peaks are clearly broader due to the decreased size of crystallite and likely root

42

2  Experimental Analysis of Titanium Drilling

Fig. 2.14  SEM micrographs of the polished and etched cross-sections of drilled holes for Exps. W183, W91, and W61

mean square strains (i.e., nanostrains) [21], resulting from the severe plastic deformation in the subsurface layer. Drilling process also changes the original texture and makes the α crystallites in the material more randomly distributed. The peaks corresponding to α (100) and (200) planes are weakened relative to the (101) planes. All peaks corresponding to β phase disappear. Because the most prominent changes are concentrated in the range of 30° and 45° 2θ diffraction angle, the close-up view of the XRD patterns along with the fitted profiles of the bulk material and four drilled hole surfaces of Exps. D183, W183, W91, and W61 are shown in Fig. 2.16 for mutual comparison.

2.6  Workpiece Drilled Surface and Subsurface Analysis

43

Square root of counts

As polished bulk material

183 m/min, 0.051 mm/rev, dry

30

40

50 60 70 Diffraction angle, 2q (°)

80

a (202)

a (004)

b (220) a (201)

a (112)

a (200)

a (103)

b (211) a (110)

b (200) a (102)

a (101)

a (002)

a (100)

b (110)

90

Fig. 2.15  X-ray diffraction patterns of the as-polished bulk material and hole surface of Exp. D183 (intensity plotted as square root of counts to help distinguish the weak peaks from the background)

Quantitative analysis by Rietveld method shows 7.3% of β in the bulk material, as labeled in Fig. 2.16. In Exp. D183, the β is reduced to 0%. The X-ray penetration depth is estimated to vary from 4 to 12 μm at 30 to 90° 2θ, respectively, for 95% of the total diffraction intensity. There are two possible causes for the disappearance of β peaks. The main cause is the transformation of a large portion of the β phase to the martensite phase. The other cause is that the residual broadened β peaks are submerged by broadened neighboring α peaks and become indiscernible. The amount of β phase increases to 13.6%, 7.8%, and 11.4% with the introduction of cutting fluid for Exps. W183, W91, and W61, respectively. These values are higher than the 7.3% β phase in the bulk material and indicates that only a small amount, if any, of the β phase transforms to α on the hole surface during drilling due to the better cooling and lubrication with the cutting fluid. Because of the broadened α peaks, the peaks corresponding to β are not obvious in XRD patterns of Exps. W183, W81, and W61 as in Fig. 2.16. Since only one or two tests were conducted for each hole, quantitative results may not be determinative, but the difference between Exps. D183 and W183 is manifested.

44

2  Experimental Analysis of Titanium Drilling

Intensity (counts)

As polished bulk material 7.3%b a profile b profile

30

35 40 Diffraction angle, 2q (°)

D183 0% b

W183 13.6% b

45

a profile b profile

a profile

D91 7.8% b

D61 11.4% b

a profile

30

35 40 Diffraction angle, 2q (°)

a profile

b profile

45

30

35 40 Diffraction angle, 2q (°)

b profile

45

Fig. 2.16  X-ray diffraction spectra of as-polished bulk material and hole edge of Exps. D183, W183, W91, and W61 and calculated profiles from 30° to 45° diffraction angle

2.6.3  Chemical Composition Analysis The wavelength dispersive spectroscopy is used to detect the possible changes in chemical composition, especially the Al as α stabilizer and V as β stabilizer, using an electron microprobe. The Al and V contents are measured at seven points randomly chosen within a region less than 10 μm from the hole surface and seven points in the region far from the hole surface (i.e., the bulk) in Exps. D183 and W183. For comparison, the Al and V contents are also measured in the bulk Ti-6Al-4V material. Table 2.3 summarizes results of average and standard deviation of the Al and V contents. No statistically significant change of Al and V composition can be observed between regions close to and far away from the hole surface, which supports the hypothesis that the β phase decomposition under dry drilling condition is a diffusionless transformation.

2.6  Workpiece Drilled Surface and Subsurface Analysis

45

Table 2.3  Comparison of Al and V content in the chemical analysis of cross-sectional subsurface layer (within 10 μm from the hole surface) in Exps. D183 and W183 and the bulk material

Al (%) V (%)

Bulk Avg 6.7 4.0

Std 0.3 0.8

Exp. D183 Avg 6.7 4.1

Std 0.6 0.1

Exp. W183 Avg 6.5 4.1

Std 0.2 0.5

The same diffusionless transformation for the decomposition of β phase is also observed in the heat treatment of Ti-6Al-4V [22]. Any β phase decomposition is more likely due to the high temperature. This matches with the same conclusion observed in turning of Ti-6Al-4V [23] but is different from the result reported in [24] for drilling of Ti-6Al-4V at low feed rate.

2.6.4  Nanoindentation Figure 2.17 shows the nanoindents and associated hardness values of the hole cross-­ section in Exp. D183, which has a 15–20 μm subsurface layer of almost 0% β phase. Figure 2.17a shows a matrix of indents in directions roughly parallel and perpendicular to the hole axis. The spacing between each indent is about 8–12 μm. Another set of nanoindentations with a line of nanoindents close to the hole surface is shown in Fig. 2.17b. Higher hardness values are found at indents closer to the hole surface. Adjacent to the hole surface, the hardness can reach 10.0 GPa. All indents are under the same 2 mN load. Figure 2.18 compares the nanoindentation hardness, H, vs. distance from the hole surface in Exps. D183, W183, W91, and W61. The layer of high hardness exists in all conditions, but the extent and the depth of high hardness layer are different. The highest hardness exists under the dry drilling condition in Exp. D183. At the region less than 5 μm from the hole surface, the hardness is over 8 GPa, which is about twice the hardness measured in the bulk. The high hardness layer is about 15–20 μm wide, which is in reasonable agreement with the microstructural observations of Exp. D183 as in Fig. 2.13. The thickness of hardened layer is significantly narrower than prior results observed in drilling at moderate speed [20] and demonstrates a benefit of high-throughput drilling. The existence of this hardened layer is the result that high strain-rate plastic deformation outweighs the thermal softening. The high temperature β phase decomposition may also contribute to the formation of this layer [19, 20]. Beyond this layer, the hardness is stabilized around 4.1–5 GPa. When the cutting fluid is supplied at the same cutting speed and feed (Exp. W183), the peak hardness reduces to 5–5.5 GPa in the subsurface layer close to the hole edge. This hardness is only slightly higher than that of the bulk material. The thickness of hardened layer is also reduced to between 5 and 15 μm. Relative to the results of Exp. D183, the benefit of cutting fluid to lubricate the tool–chip interface and reduce the temperature and plastic deformation on the hole surface is apparent.

46

2  Experimental Analysis of Titanium Drilling

Fig. 2.17  Nanoindentation on the workpiece cross-section in Exp. D183: (a) an array of indents and (b) a line of indents close to the hole edge

For Exps. W91 and W61, no significant change in the hardness profile from Exp. W183 is observed. The peak hardness remains in the range of 5–5.5 GPa as in Exp. W183. The thickness of machining affected layer is about 5 μm, which is smaller than that of Exp. W183. The decrease in layer thickness is likely the result of smaller plastic deformation and a lower strain hardening effect at high feed and lower cutting speed.

2.6.5  Burr Formation A burr is a raised edge or small piece of material remaining attached to a workpiece after a modification process. It is usually an unwanted piece of material at the exit of the hole after drilling. To get a clean finish, it has to be removed with a deburring tool. Low burr formation is another advantage of the WC-Co spiral point drill. Figure 2.19 shows pictures of the exit burr formed during drilling using HSS twist, WC-Co twist, and WC-Co spiral point drills at 18.3 m/min peripheral cutting speed and 0.051 mm/rev feed. The WC-Co spiral point drill with TiAlN coating generated similar burrs as the WC-Co spiral point drill. Due to the low thrust force in the S-shaped web, short drill point length, and large point angle of WC-Co spiral point drill, a cap is formed between Stages B and C at the exit. Efficient cutting on the periphery of the cutting edge as the drill exited the workpiece gives rise to a small residual burr as compared to the crown and flower-like exit burr generated by the HSS twist and WC-Co twist drills.

2.6  Workpiece Drilled Surface and Subsurface Analysis

Hardness, H (GPa)

12

D183

183 m/min 0.051 mm/rev Dry

W183

183 m/min 0.051 mm/rev Wet

W91

91 m/min 0.102 mm/rev Wet

8

4

0

Hardness, H (GPa)

12

8

4

0

Hardness, H (GPa)

12

8

4

0

12 Hardness, H (GPa)

Fig. 2.18 Nanoindentation hardness profile of subsurface adjacent to the hole edge in Exps. D183, W183, W91, and W61

47

61 m/min 0.152 mm/rev Wet

W61

8

4

0 0

20

40

Distance from hole wall (mm)

60

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2  Experimental Analysis of Titanium Drilling

Fig. 2.19  Burr formation of three types of drill at 18.3 m/min cutting speed (1470 rpm)

2.7  Concluding Remarks High-throughput drilling of Ti-6Al-4V with good drill life has been demonstrated feasible with the proper selection of drill, setup, and process parameters (cutting speed and feed). The fine grain WC-Co drill with S-shaped chisel edge and internal (through-the-drill) cutting fluid supply has been demonstrated to be critically important for the drill life. High MRR of 156 mm3/s with peripheral cutting speeds of up to 183 m/min can be achieved using this WC-Co spiral point drill. In comparison, a conventional HSS drill is only feasible below the cutting speed of 27.4  m/min achieving an MRR of 23.3  mm3/s. The WC-Co spiral point drill design shows advantages of low thrust force, torque, energy, and small burr size. The balance of cutting speed and feed is critical in high-throughput drilling of Ti-6Al-4V. Under the same MRR (156 mm3/s), the best drill life and surface finish results have been achieved at the peripheral cutting speed of 91 m/min and feed of 0.102 mm/rev using the 4 mm diameter WC-Co spiral point drill.

References

49

The internal cutting fluid supply through the drill is also critical for long drill life. It helps to improve the chip ejection, as demonstrated by the increased length of steady-state spiral cone chip region. The high pressure fluid delivery system may further improve the tool life for high-throughput drilling of Ti alloys. Metallurgical studies, including SEM, XRD, electron microprobe, and nanoindentation tests, are useful tools to investigate the holes and chips. High-throughput drilling decreases the size of crystallite and likely rms strains, changes the original texture, and makes the α crystallites in the material more randomly distributed. In dry drilling, the transformation of BCC β phase into martensitic HCP α phase is identified in a 10- to 15-μm wide subsurface layer adjacent to the hole surface by SEM and XRD analysis. This transformation is proved to be diffusionless, i.e., without chemical composition change. High hardness is found in this layer by nanoindentation testing. No obvious β phase decomposition occurs with the supply of cutting fluid. The high hardness layer is also narrower than that of dry drilling. The chip for drilling of Ti-6Al-4V has complicated morphology. The saw-tooth feature only forms at the outmost region of the drill cutting edge, mainly due to the variable cutting speed along the cutting edge. Narrow shear bands can be observed in the cross-sections of the chip with distinct saw teeth, but no significant change of hardness inside the chip near the shear band has been found using nanoindentation tests. As an indication of high temperature, chip light emission in high-throughput drilling of Ti alloys has been observed and particularly prominent for worn drills. This chapter provides a pathway for future experimental study of drilling of advanced materials. The drill material, coating, and geometry continue to improve. This has opened new opportunities for manufacturing engineers for breakthrough technology for drilling. To accelerate the pace of technology evolution, the drilling modeling, to be discussed in the following chapter, is a necessary engineering tool to gain fundamental understanding and create new innovations.

References 1. Stephenson DA, Agapiou JS (2016) Metal cutting theory and practice, 3rd edn. CRC Press, Boca Raton 2. Ernst H, Haggerty WA (1958) Spiral point drill-new concept in drill point geometry. ASME Trans 80:1059–1072 3. Li R, Riester L, Watkins TR, Blau PJ, Shih AJ (2008) Metallurgical analysis and nanoindentation characterization of Ti–6Al–4V workpiece and chips in high-throughput drilling. Mater Sci Eng A 472:115–124 4. Center MD (1980) Machining data handbook, 3rd edn. TechSolve, Cincinnati 5. Kitagawa T, Kubo A, Maekawa K (1997) Temperature and wear of cutting tools in high-speed machining of inconel 718 and Ti-6Al-6V-2Sn. Wear 202:142–148 6. Zareena A, Rahman M, Wong Y (2001) High speed machining of aerospace alloy Ti–6Al–4V. In: 33rd international SAMPE technical conference. Advancing affordable materials technology, Seattle, WA, vol 33. SAMPE, pp 739–750 7. Trent EM, Wright PK (2000) Metal cutting. Butterworth-Heinemann, Boston

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2  Experimental Analysis of Titanium Drilling

8. Ke F (2003) Analysis and modeling of chip ejection in deep hole drilling process. University of Michigan, Ann Arbor 9. Ulutan D, Ozel T (2011) Machining induced surface integrity in titanium and nickel alloys: a review. Int J Mach Tools Manuf 51:250–280 10. Mantle AL, Aspinwall DK (2001) Surface integrity of a high speed milled gamma titanium aluminide. J Mater Process Technol 118:143–150 11. Che-Haron CH (2001) Tool life and surface integrity in turning titanium alloy. J Mater Process Technol 118:231–237 12. Shaw MC, Dirke SO, Smith P, Cook NH, Loewen EG, Yang CT (1954) Machining titanium: a report prepared for the United States air force. MIT Press, Cambridge 13. Komanduri R, Von Turkovich BF (1981) New observations on the mechanism of chip formation when machining titanium alloys. Wear 69:179–188 14. Komanduri R (1982) Some clarifications on the mechanics of chip formation when machining titanium alloys. Wear 76:15–34 15. Xie JQ, Bayoumi AE, Zbib HM (1996) A study on shear banding in chip formation of orthogonal machining. Int J Mach Tools Manuf 36:835–847 16. Sheikh-Ahmad J, Bailey JA (1997) Flow instability in the orthogonal machining of CP titanium. J Manuf Sci Eng 119:307–313 17. Barry J, Byrne G, Lennon D (2001) Observations on chip formation and acoustic emission in machining Ti–6Al–4V alloy. Int J Mach Tools Manuf 41:1055–1070 18. Qu J, Riester L, Shih AJ, Scattergood RO, Lara-Curzio E, Watkins TR (2003) Nanoindentation characterization of surface layers of electrical discharge machined WC–Co. Mater Sci Eng A 344:125–131 19. Machado A, Wallbank J  (1990) Machining of titanium and its alloys—a review. Proc Inst Mech Eng B J Eng Manuf 204:53–60 20. Cantero JL, Tardío M, Canteli JA, Marcos-Bárcena M, Miguélez MH (2005) Dry drilling of alloy Ti–6Al–4V. Int J Mach Tools Manuf 45:1246–1255 21. Cullity BD (1978) Elements of x-ray diffraction. Addison-Wesley, Reading 22. Donachie MJ (1988) Titanium: a technical guide. ASM International, Material Park 23. Bayoumi AE, Xie JQ (1995) Some metallurgical aspects of chip formation in cutting TI-6AL-4V alloy. Mater Sci Eng A 190:173–180 24. Reissig L, Völkl R, Mills MJ, Glatzel U (2004) Investigation of near surface structure in order to determine process-temperatures during different machining processes of Ti6Al4V.  Scr Mater 50:121–126

Chapter 3

Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys

The critical technical information for the drill design and process parameter selection for drilling of Ti alloys is the spatial and temporal distributions of temperature of the drill. The high and concentrated temperature at the drill tip softens the drill material and promotes rapid diffusion wear, chemical reaction, and drill wear and edge chipping. The drill temperature can be studied either experimentally or numerically. Because the heat generation rate and drill temperature are difficult to measure directly during drilling, numerical modeling is a necessary tool to predict the temperature inside the drill. In this chapter, the inverse heat transfer method with the combination of experimental measurement and numerical modeling is presented to find the drill temperature during drilling.

3.1  Overview of Drill Temperature Analysis Methods The experimental, numerical, and inverse heat transfer methods to study the drill temperature destructions are presented in this section.

3.1.1  Experimental Measurements Experimental measurement of drill temperature has been studied for many decades. The drill tip is inside the workpiece during drilling. Measuring the surface temperature of a rapid rotating drill is technically challenging. It is even more difficult to experimentally measure the spatial and temporal temperature distributions inside the rotating drill. The non-contact thermal radiation measurement of the drill surface temperature is not feasible because the Ti work-materials are opaque to the infrared and other light frequency.

© Springer Nature Switzerland AG 2019 A. J. Shih et al., Metal and Bone Drilling - The Thermal Aspects, https://doi.org/10.1007/978-3-030-26047-7_3

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3  Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys

Thermocouple is the most common and direct experimental method to measure the drill temperature. Thermocouple is based on the thermoelectric effect, the generation of electric voltage or electromotive force (emf) due to temperature differences in the thermocouple junction of two dissimilar materials, to measure the temperature. The drill and workpiece are two dissimilar materials, which form a thermocouple junction during drilling. This drill-workpiece thermocouple method has been applied to measure the average temperature of the drill [1–4]. The repeatability and time response of this method are good, but it can only give an overall drilling temperature and cannot provide the peak and spatial distribution of the drill temperature. Another approach is to embed a thin foil inside the workpiece. During drilling, the drill cutting edge contacts the metal foil and forms a tool-workpiece thermocouple. For the electrically conductive metallic workpiece, the foil must be electrically isolated from the workpiece by sandwiching between two thin insulation layers. This method has been demonstrated to be feasible to measure the drill cutting-­edge temperature for drilling of aluminum [5]. This approach has also been successfully applied to measure the temperature in hard turning of hardened AISI 52100 bearing steel [6] and boring of cylinder liner [7]. However, in drilling Ti alloys, the drill tip temperature may exceed 1000 °C, which can melt the thin insulating layer. This multi-layer setup also changes the drilling condition by inserting three layers of different materials. Another disadvantage of this method is the requirement of extensive calibration, especially when the drill has multi-layer coating. Once the coating is worn, a new calibration curve needs to be created to convert the measured emf voltage to temperature. This approach also limits to dry drilling. The cutting fluid may influence the contact and emf voltage between the drill cutting edge and the metallic foil. The approach adopted in this chapter is to embed a miniature thermocouple tip close to the cutting edge to measure the drill temperature at a specific location during drilling [3, 8–10]. Thermocouples with two electrically insulted thin wires (as thin as 0.08 mm in diameter) and a miniature junction tip (as small as 0.1 mm in size) are commercially available and can be attached to the drill for real-time measurement of temperature during drilling. This approach requires careful preparation, for example, grinding of grooves in the hard WC-Co drill, to embed the thermocouple to avoid damaging during drilling. Since these embedded thermocouples can only measure temperature at discrete points away from the cutting edge, finite element thermal modeling of the drill temperature and the inverse heat transfer method are required to take measured temperatures as the input to predict the heat generation and drill temperature distributions. The metallurgical transformation, chemical composition change, and micro-­ hardness measurement of the drill and workpiece materials, which both subject to high temperature and undergo hardness change, can also be used to measure the drill and workpiece temperatures [11–13]. Similarly, drills coated with thermo-­ sensitive paints can be utilized for the drill temperature measurement [1, 14]. A common disadvantage of these methods is that they only measure the peak temperature. Also, these methods require destructive post-test sample analysis.

3.2  IHTM for Drill Temperature Distribution

53

3.1.2  Analytical Modeling Analytical modeling is important to study the temperature distribution in the drill. The analytical modeling of temperature distribution in the drill, which is represented as a semi-infinite body, has been reviewed in [3]. The empirical force equations and experimental data from a series of oblique cutting tests in turning are used to calculate the heat source and estimate the drill temperature. On the analysis of drill temperature as a finite domain, the finite difference method [15, 16] and finite element method (FEM) [9, 17, 18] have been applied. The FEM has emerged as the method for analytical modeling of drill temperature.

3.1.3  Inverse Heat Transfer Method There are two approaches, forward and reverse approaches, for modeling of the drill temperature. The forward approach takes initial, boundary, and surrounding conditions for a thermal model (in this case the FEM thermal model of the drill) to calculate the spatial and temporal temperature distributions of the drill. The heat inputs are usually estimated from the work done by drilling thrust force and torque. The reverse approach, as known as the inverse heat transfer method (IHTM), takes the measured temperatures at specific locations as the input to back calculate unknown parameters, which are usually the missing pieces in the drill thermal FEM. These parameters can be the heat generation at drill cutting edges, unmeasurable geometrical factors, heat transfer coefficients, and others. In IHTM of drill temperature, the drill chisel and cutting edges are divided into a finite number of elementary cutting tool (ECT) segments. Each ECT is an oblique cutting tools during drilling. The force acting on each ECT can be calculated based on experimentally measured thrust force and torque at the start of drilling when ECTs in the drill chisel and cutting edges gradually engage in the cutting action. This approach to solve oblique cutting forces in each ECT has been demonstrated in [19]. Information like chip thickness and shear angle associated with each ECT can be measured from the chip geometry. ECT and its cutting mechanics can provide some information about heat generation. The missing information for a complete drilling temperature thermal model will be solved in IHTM.

3.2  IHTM for Drill Temperature Distribution The IHTM based on thermal FEM of the drill temperature in Ti drilling is carried out in the following eight steps. • Measure the thrust force, torque, and drill temperature at specific points in a drilling test

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3  Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys

• • • • • •

Build the 3D solid model of the drill Identify the ECT of the drill chisel and cutting edges Build thermal FEM of the drill Carry out the oblique cutting analysis of each ECT Calculate the heat generation rate (identify the unknowns) Conduct the inverse heat transfer analysis to find the drill temperature distribution • For wet drilling, calculate the convective heat transfer coefficient and find the temporal and spatial drill temperature distribution These steps are further elaborated in the following sections.

3.2.1  Step 1: Experimental Inputs Figure 3.1a shows an experimental setup with a rotating 25 mm diameter Ti-6Al-4V workpiece and a stationary 9.92 mm diameter WC-Co spiral point drill. The thrust force, torque, and drill temperature are measured as inputs for IHTM solution of drill temperature. This upside-down setup is to have a stationary drill to avoid the entanglement of thermocouple wires embedded on drill for temperature ­measurement during drilling. This setup prevents the noise issue to use the slip ring or sliding contact brush to transmit the small thermoelectric emf voltage from a rotating drill to the stationary workpiece in conventional drilling setup with rotating drill.

Fig. 3.1  Experimental setup: (a) workpiece, drill, fluid hose, and dynamometer and (b) top view and coordinates of thermocouple tips on the drill flank face

3.2  IHTM for Drill Temperature Distribution

55

As shown in Fig. 3.1b, tips of two thermocouples, denoted as TC1 and TC2, are embedded in grooves hand ground on the WC-Co drill (Kennametal K285A03906) flank face and located close to the cutting edge. Two fluid jets can be supplied internally from two spiral holes inside the drill. The torque and thrust force are measured using the piezoelectric drilling dynamometer (Kistler Model 9272). Four drilling experiments, designated as D183, W183, W91, and W61, in four high-throughput drilling conditions as specified in Chap. 2, are analyzed. Symbols D and W represent the dry and wet (internal cutting fluid supply) drilling conditions, respectively. The number represents the drill peripheral cutting speed in m/min. The first experiment D183 is a dry drilling at 183 m/min peripheral cutting speed and 0.051  mm/rev feed. Using the cutting fluid (5% concentration of water-based CIMTECH 500) and maintaining the same MRR (384  mm3/s) and feed rate (4.97 mm/s) as in Exp. D183, three drilling tests, Exps. W183, W91, and W61, were conducted at 183, 91, and 61 m/min peripheral cutting speed and 0.051, 0.102, and 0.152 mm/rev feed, respectively, for drilling. The depth of drilling was 10.2 mm and the drilling time is 2.0 s in all the four experiments.

3.2.2  Step 2: Drill 3D Geometry The 3D solid model of the drill is developed to analyze the oblique cutting angles of the ECT and create the FEM mesh for drill thermal analysis. Figure 3.2 shows the solid model of the spiral point drill. Key parameters of the drill are as follows: 30° helix angle, 135° point angle, 1.9 mm point length, 1.4 mm coolant hole diameter, 52° chisel edge angle, 7° clearance angle at cutting corner, 0.43 mm width of margin, 1.4  mm chisel edge radius, and 1.8  mm chisel edge length. The drill cross-­ section profile perpendicular to the axis of the drill is measured using an optical tool-maker microscope. Using a computer-aided design (CAD) software, this measured cross-section is swiped along a spiral curve with the drill’s pitch and helix angle to generate the spiral drill body. The trajectory of a grinding wheel with drill tip grinding parameters provided by Kennametal (the drill manufacturer) is simulated to remove unwanted material and create the 3D solid model of the spiral drill point with S-shaped chisel edge. This way gives the most precise drill geometry. If the grinding parameters are not available, direct 3D scanning technologies can also be used to reconstruct the drill 3D geometry. However, accurately capturing the undercut areas or deep features around the drill point can be challenging.

3.2.3  Step 3: ECT Identification The drill chisel and cutting edges are divided into seven ECT segments based in the 3D solid model. As shown in Fig. 3.2b, two ECTs are used to represent half of the chisel edge (web of the drill), and five ECTs are used to model the cutting edge of

56

3  Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys

Fig. 3.2  Solid model of the spiral point drill (Kennametal K285A03906): (a) side view and (b) top view with seven marked ECTs

the drill in Fig. 3.1. The whole drill point is composed of 14 ECTs. Each ECT has a straight cutting edge. The length of cutting edge of the ECT at the chisel edge is 0.71 mm and at the cutting edge is 0.85 mm. Figure 3.3 shows the rake angle, inclination angle, and angle between the drill axis and ECT cutting edge of the seven ECTs. These angles are obtained from the drill’s 3D solid model since there is no existing formula to calculate these angles of the spiral point drill. The rake angle in the chisel edge is equal to −29 and −9° for ECTs 1 and 2, respectively. Compared to the conventional twist drill with 118° point angle and −59° rake angle, the spiral point drill has much lower negative rake angles and demonstrated an advantage of the spiral point drill design.

3.2.4  Step 4: Drill FEM The drill solid model is exported to a FEM software for mesh generation. Figure 3.4 shows the FEM mesh of the drill. It is modeled by 68,757 four-node tetrahedral elements. As shown in the top view in Fig. 3.4b, 13 nodes are located on the chisel edge and 11 nodes are placed on each cutting edge to achieve good resolution in the analysis of drill temperature distribution in drilling of Ti-6Al-4V. The initial condition for the FEM is the 20 °C uniform temperature in the drill. Free convection boundary condition is applied to the whole drill, on all inside

3.2  IHTM for Drill Temperature Distribution

57

Fig. 3.3  The rake angle, inclination angle, and angle between drill axis and ECT cutting edge

(through-the-drill holes) and outside surfaces. The heat flux of a vertical wall due to free convection in air is applied on the drill surface [20]: ″ qconv = B ( T − T∞ )

1.25





(3.1)

where B = 1.8 W/m2-K1.25 and T∞ = 20 °C. The boundary condition on the bottom surface at the end of the drill, opposite from the drill tip, is assumed to be maintained at 20 °C. The heat generation in drilling is applied as a line heat source along the contact length of cutting edges. The contact between drill and chip is narrow in Ti-6Al-4V drilling. Compared to the small feed per tooth, the characteristic length of the elements at the cutting edges is much larger. This allows the use of a line heat source at the cutting edge in FEM thermal analysis.

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3  Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys

Fig. 3.4  Mesh for the 3D FEM thermal model: (a) side view and (b) top view

The heat generation (marked as qf) mainly comes from friction and can be calculated as a product of the friction force (Ff) and chip velocity (Vc). These will be determined from ECT analysis.

q f = Ff Vc



(3.2)

3.2.5  Step 5: Oblique Cutting Mechanics in ECT The oblique cutting analysis is utilized to calculate the friction force and chip velocity along the chip flow direction on the ECT rake face. Starting from ECT 1 at the drill tip, ECTs sequentially engage with the workpiece at the start of drilling. After the drill moves a distance equal to the drill point length, all ECTs are engaged with the workpiece. Assuming the thrust force and torque on each ECT do not change and the workpiece does not deform during drilling, the thrust force and torque contributed by each ECT can be found by identifying the incremental increase in measured thrust force and torque at the time when an ECT is fully engaged with the workpiece. Figure 3.5 shows the oblique cutting model of an ECT. Five angles, the inclination angle λ, normal rake angle α, angle between the drill axis and ECT cutting edge

3.2  IHTM for Drill Temperature Distribution

59

FTh

Cutting direction

T ac Ff

h

Chip f

q

Fl a Fn

a Z Fc

l Y ECT

X Ft

Workpiece

Fig. 3.5  Oblique cutting model of an ECT

θ, chip flow angle η, and shear angle ϕ, are defined. According to Stabler’s rule, the chip flow angle η is assumed to be equal to the inclination angle λ. The uncut chip thickness and chip thickness are marked as a and ac, respectively. An orthogonal coordinate system with the X-axis parallel to the cutting direction and the Z-axis perpendicular to the plane determined by the X-axis and the straight cutting edge is defined for each ECT. The Y-axis is perpendicular to the X- and Z-axes to form a right-handed coordinate system. The torque, denoted as T, generates a force component Fc in the direction of the X-axis calculated as Fc = T/r, where r is the distance from the drill axis to the center of the ECT and T is the torque of the ECT. The components of the resultant force along the Y- and Z-axes are Fl and Ft respectively. The thrust force, denoted as FTh, is parallel to the drill axis and can be calculated in terms of Ft and Fl as [9]: FTh = − Fl



cos θ + Ft cos λ

cos2 λ − cos2 θ cos λ

(3.3)

The resultant force on an ECT can be decomposed into force components normal and parallel to the rake face, denoted as Fn and Ff, respectively. Ff is the friction force in the direction of chip flow on the tool rake face. Because the resultant force lies in the plane defined by Fn and Ff, Fl is related to Fc and Ft [21]:



Fl =

Fc ( sin λ − cos λ sin α tan η ) − Ft cos α tan η sin λ sin α tan η + cos λ

(3.4)

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3  Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys

Fc, Fl, and Ft are related with Fn and Ff by



0  Fl  cos λ sin λ 0   −1      0 sin α = sin cos F λ λ 0  c   F   0 0 1   0 cos α  t 

0  0 sinη   Fn  cos α  0 cosη     Ff  − sin α  1 0   

(3.5)

From Eq. (3.5), Ff can be calculated as follows:



Ff =

( cos α cos λ ) Ft + sin α Fc

(3.6)

cos λ cosη + sin α sin λ sin η

The Ft can be solved by substituting Eq. (3.3) into Eq. (3.4). Ft =

FTh ( sin λ sin α tan η + cos λ ) cos λ + Fc ( sin λ − cos λ sin α tan η ) cos θ cos2 λ − cos2 θ ( sin λ sin α tan η + cos λ ) + cos α tan η cos θ

(3.7)

The chip velocity Vc along the chip flow direction is also required to calculate the frictional heat generation. Vc is calculated from the cutting speed V = ωr, where ω is the relative rotational speed between the drill and the workpiece. Vc = V

cos λ sin φ cosη cos (φ − α )

(3.8)

The chip thickness ac corresponding to each ECT is experimentally measured and applied to determine the shear angle ϕ. tan φ =

a cos α ac − a sin α

(3.9)

where a = fd sin θ, in which fd is the feed per tooth and θ is the angle between the drill axis and ECT cutting edge.

3.2.6  Step 6: Heat Generation On the ECT cutting edge, part of the heat generated by friction is transferred to the drill. Defining K to be the heat partition factor that determines the ratio of heat transferred to the drill, the rate of heat generation on the ECT, i.e., qtool = Kqf. In this study, cutting-speed-dependent K is applied [22]:



 k K = 1 −  1 + 0.45 t  kw 

π dw Vc l

−1

  

(3.10)

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3.2  IHTM for Drill Temperature Distribution

Thermal conductivity, kt (W/m-K)

75 72 69 66 63 60 0

200

400

600

800

1000

1200

Temperature (°C)

Fig. 3.6  Thermal conductivity of the WC-Co tool (data provided by Kennametal)

where kt and kw are the thermal conductivities of the WC-Co drill and Ti-6Al-4V workpiece materials, respectively, dw is the diffusivity of Ti-6Al-4V, and l is the tool-chip contact length. All thermal properties are temperature-dependent. The tool thermal conductivity kt is shown in Fig. 3.6. The tool-chip contact length l is proportional to the chip thickness: l = sac



(3.11)

where s is the ratio of the tool-chip contact length to the chip thickness, but it cannot be determined by any means. Therefore, the value of s is the unknown to be solved by the inverse method. The value of s is assumed to be the same across the chisel and cutting edges.

3.2.7  Step 7: IHTM Solution Inverse heat transfer utilizes the temperature measured by thermocouples embedded on the drill flank surface as the input to predict the heat generation rate at the drill chisel and cutting edges. The value of s is calculated using an optimization method. The flowchart for inverse heat transfer solution is summarized in Fig.  3.7. By ­assuming a value for s, the l, K, and qtool are calculated and applied to nodes on the cutting and chisel edges of ECT. The spatial and temporal temperature distribution of the drill can then be found. The inverse heat transfer method is applied to solve s by minimizing an objective function determined by the experimentally measured and FEM-predicted temperature at specific thermocouple locations on the drill flank face. The discrepancy between the experimentally measured temperature at thermocouple j at time ti, T jti , and FEM-predicted temperature at the same thermocouple exp

location and time, T jti

est

, determines the value of the objective function:

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3  Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys

Fig. 3.7  Flow chart of the inverse heat transfer solution of drill temperature ni



nj

(

Obj = ∑∑ T jti i =1 j =1

exp

− T jti

est

)

2

(3.12)

where ni is the number of time instants during drilling and nj is the number of thermocouples selected to estimate the objective function.

3.2.8  Convective Heat Transfer Coefficient (for Wet Drilling) With the cutting fluid supply, it is necessary to estimate the convective heat transfer coefficient, h, of the cutting fluid on the drill. This is solved using the inverse heat transfer method, as illustrated by the flow chart in Fig.  3.8. The convective heat

3.3 Drill Temperature

63

Fig. 3.8  Flow chart of the inverse heat transfer solution of cutting fluid convective heat transfer coefficient

transfer coefficient h is then determined by iteration to minimize the objective function, Obj. The temperature distributions for wet drilling are obtained as well.

3.3  Drill Temperature The temporal and spatial drill temperature distributions in four high-throughput drilling conditions, Exps. D183, W183, W91, and W61 as defined in Sect. 3.2.1, are analyzed.

3.3.1  Inverse Solutions The s and heat generation rate in Exp. D183 is solved first as it is under a free convection condition. By minimizing Obj using the measured temperature at TC1, the value of s is solved as 7.0. Applying the s and temperature-dependent material properties, K and qtool vary both spatially and temporally. To compare the heat transferred to each ECT, qtool is divided by the length of the ECT cutting edge to calculate the heat generation rate per unit length of contact, denoted as q′tool. Results of q′tool of all cases after the full engagement (1.9  mm depth of drilling) are shown in

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3  Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys

Heat generation rate per unit length, q'tool (W/mm)

Exps. 30

W183 W61

D183 W91

Chisel edge

Cutting edge

20 10 0

0

0.2

0.4

0.6

0.8

1

Relative distance from drill center (r/R ) ′ Fig. 3.9  The heat generation rate per unit length qtool at seven ECTs after 1.9  mm depth of drilling

Fig. 3.9 including both dry and wet conditions. Note the coolant provides forced convection to lower the temperature but should not affect the heat generation from the cutting behavior. The difference is a result of different cutting forces and the corresponding cutting speeds. The decrease in cutting speed (and corresponding increase in feed to maintain the same MRR) leads to a lower heat generation rate q′tool (W91 and W61). Assuming s does not change with the supply of cutting fluid, the convective heat transfer coefficient h for the cutting fluid is solved using the inverse heat transfer solution with Exp. W183 and is found to be 15,000 W/m2-K. This value is in the range reported in published experimental data [23]. To quantify the discrepancy between the experimental and modeling results, the root mean square (RMS) error, eRMS, between the measured and predicted temperatures, and the percentage error, p, defined as the ratio of eRMS to the highest measured temperatures, are compared in all the four experiments. The results of eRMS and p at TC1 and TC2 are listed in Table 3.1. The low value of p shows that the IHTM can successfully minimize the objective function to find the solution. Figure 3.10 shows temperature data in the time domain. The discrepancy between the experimental and modeling results is small at thermocouples TC1 and TC2. The eRMS and p, as shown in Table 3.1, are larger in Exp. W183 than those in Exp. D183. This is primarily due to the thermocouple measurement noise induced by cutting fluid. The prediction is still accurate. For both thermocouples, p is less than 5.0%. The FEM thermal model is validated by comparing modeling results with the experimentally measured temperature at thermocouple TC2 which is not used as the input for inverse heat transfer analysis and is therefore an independent measurement. As shown in Fig. 3.10, the modeling temperature in the time domain matches well with the experimentally measured temperature at TC2 as well as TC1.

3.3  Drill Temperature

65

Table 3.1  Root mean square and percentage errors of the predicted and measured temperatures Exp. D183

TC1 9.9 1.4 31.3 4.6 33.0 4.8 7.1 1.0

eRMS (°C) p (%) eRMS (°C) p (%) eRMS (°C) p (%) eRMS (°C) p (%)

W183 W91 W61

Temperature (°C)

Temperature (°C) Temperature (°C) Temperature (°C)

Measurement

FEM

TC1

500

TC2 9.7 1.4 28.7 4.3 22.2 3.2 10.4 1.5

TC2

D183

375 250 125 0 140

W183

105 70 35 0 120

W91

90 60 30 0 100

W61

75 50 25 0

0

5

10

Drilling depth (mm)

0

5

10

Drilling depth (mm)

Fig. 3.10  Comparison of the measured and calculated temperatures at TC1 (input of inverse heat transfer analysis) and TC2 (for validation)

66

3  Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys

3.3.2  Drill Temporal Temperature Distribution Assuming the same convection coefficient h as in W183, the s in Exps. W91 and W61 remains at 7.0, the same as the value in Exp. W183. The temporal change in the ECT temperature at drill chisel and cutting edges in the four drilling tests vs. the drilling depth is shown in Fig. 3.11. When an ECT is engaged in cutting, the temperature of the ECT increases immediately. For dry drilling (Exp. D183), the ECT temperatures continue to increase after the initial rapid jump which occurs upon engagement. This is detrimental to the drill life. The chisel edge temperature is higher than that of the cutting edge only at the very beginning, when the cutting edge has not engaged in the workpiece. After drilling to a depth of 1.9 mm (the point length), ECT 7 (toward the margin) becomes the hottest ECT and remains so until the end of drilling. The peak temperature is high, 1210 °C, which is close to the limit of WC-Co tool material. As shown in Fig. 3.11, cutting fluid can reduce and maintain the drill temperature at a much lower level. Drill temperatures in Exp. W183 reaches a steady-state level shortly after the corresponding ECT is fully engaged with the workpiece. The chisel edge (ECTs 1 and 2) also has a low temperature. In Exp. W183, ECT 6 has a slightly higher temperature than that of ECT 7, which is a different trend than that of Exp.

Temperature (°C)

1200

ECT2

ECT3

ECT5

ECT6

ECT7

D183

900

ECT4

W183

600 300 0

1200

Temperature (°C)

ECT1

W91

900

W61

600 300 0 0

5 Drilling depth (mm)

10

0

5

10

Drilling depth (mm)

Fig. 3.11  Temperature distributions along drill chisel and cutting edges as a function of drilling depth

3.4 Drill Thermo-Mechanical Analysis

67

D183. The radial distance from the peak drill temperature on cutting edge to the drill margin is 0.36 and 1.09 mm for Exps. D183 and W183, respectively. This is beneficial because, away from the drill margin, ECT 6 has a smaller rake angle and stronger cutting-edge geometry than ECT 7 to withstand the high  temperature related softening of the strength of drill material. Under the same cutting speed, the internal cutting fluid supply has a significant effect on the peak drill temperature, reducing it by almost half to 651 °C after 10.2 mm of drilling.

3.3.3  Drill Spatial Temperature Distribution The spatial temperature distribution at any instantaneous time during drilling can be calculated to visualize the heat-affected condition. Figure 3.12 shows the temporal distributions of the chisel and cutting-edge temperatures immediately after the 10.2 mm depth. In comparison between W183 and D183, the result illustrates the effects of cutting fluid to reduce the drill temperature significantly. The peak drill temperature is reduced by almost half to 651 °C after 10.2 mm of drilling. As shown in the previous section, drill temperatures in Exp. W183 reaches a steady-state level shortly after the corresponding ECT is fully engaged with the workpiece. The chisel edge (ECTs 1 and 2) also has a low temperature. In Exp. W183, ECT 6 has a slightly higher temperature than that of ECT 7, which is a different trend than that of Exp. D183. The spatial temperature distribution of Exp. W183 after 10.2 mm of drilling is shown in Fig. 3.12b. The peak temperature has moved inside to ECT 6 as compared to Exp. D183 in Fig. 3.12a. The radial distance from the peak drill temperature on cutting edge to the drill margin is 0.36 and 1.09 mm for Exps. D183 and W183, respectively. The decrease in cutting speed and increase in feed have reduced the temperature at ECT 6, which has the highest temperature among all ECTs. The peak temperature, as shown in Figs. 3.12c, d, has reduced from 651 °C in Exp. W183 to 602 °C and 472 °C in Exps. W91 and W61, respectively.

3.4  Drill Thermo-Mechanical Analysis The drill temperature can be utilized to find the distortion of the drill due to combined thermal expansion and drilling forces on chisel and cutting edge. The temperature-­induced thermal stress is combined with the cutting-induced mechanical stress to estimate the potential failure region in the drill.

68

3  Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys

Fig. 3.12  Temperature distributions at the drill tip after 10.2 mm depth of drilling in Exps. (a) D183, (b) W183, (c) W91, and (d) W61

3.4  Drill Thermo-Mechanical Analysis

69

3.4.1  Drill Deformation Under high temperatures and stresses in drilling, the drill deforms both axially and radially. The increase in drill temperature expands the drill length and diameter due to thermal expansion. The force at the cutting edge decreases the drill length but increases the drill diameter. The combinational effect of temperature and stress changes the drill geometry and affects the shape of the hole. The shape of the deformed drill for Exp. D183 after 10.2 mm of drilling is shown in Fig. 3.13 with 20× amplification of deformation. The drill deformation is quantified by two parameters: the change in the drill length and the diameter. The change in length is defined by the change in total length from the drill tip to the base after imposing the temperature and cutting force on the drill. The change in diameter is the difference between the diameter of the originally round drill and the largest enclosing diameter of the drill after 10.2 mm of drilling. Table 3.2 lists the change in drill length and diameter in four drilling experiments. In all experiments, the thermal expansion effect outweighs the mechanical force effect in increasing the total length and diameter of the drill. The drill expands the most, 18.4 μm in length and 12.0 μm in diameter, in dry drilling, Exp. D183. In wet drilling, the drill deformations are not as significant, about 7  μm increase in length and 3 μm increase in diameter.

Fig. 3.13  Drill deformation after 10.2 mm drilling in Exp. D183 (scale factor of deformation: 20)

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3  Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys

Table 3.2  Drill deformation under the thermo-mechanical and mechanical-only conditions Exp. Length increase (μm) Diameter increase (μm) Length reduction by mechanical load only (mm) Diameter increase by mechanical load only (mm)

D183 18.4 12.0 0.59 0.28

W183 7.66 3.67 0.42 0.29

W91 6.84 3.43 1.17 0.38

W61 6.79 2.95 0.93 0.41

The mechanical force effect (without considering the thermal expansion effect) on the change in length and diameter is also listed in Table 3.2. The drill shortens in axial direction and expands in radial direction, but the deformation is one order of magnitude lower than that under thermo-mechanical conditions. This concludes that the effect of thermal expansion outweighs the mechanical forces in drill deformation.

3.4.2  Drill Stress and Failure Prediction The stress in the drill during the drilling of Ti-6Al-4V is solved using the thermo-­ mechanical FEM. The combination of thermal stress due to high temperature in the drill and mechanical stress caused by the cutting force applied on ECTs determines the spatial and temporal distributions of the drill stress. The 3D FEM mesh (Fig. 3.4) used for thermal modeling is applied for stress analysis. The bottom (away from the tip) of the drill is assumed to be fixed. Cutting forces in each ECT are assumed to be uniformly distributed across the edge of the ECT. These distributed forces are converted into forces on nodes comprising the cutting and chisel edges. WC-Co is a brittle material with very different tensile and compressive strengths. Three commonly used failure criteria for brittle materials are the Rankine, Mohr– Coulomb, and modified Mohr criteria. All failure criteria used three principal stresses, denoted as σ1, σ2, and σ3 with σ1 > σ2 > σ3. The maximum and minimum principal stress, σ1 and σ3, along the drill chisel and cutting edges in the four ­experiments are shown in Fig. 3.14. Under all the four drilling conditions, the drill shows high tensile (positive) σ1 and compressive (negative) σ3 at the chisel edge. A peak of high compressive principal stress σ3 is observed at the location r/R (relative distance to drill center) = 0.2. The whole cutting edge is under a state of high compression with high compressive σ1 and σ3. The Rankine criterion is the simplest among the three brittle material failure criteria. Rankine criterion, also known as maximum normal stress criterion, states that brittle material fails when the principal stress either exceeds the uniaxial tensile strength σt or compressive strength σc. The Rankine criterion can be expressed as σ1 = σt or σ3 = σc. Assuming that the maximum shear stress determines the onset of failure, the Mohr–Coulomb criterion or internal-friction theory suggests that failure occurs

3.4  Drill Thermo-Mechanical Analysis

Max. principal stress, s1 (MPa)

D183 W91

Exps.

3000

Chisel edge

2000

W183 W61 Cutting edge

1000 0 -1000

Min. principal stress, s3 (MPa)

Fig. 3.14 Maximum principal stress, σ1, and minimum stress, σ3, along the drill chisel and cutting edges after 10.2 mm depth of drilling Ti-6Al-4V

71

0 -1000 -2000 -3000 -4000

0

0.2

0.4

0.6

0.8

1

Relative distance from drill center (r/R )

when the Mohr’s circle of a point in the body exceeds the envelope created by two Mohr’s circles for uniaxial tensile strength σt and uniaxial compressive strength σc. If the Mohr envelope is simplified as a straight line, this criterion can be written as follows:



σ1 σ 3 − =1 σt σc

(3.13)

The modified Mohr criterion derives from the Rankine criterion and considers the variation of material strength with lateral compressive stress. It can be described by the following equation:



σ σ σ σ +σ3  max  1 , − 3 , 1 − 1  =1 σ σ σc  c σt  t

(3.14)

The tensile strength σt and compressive strength σc are temperature-dependent. During drilling, the drill temperature and, subsequently, the strength vary temporally and spatially. Hence, the stress limits vary from point to point in a drill. To  quantify how close the material is to failure, three dimensionless σ σ  σ σ stresses σ r = max  1 , − 3  , σ m −c = 1 − 3 , and σt σc  σt σc  σ σ σ σ +σ3  σ m − m = max  1 , − 3 , 1 − 1  associated with the Rankine, Mohr– σc   σt σc σt

72

3  Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys

Fig. 3.15  Comparison of dimensionless stresses, σ r , σ m−c , and σ m−m , after 10.2 mm depth of drilling in Exp. D183

Coulomb, and modified Mohr criteria, respectively, are defined. The closer these dimensionless stresses are to 1.0, the higher the likelihood of the material failure. Figure 3.15 compares these three dimensionless stresses in the drill after 10.2 mm drilling in Exp. D183. It is noticed that values of σ r and σ m − m are about the same, but σ m − c has much lower value. The maximum values of σ r and σ m − m are 0.91 at the cutting edge. However, the maximum value of σ m − c is only 0.71, which is located at the chisel edge. This difference lies in the fact that σ m − c does not consider the limit of normal stress. At the cutting edge, the stress state is closer to the compressive strength than to the shear stress limit as defined by the Mohr–Coulomb criterion. Based on this observation, the modified Mohr criterion is selected to analyze the drill stress because it includes the maximum normal stress limit. The contour plots of σ m − m of three wet drilling experiments are shown in Fig. 3.16. Dry and wet drilling experiments have a totally different pattern of σ m − m . In Exp. D183 (Fig. 3.15), the highest σ m − m (= 0.91) is located at the cutting edge. This is primarily due to the high compressive stress and the low tensile strength σt and compressive strength σc due to high temperature at the cutting edge. In Exps. W183, W91, and W61 (Fig. 3.16), σ m − m at the cutting edge is much smaller compared with that of Exp. D183, and the highest σ m − m is located at the chisel edge. This is due to the increase in tensile strength σt and compressive strength σc at low temperature, especially in the cutting edge. The supply of cutting fluid decreases the maximum σ m − m from 0.91 in Exp. D183 to 0.75 in Exp. W183. Under the wet drilling condition, the maximum σ m − m increases from 0.75 in Exp. W183 to 0.77 and 0.84 in Exps. W91 and W61, respectively.

3.4  Drill Thermo-Mechanical Analysis

73

Fig. 3.16  Distributions of dimensionless stress σ m−m at the drill tip after 10.2 mm depth of drilling in Exps. (a) W183, (b) W91, and (c) W61

The high tool temperature promotes the diffusion wear, while high stress induces brittle fracture. In dry drilling (Exp. D183), the temperature and dimensionless stress at the cutting edge are both high, which results in the severe drill wear at the cutting edge and short drill life. In wet drilling, the drill temperature is low, but the dimensionless stress increases with the reduced cutting speed and increased feed. Thus, the competing factors of

74

3  Modeling of Drill Temperature and Thermal Stress in Drilling of Titanium Alloys

temperature and stress in the chisel edge indicate that an optimum combination of the cutting speed and feed exists. The high-throughput drilling test using the same peripheral cutting speed but a smaller 4.97 mm diameter drill in Chap. 2 shows that the drill life is very short in dry drilling and the highest drill life occurs at 91 m/min cutting speed (0.102 mm/rev feed) with an internal cutting fluid supply. This drill life observation matches to the failure analysis results in this section.

3.5  Concluding Remarks Experimental procedures and computational models are systematically applied to predict the spatial and temporal distributions of drill temperature, stress, and failure for drilling of Ti-6Al-4V. The inverse heat transfer analysis, which utilizes experimentally measured thrust force, torque, chip thickness, and temperature at embedded thermocouple locations as inputs, can provide accurate and complete information on the drill thermal and mechanical conditions in drilling. The inverse heat transfer method is integrated with a FEM thermal model to find the heat partition on the tool-chip contact region and the convective heat transfer coefficient in wet drilling. In Ti-6Al-4V drilling, the highest temperature of the drill occurs in the cutting edge. The modified Mohr criterion predicts that the onset of drill failure initiates in the cutting edge for dry drilling and in the chisel edge for wet drilling. The supply of cutting fluid via through-the-drill holes is critical in reducing the drill temperature. Without cutting fluid, the temperature is high and continues to rise during drilling. The supply of cutting fluid maintains the drill temperature at a constant level during drilling and is able to decrease the drill peak temperature by half. The supply of cutting fluid helps to prevent premature tool failure due to high drill temperature. The maximum dimensionless stress of the modified Mohr criterion decreases from 0.91 in dry drilling to 0.75 in wet drilling at 183 m/min peripheral cutting speed in drilling. Lower cutting speed and higher feed can further reduce the drill temperature while maintaining the same MRR, but the chisel edge would undergo increasingly higher stress. This detailed analysis and prediction of drill failure is a demonstration of the systematical drill temperature measurement and analysis to gain better understanding and improve the drill design and drilling process for high-­ throughput drilling of Ti alloys.

References 1. Tueda M, Hasegawa Y, Nisina Y (1961) The study of cutting temperature in drilling: 1st report, on the measuring method of cutting temperature. Trans Jpn Soc Mech Eng 27:1423–1430 2. Watanabe K, Yokoyama K, Ichimiya R (1975) Thermal analyses of the drilling process. J Jpn Soc Precis Eng 41:1078–1083 3. Agapiou JS, Stephenson DA (1994) Analytical and experimental studies of drill temperatures. J Eng Ind 116:54–60

References

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4. Arai M, Ogawa M (1997) Effects of high pressure supply of coolant in drilling of titanium alloy. J Jpn Inst Light Met 47:139–144 5. Bono M, Ni J (2002) A method for measuring the temperature distribution along the cutting edges of a drill. J Manuf Sci Eng 124:921–923 6. Chen L, Tai BL, Chaudhari R, Song X, Shih AJ (2017) Measurement of machined surface temperature in hard turning. Int J Mach Tools Manuf 121:10–21 7. Chen L, Tai BL, Yang JA, Shih AJ (2017) Experimental study and finite element modeling of workpiece temperature in finish cylinder boring. ASME J Manuf Sci Eng 139:1–11 8. DeVries MF, Wu SM, Mitchell JW (1967) Measurement of drilling temperature by the garter spring thermocouple method. Microtec J 21:583–586 9. Bono M, Ni J (2001) The effects of thermal distortions on the diameter and cylindricity of dry drilled holes. Int J Mach Tools Manuf 41:2261–2270 10. Bagci E, Ozcelik B (2006) Finite element and experimental investigation of temperature changes on a twist drill in sequential dry drilling. Int J Adv Manuf Technol 28:680–687 11. Thangaraj A, Wright PK, Nissle M (1984) New experiments on the temperature distribution in drilling. J Eng Mater Technol 106:242–247 12. Mills B, Mottishaw TD, Chisholm AWJ (1981) The application of scanning electron microscopy to the study of temperatures and temperature distributions in M2 high speed steel twist drills. CIRP Ann 30:15–20 13. Reissig L, Völkl R, Mills MJ, Glatzel U (2004) Investigation of near surface structure in order to determine process-temperatures during different machining processes of Ti6A14V.  Scr Mater 50:121–126 14. Koch U, Levi R (1971) Some mechanical and thermal aspects of twist drill performance. CIRP Ann 19:247–254 15. Saxena U, DeVries M, Wu S-M (1971) Drill temperature distributions by numerical solutions. J Eng Ind 93:1057–1066 16. Watanabe K, Yokoyama K, lchimiya R (1977) Thermal analysis of the drilling process. Bull Jpn Soc Precis Eng 11:71–77 17. Fuh K-H, Chen W-C, Liang P-W (1994) Temperature rise in twist drills with a finite element approach. Int Commun Heat Mass Transf 21:345–358 18. Bono M, Ni J (2006) The location of the maximum temperature on the cutting edges of a drill. Int J Mach Tools Manuf 46:901–907 19. Ke F, Ni J, Stephenson DA (2005) Continuous chip formation in drilling. Int J Mach Tools Manuf 45:1652–1658 20. Orfueil M (1987) Electric process heating. Battelle Press, Columbus 21. Lin GCI, Mathew P, Oxley PLB, Watson AR (1982) Predicting cutting forces for oblique machining conditions. Proc Inst Mech Eng 196:141–148 22. Berliner EM, Krainov VP (1991) Analytic calculations of the temperature field and heat flows on the tool surface in metal cutting due to sliding friction. Wear 143:379–395 23. Kalidas S, Kapoor SG, DeVor RE (2002) Influence of thermal effects on hole quality in dry drilling, part 1: a thermal model of workpiece temperatures. J Manuf Sci Eng 124:258–266

Chapter 4

Experimental Analysis of Cast Iron Drilling with Dry and MQL Conditions

Cast irons have been broadly utilized in engineering applications. In the automotive industry, gray iron (GI), as known as the gray cast iron, is often used for engine blocks due to its high thermal conductivity and damping capability. Nodular iron, also known as ductile iron, has a higher strength and toughness than GI, and is used for many high-loading components such as crankshaft, gears, and axles. A compromise between GI and nodular iron (or the nodular cast iron) is the compacted graphite iron (CGI), which is known for its high strength for making engine smaller, stronger, and lighter. A smaller and lighter engine enables better vehicle fuel efficiency. Drilling of GI is not particularly difficult because of the graphite inside. Graphite is a natural solid lubricant which can reduce the friction between the cutting edge and workpiece. Also, GI has a high melting point to avoid the edge built­up or chip-recasting issues that occur in aluminum drilling. However, due to the high strength of CGI, excessive heat generated from material removal and chip interactions with the tool can be detrimental to the drill. This chapter presents two sets of experimental studies on dry and minimum quantity lubrication (MQL) drilling with shallow and deep holes. The first study is focused on high-speed (high-throughput) shallow hole drilling of CGI between dry and MQL conditions. The second example is focused on deep-hole drilling (without pecking cycle) of nodular irons under various MQL conditions. All tested are conducted with the state-of-the-art coated solid WC-Co drills. Detailed experimental methods and key results are presented in the following sections.

4.1  Overview of Cast Iron Drilling Flood cooling is common in drilling of cast irons. Due to the energy consumption, contamination, aerosol mist, worker health, and many other wet machining-­ associated problems, fluid cooling may not be the most economical way in high-­ volume production. Although dry drilling is possible for limited applications, the © Springer Nature Switzerland AG 2019 A. J. Shih et al., Metal and Bone Drilling - The Thermal Aspects, https://doi.org/10.1007/978-3-030-26047-7_4

77

78

4  Experimental Analysis of Cast Iron Drilling with Dry and MQL Conditions

MQL may further control the heat generation at the drill cutting zone. To enable dry and MQL drilling in the production environment, advancements in drill materials, design, and coatings as well as MQL media, fluid delivery, and compress air delivery play critical roles. Advanced drills have through-the-drill coolant holes following the spiral flutes from the drill end to the point, which allow direct application of metalworking fluid to the cutting zone. Various multi-layer tool coatings, such as TiAlN/TiN, AlCrN, and TiSiN/AlCrN, have been developed to reduce the tool wear and improve the cutting efficiency with a higher allowable cutting speed and productive. The drilling speed and feed must be optimally adjusted for MQL drilling using advanced drill and coating to maximize the drill life and productivity. Dry and MQL drilling of GI, especially shallow holes (aspect ratio less than 10), has proven to be viable, but such drilling for high-strength cast irons such as CGI has not been successfully reported in the literature due to heat-related issues. Heat is not only generated from cutting itself but also from the removed chips and surface contacts between drill and workpiece. Although there have been advanced drills that incorporate special point design, cooling channel arrangement, and coatings, these issues still remain, though may be mitigated. The root cause is that, unlike traditional flood cooling providing sufficient momentum to flush chips away and cool down the passage of flow, MQL relies solely on lubrication from the oil. Since cast irons may have had enough self-lubrication from the graphite, the key to the improved cast iron drilling is cooling and chip evacuation. Therefore, a higher through-the-drill air pressure can possibly improve drilling performance of MQL or dry conditions in cast irons. The Joule-Thomson (J-T) effect due to gas expansion from high to low pressure at the exit of through-the-drill holes of the drill tip provides some cooling to the workpiece. The air flow can also help evacuate chips. This chapter will verify the pressure effect in drilling.

4.2  Dry and MQL Drilling of CGI This section focuses on the experiments of high-speed drilling of CGI in dry and MQL conditions.

4.2.1  Drilling Tool and Experiment Figure 4.1 shows a 4-mm diameter, two-flute WC-Co drill with 135° point angle (Kennametal B255A04000YPC KCK10) used in this study. The WC-Co tool material has 1–3 μm fine grain size WC and 10% Co. The drill has a 5-μm thick multi-­ layer coating (AlCrN base layer, TiAlN/AlCrTiN middle layers, and AlCrN outer layer), an S-shaped chisel edge, three margins, and two 0.7  mm diameter spiral through-the-drill holes. Five points are identified on the chisel and cutting edges, marked as C (center), A and B (closest to the cooling holes), and D and E (near the

4.2  Dry and MQL Drilling of CGI

79

Fig. 4.1  The drill: (a) top view, (b) side view, and (c) angled view of drill tip Table 4.1  Summary of CGI drilling process parameters

Ref. [1] [2] [3] [4]

Feed rate (mm/min) 350 637 637, 716, 796 254, 478

This study 1592

Drill peripheral speed (m/min) 110 80 80, 90, 100

Drill dia. (mm) 10 10 6

L/D 2 2.2 5

Coating TiAlN TiAlN TiAlN

10

2

TiAlN/TiN, AlCrN, 80, 150 TiSiN/AlCrN TiAlN/TiN, AlCrN 100

4

6.3

Feed (mm/ rev) 0.1 0.25 0.15

Lubrication Flood Dry Flood

0.1

Flood

0.2

Dry, MQL

drill margin) for the wear study after drilling tests. Point B is closer to the cooling hole than point A. Comparison of the wear at points A and B can reveal the effect of cooling hole distance from the cutting edge on the drill wear. The drilling process parameters are selected based on the four key research publications on CGI drilling with their drilling data listed in Table 4.1. Alves et al. [1] focused on metal working fluid; Mocellin et al. [2] investigated machinability of CGI with different levels of pearlite; Oliveira et al. [3] compared different drill geometries; Paiva et al. [4] compared three types of drill coatings (TiAlN/TiN, AlCrN, and TiSiN/AlCrN). It is worth mentioned that Cr-based coatings had better drill life at a cutting speed of 80 m/min, while the drill life of multi-layered coating was better at a cutting speed of 150 m/min. Given the advanced drill with a multi-layer coating, the cutting speed is selected to be 100 m/min and feed is 0.2 mm/rev in this study, which correspond to a feed rate of 1592 mm/min and a spindle speed of 7961 rpm. This drilling speed is considered high but tolerable for a coated WC-Co drill in a dry drilling condition. Drilling experiments are conducted in a vertical machining center (Model 4020 by Fadal) with the experimental setup as shown in Fig.  4.2. The machine has a through-spindle single channel MQL capability (Coolubricator by UNIST) retrofitted from the through-coolant system. The pressure supply is up to 690 kPa (7.9 bar) applicable to both MQL and air-only conditions. The chosen MQL working fluid is Coolube 2210EP also by UNIST. Besides the setup of the workpiece, a high-speed

80

4  Experimental Analysis of Cast Iron Drilling with Dry and MQL Conditions

Fig. 4.2  Drilling experimental setup: CGI plate, hole layout, and dimensions

camera (Model FASTCAM-1024PCI by Photron) is placed next to the machine to observe drilling, chip formation, and chip  evacuation. A drilling dynamometer (Model 9272, Kistler) is set next to the test plate for force and torque measurement. CGI workpiece plates are 270 mm in length, 206 mm in width, and 32 mm in thickness. This work-material has a tensile strength of 420 MPa, elastic modulus of 140 GPa, and Brinell hardness number between 210 and 265. A surface cleanup cut of 1 mm in depth was made using a face mill to ensure a flat and smooth surface for drilling since a rough surface can degrade the drill life and affect the experimental results. Each CGI plate is designed to be drilled with 450 blind holes of 4 mm diameter, 25.4 mm depth, and 7 mm spacing. A small piece of CGI plate was mounted on a dynamometer for force and torque measurement. Three drilling experiments are conducted, marked as Exps. I, II, and III. Exp. I is a dry cutting condition; Exp. II is a dry cutting with the through-the-drill compressed air to assist cooling and chip evacuation. Exp. III is performed with MQL at 5 mL/H oil flow rate and 690 kPa compressed air supply. All three experiments use the same speed (100 m/min) and feed (0.2 mm/rev).

4.2.2  Testing Methods Drilling thrust force and torque are used to gauge the performance of a drilling process, which can be measured using a small piece of CGI plate, as shown in Fig. 4.2, on the top of the dynamometer. The thrust force is the primary contributor in advancing the drill while torque contributes to the material removal. For finding tool wear, the drill cutting edges (denoted as points A to E in Fig. 4.1) are measured under an

4.2  Dry and MQL Drilling of CGI

81

Fig. 4.3  The chip speed measurement using a high-speed camera: (a) a chip identified by the red box and its position Pn–1 at time step n–1 and (b) the same chip at position Pn in the next image at time step n

optical microscope at 100× magnification to determine the flank wear as a function of the number of holes. The drill wear is often not linear; therefore, for the first 900 holes, the flank wear is measured every 150 holes (to capture the rapid initial tool wear). After 900 holes, the flank wear is measured every 300 holes. Chip speed is another indicator on the easiness of chip evacuation during drilling. The chip evacuation phenomenon can be visualized via high-speed images recorded (2000  frames/s in this experiment). Five consecutive video images are used to estimate the chip velocity. The position of a specific chip is identified in the images. The relative change in chip position over the elapsed time in two consecutive images is analyzed using MATLAB to estimate the chip speed. Figure 4.3 illustrates steps to estimate the chip speed using two consecutive images. A box is manually selected to define the position of a chip in the image with a center position Pn. The center of the box at time n–1 is marked as Pn–1, which can be automatically obtained using the image tool in MATLAB. The chip velocity vector in the image plane can be calculated using the known time interval and positions of Pn and Pn–1. The chip speeds from four consecutive time steps are used to calculate the average chip speed. This speed indicates the ability for a chip to escape from the hole.

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4  Experimental Analysis of Cast Iron Drilling with Dry and MQL Conditions

4.2.3  Force, Torque, Drill Wear, and Chip Speed The time-series data of thrust force and torque generated for the first hole (new drill condition) in all three experiments are compared in Fig. 4.4. As shown, the results are almost identical, which indicate that effects of air cooling and MQL are not important for drilling itself. The torque data of Exp. I is slightly above the others, which implies a little more resistance in drilling and removing chips. The number of holes drilled before tool breakage is given in Table 4.2 for two repeated tests with the same drilling conditions. The drill life results show substantial differences. In Exp. I for a completely dry condition, the drill life ranges from 639 to 1742 holes. In Exp. II, the drill life significantly increases to 3150 and 2969 holes compared to those in Exp. I. The convective cooling and J-T effect of the drill as well as better chip evacuation all contribute to the improved drill life. The drill

Fig. 4.4  Comparison of the (a) thrust force and (b) torque for drilling the first hole in Exps. I, II, and III

83

4.2  Dry and MQL Drilling of CGI Table 4.2  Three CGI drilling experiments Exp. Lubrication condition I Dry (no compressed air) II Dry (with through-the-drill compressed air) III MQL, 5 mL/h oil with throughthe-drill compressed air

Drill life (number of holes before the drill breakage) Test 1 Test 2 1742 639 3150 2969 2570

2948

Fig. 4.5  The maximum flank wear in two repeated drilling tests of Exps. I, II, and III

life of 2570 and 2948 holes observed in Exp. III is, surprisingly, lower than that of Exp. II.  This indicates the potential for dry drilling of CGI using advanced coated drills. Figure 4.5 shows the maximum flank wear (either at point D or E) vs. the number of hole drilled. A horizontal line is extended from the last drill with wear measurement to the mark of the number of holes when the drill broke. Figure 4.6 shows drill wear before the failure of each condition (1500 for Exp. I; 3000 for Exp. II; 2700 for Exp. III). Overall, the chisel edge (point C) has a small flank wear (less than 50 μm), which is probably benefited from the S-shape drill chisel design. Points D and E have the highest flank wear due to the highest peripheral cutting speed and associated heat. As seen in the figures, the completely dry drilling (Exp. I) experiences a faster wear rate among three, whereas air cooling (Exp. II) and MQL (Exp. III) have a lower and similar trend. In addition, with air cooling and MQL, the drill can withstand more flank wear (up to 370 μm for Exp. II) before the catastrophic failure. This is likely due to the better chip evacuation provided by the air flow, which avoids sudden spikes of torque and force during drilling. Figure 4.7 shows the evolution of the drill flank wear at points A, B, C, D, and E quantitatively in Exp. I (Test #1), Exp. II (Test #1), and Exp. III (Test #2). The wear

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4  Experimental Analysis of Cast Iron Drilling with Dry and MQL Conditions

Fig. 4.6  The top views of three worn drills: (a) Exp. I, Test #1 (1500th hole), (b) Exp. II, Test #1 (3000th hole), and (c) Exp. III, Test #2 (2700th hole)

at all five points increases with the increase in the number of holes drilled in all experiments. For dry drilling in Exp. I, the wear at point C is similar to that at points A and B before the 750th hole. After that, slightly higher wear rates are observed at points A and B. The wear before drill breakage at points A and B is more severe than that of point C. The wears and wear rates at points D and E (margins) are the most as expected. In Exp. II (Test #1) with through-the-drill compressed air, slow wear rates can be seen at all points before 750th hole. The wear at points D and E are, as expected, higher than points A, B, and C. After the 2100th hole, wear rates at points D and E increase rapidly until tool breakage. On the other hand in Exp. III (Test #2) with through-the-drill MQL, stable wear rates at points A, B, and C are observed throughout the drilling of 2700 holes. The wears at points D and E follow the classic tool wear curve with the high wear rate in the first 300 holes, followed by a steady-state wear rate until the 2400th hole, and then a rapid wear rate is observed before the breakage of the drill. The 200 μm wear at points D and E before the drill breakage is lower than the corresponding 320–370 μm wears in two tests in Exp. II. In summary, the drill wear in drilling of CGI is greatly affected by the high peripheral cutting speed. The usage of MQL decreases drill wear and improve the drill life for high-throughput drilling of CGI. Surprisingly, through-the-drill compressed air can have a similar drill performance to that of MQL. This wear rate study reveals that chip heating and clogging may play a major role in CGI drilling. Results of average chip speed at different drilling depths are listed in Fig. 4.8. The highest average chip speed, 5.6 m/s, is measured in Exp. II, while the slowest average chip speed is 1.4 m/s in Exp. I. It is evident that compressed air in Exp. II helps the chip evacuation significantly (over a factor of 3). The average chip speed of 4.1 m/s in Exp. III is slower than that of Exp. II because the inertia of oil particle or the drag of its viscous nature could slightly reduce the air and chip speeds. The linearly fitted lines for Exps. I, II, and III indicate the tendency of chip speed change as a function of depth. There is no significant trend within the tested depth. However, it is possible that the chip speed will decrease as the depth increases due to the increase in total frictional force of the chip in the flute during evacuation.

4.2  Dry and MQL Drilling of CGI

85

Fig. 4.7  The tool flank wear at points A, B, C, D, and E for (a) Exp. I (Test #1), (b) Exp. II (Test #1), and (c) Exp. III (Test #2)

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4  Experimental Analysis of Cast Iron Drilling with Dry and MQL Conditions

Fig. 4.8  The average chip speed vs. drill depth in Exps. I, II, and III

4.2.4  Summary The combination of thermal (convective cooling, lubrication) and mechanical (drill geometry, drill coating, chip geometry, and chip evacuation) effects determines the drill life in this CGI drilling study. The thermal effects on thrust force and torque are minimal for a new drill but do change drill performance over time. Cooling and enhanced chip evacuation caused by the compressed air (Exp. II) has shown a significant improvement in drill life as compared with dry drilling (Exp. I). MQL in theory provides lubrication in machining, but it has limited effects on CGI drilling (Exp. III) compared to the air-only case (Exp. II), likely due to adequate self-­ lubrication from the graphite in CGI. The findings in this experimental study are significant as MQL has not been successful for high-strength cast iron, such as CGI, machining in the automotive industry. These difficult-to-machine materials usually require traditional flood cooling, which greatly increases the costs to set up the production line and other associated operational needs. With the advancements in drill coatings and through-the-drill cooling, dry machining of CGI is possible.

4.3  MQL Deep-Hole Drilling In deep-hole drilling, the drill cooling and chip evacuation are known challenges. Conventional deep-hole drilling often adopts the pecking cycle to allow chip evacuation. However, for a lower air pressure in MQL (480 kPa or 70 psi) compared to high-pressure through-the-drill cooling (over 2100 kPa or 300 psi), chip evacuation may become an issue in MQL deep-hole drilling. Continuously elevated temperature around the cutting zone can cause thermal damage to the drill, hole distortion,

4.3  MQL Deep-Hole Drilling

87

and entire part distortion. To mitigate the heat-related issues, Hussain et  al. [5] reported that higher cutting speed, feed rate, air pressure, and oil delivery can generate lower workpiece temperature. Agapiou [6] concluded that the lower workpiece temperature in CGI gun drilling can be achieved by higher feed and air pressure as well as better drill point design. Higher feed rates can shorten the drilling time and higher speeds can produce higher momentum for chips to travel and escape from the hole bottom. However, these can also create instantaneous thermal damage on the drill. To further understand the effect of these factors, the second part of experimental study aims to quantify drilling performance based on the thrust force, torque, and the workpiece temperature under different feed rates and air pressures using a dual-­ channel MQL delivery system [7]. Provided a long-distance travel of mist flow, the dual-channel system ensures consistent and uniform mist supply during the deep-­ hole drilling.

4.3.1  Drilling Tool and Experiment The MQL drilling experiments are conducted on the EX-CELL-O horizontal machining center (Model XHC-241) using the Bielomatik dual-channel through-­ the-­drill MQL delivery system. A schematic of the setup is shown in Fig. 4.9. The material of the cylindrical workpiece is ductile iron (nodular iron) ASTM A536 grade 80-55-06 with 40 mm in diameter and 210 mm in length. A 10-mm deep pilot hole, as illustrated in Fig. 4.9, is first drilled for guidance. A total depth of 200 mm is planned. The drill is a 10 mm diameter and 220 mm long solid WC-Co drill with 140° point angle (Model A6785TFP-10 by Titex) and a TiNAl coating. For setting up the workpiece, the cylinder is centered and clamped to a drilling dynamometer (Model 9272 by Kistler) to measure both thrust force and torque at the same time over the course of drilling. These data are sampled at 1000 Hz. In addition, five Type E thermocouples with a wire diameter of 0.127  mm (Model 5TC-TT-E-36-72 by OMEGA) are embedded in pre-drilled 1.2 mm diameter holes and filled with high thermal conductivity paste to minimize the thermal contact

Fig. 4.9  Experimental setup for MQL deep-hole drilling (unit: mm)

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4  Experimental Analysis of Cast Iron Drilling with Dry and MQL Conditions

Table 4.3  Machine settings and process parameters in four MQL deep-hole drilling experiment Test # A B C D

Machine settings Air pressure (kPa) 500 1000 500 1000

Feed rate (mm/ min) 240 240 480 480

Spindle speed (rpm) 1600 1600 2400 2400

Cutting parameters Feed (mm/ Cutting speed (m/ rev) min) 0.15 50 0.15 50 0.20 75 0.20 75

resistance. These thermocouple holes are about 3.4 mm from projected drilled hole and 40 mm apart to measure the workpiece temperature increase over time, thus to know the severity of heat generation deep into the hole. Temperatures are recorded at 10 Hz sampling rate. Four drilling conditions, denoted as A, B, C, and D in Table 4.3, include two feed rates (240 and 480 mm/min) and two air pressures (500 and 1000 kPa). The MQL flow rate is 37 mL/h. The higher air pressure (1000 kPa or 10 bar) can be achieved by an external air compressor to double the shop air pressure (500 kPa or 5 bar). Tests A and B are carried out at a slower feed rate (240 mm/min) with 50 s drilling time. Tests C and D are carried out at a faster feed rate (480 mm/min) with 25 s drilling time. Note the spindle speed is much lower than the shallow hole study in the previous section as deep-hole drilling is anticipated to damage and break the drill or wear the cutting edge rapidly during one test. More conservative spindle speeds are used (1600 and 2400 rpm were equivalent to 50 and 75 m/min cutting speed, respectively). Tests A and C are carried out at a low air pressure (500 kPa) and Tests B and D are under the high air pressure (1000 kPa).

4.3.2  Results of Force, Torque, and Temperature Rise The torque data measured during drilling is presented in Fig. 4.10. A rapid increase of torque in Test A (slow feed rate and low air pressure) due to severe chip clogging can be observed after 75  mm of drilling. The maximum torque is over 50  N-m (beyond the measurement range), more than 10 times than that at the beginning of drilling. The steady-state torque result in Test B, around 4 N-m, indicates that the boosted pressure (10 bars) can successfully eliminate the chip clogging problem. On the other hand, doubled feed rate in Tests C and D results in around 35% increase in torque compared to that in Test B. This increase coincides with the increase of feed per revolution (about 33%), which represents the chip thickness. This result also indicates that torque is independent of spindle speed. What is more, despite low air pressure in Test C (5 bars), no clogging phenomenon is observed. This is because high spindle speed produces more momentum to evacuate chips from the deep hole. Since the chips have been able to escape from the hole, the boosted pressure (Test D) does not further reduce the torque.

4.3  MQL Deep-Hole Drilling

89

Fig. 4.10  Measured torque for four drilling conditions

Temperature data at five measurement points are shown in Fig. 4.11, where the profiles from left to right are thermocouples #1 to #5 (top to the bottom), respectively. Data at #4 and #5 in Test A are missing because the machine slowed down and feed changed under the extreme spindle load as a result of chip clogging, the time-series data cannot be aligned well with the depth. In Test A, similar to the phenomena observed in the torque data, the temperature increased rapidly with the increasing drilling depth. The maximum measured temperature was around 275 °C at point #3 (at 150 mm drilling depth). Although Tests A and B have the same torque profile before the depth of 75 mm (Fig. 4.10), the temperature measurements exhibit different profiles at points #1 and #2 (at 10 and 50 mm drilling depth, respectively). The reason is that the chip accumulation cannot be reflected in the torque data until it turns to a severe clogging problem. Temperature reflects the chip accumulation earlier than torque since the heat in chips transfers into workpiece first. Torque change will not occur until excessive amount of chips jammed in the hole. For Tests C and D, the temperature profiles are similar. The higher pressure (10 bars) does not provide extra cooling to deep hole. Their temperatures are much lower than those in Tests A and B due to a faster moving heat source. However, this does not necessarily mean a lower heat generation. Theoretically, Tests C and D produce more heat than Tests A and B at the drill cutting edges.

4.3.3  Temperature Distribution and Hole Quality Based on the temperature inputs, the drilling heat generations to the hole bottom (due to cutting) and to the hole wall (due to friction and chips) can be calculated using an inverse heat transfer method, which was introduced in Chap. 3 and applied

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4  Experimental Analysis of Cast Iron Drilling with Dry and MQL Conditions

Fig. 4.11  Temperature data at five thermocouple locations in (a) Tests A and B and (b) Tests C and D

for MQL deep-hole drilling here. The step-by-step procedures are detailed in Chap. 5. These heat inputs then can be applied to the drilling finite element model to visualize the temperature distribution over time. Figure  4.12a shows four workpiece temperature distributions in Test A from 4 to 100 mm drilling depth with 32 mm increment. Figure 4.12b and c show seven workpiece temperature distributions in Tests B and C/D from 4 to 200 mm with the same 32 mm increment. By comparing the temperature change at 100 mm drilling depth, Test A has a rapid temperature rise beginning at 68 mm due to severe chip accumulation and clogging. The excessive heat results in a wide distribution of high temperature area at 100 mm. Tests C and D are shown in one figure as they have almost identical heat generation. This is another evidence that higher pressure does not necessarily increase the convective

4.3  MQL Deep-Hole Drilling

a

91

20 mm

>50 45

35 200 mm

30 25 20 15

Temperature rise (°C)

40

10 5 0

b

20 mm

36

68

>50

c

20 mm >50

40

30 25 20 15

35 30 25 20 15

10

10

5

5

0 4

36

68

100

132

164 200 mm

Temperature rise (°C)

45

40

Temperature rise (°C)

45

35 200 mm

100 mm

200 mm

4

0 4

36

68

100

132

164 200 mm

Fig. 4.12  Temperature distribution in the workpiece during drilling in (a) Test A (before the occurrence of severe chip clogging), (b) Test B, and (c) Test C/D

cooling effect in the hole. Overall, Tests C/D have the least temperature change among all cases because of the shorter drilling time. By integrating the temperature change over time along with constant density and specific heat, the total heat input for Test B is 7.89 kJ and that of Tests C/D is 4.58 kJ, which are equivalent to averaged heating powers of 158 W (for 50 s) and 183 W (for 25 s), respectively. Tests C/D have a higher heating power due to a higher chip load. All test samples are measured with the coordinate measurement machine (CMM) to determine the hole straightness and cylindricity, as the results shown in Fig. 4.13. Because of the chip clogging and associated high torque and heat, the hole geometry of Test A  appears to be very rough, likely due to excessive rubbing between chips and workpiece. The cylindricity is 0.28  mm and the largest diameter is 10.33 mm, which is considered significant in this hole size (10 mm). In comparison, Test B with high pressure aiding in chip evacuation, the cylindricity is down to 0.047 mm and the largest diameter is only 10.02 mm. Hole geometries of Tests C and D are slightly worse than Test B due to a faster feed rate, and thus more force, torque, and heat generation. Both have a similar cylindricity around 0.087  mm. However, the hole diameter deviations are all within 0.02 mm.

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4  Experimental Analysis of Cast Iron Drilling with Dry and MQL Conditions

Fig. 4.13  CMM measurements of hole geometries of (a) Test A, (b) Test B, (c) Test C, and (d) Test D

4.3.4  Summary The second part of experimental study demonstrates that the use of doubled air pressure (10 bars) effectively reduces the workpiece temperature. It is found that chips could clog intermittently in the hole when the feed and speed provide inadequate momentum for chip evacuation (Test A). Based on the temperature distribution results, such phenomenon results in extreme heat generation on the hole wall surface and rapidly increases the workpiece temperature without simultaneously changing the drilling torque. The duration prior to the significant torque change and occurrence of clogging is defined as chip accumulation, a hypothetical transition stage in an unstable drilling process. Doubled air pressure (Test B) can resolve the intermittent chip clogging problem and its associated heat generation under low drilling feed and speed. However, results also show that no further heat reduction can be achieved by increasing air pressure when no chip accumulation or clogging. Although high speed and feed rate are beneficial to both workpiece temperature and chip evacuation, it generates higher heat on the drill, which could lead to thermal damages on both workpiece and tool sides. Drill life tests are not specifically compared in this work. It is also important to note that dry and air-only drilling (like in the previous study, Sect. 4.3.2) are not recommended in deep-hole drilling. Dry drilling will certainly experience excessive chip clogging in the early drilling stage to break the drill or stall the spindle. Air-only drilling provides pressure to evacuate chips but not lubrication. Unlike shallow hole drilling, lubrication is essential and necessary during a continuous heating and cutting in deep holes.

4.4  Concluding Remarks In the first part of the experiment, a high-throughput drilling was successfully ­conducted with only compressed air. This result shows that, with an advanced coating and drill point design, it is possible to perform drilling of cast irons in a dry

References

93

condition. However, a compressed air (5 bars) is recommended to aid chip evacuation and to provide a certain degree of convective cooling in the process. This finding can potentially lead to substantial cost savings in energy consumption, chips recycling, and oil delivery in the industry and thus a more sustainable drilling process. On the other hand, dry drilling is less feasible for deep-hole drilling when the aspect ratio is larger than 10, provided its continuous heating at the hole bottom. Even in a through-the-drill MQL condition, severe chip clogging can happen anytime when the chips start to jam. The clogging of chips can cause drill and machine damage, or excessive heating and chip rubbing which can distort the hole geometry. Applying high pressure is one solution to resume the process to normal operation. However, in practice, the compressed air at 10 bars consumes lots of energy and may create unbearable noise in the work environment. Alternatively, it was found that a higher spindle speed can also help chip evacuation by providing momentum to the motion, but the trade-offs are more heat generation and slightly worse hole geometry. It is suggested that, for MQL deep-hole drilling, a process optimization should be conducted first to find proper speed and feed before going straight for high air pressure.

References 1. Alves S, Schroeter R, Bossardi RB, Andrade C (2011) Influence of EP additive on tool wear in drilling of compacted graphite iron. J Braz Soc Mech Sci Eng 33:197–202 2. Mocellin F, Melleras E, Guesser WL, Boehs L (2004) Study of the machinability of compacted graphite iron for drilling process. J Braz Soc Mech Sci Eng 26:22–27 3. de Oliveira VV, Beltrão P, Pintaude G (2011) Effect of tool geometry on the wear of cemented carbide coated with TiAlN during drilling of compacted graphite iron. Wear 271:2561–2569 4. Paiva JMF, Amorim FL, Soares P, Torres RD (2013) Evaluation of hard coating performance in drilling compacted graphite iron (CGI). J Mater Eng Perform 22:195 5. Hussain MI, Taraman KS, Filipovic AJ, Immo G (2008) Experimental study to analyse the workpiece surface temperature in deep hole drilling of aluminium alloy engine blocks using MQL technology. J Achiev Mater Manuf Eng 31:485–490 6. Agapiou J  (2010) Development of gun-drilling MQL process and tooling for machining of compacted graphite iron (CGI). Trans North Am Manuf Res Inst SME 38:73–80 7. Tai B, Stephenson DA, Shih AJ (2013) Workpiece temperature during deep-hole drilling of cast iron using high air pressure minimum quantity lubrication. J Manuf Sci Eng 135:1–7

Chapter 5

Modeling of Workpiece Temperature and Thermal Expansion in Dry and MQL Drilling

In the previous chapter we have learned that dry and minimum quantity lubrication (MQL) are viable in drilling of cast irons, but the drilling-induced heat is a great concern that can cause hole distortion expansion or other form errors of the part. For deep-hole drilling, workpiece temperature and related thermal expansion are more prominent on part accuracy. In automotive powertrain production, deep-hole drilling is common in the machining of crankshaft oil holes transmission valve body spool bores and engine block oil feed holes. The position and cylindricity on these holes are critical. In MQL drilling of precision components, the workpiece thermal distortion has been observed as significant to cause position errors in follow-up machining operations. Estimating the thermally induced form or position errors is an important task in planning the tool path and defining proper geometrical dimension and tolerance (GD&T) for the workpiece. In this chapter, two modeling methods based on the inverse heat transfer method (IHTM) are presented to predict temperature distribution and thermal distortion in the workpiece during deep-hole drilling. The first method is based on the linear invariant system. This method requires many temperature inputs along the depth but can precisely estimate the time-dependent heat generation and temperature distribution. The second method uses a polynomial function to approximate heat growth. It does not need many inputs but cannot capture abrupt heat changes. These two methods are detailed in the following sections, along with experimental validation and discussion on their limitations. Lastly, a 3D thermal distortion model is presented to apply the heat generation obtained from IHTM to predict a global part distortion in the workpiece with sequential drilling of multiple deep holes.

© Springer Nature Switzerland AG 2019 A. J. Shih et al., Metal and Bone Drilling - The Thermal Aspects, https://doi.org/10.1007/978-3-030-26047-7_5

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5  Modeling of Workpiece Temperature and Thermal Expansion in Dry and MQL…

5.1  Deep-Hole Drilling Workpiece Thermal Model Thermal analyses on drill, including analytical and finite element models, have been developed extensively in the past decades [1, 2]. In comparison, workpiece temperature in drilling has rarely been discussed. A relatively recent workpiece model, named advection model, using finite element method (FEM) was established to predict the workpiece temperature and hole distortion in dry drilling [3] with heat input from the hole bottom surface (HBS). This model may be limited to shallow holes because, as seen in the drilling experiments in Chap. 4 and Fig. 5.1, the heat input on the hole wall surface (HWS) due to friction between drill margins and workpiece, chip accumulated in the drill for evacuation can be substantial. A more accurate drilling model, therefore, is needed by considering heat generations on both HBS and HWS. Heat generation on HBS can be estimated from models based on drill geometry, operating conditions, and heat partitioning as described in Chap. 3. But the heat input on HWS is difficult to be determined due to the uncertainties of chip movement, friction, and heat partition. In this chapter, the IHTM is used to find these heat fluxes [4]. IHTM utilizes measured temperatures to find unknown heat generation and thermal properties of the system. Thermocouples are embedded in the ­workpiece

Fig. 5.1  Hole wall surface (HWS), hole bottom surface (HBS), and the 2D axisymmetric FEM mesh of the advection model for workpiece temperature simulation in drilling

5.2  Inverse Method 1: Linear Invariant System

97

near the drilled hole surface. The measured workpiece temperatures are the inputs for IHTM to calculate the corresponding heat fluxes on both HBS and HWS. Figure 5.1 is the FEM thermal model used in this chapter. This is a 2D-axisymmetric mesh using four-node linear axisymmetric quadratic element (DCAX4) in ABAQUS. This model is based on the advection model in which layers of elements are sequentially removed as the drill advances [3]. The heat generation due to material removal is applied to each subsequent layer. This so-called advection process mimics the material removal and the moving heat source applied to the HBS in drilling. Note no heat partitioning is required in this model since the advection process accounts for the removal of heat from the workpiece to chip (removed elements). Additional heat flux is applied on HWS to represent the deep-hole drilling scenario.

5.2  Inverse Method 1: Linear Invariant System 5.2.1  Concept In this method, the workpiece is divided into finite amount of segments as shown in Fig.  5.2, with each segment having a temperature input from a thermocouple, denoted as input point (IP). Two heat fluxes on the workpiece to be solved for are denoted as hb on HBS and hw on HWS in deep-hole drilling. Assuming a linear system, the total temperature rise in the workpiece at any IP i can be calculated by the superposition of the temperatures Tbi and Twi contributed by heat fluxes hb and hw, respectively, such that

T i ( t ) = Tbi ( t ) + Twi ( t )



(5.1)

To estimate these heat fluxes, hb, which is generated from drill cutting edges, will be determined first based on the measured temperature at the thermocouple closest to the hole entry surface where the heat from HWS is considered negligible. Assuming hb is a constant throughout the cutting (no wear on the tool), the temperature contributed by hb at all thermocouples can be calculated using the advection model as stated above. Then, Twi is calculated by subtracting Tbi from the measured temperature Ti. Finally, Twi at multiple IPs is used to find the time-dependent hw. The step-by-step procedure is detailed below. The heat flux hb is assumed time-independent throughout the drilling process and uniformly distributed on HBS considering no tool wear, with which the thrust force and torque are constant. Further, the heat loss via convective cooling is assumed negligible in dry or MQL conditions. Under these assumptions, the temperature response is linearly proportional to the heat input—a linear system. Therefore, the temperature at IP 1 is proportional to the temperature profile generated by a unit hb (denoted as Tu) with a scale factor k, as shown in Fig. 5.3. The scale factor k can be obtained by minimizing the objective function below. For a linear system, the solution of hb is the optimal k.

98

5  Modeling of Workpiece Temperature and Thermal Expansion in Dry and MQL…

Fig. 5.2  Segments and temperature IPs (thermocouple locations) along the hole depth in the model

Fig. 5.3  Fitting of hb using the temperature response of a unit heat input

5.2  Inverse Method 1: Linear Invariant System

99

i

min ∑ kTu ( t ) − T 1 ( t )

(5.2)

t =1



subject to k ≥ 0



The heat flux hw on HWS varies with time and drilling depth. Since the temperature Tw at one point is the accumulated result of heat fluxes from different segments at different times, the relationship between the heat flux on P segments and the temperature at IP i can be described as a linear time invariant system, such that

Twij = I ijpg hwpg

(5.3)



where Twij is the temperature response at IP i and time step j, Iijpq is a fourth-order response tensor to the heat flux impulse, and hwpq is a uniformly distributed heat flux on segment p at time step q. Note that q and j both refer to the same drilling time with q representing the time step for the heat flux segments on HWS and j representing the time step for temperature IPs. The response tensor Iijpq is generated numerically with FEM by calculating the temperature response to a unit heat flux input at every time step. The heat flux matrix hwpq is solved by minimizing the objective function p



q

min ∑∑ Twij − Twij_ exp i =1 j =1

(5.4)

where Twij is calculated by Eq. (5.3) using hwpq generated from the optimization iteration, and Tw_expij is obtained by the experimental data and Tbi. The sequential quadratic programming (SQP) method is adopted to solve the optimization problem. Since hwpq is unknown in this method, the given Tw_expij should have at least P IPs (i.e., one IP in each segment) to provide a sufficient condition for solutions. This approach uses temperature data to solve the temporal heat flux change on HWS at each segment. This is a typical IHTM that solves multiple temporal heat fluxes simultaneously. Normally, if the temperature response is sensitive to the heat input, this approach can capture rapid heat flux change within a short time. However, the spatial distribution relies on the number of segments and, at least, one thermocouple for each of them. It can be technically difficult for a considerably deep hole to achieve desired spatial distribution with many thermocouples.

5.2.2  A Case Study An experiment is conducted to evaluate this IHTM for deep-hole drilling. The experimental setup is shown in Fig. 5.4 to test the inverse method. This experiment uses a 10 mm diameter and 220 mm long solid carbide drill with 140° point angle (Model A6785TFP-10 by Titex) classified for MQL deep-hole drilling. The planned

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5  Modeling of Workpiece Temperature and Thermal Expansion in Dry and MQL…

Fig. 5.4  Experimental setup on a Cross Hüller machine

drilling is 120 mm in depth at the center of the cylindrical workpiece, 40 mm in diameter, and 150 mm in length. The work-material is a ductile iron grade 80-55-06 with 7000 kg/m3 density, 24.2 W/m-K thermal conductivity, and 506 J/kg-K specific heat. Five Type E thermocouples with 0.127 mm wire diameter are embedded in the workpiece at positions corresponding to Fig. 5.3 with a = 21 mm, b = 8.4 mm, and c = 10.5 mm. The thermocouple hole is 1.2 mm in diameter and filled with high thermal conductivity paste to minimize the thermal contact resistance. The MQL flow rate is set at 50 mL/h using a Bielomatik dual-channel through tool MQL delivery system on a Cross Hüller horizontal machining center. The spindle speed is 1600 rpm (or 50 m/min cutting speed) and the feed is 0.15 mm/rev. Using the measured temperature data at IP 1 and Eq. (5.2), the hb is found to be 2.90 MW/m2. The FEM-calculated Tbi at five IPs using obtained hb are shown in Fig. 5.5. Good agreement can be observed in the temperature rising region for each IP. The discrepancy after the peak temperature between Tbi and Ti is Twi, which is used to solve the hw. In the FEM model for this experiment, the total hole depth is divided into five segments and 80 equal time steps with 0.375 s per step. The response tensor I in Eq. (5.3) is calculated using a transient thermal FEM. As shown in Fig. 5.6, Iij11 is the temperature response of IPs to the unit heat flux applied on Segment 1 at time step 1. For q > 1, Iij1q can be estimated by shifting the results of Iij11 by (q − 1) time steps.

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Fig. 5.5  Measured temperature and calculated Tb at five IPs under MQL condition

Fig. 5.6  Response tensor Iij11 calculated by transient FEM

The entire response tensor can be estimated by this shifting technique after solving Iij11, Iij21, Iij31, Iij41, and Iij51. For a known response tensor, hwpq can generate the temperature at five IPs. Then, by comparing the calculated Twij and the experimentally measured Tw_expij, the hwpq can be searched using the objective function of Eq. (5.4). The hw can be manually set as 0 for the time steps before the drill enters the segments to reduce the amount of unknowns and to accelerate the convergence of the computation process. The optimal solutions of hw in MQL drilling at five segments and 80 timesteps are shown in Fig. 5.7. A notable increase of hw at Segment 5 implies a critical depth at which

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Fig. 5.7  Results of inverse solution

Fig. 5.8  Temperature distribution of the workpiece under MQL condition by considering heat from (a) only HBS and (b) both HBS and HWS

the effects of chip jamming or drill margin rubbing become severe. This is further confirmed by examining the measured torque from the dynamometer with a rapid increase at that depth. As discussed in Chap. 4, poor chip evacuation is a common issue in deep-hole drilling. Figure 5.8a shows the workpiece temperature distribution in every 20 time steps using the solution considering only HBS (hb). Figure  5.8b shows the workpiece temperature considering both hb and hw. HBS is usually considered as the primary heat source in almost all drilling thermal models, but this is insufficient in deep-hole drilling. The visualization results prove that the heat flux on HWS can significantly

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103

increase the workpiece temperature as the time increases. This large temperature gradient near the hole can cause thermal distortion to degrade the hole form accuracy. The average temperature over the entire model is about 10 °C higher when HWS is considered in addition to HBS. More importantly, although the surface temperatures of the workpiece (right edge of the model) are about the same in Fig. 5.8, the temperature distribution close to the drilled holed is much higher in the case when HWS is considered (Fig. 5.8b). The conventional temperature measurement on the workpiece surface, such as infrared camera, will overestimate the stability and neglect potential dimensional errors near the hole.

5.3  Inverse Method 2: Control Point Method 5.3.1  Concept The second method considers hw as a moving heat source that follows the drill into the workpiece. The spatial distribution of hw at a specific time t is described as hw(x,t) where x is the axial position from the drill cutting edge, as shown in Fig. 5.9. Multiple control points (CPs) with their positions x1, x2, x3, and x4 are assigned to define the spatial distribution of hw(x,t) via spline interpolation. At each time step, the magnitudes of four control points (denoted as CP1 to CP4) vary to update the distribution. For the control point arrangement, the position of CP4, x4, is the drilling depth, which increases with time. CP4 is always the end point of hw(x,t) and the change of heat flux is relatively small. Thus, the value of heat flux at CP4 is set as a constant. The positions of the other three points (x1, x2, and x3) are fixed. CP1 is the start point where x1 = 0. CP2 and the location of x2 determine the peak value of the entire heat flux distribution. CP3 adjusts the tailing edge shape of the heat flux between CP2 and CP4. Before the drill reaches the depth that includes CP1, CP2, and CP3, the control points are activated sequentially. In Fig. 5.10a, at the beginning of drilling with x4 ≤ x2, the shape of heat flux is assumed uniformly distributed. When the drilling depth reaches the position of CP2 (i.e., x4 > x2), as shown in Fig. 5.10b, CP1 and Fig. 5.9  The control points to determine the heat flux spatial distribution on HWS

Drill entry surface x4

CP4 CP3

x3

CP2

x2

x1 = 0 x

CP1

hw(x,t)

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Fig. 5.10  The sequence to activate the control points: (a) stage 1 when x2 ≥ x4 > 0 and (b) stage 2 when x3 ≥ x4 > x2

CP4

CP4

x

CP2 (active) CP1 (active)

x

CP1 (inactive)

x2 ≥ x4 >0

x3 ≥ x4 > x2

(a)

(b)

CP2 are activated simultaneously. Similarly, CP3 is activated and forms a shape as in Fig. 5.10 when the drilling depth exceeds x3. A spline function of hw(x,t) at a given time is determined by the piecewise cubic Hermite interpolation across all control points. In fact, the control points could be assigned in different ways while this arrangement is found to best capture the heat flux change in deep-hole drilling. The heat flux values of control points increase with the drill position in depth due to the increasing heat generation. Therefore, the heat flux of control points can be modeled as a monotonic increasing function, such as linear, bi-linear, exponential, or polynomial, depending on the fitness of the choice. Equation (5.5) is an example of a quadratic function CP 4 : hw ( x4 ,t ) = c0 CP3 : hw ( x3 ,t ) = c0 + c31 ( t − t3 ) + c32 ( t − t3 ) for t > t3 2

(5.5)

CP 2 : hw ( x2 ,t ) = c0 + c21 ( t − t2 ) + c22 ( t − t2 ) for t > t2 2

CP1 : hw ( x1 ,t ) = c0 + c11 ( t − t2 ) + c12 ( t − t2 ) for t > t2 2





where c’s are unknown coefficients, and time t2 and t3 are the time when the drilling depth reaches x2 and x3, respectively. During drilling, hw is applied to the advection FEM at the corresponding time step and drill position to calculate the temperature in the workpiece. Using the generated temperature profile at the IPs, Twi, the seven unknown coefficients (c0, c11, c21, c31, c12, c22, and c32) in Eq. (5.5) can be determined by minimizing the objective function of Eq. (5.4), which is similar to Method 1. However, the major difference is that this method is intended to estimate the “trend” of heat flux growth during the process. The quadratic function could be replaced by other functions (e.g., linear, power law, and exponential) as needed. The coefficients may not have a single set of solutions either.

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105

5.3.2  Case Study This method is validated using the same set of data in the previous section. Temperature data from the IPs are used to find the optimal solutions for the seven coefficients (c0, c11, c21, c31, c12, c22, and c32) in Eq. (5.5). Generally, more IPs can reduce the measurement errors and lead to more accurate inverse results. Solutions obtained by three and five IPs are both tested here for comparison. In addition to CP1 and CP4 being the first and last points, positions of CP2 and CP3 (x2 and x3) need to be defined manually. A properly selected position of CP2 is important to fit the temperature profile Tw_expi efficiently during the iterations. For a given Twi at certain IP, the increasing rate of temperature (dTwi/dt) begins to decrease when the maximum portion of hw passes that IP. Thus, the peak value position of the derivative of Tw_expi can be used to estimate the corresponding x2. In this model setting, the optimal x2 is found at the nodal point x = 13.5 mm, which yields the peak value positions close to those from Tw_expi for i = 1, 2, 3, 4, and 5. This further affirms the hypothesis of a constant x2. The convergence of the search process is found sensitive to the initial value c0 more than other coefficients. Thus c0 is set as an optimization parameter instead of variable. The optimization result shows that c0 = 0.01 yields the minimum objective function, among the other test values of 0, 0.01, 0.02, and 0.03. The optimized coefficients when c0  =  0.01 are listed in Table  5.1, where ∑Err is the summation of temperature discrepancy between Tw_expi and calculated Twi at all five IPs. As expected, the solution of five inputs has smaller ∑Err in comparison to the solution of three inputs. However, the overall heat flux distributions and growth, as shown in Fig. 5.11, are similar in both conditions. The dash lines indicate the positions of CP2 (x2) and CP3 (x3). The heat flux value of CP2 is the peak and increases steadily as the drill advances into the workpiece. For validation and comparison between two methods, two additional thermocouples, marked as A and B, were embedded in the workpiece at arbitrarily selected positions. The modeling results of both Method 1 and Method 2 at these two positions are shown in Fig. 5.12 for comparison. Overall the predicted data from both methods have good agreement with each other and with the experimental data. This indicates the feasibility and robustness of the presented inverse methods. Nonetheless, they both have trade-offs. Although the control point method (Method 2) does not require many thermocouple inputs for a deep hole, it loses its spatial and temporal accuracy when the cutting process encounters a rapid change, such as chip accumulation or clogging. For example, at IP 5 (which is also included in Fig. 5.12), there exists noticeable discrepancy due to significant heat flux change at that depth. Also, Method 2 requires a certain degree of trials-and-errors in the control point Table 5.1  Calculated coefficients of changing rates of control points IPs c11 (×10−2) c21 (×10−2) c31 (×10−2) c12 (×10−4) c22 (×10−4) c32 (×10−4) ∑Err (°C) All 0.085 0.110 0.240 −0.176 0.183 −0. 185 134.6 #1, #3, #4 0.023 0.065 0.216 0.155 0.282 −0.114 149.1

Fig. 5.11  Heat flux change on HWS by applying inverse solutions using (a) five IPs and (b) three IPs

Fig. 5.12  Measured and calculated temperature at Points A and B using the inverse solutions of Method 1 (linear invariant system) and Method 2 (control points)

5.4  Workpiece Thermal Distortion

107

arrangement. In comparison, Method 1 is more robust and can successfully capture the sudden temperature changes. Method 2 is more suitable for a smooth and consistent deep drilling process.

5.4  Workpiece Thermal Distortion Controlling workpiece thermal distortion is critical to achieving part dimensional accuracy and quality control in precision machining processes. The distortion is often caused by workpiece thermal expansion due to the accumulation of high-­ temperature chips on the tool or workpiece surfaces and the conduction of heat from the tool–workpiece interface. For example, for a 1 m long aluminum workpiece, an increase of 1 °C elongates it by about 24 μm. As shown in previous sections and Chap. 4, deep-hole drilling can generate a significant amount of heat on both hole bottom and wall, which conspire to degrade the GD&T form accuracy of the workpiece. Several research studies have been conducted to investigate the workpiece temperature during drilling [5–8]. However, these models are mostly under a steady-­ state condition. In the previous sections, it has been demonstrated that wall heat flux (hw) is a function of time and position. Also, there is lack of a global drilling model that predicts hole-to-hole or hole-to-workpiece thermal interactions. For this reason, this section presents a new modeling technique, named heat carrier model, for estimating workpiece temperature distribution in the event of multiple drillings [9].

5.4.1  Model Concept and Model Construction The heat carrier model is a dynamic 3D FEM in conjunction with heat transfer analysis to simulate the workpiece temperature distribution in deep-hole drilling. As shown in Fig. 5.13a, the heat carrier carries a constant hb and time-dependent hw and moves into the hole region to conduct the heat to the workpiece. The hole region is removed prior to the drilling simulation allowing the heat carrier to move into the hole. This is justified by the fact that the heat transfer in the axial direction is much slower than the drill feed rate; thus, the temperature distribution is not significantly affected by the heat carrier moving into a void space that represents the hole being drilled. This modeling concept overcomes the practical difficulty in the advection model by eliminating the need for removing 3D elements layer by layer, as shown in Fig. 5.13b. Unlike the 2D advection model (axisymmetric), which has a much simpler mesh, the number of elements increases significantly if many thin-layer regions of small 3D elements are used. In the case of drilling multiple holes in a workpiece with complex shape (such as the engine head), the advection model can be time-consuming.

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Fig. 5.13  Schematics of the (a) 3D heat carrier model and (b) 3D advection model

Fig. 5.14  The 3D heat carrier model (a) assembled heat carrier, (b) HWS heat carrier, and (c) HBS heat carrier

The heat carrier consists of HWS carrier and HBS carrier, as shown in Fig. 5.14. Both HWS and HBS carriers move at the drilling feed rate to simulate the heat conduction to the workpiece during drilling. Since the heat carrier and workpiece have different meshes, the inconsistent mesh sizes in hole surfaces may result in elements penetrating each other. Therefore, a small gap (about 1% of the drill diameter) is created between matching surfaces of the hole and the heat carrier. A zero-contact resistance condition must be defined between the surfaces. Also, the carrier should have a near-zero heat capacity to eliminate heat retention in the carrier. Note that zero heat capacity can cause numerical error in FEM.

5.4  Workpiece Thermal Distortion

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5.4.1.1  HBS Heat Carrier The HBS heat carrier has a parallelogram cross-section revolving around the centerline. The angle θ is the drill point angle. Different from the advection model that accounts for heat partitioning by the removal of elements, the carrier carries only the resultant heat that flows in the workpiece. Therefore, a modified (partitioned) heat flux, denoted as hb′, must be used. The partition factor, ζ, can be obtained numerically in the advection model. For a set of hb and hw obtained from IHTM, the total amount of heat absorption during drilling, HT, can be calculated based on the temperature rise and workpiece thermal properties. The contribution of HWS, HHWS, can be calculated by integrating hw by the time and spatial distribution. Therefore, the partition factor for heat flowing into the workpiece through HBS is described in Eq. (5.6), where A is the surface area of HBS and tf is the total drilling time.

ζ =

HT − H HWS hb At f

(5.6)

Another important consideration is the thickness of the carrier. The thickness (lb) must be long enough to emulate heat transfer around the cutting zone (i.e., the hole bottom) but not so large to retain the heat. There is no universal solution for lb, but it must be related to the workpiece thermal diffusivity and the drilling feed rate. A higher thermal diffusivity means a large heat spread-out at the hole bottom, and thus a thicker carrier is needed. A faster feed rate can “catch up” the heat transfer, so the carrier can be thinner. For finding a general guideline to determine the thickness, an index p is defined as the ratio of the thermal diffusivity to the feed rate, and the index is tested with different lb to find the optimal thickness. For example, in the case of a nodular iron work-material and 4 mm/s feed rate (Test B in Chap. 4), the material thermal diffusivity is 6.89 mm2/s and thus p index is 1.72 mm. The thickness lb of 1.6 mm was found to have a best match with the advection model among various thicknesses tested. Figure 5.15a, b shows the temperature distributions at 100 mm drilling depth in the 2D advection and heat carrier models, respectively. Temperature distributions of a 16 × 8 mm region highlighted in Fig. 5.15a, b are overlaid in Fig. 5.15c for comparison, where R2 is 0.97. 5.4.1.2  HWS Heat Carrier The HWS heat carrier is a cylindrical shell consisting of four-node thermal-elastic-­ coupled shell elements, as shown in Fig. 5.14b. The configuration of elements composes many rings along the HWS carrier. The number of rings in the axial direction on the HWS heat carrier is N, which is equal to the number of time steps of hw in the advection model for the inverse heat transfer method. The axial length of each ring in the HWS heat carrier is the distance which hw moves within one timestep in the advection model. For each time step, the spatial distribution of hw is applied on the carrier. Since the carrier retains very little heat, the applied heat flux will immediately transfer into the workpiece.

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Fig. 5.15  Temperature distributions around HBS in (a) 2D advection model and (b) 2D HBS heat carrier, and (c) the comparison of temperature results in the regions highlighted in (a) and (b)

5.4.2  Experimental Study 5.4.2.1  Experimental Method The experimental study is designed to compare the workpiece temperature distribution and thermal distortion during multiple deep-hole drillings. Aluminum 6061-T6 is chosen as the work-material in this study for a more observable thermal ­expansion. The experiment is conducted on a Fadal vertical machining center (Model VMC 4020). The feed rate and spindle speed are set at 0.2 mm/rev and 2100 rpm, respectively. A 10 mm diameter, 220 mm long solid carbide drill with oil feed holes is used. The compressed air supply for the MQL system is regulated to 5 bars. The oil

5.4  Workpiece Thermal Distortion

111

Y 12.7 25.4 Reference holes

b a

Z

Reference holes

127

#2 #1

#4 d 38.5

50.8

#3

c

18

18

152

Top view

X X

Side view

25.4

25.4

Clamping 152

Fig. 5.16  Experimental setup: (a) workpiece design for thermal distortion experiment and (b) the measurement of hole positions using dial indicator (unit: mm)

flow rate is calibrated at 60 mL/h at 2100 rpm spindle speed. Figure 5.16 shows the designed workpiece geometry to measure the workpiece thermal expansion after MQL drilling of four deep holes. The workpiece is 50.8 × 152 × 152 mm with a 25.4 mm deep and 25.4 mm wide region extending out of the bottom on one side for clamping. This design allows the workpiece to freely expand in the horizontal direction. Surface temperature at points A, B, and C are monitored during the drilling using thermocouples. Four holes, marked as #1, #2, #3, and #4, are drilled into the workpiece in sequence using the same drill. Four reference holes, marked as a, b, c, and d, are drilled 18 mm deep with a 9.5 mm diameter drill. Holes a and b were drilled prior to drilling the four deep holes. Holes c and d were drilled right after the drilling of four deep holes. The difference of distance in the X-direction between holes a and b to holes c and d and the programmed nominal X-position (127.0  mm) in the machine determines the experimentally measured thermal expansion of the workpiece. The positions of reference holes were measured using a dial indicator on the machine spindle, after the workpiece cooled to the room temperature. The accuracy of the machine’s positioning was confirmed with a Renishaw laser interferometer (Model ML 10) to be within 5 μm. This experimental method is simple without the need for CMM and can be conducted directly on the clamped workpiece to eliminate the uncertain effects of residual stress and clamping-induced distortion. The measured expansion is 61 μm on average in the experiment.

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5.4.2.2  Model Prediction Following the experimental procedures and the inverse method presented in Sect. 5.3, the heat fluxes (hb and hw) can be obtained for this drilling condition. Specifically, a 38 mm diameter and 152 mm long workpiece with five IPs are used with each thermocouple being 3.4  mm from the projected hole surface. The obtained hb is 4.5 MW/m2 and hw is a function both time and position with a maximum heat flux around 0.25 MW/m2. The 3D heat carrier model is established based on the experimental condition. For the HBS heat carrier, the diffusivity of aluminum 6061 is 74.4 mm2/s and the drilling feed rate is 7 mm/s; thus the index p is 10.6 mm. The HBS carrier thickness lb is determined to be 5.6 mm. For the HWS heat carrier, 100 rings of elements are created along the 152 mm length. This corresponds to 1.52 mm ring axial length. The 3D FEM mesh of the workpiece prior to inserting the heat carrier to hole #1 is shown in Fig. 5.17. The region for hole #1 had been removed. The heat carrier moved at a speed of 7 mm/s (feed rate of the drill) into the hole to conduct heat fluxes (hw and hb′) into the workpiece. Figure 5.18a shows the surface temperature distribution at the time when the heat carrier penetrates the bottom of the workpiece for hole #1. The highest temperature is close to the bottom of the workpiece near hole #1 due to the boundary having no material to conduct the heat. The temperature distribution in the workpiece after 6.5 s taken to retract the drill and move to the position for hole #2 is shown in Fig. 5.18b, which is also the initial temperature

Fig. 5.17  The 3D FEM mesh of the workpiece for multi-hole drilling

5.4  Workpiece Thermal Distortion

113

distribution in hole #2 analysis. Prior to drilling into hole #2, the hole material was removed and the workpiece was re-meshed. The workpiece temperature after drilling hole #2 is shown in Fig. 5.18c. Following the same procedures, the temperature distributions after drilling holes #3 and #4 were computed and are shown in Fig. 5.18d, e. The gradual increase in overall workpiece temperature can be observed as the holes are drilled sequentially. The drilled workpiece is re-meshed to the 8-node linear brick element and analyzed using thermal-elastic module to predict workpiece thermal expansion. This is a steady-state thermal-mechanical analysis assuming that the expansion occurs simultaneously with temperature rise. The FEM-predicted workpiece thermal expansion in the X-direction is shown in Fig. 5.19, where the color contour represents the displacement in X-direction. The workpiece thermal distortion across the YZ plane is almost uniform. The model-predicted thermal expansion between two sets of reference holes is 50–60 μm. This is close to the experimentally measured 61 μm considering the 5 μm uncertainty.

Fig. 5.18  Workpiece temperature distribution at (a) the end of drilling hole #1, (b) 6.5 s after the end of drilling hole #1, and the end of drilling (c) hole #2, (d) hole #3, and (e) hole #4

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Fig. 5.19  Simulated workpiece distortion in X-direction at the start of drilling the reference holes

5.5  Conclusions This chapter presents two inverse methods to determine the heat generation in deep-­ hole drilling. The inverse method is a semi-empirical approach that involves both drilling theory and actual temperature to accurately describe the heat. The inverse method can also incorporate unknowns or uncertain factors during a new drilling process. However, the challenge is the convergence of the inverse solutions. Like an optimization problem, an ideal inverse problem should have adequate inputs to find a unique and feasible set of solutions. This chapter has provided guidelines in assigning the input points and control points. Nonetheless, it is always possible to set up the inverse problem in different ways to solve the unknowns. The last part of this chapter introduces a thermal distortion modeling to enable an efficient computation of global temperature distribution. This is particularly useful when the overall part distortion is important in addition to the distortion of local features. For example, the method can be adopted to design the clamping layout to minimize thermal distortion, to select proper machining parameters, to calculate error compensation for accuracy, and to assign proper GD&T for MQL drilled deep-hole features. Although heat fluxes of this thermal distortion model are assumed repeatable at each hole drilling, it is possible to incorporate effects of drill wear and gradual increase in drilling force, torque, and heat fluxes if their relationships with time are known. One limitation of the heat carrier model is that removing the entire hole prior to the drilling possibly removes part of the heat absorbed from

References

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previous holes. The error associated with this method should be insignificant if the distance between holes is large or the drill feed rate is relatively fast compared to the heat transfer in the work-material. To mitigate this potential issue, a deeper hole can be divided into several segments and then removed sequentially. In summary, a methodology to model the heat generation and workpiece temperature and thermal expansion in deep-hole drilling has been demonstrated.

References 1. Agapiou JS, Stephenson DA (1994) Analytical and experimental studies of drill temperatures. J Eng Ind 116:54–60 2. Stephenson DA, Agapiou JS (2016) Metal cutting theory and practice, 3rd edn. CRC Press, Boca Raton 3. Bono M, Ni J (2002) A model for predicting the heat flow into the workpiece in dry drilling. J Manuf Sci Eng 124:773–777 4. Tai BL, Stephenson DA, Shih AJ (2012) An inverse heat transfer method for determining workpiece temperature in minimum quantity lubrication deep hole drilling. J Manuf Sci Eng 134(021006):1–8 5. Bono M, Ni J (2001) The effects of thermal distortions on the diameter and cylindricity of dry drilled holes. Int J Mach Tools Manuf 41:2261–2270 6. Kalidas S, Kapoor SG, DeVor RE (2002) Influence of thermal effects on hole quality in dry drilling, part 1: a thermal model of workpiece temperatures. J Manuf Sci Eng 124:258–266 7. Kalidas S, Kapoor SG, DeVor RE (2002) Influence of thermal effects on hole quality in dry drilling, part 2: thermo-elastic effects on hole quality. J Manuf Sci Eng 124:267–274 8. Fleischer J, Pabst R, Kelemen S (2007) Heat flow simulation for dry machining of power train castings. CIRP Ann 56:117–122 9. Tai BL, Jessop AJ, Stephenson DA, Shih AJ (2012) Workpiece thermal distortion in minimum quantity lubrication deep hole drilling—finite element modeling and experimental validation. J Manuf Sci Eng 134(011008):1–9

Chapter 6

Thermal Analysis of Bone Drilling in Orthopaedic Surgery

Orthopaedic surgeons perform bone drilling in day-to-day clinical operations. Bone drilling is commonly used for screw placement, microfracture, or for surface preparation to aid in joint fusion, in which multiple sequential passes are made. Although the heat generation is generally understood, such as the effects of drill diameter, speed, and feed, the differences among various drilling tools have not been looked into carefully. In this chapter, the topic is switched from metal drilling in the factory to bone drilling in the operation room at the hospital. Based on the knowledge in metal drilling, we will investigate the heat generation among different surgical tools and also the sequential drilling of bone using a clinically relevant environment. The chapter details the experimental methods, bone sample preparation, and analysis method for cadaveric bone drilling study.

6.1  Clinical Challenges Different from industrial drilling studies focused on drill wear and life, the workpiece (bone) is a major concern in surgical drilling due to the risk of heat-induced thermal osteonecrosis. Broadly defined, osteonecrosis is a disease resulting from the temporary or permanent loss of blood supply to bone tissue [1]. This absence of blood supply results in bone death, ultimately leading to collapse and non-healing [2]. Although the use of normal saline intermittent irrigation during bone drilling has been shown to decrease the maximum temperature, irrigation is not appropriate in certain clinical situations [1, 3, 4]. For example, irrigation while drilling to prepare a joint for fusion is not advised as it would wash away the bone cells while drilling through the subchondral bone. Further, unlike industrial drilling tools with through-the-drill holes, externally applied saline has limited effect on cooling for solid bone drills. Another clinical challenge is the accumulated heat during continuous or sequential drilling of multiple holes. While single-pass bone drilling is used most ­frequently © Springer Nature Switzerland AG 2019 A. J. Shih et al., Metal and Bone Drilling - The Thermal Aspects, https://doi.org/10.1007/978-3-030-26047-7_6

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6  Thermal Analysis of Bone Drilling in Orthopaedic Surgery

to aid in screw placement, multiple-pass bone drilling is also a common technique in orthopaedic surgical procedures such as preparing a joint surface for fusion, nonunion takedowns, and fenestrating eburnated bone to accept a prosthesis. In this chapter, the heat generation and its accumulated effects after repetitive sequential drilling are presented.

6.2  Comparison of Bone Drills Twist drill is a common tool for bone drilling in clinic. However, unlike the advanced drills in the manufacturing industry, most of the clinical twist drills have 90° point angle without optimization of the drill geometry. Sometimes, orthopaedic surgeons need to select special types of drills to aid different surgical needs, such as Kirschner wires (K-wires) and cannulated drills. There is a paucity of literature on K-wires and particularly cannulated drills. Few studies have looked at K-wire drilling temperature and indicated significant heat production and an associated rise in temperature over 100 °C. To assess these drills, temperature rise during drilling is an important indicator for bone necrosis. The thermal osteonecrosis is a very complex phenomenon. Several theories for the development of osteonecrosis after drilling have been studied [4, 5]. Temperature and associated exposure time have also been studied extensively [1, 3, 6–9]. Temperatures above 70 °C can result in immediate bone necrosis. Though lower temperature has also been shown to cause necrosis, its relationship to exposure time is inversely related. A temperature of 55 °C induces irreversible cell death of osteocytes after 30 s and at 47 °C after 60 s. To precisely measure the drilling performance based on these reference temperatures, the experiment must be similar to a real clinical condition and be able to account for the variations among patients, such as age and gender. The following sections detail the methods used to compare drills in a clinically relevant, while controllable, environment [10].

6.2.1  Drilling Test bed and Sample Preparation Commercial orthopaedic drills to be compared in this study include three twist drills (2.0, 2.5, and 3.5 mm in diameter), three K-wires (1.25, 1.6, and 2.0 mm in diameter), and one cannulated drill (2.7 mm in diameter). These drill sizes are all commonly used in clinical cases. Each drill is driven by a surgical hand drill at the constant full spindle rotational speed and fed at a controllable rate by a servo-linear slider. The experimental setup is shown in Fig. 6.1. A dynamometer is placed under the workpiece fixture to measure thrust force and torque, which can be used to ensure consistent cortical thickness and bone hardness among samples as well as to monitor drill wear over time. Variations among bone samples are always the major challenge in cadaveric drilling studies.

6.2  Comparison of Bone Drills

119

Fig. 6.1  The selected bone drills for comparison and the experimental setup composed of servo-­ linear actuating system, surgical hand drill device, drill, force transducer, and thermocouples

To closely mimic an in-vivo condition, test samples are prepared from non-­ embalmed cadaveric human tibia cortex. The bone is sectioned into a proper size for clamping, about 35 × 35 mm. The residual tissue on the bone surface must be completely removed to minimize the initial drilling path deviation upon surface contact. With the bone drilling setup, bone variability is tested with the 2.0 mm diameter twist drill across all samples. In this particular study, the thrust force shows a standard deviation of 0.84  N out of 16.5  N from multiple samples. This variation is considered small enough not to cause significant temperature uncertainty. For bone sample preparation, a pilot hole and two thermocouple holes are pre-­ drilled at each designated drilling spot using a computer numerical controlled (CNC) high-speed micro-drilling machine with a 0.7 mm diameter drill. The thermocouple holes 2  mm deep and 0.5 and 1.5  mm away from the hole margin to measure the temperature when the drill point fully engages. The pilot hole was 0.3 mm deep to guide the drill into the exact position without wobbling. Since the bone sample surface is not even, every hole preparation needs to be carefully referenced to the bone surface. In this experiment, thermocouples are sleeved with small metal tubes (to make it stiff) and fixed by an acrylic jig to ensure tight contact at the bottom and center of the pre-drilled holes as shown in Fig. 6.1.

6.2.2  Testing Parameters and Procedures For the drill comparison purposes, drilling speed and feed are control variables though the feed actually varies in reality. The drilling speed was maintained at the full speed like in most of the clinical cases. The feed rate is chosen by an average speed of 1 mm/s based on motion tests performed by several orthopaedic surgeons. They were asked to drill into a cortical bone with drills of different sizes (2.0, 2.5, and 3.5  mm), and the movement of hand is captured using a magnetic motion

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t­ racking system (Model trakSTAR by Ascension). The average speed after a total of 12 drillings was 1.03 ± 0.27 mm/s regardless of the drill sizes. Therefore, the constant 1 mm/s feed is selected to represent a clinical condition. For the testing procedure to mimic human body condition, the bone is first warmed to 37 ± 1 °C and kept moisturized in the wood fixture with saline solution. The solution is filled halfway up the bone thickness so that the sample is not submerged, thereby preventing the solution from acting as a lubricant and affecting temperature reading. Bone temperature is checked prior to each drilling to ensure a consistent initial condition. The drilling depth is set to 5 mm to completely penetrate through the cortical bone sample. The maximum temperature is captured when the drill tip passes the thermocouples at a depth of 2 mm instead of the surface because the initial drilling does not have a full drill tip engagement. The same procedure is applied to K-wires and twist drills. For the 2.7 mm cannulated drill, a 1.6 mm diameter guide pin (50 mm long) is first located into the drilling spot prior to drilling, which emulates the clinical practice. Power analysis is usually needed for bone drilling tests to ensure adequate number of tests to minimize the effect of sample variance. In this experiment, nine tests are performed for each drill based on an initial power analysis that mandated a minimum of eight cases for 80% power at 95% confidence. Lastly, it is important to ensure that drill wear is insignificant. An optical microscope can be used to examine cutting edges of each drill device to evaluate any cutting-edge wear that might affect heat production and temperature readings.

6.2.3  Drilling Temperature Results Temperature extracted for comparison is the peak value throughout each drilling event. Statistical analysis is applied to eight out of nine replicas with one outlier identified by the greatest deviation from the average. Figure 6.2 shows the temperature change above the initial temperature during K-wire and twist drilling with different sizes. The error bars show one standard deviation and the asterisk denotes a significant difference (p   0.05). The differences between the K-wire and twist drill are clear. Statistically significant differences (p 0.05 between TC-A, hole 5, and TC-D, hole 9 for all drilling cases. Therefore, temperature profiles of TC-A and TC-B are nearly identical to those of TC-C and TC-D. Temperatures of TC-C and TC-D do not respond to the drilling-induced heat until the second row (starting at hole 4). Temperatures of TC-A and TC-B stop rising when the drilling proceeds to the third row (starting at hole 7), though they still remain. Another useful visualization is using the average temperature at four thermocouples to interpolate the temperature field within the 5 × 5 mm region (cornered by four thermocouples) to observe both the temporal and spatial distributions. The results of the ends of drilling holes 3, 6, and 9 are shown in Fig. 6.8 (left to right). The hole in the middle is hole 5, where the data should be void after the hole is drilled. For all drills, it can be seen that the heat is propagated to TC-C and TC-D after drilling hole 3. The overall temperature fields are at or below 12 °C. After drilling hole 6, significant higher temperature field results from the use of K-wire, which ranges from 12 to 25 °C, whereas the temperature fields of the drills are still within

6.3  Heat Accumulation in Bone Drilling

127

Fig. 6.7  Temperature vs. hole position during sequential drilling with (a) 2.0  mm K-wire, (b) 2.0 mm twist drill, and (c) 2.5 mm twist drill. Error bars represent standard errors based on the six tests of each case

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Fig. 6.8  Interpolated temperature field by four thermocouples at the end of drilling holes 3, 6, and 9 with (a) 2.0 mm diameter K-wire, (b) 2.0 mm diameter drill, and (c) 2.5 mm diameter drill. The area for 2.5 mm diameter drill is larger for the same thermocouple to hole-margin distance

15 °C. Although the larger drill creates a slightly higher temperature, the difference between these two sizes (2.0 and 2.5 mm) is, again, not obvious. After drilling the last hole, the temperatures at the lower end of the region are still above 12 °C for K-wire and above 5 °C for drills. This phenomenon could result in a larger thermal dose in the system, consequently injuring bone tissues due to prolonged exposure at high temperatures. Consider that after drilling the nine holes (58 s after initiation), the average temperatures across the four thermocouples are 18.6 °C, 9.9 °C, and 11.1 °C for 2.0 mm diameter K-wire and 2.0 and 2.5 mm diameter twist drills, respectively.

6.3.4  Histology Analysis Temperature data shows that K-wire produces much more heat than the standard drills, and consequently leads to a larger area of bone damage. After drilling was completed, three selected bone samples (one from each case) were decalcified and

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Fig. 6.9  Representative photomicrographs of hole 5 of decalcified bone samples with (a) 2.0 mm K-wire, (b) 2.0 mm standard drill, and (c) 2.5 mm standard drill

sectioned to be studied microscopically. Figure  6.9 shows representative slides of bone samples drilled by a K-wire, and 2.0 mm and 2.5 mm standard drills at hole 5. The photomicrograph highlights the bony destruction encountered. The K-wire (Fig. 6.9a) demonstrates noticeably increased bony destruction and change in bony architecture when compared to the standard drill of the same size (Fig. 6.9b), correlating with increased temperatures measured during drilling as well as different drill designs. The differently sized standard drills show grossly similar bony destruction (Fig. 6.9b, c). It should also be noted that all samples have a paucity of osteocytes with empty lacunae surrounding the drill margin.

6.3.5  Discussion of the Results There are many clinical scenarios in which either K-wires or differing sizes of twist drills are utilized for repetitive sequential drilling. This study finds that K-wires produce significantly higher peak temperatures and accumulated significantly more heat than same size (2.0  mm) or even larger (2.5  mm) twist drills. K-wires produce a higher temperature rise at each drilled hole and a maximum temperature rise of over 20 °C by the ninth hole. Given the threshold of 47 °C for thermal damage, the absolute temperatures measured for the second through ninth holes are sufficient to cause necrosis. Different from the previous study concerning the maximum temperature adjacent to a hole, this current work is focused on heat accumulation, particularly between the holes. The “slow-cooker” effect can lead to a large area of necrosis. Based on the data collected from all drills, it is found that the temperature rises rapidly with each subsequent pass until the seventh hole. This shows that the second row of holes received heat input from passes 1 to 6 as the heat dispersed throughout the bone, whereas the last row of holes (7–9) is not affected by the heat dispersed into the bone during passes 1–3, but only that from passes 4 to 6. This phenomenon shows the effect of low thermal conductivity of the cortical bone that can accumulate heat over time.

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In orthopaedic surgery, there is a doubt of heat sink effect, by which the metal drills can draw or transfer the heat from bone. This is proved to be insignificant because of the similar temperature profiles and magnitudes across TC-A to TC-D. That is, regardless of the drill temperature change over time, there is a minimal heat transfer between the drill and the bone. The major thermal damage factor should still be a result of cumulative heat inside the bone from multiple passes. After studying the data, it is clear that there is a compelling argument to avoid K-wires when a clinical scenario requires multiple drill passes. The temperatures recorded for twist drills are significantly lower than those for K-wires. Two twist drills of different sizes, 2.0  mm and 2.5  mm diameter, were also tested using an identical experimental setup. Similar trends are found with these two sizes. The larger drill (2.5 mm diameter) produces slightly more heat throughout drilling; however, this is found to be statistically insignificant.

6.4  Conclusions Heat generation in bone drilling has always been a major concern in orthopaedic surgery. However, due to the inability of in-vivo tests, the difficulty in obtaining suitable cadaveric samples, and large variations in bone samples, bone drilling tests are difficult to plan to represent all clinical situations. Also, drilling is operated manually by the orthopaedic surgeon; feed rate and spindle speed are not controllable as in the industrial machining. By considering these factors, this chapter presented two most-clinically relevant experimental designs with well-defined control variables to target the clinical doubts on drill selection and heat accumulation in continuous drilling. In these experiments, real surgical drills are used; feed and speed are based on actual operational conditions; and cadaveric samples are hydrated and warmed to mimic living bones. Power analysis was also conducted to ensure adequate number of tests to minimize extraneous factors such as bone directionality, ages, and internal defects. Compared to industrial drilling analysis, bone drilling study can be time-consuming and sometimes non-conclusive. As seen in this chapter, clinical drills are very primitive compared to drills used in the manufacturing industry. There is a lot of room for the advancement and development. One example is K-wire, which has been used for over a century and well known for its severe heat generation. Cannulated drill is another example. This chapter contains quantitative comparison of their performance with regular twist drills. Although the actual temperature may vary by bone property and other human factors, the results are important for orthopaedic surgeons to make judgments in drilling motion, selection, spacing between consequent holes, and other factors. Another item that is not particularly studied, but rather important, is the drill wear. Bone drills are often reused after being sterilized. Worn drill can be a significant heat source; however, unlike in the industry, there is no standard procedure to record drill wear and predict the potential heat increase. There is a need for the future study on this topic.

References

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References 1. Pandey RK, Panda SS (2013) Drilling of bone: a comprehensive review. J Clin Orthop Trauma 4:15–30 2. Baron R, Horne WC (2005) Bone resorption: regulation of osteoclast activity. In: Bronner F, Farach-Carson MC (eds) Topics in bone biology. Springer, London, pp 34–57 3. Augustin G, Davila S, Udiljak T, Vedrina DS, Bagatin D (2009) Determination of spatial distribution of increase in bone temperature during drilling by infrared thermography: preliminary report. Arch Orthop Trauma Surg 129:703–709 4. Matthews LS, Hirsch C (1972) Temperatures measured in human cortical bone when drilling. J Bone Joint Surg 54:297–308 5. Noble B (2003) Bone microdamage and cell apoptosis. Eur Cell Mater 6:46–55 6. Augustin G, Zigman T, Davila S, Udilljak T, Staroveski T, Brezak D, Babic S (2012) Cortical bone drilling and thermal osteonecrosis. Clin Biomech 27:313–325 7. Augustin G, Davila S, Mihoci K, Udiljak T, Vedrina DS, Antabak A (2008) Thermal osteonecrosis and bone drilling parameters revisited. Arch Orthop Trauma Surg 128:71–77 8. Abouzgia MB, Symington JM (1996) Effect of drill speed on bone temperature. Int J  Oral Maxillofac Surg 25:394–399 9. Lee J, Ozdoganlar OB, Rabin Y (2012) An experimental investigation on thermal exposure during bone drilling. Med Eng Phys 34:1510–1520 10. Palmisano A, Tai B, Belmont B, Irwin T, Shih AJ, Holmes JR (2014) Comparison of cortical bone drilling induced heat production among common drilling tools. J  Orthop Trauma 29:188–193 11. Palmisano AC, Tai BL, Belmont B, Irwin TA, Shih AJ, Holmes JR (2016) Heat accumulation during sequential cortical bone drilling. J Orthop Res 34:463–470

Chapter 7

Model-Based Approach for Predicting Thermal Damage in Bone Drilling

In surgical drilling, temperature and exposure time are two critical factors in determining the thermal damage of bone, so-called necrosis. Although drilling thermal modeling has been studied extensively, the majority of existing models are two-­ dimensional and made only for single-pass drilling for analyzing the cutting zone or drill. This is especially true in the industry because the high cutting temperature can degrade tool life and work material rapidly. Despite a relatively low temperature in bone drilling, prolonged exposure under harmful temperature can cause bone necrosis. Therefore, knowing the global temperature distribution is important in this regard, but the 2D axisymmetric model cannot be directly expanded to analyze thermal interactions between multiple passes and the overall temperature distribution in a 3D complex bone geometry. Built on the experimental works in Chap. 6 and modeling work in Chap. 5, this chapter will present a 3D finite element thermal model and a thermal damage criterion to estimate necrosis in bone drilling, particularly for sequential, multiple hole drilling.

7.1  Overview of Bone Drilling Thermal Models There have been a number of studies on temperature modeling of bone drilling based on the traditional metal cutting theory. Davidson and James [1] developed thermo-mechanical equations based on machining theory coupled with the finite element method (FEM) to predict the heat generation and temperature distribution in bone. Lee et al. [2] used a finite difference method and machining theory to establish a model to predict the temperature during bone drilling. However, these models are all focused on a single hole instead of a 3D, global temperature field. Also, the heat source is often calculated based on cutting force model and mechanical-to-­ thermal energy conversion. A heat partition factor is used to determine how the heat is divided among the bone, the drill, and the bone debris, respectively. For example, Lee et al. [2] applied Boothroyd’s equation derived from metal cutting to establish © Springer Nature Switzerland AG 2019 A. J. Shih et al., Metal and Bone Drilling - The Thermal Aspects, https://doi.org/10.1007/978-3-030-26047-7_7

133

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the heat partition; Davidson and James [1] assumed a constant fraction. The selection of heat partition factor can be a major error source since it linearly scales the heat input. Therefore, an experimentally determined heat source can better reflect the actual partitioned heat. This can be referred to inverse heat transfer method (IHTM) introduced in earlier chapters. Because of the data fitting process, IHTM automatically corrects inherent errors existing in measurements, thermal properties, or model boundary conditions. As for the thermal damage criterion, it is often defined by thermal dose in the literature, which is a cumulative equivalent exposure time at 43  °C (CEM43). However, its validity as a metric is still debatable since it was initially created for cancer therapy not for bone drilling. Experimentally, temperatures above 70  °C have been seen to result in immediate bone death [3, 4], whereas irreversible cell death of osteocytes occurs after 30 s at a temperature of 55 °C and after 60 s at 47 °C [4, 5]. These three conditions produce significantly different CME43, which indicate that the original thermal dose is not applicable. Also, the threshold of 47 °C is typically used as an indicator instead of 43  °C when tissues are on the brink of destruction. Because of the aforementioned deficiencies in bone drilling simulation, there is a need to develop a generalized 3D FEM model along with a modified thermal damage criterion [6]. The modeling method can be used for evaluating a drilling process or comparing different drilling strategies such as drilling position, dwell time, drilling sequence, and cooling before intensive drilling experiments and clinical trials. It is important to note that, unlike industrial drilling focused on the optimization of speed and feed, the clinical drilling is hand held, so these typical drilling parameters cannot really be controlled.

7.2  Finite Element Thermal Model 7.2.1  Advection Method The drilling thermal model is adapted from the advection model [7], which has been described in Chap. 5. Figure 7.1 shows the overall concept in a 2D schematic. The heat flux is applied on the hole bottom surface at step i. Then, a layer of material (elements) is removed at step i + 1 and the heat is simultaneously applied on the subsequent new surface. The same cycle is repeated throughout the entire drilling process. The advantage of this model is that it considers the material removal, which carries away a portion of the heat, thus automatically accounting for heat partition. In 3D implementation, the workpiece and the region to be drilled are modeled as two separate parts, as shown in Fig. 7.2. The drilled region is a 3D configuration of advection layers, where the sequential removal of elements takes place as shown in Fig. 7.1. The workpiece can be automatically meshed but must have a predefined cylindrical space to fit the drilled region. The thermal contact between these two parts is defined to have zero resistance to ensure continuous heat flow across the

7.2  Finite Element Thermal Model

135

Fig. 7.1  Schematic drawing of the advection model for drilling heat transfer FEM

Fig. 7.2  Model configurations of the 3D heat transfer FEM for bone drilling

boundary. Two main reasons for this two-part configuration are that (1) a complex 3D geometry can be meshed using tetrahedrons without being constrained by the arrangement of advection layers and (2) the advection layers can be placed at different locations and orientations to increase the model flexibility. The advection layers are formed with an exact drill point angle and diameter. Resolution and accuracy of the temperature field next to the heat source are significantly affected by the layer thickness: finer advection layers create a more continuous movement of the heat source and also significantly increases the number of elements and steps, resulting in a heavy computational load. Numerical convergence testing should be carried out to ensure that a result could be obtained. For example, in this study, the hole size to be simulated is a 2 mm diameter hole with 1 mm/s feed rate. The thickness of each layer is set to be 0.1 mm with a step time of 0.1 s. The 0.1 mm layer thickness is found less than 1% difference in temperature,

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compared to a nearly continuous case (extremely fine mesh). Certainly, the convergence threshold can be defined by the user for the desired accuracy and computational load. On the other hand, this 3D advection method is an alternative to the heat carrier model introduced in Chap. 5. Since this is a shallow hole drilling, 3D advection model is more suitable than the heat carrier model as it eliminates the calibration steps for the heat carrier size and properties.

7.2.2  Implementation in Multi-Hole Drilling Figure 7.3a shows a clinical example for sequential, multi-hole drilling on the talus for ankle joint fusion. This example is transformed into a 3D FEM model, as seen in Fig. 7.3b, for the ease of observation on heat propagation after sequential passes. Specifically, the model is set as a 3 × 3 array of 2 mm diameter holes with 5 mm center-to-center spacing between adjacent holes. The drilling sequence follows the holes in order of their ascending numbers. The time interval between passes is set to about 1 s. The model thickness is 4 mm evenly across the surface to simulate the cortical bone. The fine meshes seen in Fig. 7.3 are the advection layers (Fig. 7.2) plugged into designated hole locations. The material properties are set within the ranges of human cortical bone [8], where the density is 2 g/cm3, the thermal conductivity is 0.5 W/m-K, and the specific heat is 1290 J/kg K. Cancellous bone and marrow are not considered in the model since the majority of the heat is expected in the cortical bone, provided a higher density and larger drilling forces. The boundary condition is set as adiabatic, given that free convection between bone and air is low and has limited effect on the

Fig. 7.3 (a) Sequential drilling in ankle fusion surgery and (b) top view of a 3D FEM model for study of sequential drilling

7.2  Finite Element Thermal Model

137

temperature inside the bone. The material of each hole is removed along with the drill pass, and all newly created surfaces are adiabatic. There are three basic assumptions made for this modeling method: first, the material properties are constant. The bone density around hole margins might change after drilling, consequently affecting the heat transfer, but the affected area is small compared to the entire operating region (i.e., a set of holes). Second, the heat flux is uniformly distributed on the hole bottom surface. The detailed spatial distribution might be generated based on the cutting-edge geometry, but the impact on the overall temperature of the operating area is assumed negligible. Lastly, the heat flux is independent of time since the drill wear is not significant under proper operating conditions. Note all these assumptions do not limit this model. They can be addressed by additional experiments for properties collection to increase the accuracy of the simulation result at the costs of time.

7.2.3  Determination of Heat Source by IHTM The heat source is defined by a constant heat flux hs, which will be determined by fitting the experimental temperature through the FEM thermal model. The IHTM searches for the optimal solution of hs to minimize the discrepancy between the model and actual temperatures, automatically compensating for errors from unknown heat loss and thermal properties. For example, the bone density is assumed homogeneous and constant (2  g/cm3). The searched hs will produce a closely matched temperature field for any deviations from real bone properties. Certainly, the same thermal model must be used for the follow-up simulations. The experimental setup of Chap. 6 for sequential, multi-hole drilling is used here for the IHTM, as shown by Fig. 7.4a. This setup consists of a surgical hand drill attached to a servomotor controlled 3-axis stage to facilitate the drilling motions. A drilling dynamometer (Model 9272 by Kistler) under the sample fixture is used to ensure a constant torque and force for the constant heat source assumption. Cortical bone samples are non-embalmed cadaveric tibia, as detailed in Chap. 6. Four K-type, 36-gauge thermocouples (Model 5TC-TT-K-36-36 by OMEGA) are placed 5 mm apart from each other, 3.5 mm from the hole center, and 2.0 mm below the bone surface, as shown in Fig.  7.4b. The plastic, transparent plate is to affix the thermocouples at proper locations during continuous drilling. The plate has an identical 3 × 3 array of holes aligned with the bone sample, allowing the drill to travel through and enter into the bone. Bone samples are placed without a specific orientation since the drilling is perpendicular to the in-plane fibrous microstructure (i.e., osteons). The drill flutes cut the bone in all directions during spinning. Two drills, a 2.0  mm diameter K-wire and a 2.0  mm diameter two-flute twist drill, are tested to obtain the temperature data. Their point angles are measured under a microscope as shown in Fig. 7.4c and modeled accordingly in the 3D FEM (Fig. 7.2). The drilling interval between passes is fixed at 1 s regardless of the distance. No drill wear presents during this calibration test.

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Fig. 7.4  Experiments for temperature collection in sequential drilling for IHTM: (a) overall setup, (b) drilled bone sample, and (c) twist drill and K-wire tips

The hs is independent of time as drill wear observed is negligible over the course of all experiments. The stainless steel drill may behave like a heat sink accumulating heat over time, but the heat that is conducted to the bone is minimal because of the large difference in thermal conductivity between the stainless steel (about 15 W/m-­ K) and the bone (about 0.5  W/m-K). Therefore, this heat transfer system can be further simplified to a single variable, time-invariant problem. The hs is obtained using the objective function defined in Eq. (7.1), where i is the thermocouple number and j is the time step. TiEXP and TiFEM are the temperatures from experiments and FEM, respectively. Each time step is set to be 0.125 s, with a total of N steps. 4



N

(

f ( hs ) = ∑∑ Ti EXP ( j ) − Ti FEM ( hs ,j ) i =1 j =1

)

2

(7.1)

Figure 7.5 shows a fitting result with IHTM for a K-wire test. The four thermocouples embedded in the bone are marked as TC1 to TC4 in Fig. 7.4b. TC1 and TC2 showed good agreement with the inverse solution. The discrepancy in the descending profiles could be caused by the actual boundary condition that wet surfaces dissipate heat to the atmosphere. However, such free-convection effect is generally slow in response and does not contribute significantly to the overall temperature distribution. The large discrepancy in thermocouple TC3 is likely due to thermocouple misalignment, drilling path deviation, or inhomogeneous local properties. It is common to see deviations of model-predicted data from experimental data due to the model assumptions and experimental uncertainties. Using multiple independent inputs (TC1–TC4) to solve a single variable can reduce such extraneous errors. Meanwhile, since these thermocouples capture the temperature in different spatial and temporal domains, they can be used to verify the assumption of constant heat flux. For example, if the actual heat increases with time, TC1 will be overestimated

7.2  Finite Element Thermal Model

139

Fig. 7.5  IHTM fit to the measured temperature profiles at four thermocouples in K-wire drilling

and TC4 will be underestimated. For all cases, it is found that the averaged deviation for a thermocouple was within ±2 °C, except for one twist drill trial with a deviation of up to 4  °C.  Overall, the data oscillated along the IHTM-obtained temperature profiles without significant offset, indicating that the heat magnitude did not change over time. Both K-wire and twist drill are repeated three times. The IHTM solutions of hs for K-wire drilling are 410, 460, and 500 mW/mm2, and for the twist drill are 420, 590, and 660 mW/mm2. The variation within the same drill could be due to the differences among bone samples, such as thickness, hardness, and density, as they are dissected from different cadavers. The average heat flux for K-wire drilling is 456  mW/mm2 and 556  mW/mm2 for the twist drill. Generally, K-wires produce more heat. In this case, the lower heat flux of K-wire is a result of a larger conical surface area at the drill-bone contact (6.3 mm2 for the K-wire and 4.4 mm2 for the twist drill). The total heat generation rate of K-wire is still about 20% higher than that of the twist drill, which agrees with the result of Chap. 6 in drilling comparison. The heat source can be obtained from various experimental setups, either a single hole or multiple holes, as long as the FEM model can represent the testing condition. Sometimes it is also important to test the obtained heat source. For example, in this study, the obtained heat sources for K-wire and twist drill can be applied to a single hole drilling to predict the temperature rises at 0.5 mm from the hole, which are 44.0 °C and 33.2 °C, respectively. The average temperature rises are 48.7 ± 4.5 °C and 35.1 ± 9.3 °C from eight replicated tests in Chap. 6. Despite some discrepancy, the estimated temperatures fall within one standard deviation of the mean value, which verifies the heat fluxes as proper values used in the numerical model.

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7.3  Thermal Damage Model 7.3.1  A Modified Thermal Dose As stated in the introduction, the original definition of thermal dose may not be applicable to bone necrosis. A modified thermal dose is proposed in this section which requires experimental data to calibrate. The original thermal dose converts the exposure time under different temperatures into a total amount of equivalent exposure time under 43 °C, such that



t 43 =

t = final

∑R

43 − T ( t )

∆t

(7.2)

t =0

where T(t) is the average temperature within a time step Δt, and R is a constant (0.5 above 43 °C and 0.25 below 43 °C). Based on the literature, bone necrosis occurs immediately at 70 °C, at 55 °C when exposed for 30 s, and at 47 °C when exposed for 60  s. However, these three points yield different thermal doses in Eq. (7.2), meaning that the thermal dose, originally developed for cancer therapy, is not suited for evaluating bone necrosis. In the modified thermal dose for bone necrosis, the threshold temperature is changed to 47 °C instead of 43 °C; the R is a function of temperature instead of a constant as in Eq. (7.2), such that



t 47 =

t = final

∑ R (T )

47 − T ( t )

t =0

∆t

(7.3)

The time-dependent function R can be found by curve fitting from multiple necrosis data. In this study, three data points from the literature are used. These three points can form a quadratic curve to distinguish damage and non-damage conditions, denoted as the function Tc(t), as shown in Fig. 7.6. The Tc is defined as the critical temperature, referring to the threshold at which necrosis begins under a certain exposure time. Along Tc(t) there should exist the same thermal dose for necrosis, such that

R ( T = Tc ( t ) )

( 47 −Tc ( t ) )

⋅ t = 60

(7.4)



where 60 is defined by 47 °C for 60 s. Based on the discrete time-critical temperature data generated from the quadratic function of Tc, R at each temperature can be solved. Then a curve fitting is applied to the R-temperature data points to find a regression model. Equation (7.5) is a result of quadratic curve fitting.

R ( T ) = −0.003T 2 + 0.0357T − 0.0695



(7.5)

7.3  Thermal Damage Model

141

Fig. 7.6  Critical temperature curve from experimental data and the modified thermal dose definition

With this model, the R-value ranges from 0.85 to 0.91 for the temperature between 47 and 70 °C. By substituting Eq. (7.5) into Eq. (7.4), a function for critical temperature can be obtained, denoted as Tc′(t) to be differentiated from Tc(t). As shown by the dashed curve in Fig. 7.6, a good agreement between Tc(t) and Tc′(t) verified a good estimation of R(T). To examine whether necrosis occurs at a specific spot, its temporal profile is first examined by upper (70 °C) and lower (47 °C) bounds to identify if there is immediate bone damage or not. If the temperature profile fully or partially existed between the bounds, the modified thermal dose, Eq. (7.3), is then applied using t47 = 60 s as the threshold. To be consistent with the simulation, a time step Δt = 0.1 s is used.

7.3.2  A Case Study: Multi-Hole Sequential Drilling In clinical sequential, multi-hole drilling as shown in Fig. 7.3, the effects of drilling sequence and time interval are never discussed besides drilling speed and feed rate. In fact, drilling speed and feed rate can hardly be controlled as humans are not CNC machines. Therefore, this section uses the developed thermal damage model to predict the bone necrosis in different drilling strategies. The first comparison studies the difference in temperature distribution between the twist drill and the K-wire. The second comparison involves cases of 1, 2, and 5 s intervals between passes. In the third comparison, an optimized sequence is defined as the maximum total travel distance of the drill, as described in Eq. (7.6), where x is the vector to describe the drilling order, e.g., {1 2 3 … 9}, and p contains the coordinate of each hole. 8



g ( x ) = ∑p ( xi +1 ) − p ( xi ) i =1

(7.6)

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7  Model-Based Approach for Predicting Thermal Damage in Bone Drilling

Fig. 7.7  Optimized drilling sequences with the first pass at (a) hole 1 and (b) hole 5

The optimized sequence guarantees the distance between two consecutive passes greater than the original sequence. Since the hole array is symmetric, all equivalent sequences can be grouped into three cases: starting at hole 1 (corner), hole 2, or hole 5 (center). This study used hole 1 and hole 5 cases as they yielded greater values in Eq. (7.6). The representative results are 1-9-4-6-7-3-8-2-5 and 5-7-3-4-6-1-9-2-8, respectively, as shown in Fig. 7.7. Though not common for such complex sequences, the purpose is to compare extreme cases with a regular sequence. 7.3.2.1  Twist Drill vs. K-wire Figure 7.8a, b shows the temperature distribution and predicted thermal damage (marked in white) for the twist drill and the K-wire, respectively. The time interval (1 s) and drilling sequences (1–9) are control variables. The temperature map shows both the final accumulated heat and a local peak value after drilling the last hole. Overall, the region affected by heat (over 47 °C) is greater in the K-wire drilling than that seen for the twist drill, as the solid contour line marked in Fig. 7.8. The K-wire also generates a local peak temperature over 65 °C while that of the twist drill is less than 54 °C. As for the predicted thermal damage, the K-wire creates a larger damaged area than the twist drill due to negatively angled cutting edges and lack of flutes to evacuate bone debris, resulting in more heat generation. The damage caused by the K-wire propagates across the first two rows and partially on the last row. The damage from the twist drill is concentrated around the margin of a hole, with about 0.5 mm thickness. The damaged areas for K-wire and the twist drill are 125.3 mm2 and 45.5 mm2, respectively. The damage caused by the twist drill is only about 36% of that of the K-wire. It is important to note that these damaged regions are exposed to harmful temperatures longer, but not necessarily to higher temperatures. 7.3.2.2  Time Interval Figure 7.9 shows the results of drilling with 2  s and 5  s time intervals between passes against the baseline of 1 s in Fig. 7.8. This comparison is performed using K-wire. The total drilling time for 1 s interval is 63 s as a result of 45 s drilling time,

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Fig. 7.8  Temperature distribution (top) and predicted thermal damage (bottom) for (a) twist drill and (b) K-wire at 10 s after drilling hole 9

8 s travel time, and a 10 s rest time after drilling. Similarly, the total times are 71 s and 95 s for 2 and 5 s time interval, respectively, with the same drilling sequence of going from holes 1 to 9. The final temperature distribution and the 47 °C contour line of these cases are all similar. The local peak temperature is about 69 °C adjacent to a hole margin. The heat from the previous hole neither increases the peak temperature nor dissipates the heat for the following hole in these cases. This phenomenon stems from the fact that the low thermal conductivity of bone slows heat transfer. However, because of the low thermal conductivity and consequentially similar temperature distribution, a longer time interval increases the total procedure time, leading to more exposure to the heat. As a result, bone damage becomes more severe for a longer time interval. The damaged area increases from 125.3 mm2 for the 1 s interval to 134.8 mm2 for the 2 s and 147.9 mm2 for the 5 s, respectively. 7.3.2.3  Drilling Sequence This study is also performed using the K-wire in order to amplify the effect of drilling sequence planning. Figure 7.10 shows the results of drilling with the two optimized sequences stated before. The interval between passes is set to be 1 s regardless

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Fig. 7.9  Temperature distribution (top) and predicted thermal damage (bottom) for K-wire drilling with time interval of (a) 2 s and (b) 5 s

of the distance. The first case aims to see the maximum possible difference if the starting spot remained the same at hole 1. The second case starting at hole 5 is anticipated to mitigate the damage, since all the surrounding heat will flow to the center if it is not drilled first. By comparing the first optimized sequence (Fig. 7.10a) with the regular sequence (Fig. 7.8a), the temperature map shows a slightly smaller 47 °C contour line, but the peak temperature is above 70 °C, meaning that this sequence concentrates the heat to hole 5 at the center. In contrast, the second case (Fig. 7.10b) can keep the peak temperature below 70 °C. From the perspective of reducing bone thermal damage, both optimized sequences eliminate the affected regions to a certain extent from the regular drilling (Fig.  7.8b). Quantitatively, the damaged area is reduced from 125.3  mm2 to 102.7  mm2 by the first sequence and to 116.2  mm2 by the second sequence.

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145

Fig. 7.10  Temperature distribution (top) and predicted thermal damage (bottom) for K-wire drilling with optimal drilling sequences of (a) 1-9-4-6-7-3-8-2-5 and (b) 5-7-3-4-6-1-9-2-8

7.3.3  Discussion on Simulation Results The numerical simulation produces several important, while sometimes counterintuitive, results. It is obvious that twist drills have a much lower risk to damage the bone than K-wires. However, if a K-wire must be used, the damaged area can still be potentially reduced by up to 18% through sequence optimization (Sect. 7.3.2.3). The optimized sequences may be clinically difficult to execute, but the result provides a guideline of an idealized drilling sequence. For example, regardless of the number of holes or the format of array, one could start the drilling from the center and then move to the corner holes, with the goal of maximizing the distance between holes. The result of time interval selection is counterintuitive. A longer time interval does not help dissipate the heat from the previous hole; instead, it extends the overall drilling duration and leads to a slow cooker effect. In comparison, a short drilling interval can effectively reduce the thermal damage. Theoretically, there should exist

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a threshold, beyond which the heat can be effectively dissipated (or conducted away) between passes. However, this threshold value would vary with the hole size, the distance between holes, bone hardness, and so on. It is difficult to conclude a rule-of-thumb for choosing a proper time interval. Clinically, finishing the hole array within a shorter time, while maintaining a regular feed rate, may be a better option. It should be noted that the limitations in these results are mainly due to the assumptions made for the model. First, the model does not emulate a varying drilling motion and trajectory that occur in the operating room. Bone properties can also vary widely from patient to patient. For example, young patients are likely to have tougher and harder bones than those of the elderly, implying more heat generation and different thermal properties. Using a more realistic in-vivo model for the IHTM will be more helpful. However, in-vivo drilling could involve heat dissipation from blood within the medullary canal which can act as another uncertainty. Secondly, the thermal dose used is modified based on limited existing data in the literature, so the estimated thermal damage remains unjustified. More clinical or experimental data is needed to refine the thermal dose model for bone. Therefore, since this model cannot be more specific without more data inputs, the comparisons of drilling strategies are performed on a relative basis. Lastly, the bone is considered only with the cortical portion. Although this is the most heated region during drilling, the layered cancellous bone may influence the results by dissipating the heat or creating a heat shielding effect across the cortical-cancellous interface. It is possible to create a detailed model when geometrical and property data are known. Nonetheless, the basic method methodology and techniques have been developed here with an aim to plan for the best drilling strategy rather than to predict any unplanned drilling outcomes.

7.4  Conclusions This chapter presents a heat transfer FEM and a modified thermal dose model for thermal damage prediction in sequential, multi-hole bone drilling. Because of the flexibility of FEM, it can be used in various drilling conditions, geometries, or drills as long as they can be parametrically defined. The modified thermal dose method is a new concept to address the deficiencies of the currently used thermal dose in almost all published works. For the practical use, the modified thermal dose should be calibrated based on the time and temperature data of a particular bone tissue while this chapter uses the published data for the demonstration purposes. Using these models, the chapter also shows the work to numerically evaluate clinically viable drilling strategies to reduce the risk of thermal damage in a sequential, multi-hole drilling operation. The results unveil a negative impact of increasing the drilling time interval, whereas a positive effect when optimizing the drilling sequence when drill selection is not available. However, it is important to note that the simulation can only provide a guideline and should not be used as a predictive

References

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drill for absolute bone damage due to inherent variations among patients, operating conditions, and manually operated motions. All produced optimization results will still need be tested and to take into account the clinical viability.

References 1. Davidson SRH, James DF (2003) Drilling in bone: modeling heat generation and temperature distribution. J Biomech Eng 125:305–314 2. Lee J, Rabin Y, Ozdoganlar O (2011) A new thermal model for bone drilling with applications to orthopaedic surgery. Med Eng Phys 33:1234–1244 3. Matthews LS, Hirsch C (1972) Temperatures measured in human cortical bone when drilling. J Bone Joint Surg 54:297–308 4. Berman A, Reid J, Yanicko DJ, Sih G, Zimmerman M (1984) Thermally induced bone necrosis in rabbits, relation to implant failure in humans. Clin Orthop Relat Res 186:284–292 5. Bertollo N, Walsh WR (2011) Drilling of bone: practicality, limitations and complications associated with surgical drill-bits. In: Biomechanics in applications. IntechOpen: INTECH Open Access Publisher, London, pp 855–861 6. Tai B, Palmisano A, Belmont B, Irwin T, Holmes J, Shih A (2015) Numerical evaluation of sequential bone drilling strategies based on thermal damage. Med Eng Phys 37:855–861 7. Bono M, Ni J (2002) A model for predicting the heat flow into the workpiece in dry drilling. J Manuf Sci Eng 124:773–777 8. Tai BL, Kao Y-T, Payne N, Zheng Y, Chen L, Shih AJ (2018) 3D printed composite for simulating thermal and mechanical responses of the cortical bone in orthopaedic surgery. Med Eng Phys 61:61–68

Chapter 8

Advancement of Surgical Bone Drills: A Case Study of Notched K-Wires

Many surgical drills still have a very basic design compared to those for metal drilling in the manufacturing industry. For example, K-wires are known for high drilling temperature, but they are still being used in orthopaedic surgery as a guidewire for cannulated drilling or a drill for fracture fixation. As described in Chap. 6, the heating problem of K-wires is due to the solid trocar design without cutting flutes to remove and evacuate bone debris. There is still room for improvement and advancement. This chapter presents a study on a modified K-wire tip, namely “notched K-wires,” to aid debris storage, thus reduce heat generation. The design and manufacturing method, and the experiment study are detailed in this chapter.

8.1  Modified K-Wires in the Literature Several modified K-wires, as shown in Fig. 8.1, have been studied to reduce heat generation in drilling. Piska [1] compared the regular K-wire with a Medin K-wire (shown in Fig. 8.1a) which has two short flutes with 20° rake angle and 30° clearance angle. Results of drilling porcine bone show that the thrust force and torque reduced by 63% and 60%, respectively, and the average bone temperature after drilling 30 holes decreased from 129 °C (regular K-wire) to 66 °C (Medin K-wire). A commercial K-wire by Smith and Nephew [2] (Fig. 8.1b) has a short segment of spiral flute at the tip and claims to be capable of decreasing temperature and enabling faster bone drilling. Furthermore, the experiment and finite element modeling (FEM) of bone temperature during drilling using a slotted K-wire (Fig. 8.1c) has shown that the thrust force and torque can be reduced by 30–40% if debris can be evacuated from slots at the K-wire tip [3]. Belmont et al. [4] have studied the effects of micro grooves along the K-wire tip (Fig.  8.1c–e) and found that the parallel groove (Fig. 8.1c) is the most effective and could decrease the thrust force by 13%. Studies by Tai et al. [3] and Belmont et al. [4] both indicate that grooves parallel to the K-wire axis are more effective in reducing the bone temperature during drilling © Springer Nature Switzerland AG 2019 A. J. Shih et al., Metal and Bone Drilling - The Thermal Aspects, https://doi.org/10.1007/978-3-030-26047-7_8

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8  Advancement of Surgical Bone Drills: A Case Study of Notched K-Wires

Fig. 8.1  The modified K-wire tips with: (a) two steep flutes, (b) two short flutes, (c) a slot, (d) two parallel channels, (e) single knurling channel, and (f) double knurling channels

and have inspired the creation of a new K-wire tip design with notches parallel to the K-wire axis. Adding a notch at the tip also helps to maintain the critical function of the K-wire to fix bone segments. This chapter will introduce various types of notched designs and investigates drilling performance in lowering the bone cutting force and temperature.

8.2  Design and Manufacturing of Notched K-wires 8.2.1  Notched K-wire Design A trocar K-wire with three bevel planes and a bevel angle of φ is selected as the baseline geometry. The notch is machined using a micro-saw on the bevel plane at the tip of K-wire, as shown in Fig. 8.2a. The tip of K-wire is defined as point O and the origin of the XY coordinate system. The center axis of the K-wire, which passes through O, is marked as line L.  As shown in Fig.  8.2a, the X-axis is across the middle of the bevel plane and the Y-axis is normal to the bevel plane. Figure 8.2b shows a side view of the bevel plane and the X- and Y-axis. The center of the micro-­ saw at the end of the cut is defined as point M. The position of M in the XY coordinate is (a, b). The parameters relevant for machining are as follows: • The outer cutting edge of the micro-saw represented by a circle (shown in Fig.  8.2b) with a diameter, D, intersecting the X-axis at point P, as shown in Fig. 8.2c; • The distance between O and P is c; • The diameter of the K-wire is d; • The tilt between L and the X-axis is the bevel angle φ, resulting in the minimum distance between point M and line L as e (Fig. 8.2b); • The length of the notch along the K-wire axially is l; • The maximum depth of notch in K-wire radial direction is h, which determines the size of the notch and affects the volume available for evacuation of debris.

8.2  Design and Manufacturing of Notched K-wires

151

(a) Y

a N

b

F M(a, b) l

D/2

O

Micro-saw O

P K-wire

X φ

P

e

c

h

G

d L

(b)

(c)

Fig. 8.2 (a) Micro-saw cutting a notch on the K-wire bevel plane and the XY coordinate, (b) configuration of the micro-saw cutting of the K-wire tip, and (c) the close-up view of a notch at the K-wire tip

The cross-sectional area machined by the micro-saw on K-wire in the XY-plane is shown in the hatched area in Fig. 8.2c. In the right triangle GOF, the angle GOF is φ, the distance of OG is b + a tanφ, and the distance OF is e.

e = ( b + a tan ϕ ) cos ϕ



(8.1)

From Fig. 8.2b, c,



e−

d D = −h 2 2

(8.2)

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8  Advancement of Surgical Bone Drills: A Case Study of Notched K-Wires

Using Eqs. (8.1) and (8.2), h=



D+d − ( b + a tan ϕ ) cos ϕ 2

(8.3)

2 If h